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Computational Chemistry Metho ds
Applications to Racemate Resolution and Radical Cation Chemistry ISBN
Computational Chemistry Metho ds
Applications to
Racemate Resolution and
Radical Cation Chemistry
een wetenschapp elijkeproeve op het gebied van de
Natuurwetenschapp en Wiskunde en Informatica
Pro efschrift
ter verkrijging van de graad van do ctor
aan de KatholiekeUniversiteit Nijmegen
volgens b esluit van het College van Decanen
in het op enbaar te verdedigen op
dinsdag januari
des namiddags om uur precies
do or
Gijsb ert Schaftenaar geb oren op augustus te Harderwijk
Promotores Prof dr ir A van der Avoird
Prof dr E Vlieg
Copromotor Prof dr R J Meier
Leden manuscriptcommissie
Prof dr G Vriend
Prof dr R A de Gro ot
Dr ir P E S Wormer
The research rep orted in this thesis was nancially supp orted by the Dutch Or
ganization for the Advancement of Science NWO and DSM
Contents
Preface
Intro duction
Intro duction
Chirality
Metho ds for obtaining pure enantiomers
Racemate Resolution via diastereomeric salt formation
Rationalization of diastereomeric salt formation
Computational metho ds for mo deling the lattice energy
Molecular Mechanics
Quantum Chemical Metho ds
Summary of used mass sp ectrometry techniques
Outline of this Thesis
References and Notes
Molden a pre and p ost pro cessing program for molecular and
electronic structures
Summary
Intro duction
Metho ds
Molden as a prepro cessor the Z matrix Editor
Molden as a p ostpro cessor
Discussion
References and Notes
The e ect of iso density surface sampling on ESP derived charges
and the e ect of adding b ondcenters on DMA derived charges
Summary
Intro duction
Metho ds
The quality of DMA derived charges versus QMESP charge
The e ect of sampling on the quality of DMA derived charges
and QMESP charges
Results
DMA derived charges
Iso density surface sampling vs Van der Waals surface sam
pling
Timings
Conclusions
Acknowledgements
References and Notes
Quantum mechanical and force eld calculations on the diastere
omeric salts of cyclic phosphoric acids with ephedrine
Summary
Intro duction
Metho ds
The crystal structures of cyclic phosphoric acid derivatives
and ephedrine
Computational metho ds
Results
Ab initio calculations on mo del systems
Lattice energy calculations using a classical force eld
Lattice energy calculations using distributed multip ole ex
pansions
Lattice energy minimizations using VASP
Lattice energy minimizations using DMol
Lattice energy minimizations using SIESTA
The relative imp ortance of separate interactions studied
with DMol
Comparison of the absolute lattice energies
Conclusions
Acknowledgements
References and Notes
The gas phase chemistry of the methyl carbamate radical cation
Summary
Intro duction
Exp erimental
Results and discussion
Energetic measurements
Theoretical methods
The unimolecular chemistry of methylcarbamate ions
Conclusions
Acknowledgements
References
Summary
Samenvatting
Dankwoord
Curriculum Vitae
Preface
This thesis deals with the application of computational mo dels to solvereal
life chemical problems Two distinct problems are tackled First the prediction of
lattice energy di erences b etween a pair of diastereomeric salts and secondly the
elucidation of the unimolecular chemistry of the methyl carbamate radical cation
While the second problem deals with relatively small molecules atoms the
rst deals with much larger molecules atoms Both systems were at the
limit of the size that could b e handled with Quantum Mechanical metho ds at
the time the calculations were p erformed This illustrates the evolution of b oth
Quantum Mechanical metho ds and computer hardware in the ten years that
lie b etween them Besides b eing di erent in size these systems also di er in
complexity While the second problem deals with isolated molecules in the gas
phase the rst deals with interacting molecules in the solid In addition the latter
involves a whole sp ectrum of intermolecular interactions from weak van der
Waals contacts ring ring interactions to strong ionic interactions and hydrogen
bridges The total energy di erences b etween diastereomeric salts however are
very small kcal mol compared to the energy di erences found b etween the
isomers and transition states of the methyl carbamate radical cation up to
kcal mol Trying to repro duce such small energy di erences as kcal mol
pushes even presentday computational metho ds to their limits
Chapter
Intro duction
This chapter deals with the background of racemate resolution via the forma
tion of diastereomeric salts In addition a brief overview will b e given of mass
sp ectrometry techniques used for the elucidation of the unimolecular chemistry
of the methyl carbamate radical cation A review of the applied computational
metho ds will also b e given
Intro duction
Chirality
Achiral molecule is a molecule that is not sup erimp osable on its mirror image
These non sup erimp osable mirror images are called enantiomers Enantiomer
pairs of a particular molecule haveidentical physical prop erties except for optical
rotation That is to say when plane p olarized light is passed through a solu
tion or crystal of one enantiomer the resulting rotation of the light p olarization
plane is equal in magnitude but in opp osite direction to that of its enantiomeric
counterpart For this reason enantiomers are also called optical isomers
The pre xes and or dextro and laevo D L which designate the di
rection of the angle of rotation are used to distinguish enantiomers Another
classi cation system the R S system designates the absolute con guration of a
stereoisomer It has largely replaced the D L notation and is used for molecules
other than amino acids Sometimes the number of chiral centers n presentina
n
molecule is more than one In this case not all of the p ossible stereoisomers are
each other s mirror image Two stereoisomers that are not each other s mirror
image are called a diastereomeric pair
In addition to essentially identical physical prop erties enantiomers also have
identical chemical prop erties except in a chiral environment such as biological
Chapter
systems where receptors enzyme systems and so forth typically havechiral
prop erties themselves The interaction of a drug molecule with the receptor or
the enzyme is very sp eci c due to their chemical and structural complementarity
and may exhibit stereoselectivity
In fact many active pharmaceutical drugs are chiral and were marketed up
till the s as racemic mixtures i e as an equal mole ratio of their individual
enantiomers The problem is that one enantiomeric form of a chiral drug may
b e medicinally b ene cial while the other enantiomeric form may b e completely
useless or even toxic Table shows some examples of the distinct biological
e ects of the two enantiomers in a racemate
An example of the latter is the drug thalidomide whichwas administered
to pregnantwomen in the s curing morning sickness in early pregnancy
One of the enantiomeric forms was found to b e medicinally b ene cial while the
other was found to b e teratogenic The result was babies b orn with severe limb
deformities Since the US Fo o d and Drugs Administration FDA and the
Europ ean Committee for Proprietary Medicinal Pro ducts have required manu
facturers to researchandcharacterise eachenantiomer in all drugs prop osed to b e
marketed as a mixture thus justifying that no safety risk exists for the racemate
From that date pro duction of new racemates ceased to b e a rational commer
cial option and instead b ecame a high risk route for pharmaceutical compagnies
In addition it led to racemic switching by pharmaceutical compagnies extend
ing a patent protection on a racemic drug by later patenting its single active
enantiomer
When the FDAvoted in favour of single isomers it did so b ecause scienti c
advances had driven chiral technology to the p oint where it b ecame realistic and
routinely p ossible to develop them
Metho ds for obtaining pure enantiomers
There are three options for intro ducing chiralityinto a synthesis
the chirality p o ol where the required con guration is present in the starting
materials used and is maintained throughout the remainder of anysynthesis
asymmetric synthesis where the single isomer pro duct is derived byintro
ducing the asymmetry directly into a non chiral material
Intro duction
Table Examples of enatiomers exhibiting di erent biological e ects
Comp ound E ect of S E ect of R
enantiomer enantiomer
Thalidomide teratogenic cures morning sickness
Propanolol blo cker contraceptive
Limonene lemon smell orange smell
Dopa Anti Parkinson toxic granulo cytop enia
Asparagine tastes bitter tastes sweet
Ketamine Anesthetic resp onsible for
side e ects
hallucination agitation
resolution metho ds where the precursor or material is provided as a racemic
mixture and has to b e separated to give the required isomer In favourable
cases the undesired isomer can b e used either by turning it backinto race
mate which can b e resolved again or byinverting its con guration so that
it to o provides the required isomer
chirality p o ol metho ds
The simplest access to single isomers is their direct isolation from natural sources
and in all cases the inherentchirality of nature in plants animals or micro or
ganisms has b een used An example is the anticancer drug Taxol presentin
the Paci c Yew tree Taxol s structural complexitymakes total chemical synthesis
impractical for drug supply However synthetic chemistry can help by attaching
asidechain that is key to Taxol s activityonto a more abundantintermediate
Baccatin I I I from the tree
Other examples are the p enicillins and cholesterol lowering agentlovastatin
which are derived by microbial fermentation In b oth cases synthetic chemistry
Chapter
has also b een applied to mo dify the fermentation pro ducts to give b etter drugs
suchasamoxicillin and simvastatin resp ectively whichhave mo di ed side
chains Apart from the pro duction of complete drugs nature also makes avail
able to the chirality p o ol useful building blo cks like the natural amino acids or
sugars L Aspartic acid for example is used to pro duce the sweetener Aspar
tame
asymmetric synthesis from a pro chiral substrate
The usual form of asymmetric synthesis takes a substrate containing no chiral
elements one that is at and transforms it via an asymmetric step into a chi
ral pro duct This has the advantage that p otentially all the material can b e
realised as the required isomer directly Suchsyntheses are often catalyzed ei
ther by enzymes fermentation or by non enzymatic catalyst For instance a
rho dium diphosphine catalyst is used to manufacture the anti parkinsonian agent
leveo dopa
resolution of racemates
There are four ways to resolve a racemic mixture in practice i Resolution via
direct crystal lisation The racemate segregates into two morphologically di erent
crystals which can b e separated either by hand Pasteur or mechanically
Direct crystallisation can also b e achieved by seeding a sup ersaturated solution
with an optically pure crystal of one enantiomer Crystals containing an excess
of the added enantiomer are often obtained This pro cedure is called resolution
byentrainment ii Kinetic resolution where the di erence in reaction rate
of two enantiomers with a single chiral enantiomer of another substance causes
enantiomeric enrichment iii Chromatographic separation The enantiomers
form intermediate diastereomeric complexes with a chiral selector whichmaybe
present in either the stationary or the mobile phase The di erence in stability
between these intermediate diastereomeric complexes results in di erent retention
behaviour thus enabling separation iv Preferential crystal lization of diastere
omeric salts A racemic acid or base is combined with a optically pure base or
acid the resolving agent resulting in the formation of two diastereomeric salts
If these salts di er su ciently in solubility they can b e separated by selective
Intro duction
crystallization of one of the salts
Racemate Resolution via diastereomeric salt formation
This metho d remains the most industrially applied metho d Typically diastere
omeric salt formation has broad applicability since b oth enantiomers are generally
available and if used in conjunction with in situ racemization allows the enan
tiomeric yield to b e signi cantly improved over the theoretical limit A
disadvantage of this approachwas that it was more of an art than a science
requiring a high degree of screening Relatively recently the requirement for com
prehensive screening of resolving agents for a sp eci c substrate was reduced by
the so called Dutch resolution technique This approach uses a mixture of
structurally di erent resolving agents to rst determine the most favored dias
teromeric salt judged by proton NMR of the crude mixture A mixture fam
ily of derivatives of the most favored structural class is used as resolving agent
For instance a mixture of mandelic malic and dib enzoyl tartaric acids could b e
used as a preliminary screen mixture If dib enzoyl tartaric acid was found to b e
the most favored salt then a mixture of functionalised dib enzoyl tartaric acids
would b e used as the family The advantages of this approach is that in more
than of all cases studied more than examples by the use of the
family approach results in higher enantiomeric excess of the substrate than
a single resolving agent alone A disadvantage however is that the increased
amount of do cumentation requirements by the Federal Drug Administration lim
its the use of this approach for large scale manufacturing
Chapter
Rationalization of diastereomeric salt formation
The resolution by diastereomeric salt formation is based on the solubility di er
ence in a pair of diastereomeric salts Frank Leusen prop osed a mo del that
links resolution e ciency to the lattice energy di erence in a diastereomeric pair
of salts Empirically the following relation was found
H r ln c c r
f p n
Where
H is the di erence in heat of fusion of the diastereomeric salt pairs
f
ln c c is the resolution e ciency
p n
c and c are the solubilities of p salt and n salt
p n
r and r are constants
The p salt is the or the salt whereas the n salt is the or the
salt Figure shows the relation b etween H and ln c c for substituted
f p n
ephedrine with substituted cyclophosphoric acid as a resolving agent the gure
was taken from the thesis of Leusen
From the Born Hab er fusion cycle it can b e deduced that the di erence in lattice
enthalpy H equals minus the di erence in enthalpy of fusion if we assume
solid
that the di erence in liquid enthalpies is small with resp ect to that of the solids
Likewise it can b e deduced that the di erence in lattice enthalpy H equals
solid
minus the di erence in solvatation enthalpies if we assume that the di erence in
enthalpy of the solutions is negligibly small
H H H r ln c c r
solid f solv p n
This thermo dynamic mo del was extended to include entropy e ects This gives
a slightly b etter correlation b etween the entropy corrected enthalpy di erence in
cor r
the solid state H and ln c c
p n
solid
The resolution via diastereomeric salt formation can thus b e quanti ed by
comparing the lattice energy of the two diastereomeric salts in a pair The lattice
energy is de ned as the amount of energy released when a mole of gaseous ions or
Intro duction
molecules are brought together from in nite separation to form a crystal Within
diastereomeric salts pairs the gas phase energy is the same Therefore di erences
in lattice energies are equivalent to di erences in the total energy of the solid
This op ens the way to prediction of the resolution e ciency of a resolving agent
by calculation of the di erence in total energy of the two diastereomeric salts in
a pair
Lattice energy calculations on diastereomeric salts have b een rep orted in the
literature bytwo groups
Leusen et al p erformed molecular mechanics calculations on three pairs of
Figure Plot of H versus ln c c Lab els indicate acid substituents
f p n
with unsubstituted ephedrine or acid base aromatic substituents
Chapter
diastereomeric salts of ephedrine with di erent cyclic phosphoric acids The
e ect of several of the CHARMm force eld parameters mainly relating
to the electrostatic interaction was investigated These are the e ect of
varying the dielectric constant the e ect of varying the cut o distance
for the electrostatic interactions and the e ect of di erentcharge schemes
The results were evaluated in terms of the ability to repro duce the X ray
structures and the energy di erences of the two diastereomers in a pair It
was concluded that electrostatic p otential derived charges ESP charges
and a su ciently large cut o distance for the electrostatic interactions
were required for a go o d repro duction of the X ray structures Still it was
not p ossible to obtain agreementbetween the exp erimental and calculated
lattice energy di erences It was concluded that the description of the
electrostatic interactions within the force eld was insu ciently accurate
and that the inclusion of p olarization terms in the force eld is essential
Hansen et al p erformed molecular mechanics calculations with several
force elds on a wide range of comp ounds including diastereomeric salts It
was concluded that force elds are generally not very go o d at repro ducing
the relative stability order of p olymorphs Hansen also concluded that it is
not generally p ossible to show that a particular charge set is sup erior i e
she showed that a given charge scheme p erformed well for some structures
and badly for others
From the ab ove it is clear that an improvement in the description of the
electrostatic interactions is crucial for improving the repro duction of the relative
stability order of diastereomeric salts and p olymorphs The aim of our work is
to nd such b etter computational metho ds
Weintend to accomplish this by p erforming molecular mechanics calculations
with improved description of the electrostatic interactions and by the use of
quantum mechanical metho ds that can deal with p erio dic b oundary conditions
appropriate for a crystalline lattice
Weevaluate these metho ds on a subset of two of the diastereomeric salt pairs
used by Leusen These are the salt pairs of ephedrine with cyclic phosphoric acid
and ephedrine with chlorine substituted cyclic phosphoric acid
Intro duction
Computational metho ds for mo deling the lattice en
ergy
This section discusses the computational metho ds applied Molecular Mechanics
and Quantum Mechanics metho ds
Molecular Mechanics
The molecular mechanics metho d is used to calculate molecular structures and
relative energies of conformers using concepts from classical mechanics Electrons
are not explicitly included in molecular mechanics which is justi ed on the basis
of the Born Opp enheimer approximation stating that electronic and nuclear mo
tions can b e uncoupled from one another and considered separately Thus the
nuclei may b e viewed as moving in an average electronic p otential eld
Alternatively Molecular mechanics can b e thought of as a ball and spring
mo del of atoms and molecules with classical forces b etween them These forces
are describ ed by p otential energy functions dep ending on structural features such
as b ond lengths b ond angles and torsional angles The p otential energy func
tions contain a numb er of parameters which are t to repro duce exp erimental
prop erties
The total energy E of a molecule or a cluster of molecules is divided into
tot
several parts one of which is attributed to b ond stretching E one to b ond
bond
angle b ending E one to torsional deformations E one to van der
ang le tor sion
Waals interactions E and one to electrostatic interactions E
vdW C oulomb
MM
E E E E E E
bond ang le tor sion vdW C oulomb
A more re ned force eld will also include cross terms such as stretch b end
torsion stretch etc Finally other terms suchashydrogen b onding have b een
used to takeinto account phenomena that are not prop erly accounted for oth
erwise The rst three terms in Eq are strictly intramolecular contributions
while the latter two are also involved in intermolecular interactions Since the
crystal packing is strongly in uenced byintermolecular interactions we will lo ok at these in more detail
Chapter
Van der Waals p otentials
The disp ersion attractive part of the van der Waals p otential is usually de
scrib ed by a term with an inverse sixth p ower of the distance whereas the re
pulsive part is describ ed byaninverse twelfth p ower term Lennard Jones
function Eq or alternatively byanexponential function Exp onential or
Buckingham p otential Eq
r r
E D
vdW
r r
E A exp Br Cr
vdW
where D is the well depth r is the minimum energy interaction distance r is
the interactomic distance b etween the interacting atoms and A B and C are
parameters
Electrostatic p otentials
The electrostatic interactions are in most force elds accounted for by a Coulom
bic p otential energy function using partial atomic charges
Q Q
i j
E
C oulomb
r
ij
where r is interatomic distance b etween atoms i and j Q and Q representthe
ij i j
atomic p ointcharges and is the MM equivalent of the dielectric constant
Most force elds use a quick calculation of p ointcharges based on electroneg
ativityrules Several metho ds exist to determine p ointcharges from a Quan
tum Mechanical QM calculation These metho ds can b e sub divided into a class
where charges are determined bysomescheme that partitions the electron den
sityover the atoms Mulliken Bader Hirshfeld and a class where charges
are optimized to repro duce the QM electrostatic p otential ESP by employing
a least squares t of the mo del p otential on p ointcharges based and the QM
p otential Metho ds in the latter class di er mainly byhow and where the electro
static p otential is sampled in the surrounding molecular space Wedevelop ed
and implemented two new schemes for deriving ESP charges see chapter
Intro duction
Charges t to repro duce the Distributed Multip ole Analysis DMA derived
electrostatic p otential
ESP charges derived by sampling the electrostatic p otential on a number
of surfaces with constant electron density so called iso density surfaces
We used the DREIDING force eld with a numb er of di erentcharge sets
to p erform minimizations and lattice energy calculations on diastereomeric salts
of ephedrine with cyclic phosphoric acid see chapter
The Coulombinteraction of twocharge distributions can b e describ ed more
accurately than in Eq as a multip ole expansion in the form
X
m m
l l
l l R Q U Q S
l m elec l m
l l l l
l l m m
Where l l denotes the numerical factor l l l l the
multip ole moments Q describ e the charge distributions and S is a function
lm
of the relative orientation of molecules
Equation reduces to equation when l and l are zero When one of the
charge distributions is represented byonlyapointcharge of charge l
Q Equation reduces to a DMA derived electrostatic p otential
The DMAREL package was sp eci cally designed for crystal structure sim
ulations using distributed multip ole expansions We used the DMAREL program
to p erform force eld minimizations and lattice energy calculations on diastere
omeric salts of ephedrine with cyclic phosphoric acid see chapter
The calculation of the electrostatic p otential ESP charges distributed multi
p ole moments as well as the interfacing to the DMAREL package has b een built
into our program MOLDEN see chapter
Quantum Chemical Metho ds
Hartree Fock Theory and p ost Hartree Fockmethods
In the Hartree Fock HF metho d the exact electronic Hamiltonian is approx
imated by the Fock op erator whichsolves an electron s wave function in the
average eld of all the other electrons
Chapter
Z
X
r Z
A
r dr r
i
jr R j jr r j
A
A
Z
X
r r
j i
r r dr
j i i
jr r j
j
where the rst two terms are the kinetic energy and the electron nucleus at
traction of a single electron The third term the Coulomb operator represents
the average repulsion of electron by all other electrons The last term the
exchange operator arises as a direct consequence of including the Pauli prin
ciple through the use of an antisymmetrized wavefunction approximated bya
single determinantwavefunction Since the orbitals dep end on the Coulomb
i
and exchange op erators and the Coulomb and exchange op erators dep end on
the orbitals the Hartree Fock equations havetobesolved iteratively until self
consistency is achieved i e until the input orbitals are equal within a certain
tolerance to the output orbitals
In practice the molecular orbitals MO s are expanded as a linear com
bination of atomic orbitals AO s The expansion co e cients are adjusted to
minimize the exp ectation value of the total energy with the exact electronic
Hamiltonian
The primary de ciency of the Hartree Fock theory is the inadequate treat
ment of the correlation b etween motions of electrons While correlation of the
motions of electrons with the same spin is partially taken into accountby virtue
of the determinantal form of the wave functions single determinantwavefunc
tions do not takeinto account the correlation b etween electrons with opp osite
spin As a consequence the calculated Hartree Fock energies will b e higher than
the exact values The di erence b etween the Hartree Fock and exact energy is
called the correlation energy
E exact E Hartree Fock E correlation
Several metho ds exists that can include correlation e ects using the Hartree
Fock single determinantwavefunction as starting p oint These p ost Hartree Fock
metho ds include con guration interaction CI and the M ller Plesset p erturba
tion series MP MP see Szab o and Ostlund
Intro duction
DensityFunctional Metho ds
The conventional ab initio metho dology is based on the approximate solution of
the many electron Schr odinger equation Hohenb erg and Kohn have shown that
the total energy can directly b e expressed as a functional of the electronic charge
density This concept lies at the hart of the density functional theory DFT
Instead of working with a complex N dimensional wavefunction describing the
behaviour of each electron in an N electron system DFT allows us to work with
a simple three dimensional function the total electronic density r
Kohn and Sham KS intro duced a practical approach to p erforming DFT
calculations In the KS approach r of an N electron system with N spin
up and N spin down electrons is expressed as the sum of the square mo duli of
and singly o ccupied orthonormal Kohn Sham molecular orbitals
i
i
N N
X X
j r j j r j r r r
i
i
i i
The unknown energy functional E r is partitioned into three terms
E r U r T r E r
XC
where U r is the classical electrostatic energy the sum of the electron nucleus
attractions and the electron electron Coulomb repulsions
ZZ Z
X
r r Z r
A
dr dr dr U r
jr R j jr r j
A
A
The next term T r is the kinetic energy of the electrons
Z
N
X X
r T r r dr r
i i
i
The last term E r is the yet to b e de ned exchange correlation XC
XC
energy functional
Applying the condition that the energy functional is minimizedby the ground
state density yields the one electron KS equations
Z
X
E r r Z
XC A
r dr r r
i
i i
jr R j jr r j r
A A
Chapter
Just as the Hartree Fock equations these equations havetobesolved iteratively
until self consistency is achieved i e until the input densities and orbitals are
equal within a certain tolerance to the output densities and orbitals
Until now weavoided dealing with the precise nature of the XC energy
functional E r The simplest approximation to E r is the Lo cal
XC XC
Spin Density Approximation LSDA In LSDA E r is approximated by
XC
Z
E r r r r dr
XC XC
where r r is the exchange and correlation energy density p er parti
XC
cle It is only a function of r and r at that sp eci c p oint r in space The
value of r r has b een determined for a homogeneous gas of inter
XC
acting electrons as a function of the total density by means of quantum Monte
Carlo metho ds The problem with the LSDA is its systematic overestima
tion of binding energies and its p o or description of the hydrogen b ond To
solve these problems one must adopt gradient corrected XC energy functionals
Within the Generalized Gradient Approximation GGA not only dep ends
XC
on the density r but also on the gradients of the density r r and r r
so that E r is nowgiven by
XC
Z
E r r r r r r r r dr
XC XC
Several gradient corrected exchange and correlation energy functionals exist
They are formulated to address either the exchange or the correlation comp o
nentof E r Commonly used gradient corrected exchange functionals are
XC
thoseofPerdew and Wang and Becke Popular gradient corrected correlation
functionals are those of Perdew and Lee Yang and Parr LYP Typically a
combination of one of the exchange and one of the correlation gradient corrected
XC energy functionals is used Finally the hybrid B LYP functional deserves
to b e mentioned The B LYP functional is a mix of the exact exchange
energy obtained in the same fashion as in a Hartree Fock calculation the
LSDAXC energy and the gradient corrected LSDA exchange Becke and
Intro duction
correlation LYP energy Theweight of these three comp onents is optimized to
repro duce a set of highly accurate exp erimental data
QM calculations on solids
When p erforming QM calculations on solids the one electron wavefunctions r
j
must re ect the translational symmetry of the lattice Blo ch s Theorem states
that this condition is satis ed when
k k
r T exp ik T r
k
where T is a direct lattice vector k is a recipro cal lattice vector and is a Blo ch
function BF The irreducible part of the recipro cal space spanned byvectors k
k space is called the First Bril louin Zone The Brillouin zone can b e sampled
in a nite number of k p oints to obtain go o d approximations to the total energy
The one electron orbitals in a total energy calculation are most often ex
panded in a set of basis functions f r g
i
X
c r r
i j i j
i
In practical calculations one has to truncate the summation at some prefer
ably small numb er and it therefore b ecomes imp ortant to use a basis set for
which the error in the representation of the orbitals is quickly converging with
the numb er of functions The use of a small basis set reduces the time of com
putation and the memory requirements Two basic typ es of functions are used
for the expansion in Eq lo calized functions or atomic orbital AO based
BF s and plane waves For atomic orbitals Gaussian typeorbitalsornumeri
cal orbitals can b e used An example of the rst is the program CRYSTAL
and examples of the second are the programs DMol and SIESTA Atomic
orbitals closely resemble the orbital b ehavior near the nucleus where the valence
orbitals strongly oscillate in order to stay orthogonal to the core orbitals Many
plane waves would b e necessary to simulate this oscillatory b ehaviour The use
of pseudop otentials pseudo orbitals greatly reduces the numb er of plane waves
required in the expansion esp ecially when ultra soft pseudop otentials are used
see b elow
Chapter
The expression for the expansion of the wave functions in a plane wave basis
set is
X
c exp i k G r r
j kG j k
G
The sum is over all recipro cal space vectors G and the wavevector k de
termines a p oint in the rst Brillouin zone The expansion co e cients can b e
shown to approach zero for large values of the kinetic energy of the plane waves
jk Gj as the energy otherwise b ecomes unb ounded This suggests a trunca
tion pro cedure where all plane waves b elow a given kinetic energy are included
and plane waves ab ove the chosen threshold are discarded This yields a nite
numb er of plane waves p er k p oint VASP is an example of a program that
uses plane waves in combination with ultra soft pseudop otentials
Despite the fact that many more basis functions are always required to expand
an orbital in plane waves than if atom centered basis functions were used the
use of plane waves is still advantageous for several reasons These include the use
of very e cientFast Fourier Transform FFT algorithms in the iterative eigen
value solver as well as the conversion back and forth from real to recipro cal
space The kinetic nuclear attraction and Coulomb repulsion contributions to the
total energy are calculated in recipro cal space while the exchange correlation
contribution is calculated in real space
The number of Fourier grid p oints necessary is determined by the oscillations
in the density The density requires a grid with twice the linear size of the grid
required by the wave functions b ecause the squaring of the wave functions to
obtain the density doubles the frequencies of the Fourier comp onents
Tosave time on computations one can often b ene t from doing all the calcu
lations related to the wave functions on a coarse Fourier grid and transp ort the
wave functions to a denser grid in recipro cal space byFourier interp olation b e
fore doing the few calculations related to the electron density This double grid
technique b ecomes esp ecially imp ortant for larger calculations in the ultrasoft
scheme b ecause the ultrasoft wave functions are much softer than the augmen
tation charge density
Intro duction
Pseudop otentials
One wayofavoiding much of the computational exp ense asso ciated with the all
electron approachisby describing the core region in terms of xed atomic orbitals
that p erturb but are not necessarily p erturb ed by the valence region This is
known as the frozen core approximation The same goal can b e achieved through
the use of pseudop otentials
Figure An illustration of the actual valence wavefunction and electronic p o
tential solid lines plotted against distance r from the atomic nucleus The cor
resp onding pseudo wavefunction and p otential is plotted dashed lines
pseudo
Outside a given radius r the actual and pseudo wavefunctions are identical c
Chapter
In the norm conserving pseudop otential approach pseudo wavefunctions
are constructed which are equal to the actual valence wavefunctions b eyond some
de ned core radius r but di erent inside r while retaining an identical norm
c c
i e net charge density within the sphere of radius r See gure
c
Vanderbilt removed the norm conservation criterion of the pseudop o
tential so that the pseudo wavefunctions inside r could b e made as soft as p ossi
c
ble Ultrasoft His approach greatly reduces the numb er of plane waves required
in the expansion of the wavefunction Since the pseudo wavefunctions are no
longer normalized one has to correct for the missing charge densityby adding
so called augmentation charge density
Summary of used mass sp ectrometry techniques
Chapter of this thesis deals with the unimolecular chemistry of the methyl
carbamate radical cation studied by mass sp ectrometry techniques and ab initio
molecular orbital calculations This was a joint pro ject b etween the Theoretical
Chemistry and Mass Sp ectrometry groups of the University of Utrecht Belowis
a summary of the applied mass sp ectrometry techniques
In the ionization chamb er of a mass sp ectrometer the sample M is ionized
by electrons Ejection of an electron from the sample molecule leads to a radical
cation
e M e M
The minimum energy required for ionization is the Ionization Energy IE From
a
the IE M and the heat of formation H of the sample M the heat of
f
formation of the ion H M can b e derived
f
IE M H M H M
f f
The molecular ion M can also fragmentinto a daughter ion M and a neutral
a
The heat of formation is de ned as the enthalpychange H for the formation of mol
f
of a substance in the standard state from the most stable forms of its constituent elements in their standard states
Intro duction
M
M M M
The energy at which the daughter ion M rst app ears is called the App earance
Energy AE From the AE M the heat of formation of the ion M can b e
derived via the following relation assuming the other H s are known
f
H M H M AE H M
f f f
into the ion M Figure Energy diagram for the fragmentation of an ion M
and neutral M Arrows indicate the App earance Energy AE and the reverse
activation energy E
The ab ove only holds if no reverse reaction energy barrier is involved and the
lies b elow the heat of formation of the pro ducts see heat of formation of M
gure The presence of an energy barrier results in a higher value for the AE
whichthenyieldsvaluable information ab out the barrier After passage of the
barrier at least the reverse activation energy is transferred to the fragmentation
pro duct in the form of internal and kinetic energy This kinetic energy release
Chapter
hT i is observable and can b e derived from the broadening of the metastable ion
p eak Metastable ions are ions to which relatively little energy is transferred by
the ionizing electron The lifetime of these ions is such that they can undergo
rearrangements but fragment somewhere inside the mass sp ectrometer
Stable ions can b e forced to fragmentby Col lision Activation CA with a
target gas Information ab out the identity of an ion can also b e retrieved byinves
tigating the stability of its neutral counterpart with Neutralization Reionization
Mass Spectrometry NRMS In this exp eriment the ion is neutralized and sub
sequently reionized again Finally the neutrals released during ion fragmenta
tion can b e studied by Col lision Induced Dissociative Ionization Mass Sp ectra
CIDI
Outline of this Thesis
Chapter deals with the Molden package our visualization program of molecular
and electronic structure This program has b ecome central to this research
It is used to calculate a numb er of di erenttyp es of charges the electrostatic
p otential Distributed Multip oles Z matrix constructs to imp ose translational
and screw typ e of symmetry forinterfacing with DMAREL and VASP and for
manipulation of crystal structures
Chapter deals with the developmentoftwonewpoint charge mo dels
Charges t to repro duce the Distributed Multip ole derived electrostatic
potential
ESP charges derived by sampling the electrostatic p otential on a number
of surfaces with constant electron density
Chapter deals with the Quantum Mechanical and Force Field calculations on
Diastereomeric Salts
Chapter deals with the unimolecular chemistry of the methyl carbamate radical
cation investigated byacombination of mass sp ectrometry techniques and ab initio molecular orbital calculations
Intro duction
References and Notes
U Hacksell ATextbook of Drug Design and Development ch Structural and physico
chemical fctors in drug action New York Harwo o d Academic Publishers
Chirality
M Gross Chemical Analysis Vol The ImpactofStereochemistry on Drug Devel
opment and Use ch Chapter Enantioselective analysis and the regulation of chiral
drugs New York John Wiley rm Sons Inc
CPMP Note for Guidance Investigation of Chiral Active Substances Brussels
Commision of the Europ ean Union I I I EN Final
De Camp W H Chirality
Vermeulen A M Belpaire F M Mo erman E de Smet F Bogaert M G Chirality
Enders D Ho mann R W Chemie in unzerer Zeit
Cotzias G C Papavasiliou P S Gallene R N Engl J Med
White P F Ham J Way W L Trevor A J Anesthesiology
Pirkle W H Pochapsky T C Chem Rev
Okamoto Y Kaida Y J Chromatogr
Nathwani D Wo o d M J Drugs
Ho man W F Alb erts A W Anderson P S Chen J S Smith R L Willard A K J
Med Chem
Tou J S Vineyard B D J Org Chem
Crosby J Tetrahedron
Knowles W S Sabacky M J Vineyard B D Weinkau D J J Am Chem So c
Pasteur L Ann Chim et Phys
Jacques J Collet A Wilen S H Enantiomers Racemates and Resolutions Malabar
Florida Krieger Publishing Company
Taylor D R Maher K J Chromatographic Science
Vries T Wynb erg H van Echten E Ko ek J ten Ho eve W Kellog R M Broxter
man Q B Minnaard A Kaptein B van der Sluis S Hulshof L Ko oistra J Angew
Chem Int Ed
F Leusen Rationalization of racemate resolution a molecular model ling study Nijmegen
Ph D thesis
Bro oks B R Bruccoleri R E Olafson B D States D J Swaminathan S Karplus M
J Comput Chem
L Hansen Structural Investigations of Diastereomeric Salts TheRoyal Danish Scho ol of
Pharmacy Ph D thesis Del Re G J Chem So c London
Chapter
Gasteiger J Marsili M Tetrahedron
Mulliken R S J Chem Phys
R Bader Atoms in Molecules A Quantum Theory Oxford Oxford University Press
Hirshfeld F L Theor Chim Acta
Breneman C M Wib erg K B J Comp Chem
Besler B H Merz K M Kollman P A J Comp Chem
Schaftenaar G No ordik J H J Comp Aided Molecular Design
Mayo S L Olafson B D Go ddard I I I A J Phys Chem
Stone A J Chem Phys Lett
Price S L Stone A J Alderton M Molec Phys
Co omb es D S Price S L Willo ck D J Leslie M J Chem Phys
Willo ck D J Price S L Leslie M Catlow C R A J Comp Chem
Schaftenaar G No ordik J H J Comp Aided Molecular Design
A Szab o and N Ostlund Modern Quantum Chemistry Introduction to AdvancedElec
tronic Structure Theory New York McMillan
Hohenberg P Kohn W Phys Rev B
Kohn W Sham L J Phys Rev A
Vosko S H Wilk L Nusair M Can J Phys
Cep erley D M Phys Rev B
Cep erley D M Alder B J Phys Rev Lett
Johnson B G Gill P M W Pople J A J Chem Phys
Becke A D J Chem Phys
Becke A D J Chem Phys
Sim F St Amant A Papai I Salahub D R J Am Chem So c
Perdew J P Wang Y Phys Rev B
Becke A D Phys Rev A
Perdew J P Phys Rev B
Lee C Wang W Parr R G Phys Rev B
Becke A D J Chem Phys
Becke A D J Chem Phys
Becke A D J Chem Phys
Dovesi R Saunders V R Ro etti C Causa M Harrison N M Orlando R
Apra E Crystal Electronic Structure Structure of Perio dic Systems User Manual
http gserv dl ac uk TCSC Software CRYSTAL
Delley B J Chem Phys
Sanchez Portal D Ordejon P Artacho E Soler J M Int J of Quant Chem
Intro duction
Kresse G Hafner J Phys Rev B
Car R Parrinello M Phys Rev Lett
Kresse G Furthmuller J Comput Mat Sci
Ihm J Zunger A Cohen M L J Phys Chem
Laasonen K Pasquarello A Car R Lee C Vanderbilt D Phys Rev B
Hamann D R Schluter M Chiang C Phys Rev Lett
Vanderbilt D Phys Rev B
Holmes J L Mommers A A de Koster C Heerma W Terlouw J K Chem Phys
Lett
Beynon J H Gilb ert R Application of Transition State Theory to Unimolecular Reac
tions Chichester Wiley Interscience
Terlouw J K Schwarz H Angew Chem Int Ed Engl
Burgers P C Holmes J L Mommers A A Terlouw J K Chem Phys Lett
Chapter
Chapter
Molden a pre and p ost pro cessing program
for molecular and electronic structures
This chapter has b een repro duced with kind p ermission from G Schaftenaar J H No ordik J
c
Comp Aided Molecular Design Kluwer Academic Publishers
Summary
Molden is a software package for pre and p ostpro cessing of computational chem
istry program data Interfacing to the ab initio programs GAMESS US UK and
GAUSSIAN and to the Semi Empirical package MOPAC is provided The em
phasis is on computation and visualization of electronic and molecular prop erties
but e g reaction pathways can b e simulated as well Some molecular prop erties
of interest are pro cessed directly from the output of the computational chemistry
programs others are calculated in MOLDEN b efore display The package fea
tures di erent options to display MOLecular electronic DENsity each fo ccusing
on a di erent structural asp ect molecular orbitals electron density molecu
lar minus atomic density and the Laplacian of the electron density To display
di erence density either the spherically averaged atomic density or the oriented
ground state atomic density can b e used for a numb er of standard basis sets The
quantum mechanical electrostatic p otential or a distributed multip ole expansion
derived electrostatic p otential can b e calculated and atomic charges can b e tted
to these p otentials calculated on Connolly surface s Reaction pathways and
molecular vibrations can b e visualized Input structures can b e generated with
a Z matrix editor Avariety of graphics languages is supp orted XWindows
p ostscript VRML and Povray format
Chapter
Intro duction
Quantum chemistry programs like Gaussian and Gamess US UK and the
semiempirical program Mopac have b ecome widely accepted as valuable to ols
in elds as diverse as drug design synthesis planning and material science The
continuous sp eedup of computer hardware has made calculations on systems of
interest tractable to the b enchchemist This b enchchemist however is often
discouraged from using these computational to ols b ecause of the use of unfamiliar
concepts or complicated user interfaces Some vendors of computational chem
istry programs are simpli ng the use of their pro duct bythedevelopmentofa
customized graphical interface For example GaussView SYBYL from Trip os
or CERIUS from MSI provide interfaces to one or more computational chemistry
packages High quality computer graphics is playing an increasingly imp ortant
role in computational chemistry Visualization of computational results is often
the most imp ortantroadtointerpretation
The program Molden adds the p ower of computer graphics to the interpre
tation of the calculations Other visualization programs feature sophisticated
routines to display structural details but Molden is quite unique in its coverage
of features of the electronic structure Molden has b een designed as a general pur
p ose to ol to overcome the barriers which might hamp er the use of computational
chemistry techniques and programs It facilitates the access to these programs
via interactive preparation of program input
Molden do es not only visualize results pro duces by other programs but it
also can calculate several interesting quantities which those programs do not
provide or require multiple invo cations of those programs From nowonwe
will refer to rst form of visualization as direct visualization and the second
form as indirect visualization Prerequisites for indirect visualization such as
the atomic co ordinates the basis set the molecular orbital co e cients and the
numb er of electrons are read from the program outputs
Quantities calculated by Molden are
the electrostatic p otential ESP
ESP charges a tofpointcharges to repro duce the electrostatic p otential
the Distributed Multip ole Analysis DMA
Molden a pre and p ost pro cessing program for molecular and
electronic structures
the orbitals the molecular density or the di erence density
the Laplacian of the electron density
Other quantities visualized by Molden directly available from the output of
computational chemistry programs include the intermediate and nal results of a
geometry optimisation or saddle p oint lo cation together with related information
such as energies forces and convergence data the self consistent eld convergence
and normal mo des
Although mainly designed as a pre p ost pro cessing to ol for the computa
tional chemistry programs mentioned b efore and with a fo cus on the electronic
structure Molden also provides more general applications to the user Current
options include
visualization of protein structures as available from the Bro okhaven Protein
Data Bank
visualization of information on protein secondary structure elements such
as alpha helices b eta sheets or random coil When such information is
not available from the PDB entry it is generated according to the metho d
describ ed in an early version of the VADAR program
visualization of crystal structures from the Cambridge Structural Database
as sp eci ed in the FDAT le format including the generation of symme
try equivalent p ositions and a unit cell and the displayofmultiple unit
cells
Supp orted le formats also include the XMOL format and the Chemx format
User do cumentation and details of the graphics and visualization asp ects of
the program are available as a Web do cument
URL http www caos kun nl schaft molden molden html
The appreciation of the program by b oth computational and b enchchemists
may b e illustrated by more than installations worldwide
Chapter
Metho ds
Molden as a prepro cessor the Z matrix Editor
Preparation of input for computational chemistry programs often is a problem for
even the computer literate b enchchemist The structure of an input le can b e
quite complex due to the large numb er of supp orted options and the sometimes
complicated rules for parameter sp eci cation Either cartesian co ordinates or
a Z matrix can b e used for the sp eci cation of the molecular geometry In the
Z matrix approach atom p ositions are de ned with resp ect to previously de ned
atoms by means of internal co ordinates such as b ond distances b ond angles and
dihedral angles For small molecules a Z matrix can often b e constructed by
hand but for larger molecules this quickly b ecomes tedious and complex
Molden s Z matrix Editor presents the user complete control over the molecu
lar geometry Mo di cations in internal variables are immediately re ected in the
displayed structure and mo di cations in the structure are immediately incorp o
rated in the current Z matrix New structures can b e built adding one atom at
a time or by using internally or externally stored fragments Internal co ordinates
can b e sp eci ed to b e variable constant or linked to other internal co ordinates
In the latter case two or more internal co ordinates are describ ed with one vari
able This is particulary useful in the construction of Z matrices that re ect the
molecular symmetry Geometries constructed with the Z matrix editor can b e
saved as a Z matrix or using cartesian co ordinates Figure shows an example
display with b oth a molecule display and the corresp onding Z matrix window
Molden a pre and p ost pro cessing program for molecular and
electronic structures
Figure Molden s Z matrix Editor option The left screen window displays
the editable molecule the right screen window the corresp onding Z matrix and
the edit control buttons
Molden as a p ostpro cessor
Molden pro cesses numerical information pro duced by computational chemistry
programs This pro cessing can result in direct visualization if all necessary in
formation is already available If such is not the case additional visualization
information will b e calculated in an intermediate computational step
Visualization of reaction paths and normal mo des
The use of Molden for the animation of reaction paths and normal mo des of
vibration of molecules are examples of direct visualization
During a reaction the molecular geometry generally will change These ge
ometrical or conformational changes are correlated with changes in the total
energy Molden can visualize reaction paths from Internal Reaction Co ordinate
Chapter
IRC calculations optimization and or saddle runs Molden complements such
an animation with a plot of the energy versus geometry p oint
Information on conformational exibility resulting from thermal motion is
present in the output of computational chemistry programs in the form of nor
mal mo des and their frequencies Molden displays normal mo des as a series of
geometries The starting geometry is gradually distorted by scaling the atomic
displacementvectors that make up a normal mo de Molden allows the animation
to b e saved in the form of a VRML scene or a series of GIF les The latter can
be converted with external programs to commonly used animation le formats
also known as gifanim such as GIF a
Figure shows the racemization of hexahelicene as an example of direct
visualization
Figure Racemization of hexahelicene The left hand window of the screen
shows the animation In the right hand window an energy plot is displayed
simultaneously By selecting a p osition on the energy plot the corresp onding
molecular geometry will b e displayed
Molden a pre and p ost pro cessing program for molecular and
electronic structures
Some of Molden s options for the display of electronic structural informa
tion require information not directly available from the computational chemistry
program output In particular the handling of the electron density and charge dis
tribution are far from trivial and require closer attention Generally one or more
additional computational steps are required to generate the required information
Visualization of electron densities
Di erence density
Plots of the di erence or deformation density are often used to visualize the
e ects of chemical b onding In these plots of molecular densityminus spherical
atomic density the accumulation and depletion of electron density during b ond
formation is shown A classic example is the formation of banana shap ed b onds
in cyclopropane as shown in Figure
For some molecules it has b een shown that the standard deformation
density is small or even negative for certain covalent b onds indicating that the
use of spherically symmetric atomic ground state densities is not always the b est
atomic reference Although atomic ground states are spherically symmetric some
degenerate atomic ground states are actually linear combinations of nonspherical
oriented comp onents This degeneration can b e lifted even at large interatomic
distances where the very weak long range in uence of other atoms has an ori
enting e ect on the free atom with a degenerate ground state In such cases it is
b etter to use the oriented nonspherical comp onents of the spherically symmetric
ground states Molden incorp orates two algorithms for the construc
tion of the di erence density maps The rst uses spherically symmetric atomic
densities and the second uses oriented non spherically symmetric atomic densities
The rst algorithm is describ ed b elow
The total molecular electron density is de ned as the sum over the densities
of the o ccupied Molecular Orbitals MO s
X X X X X X
nocc MO nocc c c AO AO P AO AO
i i ir is r s rs r s
i
r s r s
i i
where each MO is a linear combination of Atomic Orbitals AO with co e
i r
cients c Each MO is o ccupied with nocc electrons P are the elements of
ir i i rs
Chapter
C
C
C
Figure Cyclopropane sto g basisset Molecular densityminus Atomic density
The standard approach displays the correct density distribution with banana
b onds an increase of electron density p ositioned outside the C C b ond axes
solid contours and a depletion of electron density in the inner ring around the
carb on atoms dashed contours
the electron density matrix
X
P nocc c c
rs i ir is
i
For the H molecule where the simplest wavefunction consists of a doubly o ccu
pied MO consisting of an s orbital on atoms a and b this leads to
MO fc s c s g
a b
and the electron densityisgiven by
n o
c s c c s s c s
a b
a b
Molden a pre and p ost pro cessing program for molecular and
electronic structures
or in matrix form
s c c c
a
A A
s s
a b
s c c c
b
where the matrix in the center is the electron densitymatrixP P can b e thought
of as comp osed of a set of atomic matrices i e matrices refering to the same AO
pro ducts as those available to the free atoms
c
A
c
and the overlap density matrix with matrix elements refering to pro ducts of AO s
centered on di erent atoms
c c
A
c c
Wenow de ne the di erence or deformation density as the molecular density
minus the spherical atomic density In the case of the H molecule this b ecomes
c c c
A
c c c
If an atomic groundstate is not spherical symmetric a di erence density plot
will show a misleading decrease in electron density along some b onds E g in
the case of H O Figure accumulation of charge densityisabsent along the
O O axis the x axis in the molecular frame In this example oxygen has a P
ground state One of the not spherical symmetric comp onents is p p p Here
x y z
the electron density has a maximum along the x axis Subtracting a spherically
can in such a case result in subtracting to o much p p symmetricatom p
z y x
density in the y and z directions and to o little in the x direction In general if an
atom in a molecule has retained much of its ground state character it will have
a preferred orientation The e ect is most pronounced for the atoms O F S and
Cl whereas for example C usually has retained most of its spherically symmetric
character
Chapter
H
O O
H
Figure H O sto g molecular densityminus spherical atomic density stan
dard approach Misleading density plot as a result of neglecting the directional
character of atomic density Accumulation of charge density solid contours is
absent along the O O axis
Molden a pre and p ost pro cessing program for molecular and
electronic structures
The algorithm in molden that uses oriented non spherically symmetricatomic
densities mo di es the atomic density D of O F S and Cl atoms such that the
atom
sum of D i j D i j b ecomes minimal with D b eing the atomic
mol atom mol
part of the molecular density matrix and i and j running over the p p p atomic
x y z
orbitals Application of this approachtotheH O molecule results in the plot
shown in Figure with the exp ected increase in electron density along the O O
axis
The electron density di erence function to b e minimized b ecomes in matrix
form
Mol Atom
D D D D D D R R R
xx xy xz xx xy xz xx xy xz
B C B C B C
B C B C B C
D D D D D D R R R
yx yy yz yx yy yz yx yy yz
A A A
D D D D D D R R R
zx zy zz zx zy zz zx zy zz
Where matrix R is a rotation matrix de ned by three euler angles The sum
P P
D is the quantity that of the squares of this di erence matrix
ix y z j x y z
ij
is actually minimized
The atomic density matrices are stored internally for a numb er of frequently
used basis sets and elements
Molecular orbitals
The second Molden option related to orbital display is the visualization of orbitals
suchasfrontier molecular orbitals as used in Frontier Molecular Orbital FMO
theory calculations
Figure shows the HOMO in the Diels Alder cycloaddition transition state
of butadiene with ethylene which FMO theory predicts to b e a HOMO LUMO
reactantcombination
The Laplacian of the electron density
A third Molden option for the display of orbital related electron density informa
tion is the Laplacian of the electron density Bader showed how this quantity
Chapter
H
O O
H
Figure H O sto g Molecular densityminus Oriented Oxygens with prop er
treatment of directional character of atomic density resulting in the accumulation
of density solid contours along the O O axis
Molden a pre and p ost pro cessing program for molecular and
electronic structures
can provide interesting information ab out the chemical b ond Most computa
tional chemistry programs havenoprovision to calculate it
In Molden the Laplacian is calculated according to the following equations By
de nition the Laplacian of the electron density is the trace of the second deriva
tive matrix of the density
X X
P AO AO r
rs r s
x y z x y z
r s
The Atomic Orbitals AO s are constructed as a linear combination of carte
sian gaussian typ e orbitals gto s with xed co e cients and exp onents
lmn
l m n
N x y z exp x y z
lm n lm n
N is the normalisation constant
lmn
lmn
l m n
N
lmn
l m n
The calculation of the Laplacian now breaks down into derivatives over pro d
ucts of gto s
j j i i i j
i j
x x x x x
The explicit formulas for the rst and second derivatives over primitive gaus
sians are given by
l
lm n
x
lmn
x x
l l
lmn
x
lm n
x x x
Derivatives over y and z followby analogy The last two equations do not
hold for x and in Molden this has b een solved programmatically by letting x
y or z b e the smallest p ossible numb er within machine precision for these cases
The recovery of the shell structure by the Laplacian in carb on monoxyde is
shown in Figure
Chapter
Figure Higest Occupied Molecular Orbital of a Diels Alder cycloaddition
transition state of butadiene with ethylene Shown are the contour surfaces of
orbital amplitude Blue and Red
Molecular charge distribution
Distributed Multipole Analysis
The calculation of the interaction energy of two molecules as implemented in all
force eld based programs is crucially dep endent on a correct description of the
Molden a pre and p ost pro cessing program for molecular and
electronic structures
electrostatic contribution Most force eld metho ds describ e this term as a sum
of coulombinteractions b etween partial atomic charges This however do es not
takeinto account the fact that an atom in the eld of other atoms is p olarized
and exerts an electric force which is not equal in all directions By representing
the molecular charge distribution byasetofpointmultip oles on a number of
centers often atomic centers the electrostatic interaction can b e mo deled far
more accurately
Chapter
Figure CO sto g surface of constant Laplacian showing the s and
valence shells of carb on and oxygen
Such a mo del automatically includes the e ect of lone pair and electron
density on the intermolecular forces and is widely used to mo del complexes of
p olar and aromatic molecules for the prediction of protein side chain struc
tures and nucleic acid base pairs and crystal structures Calculations in the
references quoted were p erformed with the Orient and DMAREL packages
where the latter is sp eci cally designed for crystal structure simulations
in a The Distributed Multip ole Analysis has b een describ ed by Stone
general way but explicit formulae for the required integrals have not b een re
p orted in the literature Molden has incorp orated the calculation of multip ole
moments according to the following formalism
The coulombinteraction of twocharge distributions can b e expressed as a
Molden a pre and p ost pro cessing program for molecular and
electronic structures
multip ole expansion in the form
X
m m
l l
U l l R Q Q S
elec l m l m
l l l l
l l m m
Where l l denotes the numerical factor l l l l the
Q describ e the charge distributions and S is a function of the relativeorienta
lm
tion of molecules The Q are complex for m
lm
m
p p
Q iQ Q Q iQ Q
lmc lms l m lmc lms l m
A molecular charge distribution can b e describ ed as set of multip ole expan
sions at centers T where T consists of atomic centers and centers due to in
teratomic overlap density According to the gaussian pro duct theorem the
A B
pro duct of two gaussian typ e orbitals and centered at atomic p ositions
A and B and with exp onents and is itself a gaussian function centered at
point T given by
T A B
In Mo dern Ab Initio programs the AO s are group ed in shells where the s p
and or d orbitals in a shell are a xed linear combination of the same primitive
gaussians and therefore all contribute to a given site T asso ciated with a pro duct
of primitive gaussians The Q are calculated as the exp ectation value of the
lm
regular spherical harmonics
X X
Q T P d d h jR j i Q T P d d h jR j i
lmc rs ri sj i lmc j lms rs ri sj i lms j
rs rs
Here P is an element of the density matrix r and s run over all AO s within
rs
shell I and I I resp ectively and eachAO is expressed as a linear combination of
P
d gaussian primitive functions AO
ri i i i
r
Amultip ole expansion ab out the p oint T can b e represented as a multip ole
expansion ab out any other p ointSby means of the formula
Chapter
k l
X X
l m l m
A A
Q T R S T Q S
kq lk mq lm
k q k q
q k k
Thus the proliferation of expansion centers can b e reduced by shifting some or
all of the overlap charge distribution to the atomic centers Molden o ers three
schemes for shifting the overlap charge distribution
shift all overlap density to the atomic sites default
shift all overlap density to the nearest atomic site or to a site halfway
between the b onds
only shift overlap densitybetween non b onded atoms
Molden calculates the multip ole moments up to the hexadecap ole rank
since explicit terms in equation are only available upto hexadecap ole moment
Wenow turn to explicit formulae for the integrals of typ e h jR j i The
i lmc j
regular spherical harmonics can b e written as a linear combination of p owers of
P
l m n
r r r
g x y z and cartesian co ordinates R
r
r
X
l m n
r r r
g h jx h jRj i y z j i
r i i j j
r
n m l
r r r
j i can b e derived in analogy for that of the z y An expression for h jx
j i
overlap integral as describ ed by Saunders
A l m n B
r r r
AB I I I h jx y z j i exp
x y z
l m n l m n
in which
Z
l l
X
il x
r
x e TA TB dx I f l l
x x x i
i
l l
X
i l
r
TA TB i l f l l
x x r i
il
r
i
Molden a pre and p ost pro cessing program for molecular and
electronic structures
with k for o dd k and k for even k TA is the x comp onentof
x
the vector connecting atomic center A with the center of the gaussian pro duct T
TB is the x comp onentofthevector connecting atomic center B with the center
x
of the gaussian pro duct T AB A B A B l l
and
ij k
X X
l l
l i l j
A A
TA TB TA TB f l l
x x k
x x
i j
i l j l
Expressions for I and I can b e obtained by replacing l with m and n re
y z
sp ectively and replacing x by y and z resp ectively Molden can thus calculate dis
tributed multip ole moments for Ab Initio wavefunctions as read from the outputs
of the b eforementioned Computational Chemistry packages These distributed
multip ole moments can b e used to calculate an approximate electrostatic p oten
tial using the expression for the coulombinteraction of twomultip ole expansions
describ ed ab ove The distributed multip ole moments are also used to generate input for the DMAREL program
Chapter
The Electrostatic Potential and ESP derived charges
Since the ma jority of force eld packages is not capable to deal with distributed
multip oles p oint atomic charges are frequently used to describ e the electrostatic
comp onent of the energy in force eld calculations One way to obtain these
charges is by tting an atom centered monop ole approximation to the molecular
electrostatic p otential MEP The MEP can b e used to predict the sites in a
molecule which are most reactivetowards protonation or more generally towards
an electrophilic attack
As rst de ned by Bonaccorsi et al the MEP V r represents the value
at rst order of p erturbation of the interaction energy b etween molecule M and
a proton lo cated in r
Z
X
r Z
a
dr V r
jr r j jr r j
a
The rst term corresp onds to nuclear repulsion from the nuclei with charge Z
a
and the second originates from electronic attraction b etween the proton and the
electron density The latter is equivalent to the Nuclear Attraction Integrals
NAI required for the construction of the electron Fock matrix in Hartree
Fock calculations The algorithm currently implemented in Molden calculates
the NAI s utilizing the Rys Polynomial Metho d and a scheme develop ed by
Besler et al where the MEP is calculated on a numb er of Connolly surfaces
generated by scaling the Van der Waals radii of the atoms Fitting is accomplished
by a least squares pro cedure It has b een noted that charges computed by sucha
pro cedure may b e conformationally dep endent and pro cedures exist which allow
for the tting of charges to multiple conformations It has also b een noted
that sometimes not all charges can b e determined with the simple least squares
pro cedure By application of a singular value decomp osition on the least squares
matrix an estimate of the number of charges that can b e assigned with statistical
validity can b e obtained Both the tting of charges to multiple conformations
and the singular value decomp osition approachhave not yet b een used in Molden
Molden a pre and p ost pro cessing program for molecular and
electronic structures
Figure The Molecular Electrostatic Potential for the water molecule
MEP Hartree grey area
Molden calculates the MEP for a variety of plots the D contour plot the
D iso contour plot as in Figure and color co ded on a Van der Waals surface
Chapter
Discussion
Wehave presented a description of the current state of development of Molden
The animation options and the treatment of di erence density the Laplacian of
the electron density the distributed multip oles and the electrostatic p otential
have b een extended and where necessary theoretically underpinned Ongoing
development include the incorp oration of charges tted to the DMA derived elec
trostatic p otential Preliminary calculations haveshown that the computational
costs of the pro cedure are orders of magnitude less than those of the traditional
ESP charge calculations The lo cation of extrema on the electrostatic p otential
map the interfacing to the DMAREL program and visualization of the spin den
sity are other Molden developments Some computational chemistry programs are
being interfaced to Molden e g the Quantum Theory Pro ject the MOLPRO
package and the ADF package Prof A Bencini Inorganic Computational
Chemistry University of Florence Molden has established a sizeable user base
world wide
Acknowledgements
The investigations rep orted in this pap er were supp orted by the Netherlands
Organization for Chemical Research NWO CW within the framework of the
PPM CMS Crystallization pro ject CMS c The CMS c pro ject is a Dutch
research collab oration with academic and industrial partners fo cussing on pre
comp etitive researchinto mo deling packing morphology and industrial crys
tallization of organic comp ounds Pro ject information is a accessible at URL
http www caos kun nl cmsc
Molden a pre and p ost pro cessing program for molecular and
electronic structures
References and Notes
Frish M J Trucks G W Head Gordon M Gill P M W Wong M W Foresman J B
Johnson B G Schlegel H B Robb M A Replogle E S Gomp erts R Andres J L
Raghavachari K Binkley J S Gonzalez C Martin R L Fox D J Defrees D J
Baker J Stewart J J P Pople J A Gaussian Gaussian Inc Carnegie O ce Park
Pittsburgh PA
Schmidt M W Boatz J A Baldridge K K Koseki S Gordon M S Elb ert S T
Lam B GAMESS Program No Indiana University Blo omington Indiana
Guest M F Kendrick J van Lenthe J H Sho e el K Sherwood P GAMESS UK
Users Guide and Reference Manual Computing for Science CFS Ltd Daresbury Lab o
ratory
Stewart J J P QCPE Bull
Nielsen A B Holder A J GaussView User s Reference Gaussian Inc Carnegie O ce
Park Carnegie PA USA
Trip os Asso ciated Inc St Louis USA
Molecular Simulations Inc Scranton Road San Diego CA USA Cerius User Guide
March
Schaftenaar G QCPE Bull
Bernstein F C Ko etzle T F Williams G J B Meyer E Bryce M D Rogers J R
Kennard O Shikanouchi T Tasumi M J Mol Bio
Wishart D S Willard L Richards F M Sykes B D VADAR A ComprehensivePro
gram Suite for Protein Structural Analysis Protein Engineering Network of Centres of
Excellence University of Alb erta
Allen F H Bellard S A Brice M D Cartwright B A Doubleday A Higgs H Hum
melink T Hummelink Peters B G Kennard O Motherwell W D S Ro dgers J R
Watson D G Acta Crystallogr Sect B
Allen F H Johnson O Macrae C F Smith J M Motherwell W D S Galloy J J
Watson D G Rowland R S Edgington P R Garner S E Davies J E Mitchell G F
CSD System Do cumentation Cambridge Crystallographic Data Centre Union Road
Cambridge CB EZ UK
Minnesota Sup ercomputer Center Inc Minneap olis MN XMol Users Manual
Chemical Design Ltd Oxon England Chem X Reference Guide Volume I I I
GRAPHICS INTERCHANGE FORMATVersion a Columbus Ohio CompuServe
Incorp orated
Stewart R F J Chem Phys
Hirshfeld F L Acta Crystallogr Sect B
Kunze K L Hall M B J Am Chem So c
Schwarz W H E Ruedenb erg K Mensching L J Am Chem So c
F L Hirshfeld Crystal lography Reviews vol ch Electron density distributions in
molecules England Gordon and Breach
Bader R F W Keaveny I Cade P E J Chem Phys
Schwarz W H E Valtazanos P Ruedenb erg K Theor Chim Acta
Chapter
Ro othaan C C J Rev Mo d Phys
I Fleming Frontier Orbitals and Organic Chemical Reactions New York Wiley
R Bader Atoms in Molecules A Quantum Theory Oxford Oxford University Press
Bader R F W Pop elier P L A Keith T A Angewandte Chemie Intl Ed Eng
Bader R F W Gough K M Laidig K E Keith T A Molec Phys
Bader R F W Gillespie R J MacDougall P J J Am Chem So c
Clementi E Davis D R J Chem Phys
Stone A J Chem Phys Lett
Price S L Stone A J Alderton M Molec Phys
Buckingham A D Fowler P W Can J Chem
Price S L Stone A J J Chem Phys
Mitchell J B O Nandi C L Thornton J M Price S L Singh J Snarey M J Chem
So c FaradayTrans
Price S L Lo Celso F Treichel J A Go o dfellow J M J Chem So c FaradayTrans
Co omb es D S Price S L Willo ck D J Leslie M J Chem Phys
Stone A J Dullweb er A Pop elier P L A Wales D J Orient a program for studying
interactions b etween molecules version UniversityofCambridge
Willo ck D J Price S L Leslie M Catlow C R A J Comp Chem
Boys S F Pro c R So c
V Saunders Computational Techniques in Quantum Chemistry and Molecular Physics
ch An Intro duction to Molecular Integral Evaluation Dordrecht Reidel
Bonaccorsi R Scro cco E Tomasi J J Chem Phys
Dupuis M Rys J King H F J Chem Phys
King H F Dupuis M J Comp Phys
Besler B H Merz K M Kollman P A J Comp Chem
Bayly C I Cieplak P Cornell W D Kollman P A J Phys Chem
Francl M M Carey C Chirlian L E J Phys Chem
URL http www qtp u edu
Werner H J Knowles P J User s manual for MOLPRO Insititut fur Theoretische
Chemie Universitat Stuttgart and Scho ol of Chemistry University of Birmingham
Baerends E J Ellis D E Ros P Chem Phys
Chapter
The e ect of iso density surface sampling on
ESP derived charges and the e ect of adding
b ondcenters on DMA derived charges
This chapter has b een repro duced with kind p ermission from G Schaftenaar J H No ordik J
c
Comp Aided Molecular Design Kluwer Academic Publishers
Summary
The e ect of sampling the electrostatic p otential around a molecule on the quality
of electrostatic p otential derived charges is investigated In addition the e ect of
the numb er of expansion sites in a Distributed Multip ole Analysis on the quality
of charges tted to the DMA derived electrostatic p otential is investigated Sam
pling on constant electron density surfaces gives a b etter t b etween the quantum
mechanical p otential and the p otential derived from the tted charges compared
to sampling on a Van der Waals surface comp osed of intersecting spheres The t
between the electrostatic p otential derived from p ointcharges and the quantum
mechanical p otential b ecomes p o orer with an increasing quality of the employed
basis set The inclusion of b ondcenters into the calculations improves the t
between the Quantum Mechanical electrostatic p otential and the DMA derived
potential The numb er of expansion sites needed for an accurate approximation
of the QM electrostatic p otential increases with increasing quality of the used
basis set
Intro duction
Classical force eld metho ds use Coulomb s law to describ e the electrostatic inter
actions of molecules This requires the use of p ointcharges Most force elds use
Chapter
aquick calculation of p ointcharges based on electronegativity rules Several
metho ds exist to determine p ointcharges from a Quantum Mechanical QM
calculation These metho ds can b e sub divided into a class where charges are
determined by some scheme that partitions the electron densityover the atoms
Mulliken Bader Hirshfeld and a class where charges are optimized to re
pro duce the QM electrostatic p otential ESP by employing a least squares t
of the mo del on p ointcharges based p otential and the QM p otential From
nowonwe will refer to these charges as QMESP charges Metho ds in the latter
class di er mainly byhow and where the electrostatic p otential in sampled in the
surrounding molecular space These metho ds sometimeshave problems with
statistically p o orly determined charges on buried centers The RESP metho d
was develop ed to deal with this problem by allowing the simultaneous t of
charges for multiple conformations
However using p ointcharges to describ e electrostatic contributions neglects
the fact that an atom in the eld of other atoms is p olarized and exerts an electric
force which is not spherically symmetric By representing the molecular charge
distribution as a set of multip oles on a number of centers the electrostatic interac
tion can b e mo deled far more accurately Stone has describ ed a generally
applicable metho d for the determination of distributed multip ole moments from
electron density determined using Quantum Mechanics QM However most
force eld metho ds cannot handle multip oles and rely on atomic partial charges
to describ e electrostatic interactions Exceptions are the tinker package byPon
der and the DMAREL program The distributed multip oles can still b e useful
for p ointcharges based force elds since the DMA derived electrostatic p otential
can b e used to obtain DMA derived charges DMAESP charges The advantage
of these DMAESP charges over the conventional QMESP charges is a decrease
in computational cost of a two orders of magnitude A pro cedure to calculate
the DMAESP charges is available in our program Molden and has recently b een
develop ed indep endently by Winn et al DMAESP charges are not equivalent
to the monop oles which are the lowest rank of multip oles resulting from a Dis
tributed Multip oles Analysis These monop oles su er from the same de ciency
as charges derived from a Mulliken p opulation analysis in which the overlap
density is equipartitioned over the contributing atoms which is a quite arbitrary
choice as explained by Williams In the DMA approach the overlap densityis
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
shifted see formula from the previous article to the nearest expansion
site In the standard approach this expansion site is an atomic site whichis
an equally arbitrary choice as equipartitioning The rst ob jective of this work
is to evaluate the quality of DMAESP charges in comparison with conventional
QMESP charges
The second ob jective of this work is to improve the quality of b oth ESP and
DMAESP charges by b etter sampling of the QM or DMA derived electrostatic
p otential around the molecule
Metho ds
The quality of DMA derived charges versus QMESP charge
The agreementbetween of DMAESP charges and conventional QMESP charges
is limited byhowwell the DMA derived electrostatic p otential approximates the
QM electrostatic p otential From nowonwe will refer to the QM electrostatic
p otential as true p otential Not shifting the overlap density to atomic sites
should in priciple pro duce the b est agreementbetween the DMA p otential and the
QM p otential This metho d is only tractable for the smallest molecules b ecause
the number of overlap sites scales with the square of the numb er of primitive
cartesian gaussians used to describ e the electron density and thus increases with
basis set quality It is exp ected that increasing the numb er of expansion sites will
systematically improve the agreementbetween the true electrostatic p otential
and the DMA derived p otential and that more expansion sites are needed as the
quality of the basis set increases We will compare the agreementbetween the
DMAESP charges with those of the true ESP equivalent for twoDMAvariants
the standard approach with only atomic expansion sites and a variant where
b ondcenters have b een added
The quality of the DMA derived p otential can b e insp ected by visualizing
the di erence b etween the QM p otential and the DMA derived p otential The
qualityofthecharges will b e judged by the ro ot mean square of the di erence
in atomic partial charges derived from the QM p otential and the DMA derived
potential Qrms for a test suite of molecules The mathematical background of
electrostatic p otentials the charge tting pro cedure and the Distributed Multi
Chapter
p ole Analysis are covered earlier in some detail The methylammonium
propanol salt of a cyclic phosphoric acid the so called pa complex has highly
lo calized charges the phosphorus is strongly p ositiveandtwooftheoxygens
b onded to it carry a nearly full negativecharge An additional p ositivecharge
is lo cated on the nitrogen atom and the complex has twohydrogen b onds see
Figure For an accurate QM calculation di use functions on the negatively
charged oxygens are required This complex will serve as a test case for a highly
inhomogeneous electrostatic p otential
H H
C H
H H H C H C
N C H H OH H H H
O2 O1
P
O3 O4
H H C C H H C H
H
Figure Test suite pa complex with highly lo calized charges
The e ect of sampling on the quality of DMA derived charges
and QMESP charges
The second ob jective of this work is an attempt to improve the qualityofboth
ESP and DMAESP charges by b etter sampling of the QM or DMA derived
electrostatic p otential around the molecule The quality criterion in all ESP
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
metho ds is a minimal quadratic sum of the deviation of the mo del p otential from
the QM electrostatic p otential at the p oints used in the t Henceforth wewill
refer to it as the go o dness of t or GOF
Figure Isop otential surfaces p otential Hartree yellow Hartree
red of the cytosine molecule for three typ es of p otentials a the QM electro
static p otential b the DMA derived p otential and c the ESP charges derived
p otential
s
P
m
c o
V V
i i
i
GO F
n
c o
the mo del p otential whichisgiven is the QM electric p otential and V where V
i i
by Coulomb s law
n
X
q
j
c
V
i
r
ij
j
where i runs over the p oints sampling the electric p otential m in total and
j runs over the number of charges to b e tted n in total r is the distance ij
Chapter
between p ointcharge j and sampling p oint i Large p otentials and large devia
tions tend to b e strongly expressed in the GOF giving unfairly great weights to
the p oints nearby atoms This may ultimately result in a p o or t of the p otential
at the sampling p oints with small p otentials and a decrease in quality of the
charges asso ciated with it It is therefore crucial for the quality of the t not
to oversample large p otential values Williams exp erimented with the limit of
the inner b oundary of the Van der Waals surface The t to the QM p otential
rms and rrms b ecame worse at the smaller b oundary and b etter at the larger
b oundary Singh and Kollman lo cated p otential grid p oints in equally spaced
shells lo cated at and times the Van der Waals radii However
using sucha Van der Waals surface one uses the same Van der Waals radii re
gardless of the di erent atomic environments In contrast to a neutral oxygen a
negatively charged oxygen atom is likely to have an electrondensity distribution
that extends further into space which corresp onds with a slightly larger Van der
Waals radius Using a smaller radius will result in sampling p oints with a higher
electron density with resp ect to the neutral oxygen This in turn could lead to
oversampling of high ESP values for some of the oxgygen atoms with resp ect to
others The magnitude of this e ect will increase with increasing level of detail
of the basis set since a more exible basis set allows the atoms to extend further
into space
Toavoid these problems we prop ose to sample the electrostatic p otential
on a numb er of surfaces with constant electron density or iso density surfaces
This has the advantage of minimizing electron cloud p enetration e ects As two
molecules approacheach other their p otentials are distorted by electron cloud
p enetration e ects Using iso density surfaces ensures that lo cal di erences in
electron cloud p enetration are small in the area where the electrostatic p otential
is sampled The values of the electron density are chosen such that the iso density
surfaces approach b est the Van der Waals shells employed by Singh and Kollman
Sampling also e ects the quality of DMAESP charges as compared to QMESP
charges The QM p otential and the DMA derived p otential and the ESP charges
derived p otential b ehave di erently near the atoms See Figure When r
the distance to a particular atom is small the QM p otential is a function of the
nuclear charge divided by r whereas a charges derived p otential and the DMA de
rived p otential in rst approximation are a function of partial charge divided by
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
r Sampling to o close to the atoms will therefore reduce the quality of DMAESP
charges As discussed ab ove b oth the quality of the QMESP DMAESP charges
and the corresp ondence b etween QMESP and the DMAESP are dep endent on the
quality of the basis set used therefore we will present the basis set dep endency
as a separate topic QMESP charges mentioned in this work were all calculated
using the scheme by Singh and Kollman
Figure Graphical illustration of the di erence b etween the QM electrostatic
p otential and the DMA p otential with only atomic expansion sites for the cytosine
molecule Shown as surfaces with constant p otential v v yellow and v
red v Hartree kcal mol
Chapter
Figure The di erence of the QM electrostatic p otential and the QMESP
charges derived p otential a the DMA p otential derived with atomic expansion
sites only b and the DMA p otential derived with atomic and b ond centers
expansion sites c Shown as surfaces with constant function values v v
yellow and v red v Hartree kcal mol for gures b and c
v Hartree kcal mol for gure a Also shown is the surface with
constant densityvalue e B ohr blue color
Results
DMA derived charges
In Table twovariants of DMAESP charges are compared with the true
QMESP charges charge set using the ro ot mean square di erences of the
atomic partial charges Qrms as criterion In the rst variant only the atoms
were used as expansion sites charge set In the second variant in addition
b ondcenters were included as expansion sites charge set Both Van der Waals
surface sampling and the iso density surface sampling were p erformed They are
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
designated byVDW and ISO resp ectively
Table Comparison of the ro ot mean square Qrms of the di erence b etween
DMAESP charges and QMESP charges for twotyp es of electrostatic p otential
sampling van de Waals surface sampling VDW and iso density surface sam
pling QMESP charges DMA with atomic expansion sites DMA with
b ondcenter sites added
VDW VDW ISO ISO
compound Qr ms Qr ms Qr ms Qr ms
H O
tetr ahy dr of ur an
metoxy methy l
metoxy tetr ahy dr of ur an
cy tosine
pa compl ex
benz ene
g
g
A comparison of the charges calculated with the two DMA variants shows that
the addition of b ondcenters charge set to only atomic expansion sites charge
set reduces the Qrms values for b oth VDW surface sampling and iso density
surface sampling The di erence in Qrms values is ab out a factor for VDW
surface sampling and ab out a factor for iso density surface sampling clearly
showing the improved charges resulting from the iso density surface sampling
In Figure the overall di erence b etween the QM p otential and the DMA
p otential with atomic expansion sites only is illustrated graphically for the cyto
sine molecule This di erence is p ositive yellow near the atoms and negative
red b etween the atoms i e the region of space closest to the b ondcenters
Chapter
This observation suggested that the agreementbetween b oth p otentials could b e
improved by adding expansion sites at the b ond centers
The improvement of the t is presented graphically in Figure whichshows
the di erence function b etween the QM electrostatic p otential and three derived
p otentials
a The electrostatic p otential derived from QMESP charges
b The DMA derived p otential with atomic expansion sites only
c The DMA derived p otential with atomic and b ond centers expansion
sites
Figure clearly shows that the error resulting from sampling the space
outside the iso density surface is larger for the DMA derived p otential with only
atomic expansion sites b than for the p otential derived with b ondcenter ex
pansion sites added c The error surfaces extend further into space for smaller
absolute values of the error v This can b e understo o d if one considers that close
to the atomic sites the di erence function always b ecomes strongly p ositivebe
cause of the di erent b ehaviour of the QM p otential and the derived p otentials
in this region as discussed ab ove It can also b e seen that the DMA derived
p otentials are in far b etter agreement with the QM p otential than the QMESP
charges derived p otential
Iso density surface sampling vs Van der Waals surface sampling
For the pa complex in our test suite distances of di erentoxygen atoms to the
surface with densityvalue e B ohr are given in Table It can b e seen
that the extension in space varies up to Angstrom from a hydroxyl oxygen
OH to the negatively charged oxygen b onded to phosphorus O
For the same comp ound this iso density surface for two di erent basis sets
g and g and a Van der Waals surface of intersecting spheres scaled by
a factor of are shown in Figure This Van der Waals surface approximates
the iso density surface quite well for the medium sized basis set but it lays well
inside the iso density surface of the bigger basis set
Van der Waals surface sampling will include more higher density p oints for the
medium size basis set than for the larger basis set This is equivalent to sampling
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
Figure Iso density surface with densityvalue e B ohr for two di erent
basis sets g top and g b ottom The electrostatic p otential is color
co ded on the surface p ositivevalues orange negativevalues blue The Van der
Waals surface of intersecting spheres with a Van der Waals radius scaled bya
factor is shown as a solid surface
Chapter
Table Distance to the surface with constant density for di erentoxygen
atoms in the pa complex
Atom Distance in Angstroms to iso density surface
density e B ohr
OH
O
O
O
O
more p oints with a lower electrostatic p otential since higher electron density
means more shielding of the nuclear charge Only for the medium quality basis
set iso density surfaces at densityvalues and e B ohr
are fairly well approximated byVan der Waals surfaces lo cated at and
times the Van der Waals radii resp ectively
Comparison of the go o dness of t b etween VDW surface sampling and iso
density surface sampling See table shows that the iso density surface sam
pling yields signi cantly b etter go o dness of t values There is also a general
trend towards b etter corresp ondence with the QM dip ole moment when iso den
sity surface sampling is used although this trend is not as strong as with the
GOF values
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
Table Comparison of the Van der Waals surface sampling VDW and the
iso density surface sampling ISO based on the GOF s in kcal mol and the
di erences D between the dip olemoment based on charges and the quantum
mechanical dip ole moment D bothinDebye
VDW ISO VDW ISO
C ompound GO F GO F D D D
H O
tetr ahy dr of ur an
metoxy methy l
metoxy tetr ahy dr of ur an
cy tosine
pa compl ex
benz ene
g
g
Chapter
Figure The di erence function of the QM electrostatic p otential g basis set and a QMESP charges derived
p otential b c d three variants of the DMA derived p otential Shown as surfaces with constant function value
v for the pa complex v yellow and v red v Hartree kcal mol for b c d and v
Hartree kcal mol for a the surface with constant densityvalue e B ohr is shown in blue
Figure The di erence function of the QM electrostatic p otential g basis set and a QMESP charges
derived p otential b c d three variants of the DMA derived p otential Shown as surfaces with constant function
value v for the pa complex v yellow and v red v Hartree kcal mol for b c d and
v Hartree kcal mol for a the surface with constant densityvalue e B ohr is shown in blue
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
Figure The di erence function of the QM electrostatic p otential g basis set and DMA derived p otential a
front side view and c back side view of pa complex for b ond center sites only b and d idem with hydrogenbond
center sites added Shown are surfaces with constant function value v v yellow and v red v Hartree
kcal mol The surface with constant densityvalue e B ohr is shown in blue
Figure The di erence function of the QM electrostatic p otential g basis set and DMA derived p oten
tial a front side view and c back side view of pa complex for b ond center sites only b and d idem with
hydrogenbond center sites added Shown are surfaces with constant function value v v yellow and v red v
Hartree kcal mol The surface with constant densityvalue e B ohr is shown in blue
Chapter
Basis set quality in uences the t b etween the QM electrostatic p otential and
derived p otentials This e ect is clearly shown bytheGOFvalues presented in
Table The e ect is most pronounced for Van der Waals surface sampling
There the GOF b ecomes signi cantly worse with increasing basis set quality
For iso density surface sampling the GOF is not only b etter but also do es not
signi cantly increase with increasing basis set quality
Table The GOF in kcal mol as a function of the basis set qualityforVan
der Waals surface sampling VDW and iso density surface sampling ISO Data
presented are for the pa complex
VDW ISO
basis set GO F GO F
sto g
g
g
Besides e ecting the t basis set quality also e ects the reliabilityofthe
DMAESP charges Indep endent of sampling metho d and the DMA variant used
the deviation of DMAESP charges from QMESP charges deteriorates with in
creasing basis set quality as shown by the Qrms values in Table
The larger the basis set one selects to calculate the QM electrostatic p otential
the less is the t with derived p otentials and the less charges can b e approximated
byany less compute intensive metho d However by addition of more expansion
sites to the DMA analysis DMA derived p otentials can b e systematically im
proved
The deteriorating agreement with increasing basis set exibilitybetween QM
electrostatic p otential and derived p otentials and the improvementin tby
adding additional expansion sites is illustrated graphically in Figures
and The decrease in t is understo o d by considering that the ratio
atomic plus overlap sites versus atomic plus b ond center sites b ecomes increas
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
Table Ro ot mean square values Qrms of the deviation of DMAESP charges
from QMESP charges as a function of basis set quality and sampling metho d Van
der Waals surface sampling VDW and iso density surface sampling ISO Data
for the pa complex QMESP charges DMA with atomic expansion sites
DMA with b ondcenter sites added
VDW VDW ISO ISO
basis set Qr ms Qr ms Qr ms Qr ms
sto g
g
g
ingly unfavorable with increasing exibility of the basis set used Figures
g basis set and g basis set show the di erence function b etween
the QM electrostatic p otential and four derived p otentials for the molecular pa
complex
a The electrostatic p otential derived from ESP charges
b The DMA derived p otential with atomic expansion sites only
c The DMA derived p otential with atomic and b ond centers expansion
sites
d The DMA derived p otential with atomic b ond center and hydrogen
b ond center expansion
Comparison of Figures and shows the basis set e ect the systematic
improvement as a result of the addition of expansion sites is clearly illustrated in
going from a to d in b oth Figure and
The improvement of the t b etween the QM electrostatic p otential and DMA
derived p otentials as an e ect of the addition of hydrogenb ond center expansion
Chapter
sites on top of atomic and b ond center sites is shown in more detail in Figures
and where we zo om in on p otentials c and d ab ove
The e ect of the addition of hydrogen b ond center expansion sites on the
quality of the t is most signi cantattheback side of the molecule where the
spacial extension of electron density is less pronounced The lo cations where the
DMA derived p otential still deviates from the QM p otential could b e identi ed
as oxygen lone pair sites
Timings
Table shows a comparison of times needed to calculate QMESP charges
t and DMAESP charges t as a function of the numb er of basis
QM E S P DM AESP
functions used to describ e the QM electron density The ratio t t
QM E S P DM AES P
increases in favor of the DMAESP charges with increasing numb er of basis func tions ranging from for small systems to for larger systems
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
Table Comparison of the calculation time of QMESP charges t and
QM E S P
DMAESP charges t as a function of numb er of basis functions used
DM AES P
Timings are in seconds
C ompound t t t B asis
QM E S P DM AESP QM E S P
t F unctions
DM AESP
H O
benz ene
cy tosine
tetr ahy dr of ur an
metoxy methy l
metoxy tetr ahy dr of ur an
pa compl ex
g
g
Conclusions
Calculations on a set of test molecules with wide varietyofcharge distributions
were p erformed to establish the quality of the DMA derived electrostatic p oten
tials and the e ect of the sampling metho d on the qualityofcharges tted to
a DMA derived p otential The advantage of DMAESP charges over the con
ventional QMESP charges is a decrease in computational cost of a few orders
of magnitude It was found that the quality of the DMA derived electrostatic
potential can b e systematically improved by adding additional expansion sites
to the DMA analysis and that more sites are needed with increasing basis set
quality The same pro cedure improves the DMAESP charges as well Sam
pling the electrostatic p otential on iso density surfaces instead of sampling on a
Van der Waals surfaces improves b oth ESP and DMAESP charges Using the
Chapter
iso density sampling metho d and a su ciently large numb er of expansion sites
DMAESP charges can b e calculated in go o d agreement with the conventional
QMESP charges with typical errors b eing smaller than one p ercent
Acknowledgements
The investigations rep orted in this pap er were supp orted by the Netherlands
Organization for Chemical Research NWO CW within the framework of the
PPM CMS Crystallization pro ject CMS c The CMS c pro ject is a Dutch
research collab oration with academic and industrial partners fo cussing on pre
comp etitive researchinto mo deling packing morphology and industrial crys
tallization of organic comp ounds Pro ject information is a accessible at URL
http www caos kun nl cmsc
The e ect of iso density surface sampling on ESP derived charges and
the e ect of adding b ondcenters on DMA derived charges
References and Notes
Del Re G J Chem So c London
Gasteiger J Marsili M Tetrahedron
Mulliken R S J Chem Phys
R Bader Atoms in Molecules A Quantum Theory Oxford Oxford University Press
Hirshfeld F L Theor Chim Acta
Breneman C M Wib erg K B J Comp Chem
Besler B H Merz K M Kollman P A J Comp Chem
Bayly C I Cieplak P Cornell W D Kollman P A J Phys Chem
Stone A J Chem Phys Lett
Price S L Stone A J Alderton M Molec Phys
Ponder J W Richards F M J Comp Chem
Willo ck D J Price S L Leslie M Catlow C R A J Comp Chem
Winn P J Ferenczy G G Reynolds C A J Phys Chem
D E Williams Reviews in Computational Chemistry ch Net Atomic Charge and Mul
tip ole Mo dels for the ab initio Molecular Electric Potential New York VCH Publishers
Inc
Schaftenaar G No ordik J H J Comp Aided Molecular Design accepted for publication
Cox S R Williams D E J Comp Chem
Singh U C Kollman P A J Comp Chem Colonna F Evleth E J Comp Chem
Chapter
Chapter
Quantum mechanical and force eld calculations
on the diastereomeric salts of cyclic phosphoric
acids with ephedrine
Summary
Wehave calculated the relative lattice energies of the diastereomers of cyclic phos
phoric acid and its chlorine derivative with ephedrine with various computational
mo dels and compared them with exp erimental data All computational mo dels
gave go o d structural agreement with the exp eriment but only some mo dels repro
duced the exp erimental stability order Calculations with the DREIDING force
eld in combination with several charge sets failed to repro duce the exp erimental
stability order of the diastereomers By using distributed multip oles to mo del
the electrostatic interactions in force eld calculations the correct stability order
was repro duced in one case but the results are very sensitive to the factor used
for scaling the electrostatic interactions and to conformational energy corrections
of the rigid b o dies Quantum mechanical calculations with the DMol density
functional package predict a correct stability order for one pair of diastereomers
but fail to p osition a third p olymorph correctly Similar calculations with the
VASP and SIESTA density functional packages predict the stability order of all
diastereomers correctly at the p oint in k space With b etter k space sampling
however the agreementbetween theory and exp eriment b ecomes less An ex
p erimentally unknown chlorine free analogue of the exp erimentally most stable
chlorine containing diastereomer was calculated to b e the least stable Mo del
systems of the twotyp es of hydrogen b onded chains observed in a series of dia
stereomeric salts with screw and translational symmetry were optimized at the
Hartree Fock and density functional level The exp erimentally most frequently
Chapter
o ccurring hydrogen b onded chain with screw axis symmetry was calculated to b e
the most stable
Intro duction
During the synthesis of optically active comp ounds one often obtains a racemic
mixture of stereoisomers These stereoisomers or enantiomers mayhavevery dif
ferent biological activities In the worst case the undesired enantiomer maybe
highly toxic or even teratogenic The Softenon a air was a dramatic example
of this One way of purifying a racemic mixture is to add a so called resolving
agent to the mixture The resolving agent is necessarily also an optically active
comp ound that forms diastereomeric salts with the enantiomers of the racemic
mixture A go o d resolving agent yields diastereomeric salts with very di erent
solubilities This metho d is known as selective crystallization of diastereomers
In his Ph D thesis Leusen proved that chiral discrimination is not a solution de
termined prop erty but manifests itself mainly in the solid state He established
a mo del that links the resolution e ciency to the crystal lattice energy di erence
between diastereomeric salt pairs Leusen tried to mo del the lattice energy di er
a
ences b etween ve diastereomeric salt pairs of ephedrine and a cyclic phosphoric
b
acid with molecular mechanics force eld calculations A go o d agreementbe
tween calculated and exp erimental structures was found The calculated energy
di erences however were not in agreement with exp eriment and in some cases
the stability order was predicted incorrectly He concluded that the description
of the electrostatic interactions within the force eld was insu ciently accurate
and that the inclusion of p olarization terms in the force eld is essential Whilst
Leusen worked on a system with highly lo calized charges Hansen p erformed sim
ilar calculations on a much wider range of comp ounds including diastereomeric
salts She concluded that force elds are generally not very go o d at repro ducing
the relative stability order of p olymorphs Limitations of the force elds are their
inabilities to handle crystals of comp ounds containing phosphorous or sulpher
as used by Leusen Hansen also concluded that it is not generally p ossible to
show that a particular charge set is sup erior i e she showed that a given charge
a
methylamino ethyl b enzyl alcohol
b
dimethyl hydroxy phenyl dioxaphosphorinane oxide
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
scheme p erformed well for some structures and badly for others From the ab ove
it is clear that an improvement in the description of the electrostatic interactions
would b e crucial for improving the repro duction of the relative stability order of
diastereomeric salts and p olymorphs The aim of our work is to nd suchbetter
computational metho ds
This may b e accomplished in a number of ways
using force eld calculations with improved mo dels of p ointcharges by
mo delling charges according to quantum mechanical derived electro
static p otentials of the anion cation complexes of the diastereomeric
salts instead of the ions alone In this wayweintend to incorp orate
some p olarization of the anion by the cation and vice versa
doing the same for multiple conformations of the ions and or the anion
cation complex
improving the quality of the mo dels of the charges by b etter sampling
of the quantum mechanical electrostatic p otential This is accom
plished by sampling the p otential on iso density surfaces as opp osed to
the often used used sampling on a van der Waals surface
employing force eld calculations with distributed multip oles instead of
pointcharges to describ e the electrostatic interactions
using quantum mechanical co des that can deal with p erio dic b oundary
conditions appropriate for a crystalline lattice
Weevaluated these metho ds on a subset of two of the diastereomeric salt pairs
used by Leusen These are the salt pairs of ephedrine with cyclic phosphoric acid
CPA and ephedrine with chlorine substituted cyclic phosphoric acid ClCPA
Accurate exp erimental geometries and relative lattice energies are available for
these systems
The second ob jective of our work is to understand the relative stabilities of
subsystems of the di erent crystal packings of these diastereomeric salts in par
ticular the two di erenttyp es of hydrogen b onded chains found in these crystals
Chapter
Metho ds
The crystal structures of cyclic phosphoric acid derivatives and
ephedrine
Wehave studied a subset of two of the diastereomeric salt pairs used by Leusen
These are the diastereomeric salts pairs of cyclic phosphoric acid with ephedrine
CPA E and chlorine substituted cyclic phosphoric acid with ephedrine ClCPA
E The reason for limiting ourselves to these structures is the computational cost
of the quantum mechanical calculations involved These two particular pairs of
diastereomeric salts were chosen on the basis of extreme di erences in lattice
energies The highest di erence in exp erimental lattice energy was found for
the salt pair of chlorosubstituted cyclic phosphoric acid ab out kcal mol and
lowest zero within exp erimental error for unsubstituted cyclic phosphoric acid
Whilst the rst stands the b est chance of b eing outside the error range inherent
in the di erent computational metho dologies the second can b e used as a null
calibration Table shows the absolute and relative exp erimental heats of
cor r
formation and the entropy corrected lattice enthalpy di erence H as de ned
solid
by Leusen for the diastereomers of CPA E and ClCPA E Throughout this article
cor r
weusethe H data for comparison with calculated lattice energy di erences
solid
The structures of diastereomeric salts pair CPA E have the reference co des
FIMVEC and FILGAI in the Cambridge Structural Database CSD The struc
tures of diastereomeric salts pair ClCPA E have the CSD reference co des FIM
TUQ and FIMVAY Table includes the names of the salts used by Leusen et
al
The structure SUMWEC is a p olymorph of the FIMVAY structure It was
discovered after the publication of Frank Leusen s Ph D thesis No solubility
cor r
data have b een published for this p olymorph so its H value can not b e
solid
cor r
calculated The di erence b etween the relative heats of formation and H
solid
is very small for the diastereomers FILGAI and FIMVEC So wehave used the
relative heat of formation for the structurally very similar SUMWEC Figure
shows deprotonated CPA and protonated ephedrine the forms in which they are
present in the diastereomeric salts with a rough indication of the charge centres
Figure shows the exp erimental structures of the diastereomers of CPA
FIMVEC FILGAI and ClCPA FIMTUQ SUMWEC FIMVAY with ephedrine
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Absolute and relative exp erimental heats of formation and the entropy
cor r
corrected lattice enthalpy di erence H in kcal mol of the diastereomers
solid
of CPA E and ClCPA E
cor r
Name r ef code H H H
f f
solid
CPA E
IN AP FIMV EC
IN AM F I LGAI
ClCPA E
CLINAP FIMTUQ
CLAM SU M W EC
CLINAM FIMV AY
The diastereomeric salt pairs are structurally similar This can b e seen
in Figure which shows the match of the salt pair of the unsubstituted
CPA FIMVEC FILGAI and the match of the salt pair of ClCPA FIMTUQ
SUMWEC All ve crystal structures adopt the P space group characterized
byatwo fold screw axis along the crystallographic b axis Apparently this crys
tal packing can accommo date b oth enantiomers of ephedrine without to o much
strain
There is also a strong structural similaritybetween the unsubstituted and
chlorosubstituted CPA salts This can b e seen in Figure which shows the
matchbetween the unsubstituted cyclic phosphoric acid salt FIMVEC with its
chlorine derivative counterpart FIMTUQ and the matchbetween the unsubsti
tuted cyclic phosphoric acid salt FILGAI and its chlorine derivative counterpart
Chapter
+ O N O - + P - O O O
EPHEDRINE CYCLIC PHOSPHORIC ACID
Figure Cyclic phosphoric acid and ephedrine in protonated and deprotonated
forms with a rough indication of the charge centres
SUMWEC This shows that the larger chlorine can b e accommo dated with little
strain
These four crystal structures all adopt the same crystal packing It is char
acterized by a screw symmetrichydrogen b onded chain as shown in Figure
This crystal packing is adopted in eight structures studied by Leusen
The most stable chlorosubstituted CPA salt FIMVAY adopts a very di er
ent crystal packing characterized byhydrogen b onded chains with translational
symmetry asshown in Figure
Figures and show simpli ed forms of the hydrogen b onded chains with
translational and screw symmetry resp ectively NO and NO are de ned as
the vectors from the ephedrine nitrogen hydrogen b ond donor to the phosphoric
acid oxygen hydrogen b ond acceptor With screw symmetry the twovectors are
distinct Whilst NO runs roughly parallel with the chain NO is more or less
p erp endicular to the chain direction With translational symmetry the di erence
between the two is not very distinct
The vector lengths of NO NO pairs in eight diastereomers with a screw
symmetric H b ond chain have a more or less linear relationship in which the
structure with the translational symmetricH bondchain do es not t see Fig
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
A A
C O C O
B B
FIMVEC FILGAI
A A A
C C O O B B B O C
FIMTUQ SUMWEC FIMVAY
Figure The exp erimental structures of the diastereomers of CPA E
FIMVEC FILGAI and ClCPA E FIMTUQ SUMWEC FIMVAY corresp ond
ing CSD reference co des in parenthesis
Figure shows the average lengths of NO and NO as a function of the
numb er of o ccurences N in diastereomers The diastereomers with screw sym
metric H b onded chains form a cluster with a mean distance of A
which is quite di erent from the diastereomer displaying translationally symmet
ric H b onded chains Apparently the screw symmetric chain has some comp en
satory exibility in the lengths of the NO and NO vectors when NO shortens
Chapter
A A
O O C C B B
FIMVEC-FILGAI FIMTUQ-SUMWEC
Figure Matchbetween the diastereomer pairs of CPA E FIMVEC FILGAI
and diastereomer pairs of ClCPA E FIMTUQ SUMWEC
NO lengthens and vice versa Some reservations ab out these conclusions how
ever are in order since the limited numb er of data p oints do es not allow for
truely reliable statistics
Computational metho ds
Classical force eld metho ds use Coulomb s law to describ e the electrostatic in
teractions of molecules This assumes the use of p ointcharges Most force elds
use a quick calculation of p ointcharges based on electronegativity rules Sev
eral metho ds exist to determine the value of lo cal p ointcharges from a quantum
mechanical QM calculation These metho ds can b e sub divided into a class
where charges are determined bysomescheme that partitions the electron den
sityover the atoms Mulliken Bader Hirshfeld and a class where charges
are optimized to repro duce the QM electrostatic p otential ESP by employing a
least squares t of the mo del p otential based on p ointcharges to the QM p oten
tial Metho ds in the latter class di er mainly byhow and where the electrostatic
p otential is sampled These metho ds sometimeshave problems with numeri
cally p o orly determined charges on buried centres The restrained ESP metho d
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
A A
O O C C B B
FIMVEC-FIMTUQ FILGAI-SUMWEC
Figure Matchbetween the diastereomers of CPA E FIMVEC and FILGAI
and their ClCPA E counterparts FIMTUQ and SUMWEC
RESP was develop ed to deal with this problem by allowing the simultane
ous tting of charges for multiple conformations In our work wetried rstlyto
improve the description of the electrostatic interactions by using ESP charges t
to the quantum mechanical electrostatic p otential of the anion cation complex of
the diastereomeric salts instead of the ions alone as done by Leusen In this
way one might exp ect to incorp orate some p olarization of the anion caused by
the cation and vice versa We also tried to improve the electrostatics using the
RESP metho d and nally we tried to improve the quality of the charges by b et
ter sampling of the quantum mechanical electrostatic p otential We accomplished
this by sampling the p otential on iso density surfaces as opp osed to sampling on
avan der Waals surface Wehave already develop ed this metho d for the same
purp ose In combination with these charges we use the DREIDING force
eld as implemented in the Cerius program for energy minimizations of the
cell parameters and the atomic p ositions
However using p ointcharges to describ e electrostatic contributions neglects
the fact that an atom in the eld of other atoms is p olarized and pro duces an
electric force which is not spherically symmetric By representing the molecular
Chapter
A
C
B O
Figure Example of the crystal packing class with screw symmetrichydrogen
b onded chains along the b axis Three unit cells are shown along this axis
charge distribution as a set of multip oles on a number of centres the electrostatic
interaction can b e mo delled far more accurately Stone describ ed a generally
applicable metho d for the determination of distributed multip ole moments from
aquantum mechanically determined electron density However most force eld
metho ds cannot handle multip oles and rely on partial charges to describ e elec
trostatic interactions Exceptions are the TINKER package byPonder an
adaptation of the TINKER package by Mo oij et al incorp orating p olarizable
multip oles and the DMAREL program Our computational chemistry pro
gram MOLDEN was adapted to calculate distributed multip ole moments from
a quantum mechanical wavefunction and to interface with b oth the Mo oij ver
sion of TINKER and the DMAREL program Only intermolecular interactions
can b e optimized with DMAREL the intramolecular conformations remain rigid
We used the DMAREL program to p erform force eld minimizations of the cell
parameters and the rigid b o dies of the ephedrine and cyclic phosphoric ions
The metho ds describ ed ab ove all use the prop erties of the isolated ions or
complexes to describ e the p erio dic system In a more complete description of
a p erio dic system the ions complexes feel the presence of their symmetry and
translationally related copies resulting in p olarization and or charge transfer
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
A
C O B
Figure Example of the crystal packing class with translationally symmetry
hydrogen b onded chains along the b axis Three unit cells are shown along this
axis
e ects Quantum mechanical packages that can handle p erio dic systems incor
p orate these e ects These packages usually employ density functional theory
DFT for the energy evaluation Unlike the Hartree Fock HF metho d
that completely neglects electron correlation within DFT it can b e taken into
account to a large extent DFT is computationally less demanding than other
metho ds for incorp orating electron correlation such as the p ost HF singles and
doubles con guration interaction SDCI and second order M ller Plesset p er
turbation theory MP
Table shows a summary of the strengths and weaknesses of the density
functional theory DFT in terms of the di erenttyp es of interaction present
in the system studied Hydrogen b onding is well describ ed by DFT when used
within the generalized gradient approximation GGA The lack of long range
disp ersion in exchange correlation functionals within the generalized gradientap
proximation yields a purely repulsivevan der Waals p otential Meijer and
Hobza rep orted that frequently used exchange correlation functionals yield a
purely repulsive b enzene dimer p otential From these considerations it can b e
Chapter
NO1
NO2
Figure Small mo del translationally symmetric H b onded chain used for ge
ometry optimizations
concluded that di erences in lattice energy b etween diastereomeric salts can only
b e calculated accurately with DFT if the contributions to the total energy from
ring ring and van der Waals interactions in the di erent diastereomers are very
similar Recently Rovira corrected for the lack of long range disp ersion by
adding a empirical correction term to the total energy Thishowever requires
extensive calibration of the correction term with MP calculations
We used the density functional packages VASP SIESTA and DMol to op
timize the atomic p ositions in the cell keeping the cell parameters xed at the
exp erimental values VASP is the ab initio total energy and molecular dynamics
program Vienna Ab Initio Simulation Program develop ed at the Institut fur
Theoretische Physik of the Technische Universit at Wien VASP is a den
sity functional co de using a plane wave basis set The interaction b etween ion
cores and electrons is describ ed using ultrasoft Vanderbilt pseudop otentials US
PP so only the valence electrons are treated explicitly VASP allows the
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
NO1
NO2
Figure Small mo del screw symmetric H b onded chain used for geometry
optimizations
simultaneous optimization of atomic p ositions and cell parameters The DMol
package uses atom centred numerical basis functions and a numerical integration
scheme for matrix elements The numerical integration has the prop ertythatthe
computational e ort can go down with decreasing overlap of the basis functions
This prop erty allows us to p erform all electron calculations on our atom sys
tems the asymmetric unit contains only atoms but DMol cannot handle
p oint group symmetry No core pseudo p otentials were used since DMol only
provides them for elements Sc through Lr DMol do es not allow the optimization
of cell parameters
The SIESTA package also uses atomic numerical basis functions and nu
merical integration Exploiting the spatial lo calization of the atomic basis set the
computational cost necessary for the calculation and storage of the self consistent
Hamiltonian matrix is made to scale linearly O N with the number of elec
trons N in the unit cell Furthermore for insulators the evaluation of the density
and total energy can b e also e ciently p erformed in O N op erations using the
Chapter
NO1 vs NO2 Trans Screw o NO2 (A) (NO1 + NO2) / 2 = 2.83 3.00
2.95
2.90
2.85
2.80
2.75
2.70
2.65
2.60 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 o
NO1 (A)
Figure Relation b etween the lengths of the exp erimental vectors NO and
NO for a numb er of diastereomers with H b onded chains with screw and trans
lational symmetry See Figures and for the de nitions of NO and NO
recently develop ed O N techniques In the presentwork however due to
the need of computing highly accurate total energies wehave decided to use a
standard diagonalization of the Hamiltonian The interaction b etween ion cores
and electrons is describ ed using the norm conserving Troullier Martins pseudop o
tentials
The PW GGA exchange correlation functional was used with b oth DMol
and VASP The PBE GGA exchange correlation functional was used with
SIESTA
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
(NO1 + NO2) / 2
N 4
3
Screw
2 o Mean 2.83 +/- 0.03 A
Trans
1
0 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 o
(NO1 + NO2) / 2 A
Figure The average of distances NO and NO as a function of the number
of o ccurrences N in diastereomers of derivatives of CPA E nine in total The
diastereomers with H b onded chains with screw and translational symmetry form
separate clusters See Figures and for the de nitions of NO and NO
Another imp ortant asp ect to consider when p erforming quantum mechanical
calculations on p erio dic systems is the sampling of the k space DMol only
c
considers one sp ecial p oint in the k space the p oint With the VASP and
SIESTApackages it is p ossible to sample the k space over more p oints than just
employing the metho d develop ed by Monkhorst and Pack We use the
c
This is the case for the DMol version supplied to us under courtesy license from MSI
The DMol versions and higher do allow for k space integration
Chapter
Table Strengths and weaknesses of the density functional metho d
I nter action I ncl uded C omment
Ionic complexes
Hydrogen b onds provided non lo cal DFT is used
Phenyl phenyl ring See reference
van der Waals Purely repulsivevan der Waals p otential
k p oint for geometry optimization with VASP and investigated the dep endence
of the relative lattice energies of the diastereomeric salts by p erforming single
p oint energy calculations with Monkhorst Pack sampling of the k space
on optimized geometries
Computational resources for the SIESTA calculations allowed us to p erform
geometry optimizations with xed cell dimensions at various levels of k space
sampling as well as to investigate the in uence of the simultaneous optimization
of cell parameters and atomic p ositions on the relative energies of the ClCPA E
diastereomers
All the ab ove mentioned packages use Ewald summation or related schemes
to do the lattice sums of the long range electrostatic interactions
Results
Ab initio calculations on mo del systems
The next section will deal with the construction of the mo dels in two steps It will
b e followed by a section discussing the results of the calculations on the mo dels
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Mo del construction
Step
As explained ab ove the most imp ortantinteraction in these diastereomers is in
the hydrogen bridged chains running along the crystallographic b axis These
chains consist of ionic complex units of protonated ephedrine and the anion of
cyclic phosphoric acid Twotyp es of chains are found one with screw symmetry
and the other with translational symmetry only Mo del structures three com
plexes units long were constructed for b oth screw symmetric and translationally
symmetric forms see Figures and resp ectively These mo dels were op
timized keeping their resp ective symmetries at b oth Hartree Fock and density
functional level of theory
The screw and translational symmetries were imp osed using a sp ecial con
struction of internal co ordinates within the Z matrix description of the molecular
geometry Table shows this Z matrix construction Displayed in normal font
are the atom lab els with a numerical subscript denoting the numb er of the com
plex unit they b elong to The rst column de nes the atom The second fourth
and sixth columns sp ecify the atomic connectivity with resp ect to previously de
ned atoms The lab el X denotes a geometrical auxiliary atom or dummy
atom Displayed in b old are the internal variables some of which are kept
constant numeric values and the string CONST The third fth and seventh
columns hold the internal variables of typ e b ond distance b ond angle and dihe
dral angle resp ectively The automatic generation of these Z matrix constructs
was built into our mo delling program MOLDEN
The implementation of symmetry in this way is only an approximation since
The three complexes units in the chains have di erentenvironments The
system in this mo del is therefore not truly p erio dic but only quasi p erio dic
In in nitely long chains each complex unit would have nearest neighbor
interactions with the complex units b efore and after it in the chain In
the three unit chain this is only true for complex unit Complex unit
interacts only with the complex unit after it and complex unit interacts
only with the complex b efore it So in the three unit long chains there are
only twointercomplex interactions with and with whereas in
Chapter
Table The Z matrix construction to implement fold screw and translational
symmetry
X
X X xx
A X dx X
B A d X angx X dihx
C B d A ang X dihx
X X xx A X
A X dx X A CONST
B A d X angx X dihx
C B d A ang X dihx
X X xx A X
n n n n
A X dx X A CONST
n n n n
B A d X angx X dihx
n n n n
C B d A ang X dihx
n n n n
For screw symmetry CONST
For translational symmetry CONST and xx is a constant
in nitely long chains there would b e three intercomplex interactions for
every three complex units
Since the mo del system is only three units long the lattice sums over the
electrostatic and other long range interactions b etween one complex unit
and all of its symmetry related copies are not complete
Step
After optimization these smal l model chains aswe call them from here on were
expanded with cyclic phosphoric acid rings and methyl groups at the ephedrine
like part see Figures and We will refer to them as expandedmodel
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
chains The corresp onding complex units will b e referred to as model complexes
from here on The full optimization of the expanded mo del chains was not feasible
due to limited computer resources Therefore we constructed the expanded mo del
chains from the optimized small mo del chains and mo del complexes
Figure Expanded mo del screw symmetric H b onded chain used for single
p oint energy calculations
The mo del complexes were fully optimized at b oth Hartree Fock and density
functional level of theory see Figure The values of internal variables thus
obtained for the cyclic phosphoric ring and the ephedrine methyl groups were used
in the construction of the expandedmodel chains Finally single p oint energy
calculations were p erformed for the expanded mo del chains at the Hartree Fock
density functional and MP level of theory MP only at the expanded version
of the Hartree Fock optimized small mo del chain geometry
Chapter
Figure Expanded mo del translationally symmetric H b onded chain used
single p oint energy calculations
Mo del calculations
The in uence of the basis set sup erp osition error BSSE on the relative ener
gies of the mo del complexes with resp ect to its constituent ions was investigated
using the counterp oise metho d All density functional calculations were done
using the B LYP exchange correlation functional within the program Gaus
sian The B LYP functional has b een rep orted to give go o d energetic results
for hydrogen b onded systems even in combination with a medium sized basis
set such as G d p A customized basis set derived from the G d p
basis set was used for geometry optimizations
The use of di use basis functions on all atoms leads to linear dep enden
cies so they were used only on the oxygen atoms Without di use basis
functions on the oxygens one of the hydrogens attached to the ephedrine
nitrogen migrates back to cyclic phosphoric acid oxygen during geometry optimization
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
2_fix 2
8.6 4.3 1
0.0
Figure Mo del complexes optimized at the density functional level of theory
with the B LYP functional and a customized basis set with their relative energies
at the same level of theory corrected for the BSSE
In addition the hydrogen p olarization functions were used only for those
hydrogen atoms that are involved in hydrogen b onding
Figure shows the fully optimized geometries of the mo del complexes at
the B LYP density functional level together with their relative energies corrected
for BSSE The mo del complex corresp onding to the screw symmetric hydrogen
b onded chain lab elled was found to b e kcal mol more stable than its
translationally symmetric chain counterpart lab elled Figure shows the
remarkable agreementbetween the optimized structure of mo del complex grey
and the corresp onding part of the exp erimental structure FILGAI black The
fully optimized structure of mo del complex do es not match the exp erimental
structure very well In the exp erimental structure the orientation of the cyclic
phosphoric ring is such that one of the oxygens connected to the phosphorus atom
Chapter
can interact with the next complex in the hydrogen b onded chain
A O B
C
Figure Matchbetween B LYP optimized mo del complex grey and ex
perimental structure FILGAI
Figure shows the improved matchbetween mo del complex grey opti
mized while restraining the torsional angle that determines the orientation of the
cyclic phosphoric ring to the exp erimental value with the exp erimental structure
x in gure FIMVAY black The partially xed mo del complex lab elled
is kcal mol less stable than mo del complex Mo del complex and the
partially xed mo del complex can b e considered as the geometrical building
blo cks of hydrogen b onded chains with screw chain and translational chain
symmetry resp ectively
In tables and the absolute and relative energies at the Hartree Fock
B LYP and MP level of theory are given for the small mo del chains chain and
chain the expanded mo del chains and the mo del complexes and For the
small mo del chains and the mo del complexes the fully optimized geometries at
the Hartree Fock level of theory were used employing the customized basis set
describ ed ab ove For the calculation of the single p oint energies the G d p
basis set was used The energy di erence b etween the mo del complex and
partially xed mo del complex and kcal mol for HF B LYP and
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Figure Matchbetween B LYP optimized mo del complex grey and ex
p erimental structure FIMVAY
MP is largely conserved b etween the twochains The energy di erences b etween
the small mo del chains are and kcal mol p er complex for HF B LYP
and MP resp ectively The energy di erences b etween the expanded mo del chains
are and kcal mol p er complex for HF and B LYP resp ectively Hartree
Fock and B LYP calculations agree within kcal mol
In Table the absolute and relative energies at the B LYP level of theory
are given for the fully optimized small mo del chains chain and chain the
expanded mo del chains and the fully optimized mo del complexes and All
optimizations were p erformed at the B LYP level of theory using the customized
basis set describ ed ab ove For the single p oint energies the G d p basis
set was used The BSSE corrected relative energies are included for the mo del
complexes The largest correction was kcal mol which is in the range of the
error in the exp erimental lattice energies The energy di erence b etween the two
unit complexes kcal mol is largely conserved b etween the two small mo del
chains kcal mol for units kcal mol p er unit
Figure shows the excellentmatchofthe ab initio B LYP translational
typ e H b onded chain with the diasteromer of the chlorine derivativeofCPA with
Chapter
Table Absolute energies in Hartrees at di erentlevels of theory employing
the G basis set for mo del complexes and mo del chains optimized at the
Hartree Focklevel of theory using a customized basis set
compound E E E
HF B LY P MP
compl ex
compl ex
compl ex
fixed
chain
chain
chain
expanded
chain
expanded
ephedrine CSD reference co de FIMVAY Figure shows the match of the
ab initio B LYP screw typ e H b onded chain grey with the diasteromer of
doubly substituted chlorine derivativeofCPA with ephedrine black with CSD
reference co de KOSYIA The ab initio geometry displayed is of an intermediate
structure kcal mol less stable than the nal optimized structure The match
of the nal optimized structure with KOSYIA is less go o d Probably the omission
of methyl groups on the ephedrine likepartofthechain during the optimization
allows low energy geometries that would no longer b e low energy geometries if the
structure were to b e expanded with these methyl groups This is con rmed bythe
relative energies of the fully expanded mo del chains in table denoted by
isonly kcal mol more stable than the The screw typ e chain chain
expanded
versus kcal mol in the unexpanded translational typ e chain chain
expanded
case In chain there is a close contact of Abetween a methyl group expanded
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Relative energies in kcal mol at di erentlevels of theory employing
the G basis set for mo del complexes and mo del chains optimized at the
Hartree Focklevel of theory using a customized basis set
compound E E E
HF B LY P MP
compl ex
compl ex
compl ex
f ixed
chain
chain
chain
expanded
chain
expanded
hydrogen and an atom on the cyclic phosphoric ring that is clearly energetically
unfavourable This is also supp orted by the relative energies of the not fully
expanded mo del chains denoted by where not fully expanded means that
only cyclic phosphoric rings are added and not methyl groups Figure com
pares the calculated NO and NO distances as de ned in Figures and
with the exp erimental NO and NO distances found in eight diastereomers with
H b onded screw symmetricchains and one with translational symmetry The cal
culated NO NO pair for the H b onded screw symmetric chain lies within the
same area as the corresp onding exp erimental values The calculated NO NO
pair for the H b onded translationally symmetric chain and its exp erimental coun
is terpart lie well outside this area The screw typ e chain chain
expanded
This kcal mol more stable than the translational typ e chain chain
expanded
matches the small mo del chains This shows the limitations of using a mo del
Chapter
Table Absolute and relative energies in Hartrees and kcal mol resp ectively
at B LYP level of theory for mo del complexes and mo del chains geometry opti
mized at the B LYP level of theory using a customized basis set
compound E E E
Abs Rel Rel BSSE
compl ex
compl ex
compl ex
fixed
chain
chain
chain
expanded
chain
expanded
chain
expanded
chain
expanded
small cyclic phosphorus rings
small cyclic phosphorus rings methyl system that is to o small to describ e a large system
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Figure Match of the ab initio translationally symmetric H b onded chain
with one diasteromer of ClCPA E CSD refco de FIMVAY
KOSYIA B3LYP NO1 2.788 2.720
NO2 2.904 2.895
Figure Matchoftheab initio screw symmetric H b onded chain interme
diate geometry kcal mol away from the optimum with the diasteromer of
doubly substituted chlorine derivate of CPA E CSD refco de KOSYIA
Chapter
NO1 vs NO2
Experimental: Screw Trans
o Calculated: Screw Trans NO2 (A) 3.00
2.95
2.90
2.85
2.80
2.75
2.70
2.65
2.60 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 o
NO1 (A)
Figure The exp erimental distances NO and NO for a numb er of dia
stereomers with H b onded chains with screw and translational symmetry com
pared with the calculated NO and NO distances See gures and for the de nition of NO and NO
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
In conclusion one can say that the screw typ e chain is roughly kcal mol
p er complex unit more stable than the translational typ e chain The exclusion of
certain parts of the large system can cause the optimized structure of the mo del
system to deviate from the optimal structure of the large system which in turn
can cause the expanded mo del to have an unrealistic geometry
Lattice energy calculations using a classical force eld
The following charge sets were used in combination with the DREIDING force
eld
set ESP t on the whole complex
set ESP t on the whole complex combined with the RESP metho d
set ESP t on the ions
set ESP t on the ions combined with the RESP metho d
set ESP sampled on iso density surfaces t on the ions
set ESP sampled on iso density surfaces t on the ions combined with
the RESP metho d
The charge sets and were derived from a QM calculation of the partially
optimized complexes at the Hartree Focklevel using the customized basis set
discussed earlier where partially optimized means that the internal variables
whichwere thought to b e sensitive to the crystal environmentwere kept xed
while all others were relaxed In this way the in uence of errors in the exp eri
mental crystal structures on the charge distribution is minimized Several of the
crystal structures contained p o or hydrogen p ositions with for example hydro
gens connected to a phenyl ring having an H C C b ond angle of instead of
the common These optimizations were computationally demanding so we
decided not to include the SUMWEC structure in these calculations
Table shows the total charge on the CPA substructure in the diastereomers
of CPA E and ClCPA E for charge sets and The total electronic charge on
CPA is roughly which is signi cantly less than the value for an isolated
Chapter
Table Total charge on the CPA substructure in the diastereomers of CPA E
and ClCPA E for charge sets and
Ref code set set
FIMVEC
FILGAI
FIMTUQ
FIMVAY
CPA anion This charge transfer e ect can b e seen as a dep olarization of the
complex with resp ect to the isolated ions
Table shows the absolute and relative lattice energies and p ercentage er
rors in lattice parameters of the diastereomers of CPA E and ClCPA E optimized
with the DREIDING force eld in combination with charge set Ewald
summation was used for the non b onded interactions The default settings were
used The inter and intra molecular geometry are optimized simultaneously
The structural agreementbetween calculated and exp erimental structures is rel
atively go o d with errors on average around p ercent The only unfavourable
exception is the b parameter of the FIMVEC structure which is around p ercent
in error The agreementbetween the calculated and exp erimental lattice energies
is however very p o or b oth in the magnitude of the energy di erences b etween
the diastereomeric salt pairs FIMVEC FILGAI and FIMTUQ FIMVAY and the
relative stability order of the latter Exp erimentshows the FIMVAY structure
to b e kcal mol more stable than the FIMTUQ structure while DREIDING
calculates it to b e kcal mol less stable
As shown in Table charge set gives an even b etter structural agree
ment with the exp eriment than charge set In addition the magnitude of the
energy di erences b etween the diastereomeric salt pairs FIMVEC FILGAI and
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Absolute and relative lattice energies and p ercentage errors in lattice
parameters of the diastereomers of CPA E and ClCPA E calculated with the
DREIDING force eld using charge set
Ref code a b c E E
abs rel
kcal mol kcal mol
FIMVEC
FILGAI
FIMTUQ
FIMVAY
FIMTUQ FIMVAY are more in agreement with exp eriment The relative sta
bility order of the FIMVAY and FIMTUQ structures is still predicted wrongly
however
All other charge sets also give go o d structural agreementbetween calculation
and exp eriment Table lists the relative lattice energies for the diastereomers
of CPA E and ClCPA E for all the six charge sets All charge sets givean
incorrect order of stability for the salt pair FIMTUQ FIMVAY The predicted
energy di erence ranges from to kcal mol Clearly the DREIDING force
eld is extremely susceptible to variations in the p ointcharges The reason for
this can b e found in Table which lists the intermolecular part of the relative
lattice energies for the various charge sets The intermolecular part of the relative
lattice energies for the salt pair FIMTUQ FIMVAY with the exception of charge
set is muchlessvariable than the total relative lattice energies and ranges from
to kcal mol Charge set b ehaves di erently b ecause it is the only charge
set for which the total charge on the ions is di erent for FIMTUQ and FIMVAY
versus Obviously this charge transfer e ect has a large e ect on the
intermolecular interaction of the anion and cation The large variation in the total
Chapter
Table Absolute and relative lattice energies and p ercentage errors in lattice
parameters of the diastereomers of CPA E and ClCPA E calculated with the
DREIDING force eld using charge set
Ref code a b c E E
abs rel
kcal mol kcal mol
FIMVEC
FILGAI
FIMTUQ
FIMVAY
relative lattice energies must b e attributed to variations in the intramolecular
contributions to the total relative lattice energies The DREIDING force eld
includes intramolecular charge charge interactions for atoms which are more than
two b onds away from each other Since ESP charges are designed to repro duce
the electrostatic p otential outside the molecule there is no reason to assume
they should b e optimal for repro ducing intramolecular energies An insp ection of
the individual charges in all six charge sets shows that some charges asso ciated
with atoms not very close to the molecular surface show large variations b etween
the di erent sets variations of sometimes accompanied by sign reversal
This is probably b ecause these charges contribute little to the actual value of the
charges derived electrostatic p otential at the molecular surface particularly in the
case of the ions where the p otential is dominated by a few strong charge centres
Although these large charge variations mayhave little e ect on the p otential
at the molecular surface they mayhave a large e ect when used to calculate
intramolecular charge interactions
In conclusion one can say that only tting charges on the complexes rather
than the ions in combination with tting on multiple conformations RESP
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Relative lattice energies in kcal mol for the diastereomers of CPA E
and ClCPA E calculated with the DREIDING force eld using various charge
sets
set set set set set set exp
E
F I LGAI FIMV EC
E
FIMV AY FIMTUQ
Table Intermolecular part of the relative lattice energies in kcal mol for
the diastereomers of CPA E and ClCPA E calculated with the DREIDING force
eld using various charge sets
set set set set set set
E
F I LGAI FIMV EC
E
FIMV AY FIMTUQ
gives lattice energy di erences b etween diastereomeric salt pairs of the correct
magnitude but the relative stability order is still incorrect The use of iso density
sampling of the electrostatic p otential do es not yield a systematic improvement
over van der Waals surface sampling for this system
Chapter
Lattice energy calculations using distributed multip ole expan
sions
The DMAREL package incorp orates electrostatic contributions to the inter
action energy via interacting multip ole expansions Only intermolecular inter
actions can b e optimized with this metho d the intramolecular conformations
remain rigid Calculations with the DMAREL package were done for our mo del
system the diastereomeric salts of CPA E and ClCPA E cho osing the cyclic
phosphoric and ephedrine parts as rigid b o dies The multip ole expansions were
externally generated via our MOLDEN package The repulsion disp ersion pa
rameters for hydrogen carb on nitrogen and oxygen provided with the program
were used the parameter set named FIT DMA in reference The program
provides no such parameters for chlorine and phosphorus atoms For chlorine
the parameters were taken from Williams et al As with the parameters for
hydrogen carb on nitrogen and oxygen these parameters were optimized in the
presence of atomic charges in the nonb onded p otential For phosphorus no such
parameters were available In our mo del system phosphorus do es not have close
intermolecular contacts since it is tetrahedrally surrounded byoxygens The
exact values of the phosphorus parameters therefore will have little e ect on
the relative energies of the diastereomers Wechose the chlorine parameters to
describ e the repulsion disp ersion interactions of phosphorus
Cox and Williams found that most Hartree Fockwavefunctions with split
valence basis sets overestimate molecular dip ole moments They intro duced a
dip ole scaling factor of which is widely used in molecular mo deling The
authors of DMAREL concluded that scaling of the multip oles with a factor of
provides the b est predictions of the lattice energies of the non hydrogen b onded
molecules but generally underestimates the lattice energies of hydrogen b onded
molecules Since our mo del system contains b oth hydrogen b onds and ionic
interactions we also investigated the in uence of the multip ole scaling factor on
the lattice energies
Tables and show the absolute and relative lattice energies
and p ercentage errors in lattice parameters of the diastereomers of CPA E and
ClCPA E calculated with the DMAREL program using factors of and
resp ectively to scale the multip ole moments
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Absolute and relative lattice energies and p ercentage errors in lattice
parameters of the diastereomers of CPA E and ClCPA E calculated with the
DMAREL program using a factor of to scale the multip ole moments
Ref code a b c E E
latt rel
kJ mol kcal mol
FIMVEC
FILGAI
FIMTUQ
SUMWEC
FIMVAY
Chapter
Table Absolute and relative lattice energies and p ercentage errors in lattice
parameters of the diastereomers of CPA E and ClCPA E calculated with the
DMAREL program using a factor of to scale the multip ole moments
Ref code a b c E E
latt rel
kJ mol kcal mol
FIMVEC
FILGAI
FIMTUQ
SUMWEC
FIMVAY
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Absolute and relative lattice energies and p ercentage errors in lattice
parameters of the diastereomers of CPA E and ClCPA E calculated with the
DMAREL program using a factor of to scale the multip ole moments
Ref code a b c E E
latt rel
kJ mol kcal mol
FIMVEC
FILGAI
FIMTUQ
SUMWEC
FIMVAY
The exp erimental structures are repro duced with an r m s error in the lat
tice parameters of roughly as compared to with DREIDING with the
exception of the FIMVAY structure Esp ecially at the higher scaling constants
large errors up to in individual lattice parameters were found for FIMVAY
Table shows the r m s of the p ercentage error in lattice parameters for each
structure as a function of the factor used to scale the multip ole moments ranging
from to The b est r m s average over all ve stuctures is obtained with
a scaling constantof
The calculated relative energies are of the correct magnitude kcal mol
for the ClCPA E diastereomers but to o large for the CPA E diastereomers
kcal mol The relative stability orders of FIMVAY with resp ect to FIMTUQ
are not correctly predicted except with a multip ole scaling constant of Here
Calc
FIMVAY is predicted to b e more stable than FIMTUQ E
FIMV AY F IMTUQ
Expt
kcal mol versus E
FIMV AY FIMTUQ
Lattice energy di erences have to b e corrected for the energy di erences of
the rigid b o dies of diastereomeric salt pairs since these are not considered in
the DMAREL approach When treating the constituents of the complexes as
Chapter
Table The ro ot mean square of the p ercentage error in lattice parame
ters calculated with the DMAREL program for the diastereomers of CPA E and
ClCPA E as a function of the factor used to scale the multip ole moments In
parentheses the average is given for when the diastereomer FIMVAY is excluded
Ref code scal e
FIMVEC
FILGAI
FIMTUQ
SUMWEC
FIMVAY
av er ag e
rigid b o dies only their conformational energy di erences need to b e considered
Table shows the relative energies calculated with the DMAREL program for
the diastereomers of CPA E and ClCPA E corrected for conformational energy
di erences as a function of the factor used to scale the multip ole moments The
conformational energy di erences b etween the complex parts see Table
were calculated at the density functional level of theory with the DMol pro
gram with geometries resulting from p erio dic ion relaxation calculations from
d
the VASP program There is a remarkable agreementbetween the results with
scaling factor and the results discussed b elow for DMol lattice energy cal
culations see Table The conformational energy corrections dominate the
d
We could use neither the DMol nor the VASP program for b oth the energy calculations
and geometry relaxations with p erio dic b oundary conditions Because of limited computer
resources the structures of FILGAI and FIMVEC could not b e optimized with the DMol pro
gram The VASP program on the other hand has no provisions for non p erio dic calculations
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Relative energies in kcal mol calculated with the DMAREL program
for the diastereomers of CPA E and ClCPA E corrected for conformational energy
di erences as a function of the factor used to scale the multip ole moments
Ref code scal e E
exp
FIMVEC
FILGAI
FIMTUQ
SUMWEC
FIMVAY
lattice energy di erences b etween the diastereomers In the single case of the
conformational energy correction of SUMWEC with resp ect to FIMTUQ a cor
rection of up to kcal mol was found The relative lattice energy of SUMWEC
with resp ect to FIMTUQ calculated with the DMol program is only half of this
kcal mol whilst exp erimentally it is found to b e kcal mol This suggests
that the conformational energy corrections calculated with DMol may b e insuf
ciently reliable at least in some cases The lattice energy calculations with the
DMol and VASP programs are discussed in detail in following sections
Chapter
Table Conformational energy di erences b etween complex parts of the dia
stereomers of CPA E and ClCPA E calculated at the density functional level
program with the geometries resulting from p erio dic of theory with the DMol
ion relaxation calculations with the VASP program
Ref code E E E E
ephedr inepar t cy clicphosphor icpar t tot Rel
FIMVEC
FILGAI
FIMTUQ
SUMWEC
FIMVAY
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Lattice energy minimizations using VASP
The crystal structures of the diastereomers of CPA E and ClCPA E were opti
mized with VASP while keeping cell dimensions xed at the exp erimental values
The wave functions are expanded in a plane wave basis set Only waves for which
jk K j E are included An E of Ry was required The pseudop oten
cut cut
tials were optimized for use with the PW exchange correlation functional
We to ok esp ecially care to accurately describ e the augmentation charges of the
ultra soft pseudop otentials Non linear core corrections were employed for the
elements chlorine and phosphorus The non lo cal pro jections were carried out in
real space
The results of these calculations at the p oint in k space are presented in Fig
ure and Table Figure shows the matchbetween VASP optimized
and exp erimental structures of the diastereomers of CPA E and ClCPA E with
CSD reference co des FIMVEC FILGAI FIMTUQ SUMWEC FIMVAY
The agreementbetween calculated and exp erimental structures is very go o d
with the exception of the hydrogen p ositions This is not surprising since the
hydrogen p ositions determined by X ray di raction are always less accurate than
those of the heavier elements Sp ecially in the case of FIMVEC and FIMTUQ
where in the exp erimental structures some hydrogen connected to the ephedrine
phenyl ring make CCH angles of and where they should typically b e
around In the case of FIMVAY a small deviation was found in the torsion
angle de ning the orientation of the phenyl with resp ect to the cyclic phosphoric
ring to which it is attached Table shows absolute and relative energies of
the diastereomers of CPA E and ClCPA E as calculated with the VASP package
Included for comparison are the exp erimental energies Agood agreement between
theory and experiment is found FIMVAY is predicted to b e the most stable
chlorine containing diastereomer Also the energy di erences b etween FIMVEC
and FILGAI and its chlorine analogues FIMTUQ and SUMWEC were found to
b e within the exp erimental error
This table also contains a FIMVAY analogue FIMVAY is the most stable
chlorine containing diastereomer However its non chlorine analogue is unknown
suggesting that it is less stable than FIMVEC or FILGAI The non chlorine FIM
VAY analogue was optimized with VASP keeping its lattice parameters at the
Chapter
A A
C C
O O B B FIMVEC FILGAI
A A A
C C
O O C O B B B
FIMTUQ SUMWEC FIMVAY
Figure Matchbetween VASP optimized grey and exp erimental black
structures with CSD refco des FIMVEC FILGAI FIMTUQ SUMWEC FIM
VAY
exp erimental values found for FIMVAY The calculated structure was indeed
found to b e less stable than FIMVEC and FILGAI by and kcal mol re
sp ectively Figure shows the matchbetween the VASP optimized structures
of FIMVAY and its non chlorine analogue The two structures are very similar
except for the torsion angle that de nes the orientation of the phenyl with resp ect
to the cyclic phosphoric ring to whichitisattached
This can b e seen even more clearly in Figure where the di erence in
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Absolute eV and relative kcal mol energies of the diastereomers
of CPA E and ClCPA E with atomic p ositions optimized at the density func
tional level of theory with the VASP program keeping cell dimensions xed at
exp erimental values and only p ointwas used for the k space sampling Ex
p erimental energies are also shown for comparison Included is the non chlorine
analogue of FIMVAY optimized using the FIMVAY cell
Ref code E E E
Exp
FIMVEC
FILGAI
FIMVAY analogue
FIMTUQ
SUMWEC
FIMVAY
orientations of the phenyl rings is shown b etween FIMVAY black and its non
chlorine analogue grey In FIMVAY there is a close contact A b etween
the chlorine connected to one ring and a hydrogen connected to its translational
copy In its non chlorine analogue the phenyl rings have turned away toyield
amuch less close contact of Abetween a hydrogen connected to one ring
and a hydrogen connected to its translational copy This clearly suggests that an
energetically favourable interaction in FIMVAY is substituted by an energetically
unfavourable interaction in its non chlorine analogue
Just by lo oking at the partial ESP charges of the FIMVAYchlorine and
the hydrogen with which it is in close contact and resp ectively
one would say they havea weak favourable electrostatic interaction For the
same reason the twohydrogens in the non chlorine FIMVAY analogue should
Chapter
A
C O
B
Figure Matchbetween VASP optimized structures of FIMVAY and its non
chlorine analogue
2.426
3.725
Figure Comparison of the orientations of the phenyl rings connected to the
cyclic phosphoric rings of the VASP optimized structures of FIMVAY and its
non chlorine analogue
havea weak repulsive electrostatic interaction is the typical value of the
ESP charge of a hydrogen connected to a phenyl ring Wehave searched the
Cambridge Structural Database for the numb er of o ccurrences N of a chlorine
connected to a phenyl ring having a close contact with a hydrogen connected
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
to another phenyl ring The results are displayed in Figure If the spatial
distribution of nonb onded atoms were random the probability of nding an atom
at a certain distance increases with the surface area of a sphere whose radius is
that distance In practice however one often nds a more or less well de ned p eak
sup erimp osed on a monotonic rising alb eit not with the square of the distance
background In our case a small p eak is found at a distance of A This is an
indication for the existence of a weak energetically favourable interaction for such
acontact In the exp erimental structure of FIMVAY this close contact is at A
in agreement with the statistical analysis However the close contact in the VASP
optimized structure is at a much smaller value A This seems to suggest
that the description of this typ e of interaction using the current approximations
to the density functional is not accurate enough or p erhaps that in spite of the
large unit cell it could require a b etter k sampling than the one used here
k p oint
Finally the in uence of b etter k space sampling on the relative lattice energies
was investigated We discussed the results at the k p oint in detail since it allows
for a b etter comparison with the DMol calculations which are only p ossible
at the k p oint Table shows the absolute and relative energies of the
diastereomers of CPA E and ClCPA E with k space sampling of
which yields two inequivalent k p oints in the irreducible part of the Brillouin
e
zone The atomic p ositions are directly taken from the calculation previously
describ ed i e optimized using only k p oint for the k sampling and keeping
the cell dimensions xed at the exp erimental values
For comparison the energies with the k space sampling at and exp erimental
energies are given
The b etter sampling has a small e ect kcal mol or smaller on all struc
tures except FIMVAY Where FIMVAY is the most stable structure at
kcal mol more stable than FIMTUQ at k space sampling FIMVAY
is the least stable structure kcal mol less stable than FIMTUQ The abso
lute energy of the FIMVAY structure is raised by only kcal mol going from
to k space sampling indicating that the k space
sampling is su cient Insp ection of the forces on the atoms at the
e
in principle yields eight k p oints but time reversal symmetry reduces this number
to four k p oints and p oint group symmetry reduces this number to two k p oints
Chapter
N 450
400
350
300
250
200
150
100
50
0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
o
CLH (A)
Figure The numb er of o ccurrences N of a chlorine connected to a phenyl
ring having a close contact with a hydrogen connected to a phenyl ring in the
CSD as a function of the distance of the close contact CLH Angstrom units
level on all six structures shows that they are very small except for the FIMVAY
structure
The three chlorine containing diastereomers FIMVAY FIMTUQ and SUMWEC
were optimized at the k space sampling The results are displayed in
Table Lack of computer resources prevented us from p erforming the opti
mization of all six structures at the level but we feel this is justi ed in
view of the small forces found at the level for all except the FIMVAY
structure
As exp ected the structural and energetical changes of FIMTUQ and SUMWEC
up on optimization are negligible On optimization FIMVAY is only kcal mol
less stable than FIMTUQ at the level At the level the
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Absolute eV and relative kcal mol energies of the diastereomers
of CPA E and ClCPA E with k space sampling of two p oints at
atomic p ositions taken from the optimization with the k space sampling at
and cell dimensions xed at the exp erimental values For comparison
the energies with the k space sampling at and exp erimental energies are given
All calculations were p erformed at the density functional level of theory with the
VASP program
Ref code E E E E
xx xx Exp
FIMVEC
FILGAI
FIMVAY analogue
FIMTUQ
SUMWEC
FIMVAY
SUMWEC structure is the most stable of the diastereomeric salts of ClCPA E
b eing kcal mol more stable than FIMTUQ Surprisingly the relative sta
bility of the non chlorine containing FIMVAY analogue do es not change at the
level However the structural agreement of the exp erimental and VASP
optimized FIMVAY structure is improved going from k p ointto
k space sampling The dihedral angle de ning the orientation of the phenyl ring
containing the chlorine with resp ect to the cyclic phosphoric ring changes from
at the k p ointto at the k space sampling The
latter is only in error with the exp erimental value The close con
tact of the chlorine connected to the phenyl ring with the hydrogen connected
to its symmetry copy is also improved Atthe k space sampling it
Chapter
Table Absolute eV and relative kcal mol energies of the diastereomers
of ClCPA E optimized at k space sampling of two p oints with cell
dimensions xed at the exp erimental values For comparison the energies with
the k space sampling at and exp erimental energies are given All calculations
were p erformed at the density functional level of theory with the VASP program
Ref code E E E E
xx xx Exp
FIMTUQ
SUMWEC
FIMVAY
is A compared to A in the exp erimental structure The results for the
dihedral are summarized in Table
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Dihedral de ning the orientation of the chlorine containing phenyl
ring with resp ect to the cyclic phosphoric ring for the structures FIMVAY and the
non chlorine containing FIMVAY analogue exp erimental versus VASP optimized
values at k space sampling and
str uctur e D ihedr al Ang l e inD eg r ees
FIMVAY Exp eriment
FIMVAY VASP optimized at
FIMVAY VASP optimized at
FIMVAY analogue VASP optimized at
Chapter
Table Absolute Hartrees and relative kcal mol energies of the diastereo
mers of ClCPA E with atomic p ositions optimized at the density functional level
of theory with the DMol program keeping cell dimensions xed at the exp eri
mental values compared with exp erimental energies
Ref code E E E
Exp
FIMTUQ
SUMWEC
FIMVAY
Lattice energy minimizations using DMol
Table shows the absolute and relative energies of the diastereomers of ClCPA
E with atomic p ositions optimized at the density functional level of theory with
the DMol program while keeping cell dimensions xed at the exp erimental
values compared with exp erimental energies These density functional calcu
lations were p erformed within the generalized gradient approximation GGA
employing the PW functional the same as used with VASP and the double
numeric with p olarization DNP basis set Due to limited computer resources
only the diastereomers ClCPA E were optimized Each optimization to ok more
than six months of computer time on our lo cal machine a Silicon Graphics Power
Challenge
In agreement with exp eriment FIMVAY is calculated to b e more stable than
FIMTUQ However SUMWEC is calculated to b e the most stable diastereomer
though exp erimentally it is equally stable as FIMTUQ Figure shows the
matchbetween the DMol optimized and exp erimental structures of the dia
stereomers of ClCPA E with CSD reference co des FIMTUQ SUMWEC and
FIMVAY The agreementbetween calculated and exp erimental structures is very
go o d with the exception of the hydrogen p ositions as mentioned earlier
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
A A A
C C
O O B B B O
FIMTUQ SUMWEC FIMVAY
Figure Matchbetween DMol optimized grey and exp erimental black
structures with CSD refco des FIMTUQ SUMWEC FIMVAY
Table shows the comparison b etween the DMol relative energies kcal mol
of the diastereomers of ClCPA E calculated resp ectively at the geometries op
timized with the VASP and DMol packages The e ect of the di erent ge
ometries on the relative energies is negligible largest di erence kcal mol
This suggests that the di erence in relative stability order for the diastereomers
of ClCPA E found with VASP and DMol is due to di erences in the waythe
energy is calculated Obvious di erences b etween the two metho ds are the all
electron calculation for DMol versus the pseudop otential calculation of VASP
and the use of di erent basis sets atom centred numerical basis functions with
DMol versus plane waves with VASP
Chapter
Table Comparison b etween the relative energies kcal mol of the diastereo
mers of ClCPA E calculated resp ectively at the geometries optimized with the
VASP and DMol packages b oth using only for the k space sampling The
energies were calculated at the density functional level of theory with the DMol
package
Ref code E E
VASP Geom
DM ol Geom
FIMTUQ
SUMWEC
FIMVAY
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Relative energies kcal mol of the diastereomers of ClCPA E op
timized at various levels of k space sampling with cell dimensions xed at the
exp erimental values calculated with the SIESTA VASP and DMol programs
For SIESTA a column is added containing the relative energies of the simultane
ous optimization of atomic co ordinates and cell dimensions at the x x k space
level For comparison the exp erimental energies are given
P r og r am Ref code E E E E E
xx xx xx E xp
Opt Cell
SIESTA
FIMTUQ
SUMWEC
FIMVAY
VASP
FIMTUQ
SUMWEC
FIMVAY
DM ol
FIMTUQ
SUMWEC
FIMVAY
Lattice energy minimizations using SIESTA
Table shows the relative energies of the diastereomers of ClCPA E optimized
at various levels of k space sampling with cell dimensions xed at the exp erimen
tal values calculated with the SIESTA program For comparison the VASP
DMol and exp erimental relative energies are shown For SIESTA a column is
added containing the relative energies of the simultaneous optimization of atomic
co ordinates and cell dimensions at the k space level The SIESTAcal
culations were p erformed within the generalized gradient approximation GGA
employing the PBE functional and the double p olarized basis set
The SIESTA results are in go o d agreement with the VASP results with
Chapter
di erences in relative energies no bigger than kcal mol at the k p ointand
kcal mol at the k space level With b oth VASP and SIESTA
the FIMVAY diastereomer is calculated to b e the most stable at the k p oint
Whereas with DMol the SUMWEC diastereomer is calculated to b e the most
stable with a di erence in relative energy b etween DMol and SIESTAof
kcal mol
The SIESTA relative energies do not signi cantly change going from
to k space level This is in agreement with our conclusion from
the VASP results that the k space sampling is su cient As with
VASP the agreementbetween the SIESTA and exp erimental relative energies
becomes worse when going from the k p ointto and higher k space
sampling Figure shows the matchbetween the SIESTA optimized structures
at k space level and exp erimental structures of the diastereomers of
ClCPA E with CSD reference co des FIMTUQ SUMWEC and FIMVAY The
agreementbetween calculated and exp erimental structures is very go o d with the
exception of the hydrogen p ositions as was the case with VASP and DMol optimized structures
A A A
C C O B O C B B O
FIMTUQ SUMWEC FIMVAY
Figure Matchbetween SIESTA optimized structures at k space
level grey and exp erimental black structures with CSD refco des FIMTUQ
SUMWEC FIMVAY
When atomic co ordinates and cell dimensions are simultaneously optimized at
the k space level the di erence b etween the exp erimental and calculated
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Exp erimental and SIESTA optimized lattice parameters of the dia
stereomers of ClCPA E The atomic co ordinates and cell dimensions were si
multaneously optimized at the x x k space level The last column shows the
percentual increase in volume going from exp erimental to calculated structures
Ref code a b c Vol
A A A D eg r ees
FIMVAY
Exp
SIESTA
FIMTUQ
Exp
SIESTA
SUMWEC
Exp
SIESTA
results increases The exp erimentally most stable ClCPA E diastereomer is again
calculated to b e the most unstable One reason for this may b e an inabilityof
the current GGA functionals to describ e ring ring interactions prop erly
Table shows the exp erimental and SIESTA optimized lattice parameters
of the diastereomers of ClCPA E The atomic co ordinates and cell dimensions
were simultaneously optimized at the x x k space level The calculated a b
and c values are always bigger with resp ect to exp eriment As a result
the calculated cell volume is increased with with resp ect to exp eriment
The relative imp ortance of separate interactions studied with
DMol
To determine the relative imp ortance of the separate interactions that playa role
in the relative stabilities of the crystal packings with hydrogen b onded chains of
translational and screw symmetry we p erformed a series of single p oint energy
calculations on the mo di ed DMol optimized structures of the two b est repre
Chapter
sentatives of these packings FIMVAY and FIMTUQ As discussed in previous
sections the relative abundances of the crystal packing with hydrogen b onded
chains of screw symmetry and translational symmetry and the ab initio calcula
tions on mo del systems of these chains suggest that the hydrogen b onded chains
with screw symmetry are much more stable In the case of FIMVAY and FIM
TUQ this stability order is reversed with resp ect to exp eriment We designed
mo di cations in suchaway that the contribution of separate interactions on the
total relative stability order could b e studied These mo di cations are of two
typ es in some cases combined
Cell dimensions a and c increased to A thus excluding interactions in
the a and c directions
stripping parts of the system and capping cut b onds with hydrogen atoms
Table shows the relative energies of comparable subsystems of the dia
stereomers FIMVAY and FIMTUQ In cases where the subsystem contains chlo
rine relative energies of the subsystems are also given but with chlorine substi
noC l
The entry lab elled A gives the relative energies of tuted byhydrogen E
Rel
the unmo di ed FIMVAY and FIMTUQ crystals with the energy minimized with
resp ect to atomic co ordinates at the density functional level of theory employing
the PW functional and the DNP basis set with the DMol package The
unmo di ed FIMVAY crystal is kcal mol more stable than the FIMTUQ crys
tal in agreement with the exp erimental value of kcal mol When we increase
the lattice parameters a and c to A system lab elled B the subsystems of
FIMVAY and FIMTUQ are almost equally stable The interactions in the a and
c directions are all ring ring interactions Apparently they are more favourable
for FIMVAY than for FIMTUQ
The subsystem B of FIMVAY consists of twohydrogen b onded chains with
translational symmetry These twochains are related by a screw axis transforma
tion see Figure In the FIMVAY subsystem C thesetwochains have b een
separated in sucha way that they are equally distant from each other as from
their copies in neighb ouring cells thus the interaction b etween these twochains
is switched o This subsystem is kcal mol less stable than the FIMTUQ sub
system B Apparently the twohydrogen b onded chains with translational sym
metry in FIMVAYhavea favourable interaction of kcal mol This
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Table Relative energies in kcal mol calculated with the DMol program for
the diastereomers of CPA E and ClCPA E and a numb er of its mo di cations
noC l
Label D escr iption E E
Rel
Rel
A FIMVAYminus FIMTUQ
B FIMVAYminus FIMTUQ a c A
C B two FIMVAY H b onded chains separated
D C chains stripp ed of phenyl ring
E D chains stripp ed of cyclic phosphorus rings
B C two FIMVAY H b onded chains separated minus
conjoined
F FIMVAY structure E separated minus joined
G FIMVAY ephedrine phenyls only
separated minus joined
H FIMVAYchlorine substituted phenyl rings only
a b c A minus a c A b A
I H with chlorines substituted byhydrogens
p ertaining to same structures with Cl substituted byH
is con rmed by comparing directly the energies of the FIMVAY subsystems with
joined chains versus separated chains entry B C in Table This interaction
of the twoFIMVAYhydrogen b onded chains apparently has twocontributions
the phenyl phenyl interaction of the ephedrines and the electrostatic interaction
of the highly charged centres in the core of these twochains This contention is
supp orted by the calculation on subsystems G and F The subsystems G are the
ephedrine phenyl rings of FIMVAY only separated or joined The joined FIM
VAY subsystem is kcal mol more stable than the separated one This is in
contradiction with rep orts in the literature on the disabilityofa number of DFT
Chapter
functionals to describ e this interaction as favourable as discussed earlier The
subsystems F are the FIMVAY H b onded chains with translational symmetry
separated and joined In addition all the phenyl rings and cyclic phosphoric rings
have b een stripp ed away In this way only the electrostatic interaction b etween
the highly charged centres in the core of the hydrogen b onded chains is studied
It app ears that the two FIMVAYchains can gain kcal mol by electrostatic
interaction
- ++
B ++ - - ++
O ++ - - ++
++ -
Figure The two translationally symmetric hydrogen bridged chains of the
FIMVAY diasteromer separated by a dashed line The interaction b etween these
twochains has contributions from the phenyl phenyl interaction green and the
electrostatic interaction of the highly charged centres in the core of the twochains
black
If we strip the phenyl rings of the subsystems C of FIMVAY and FIMTUQ
we get subsystems D and if we strip even the cyclic phosphoric rings we get sub
systems E These subsystems are nowidentical in comp osition to the expanded
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
see gures and and small mo del systems see gures and we
used for our ab initio study of three complex hydrogen b onded chains of transla
tional symmetry FIMVAY and screw symmetry FIMTUQ In this study we
found the screw symmetric H b onded chains to b e much more stable by roughly
kcal mol p er complex unit see Table Subsystem D of FIMVAYis
kcal mol less stable than subsystem D of FIMTUQ Subsystem E of FIMVAY
is kcal mol less stable than subsystem E of FIMTUQ This is in qualitative
agreement with results for the mo del calculations We did not exp ect that b oth
typ es of calculation would yield absolute quantitative agreement since in the
mo del systems were optimized with no interactions in the a and c directions and
lacked the phenyl rings on the cyclic phophoric ring and on the ephedrine
Comparing the relative energies of the subsystems A to C with the same
noC l
systems with the chlorine substituted byhydrogen E versus E we
Rel
Rel
nd that the relative energies all shifted by kcal mol in favour of the
FIMTUQ subsystems Clearly the substitution of chlorine byhydrogen has a
lo cally destabilising e ect This is con rmed by the relative energies of the FIM
VAY subsystems consisting of only the phenyl rings containing the chorine with
a b c A versus the same system with b A the exp erimental value
lab elled H We nd that the rst system where the chloro phenyl rings still have
interactions is kcal mol more stable Lo oking at the relative energy of the
same systems when chlorine is substituted byhydrogen entry I we nd that
the rst system where the phenyl rings still haveinteractions is kcal mol
less stable This is in agreement with the results of the VASP calculations for the
diastereomers of CPA E Here we found that the no chlorine FIMVAY analogue
was kcal mol less stable than the no chlorine FIMTUQ analogue FIMVEC
see Table
Comparison of the absolute lattice energies
The lattice energy is de ned as the amount of energy released when a mole of
gaseous ions or molecules are brought together from in nite separation to form
a crystal For diastereomeric salts the gas phase energy is the same Therefore
di erences in lattice energies are equivalent to di erences in the solid state energy
Upto this p oint when we discussed relative lattice energies we actually discussed
Chapter
Table Comparison of the absolute lattice energies kcal mol calculated
with the DREIDING DMAREL and DMol for the diastereomers of ClCPA E
Ref code E E E
DREI DI N G DM AREL
DM ol
FIMTUQ
SUMWEC
FIMVAY
relative solid state energies with the exception of the DMAREL calculations In
order to calculate the absolute lattice energies we need to subtract the energy of
the gas phase ions from the solid state energy
Table shows the comparison of the absolute lattice energies kcal mol
calculated with DREIDING DMAREL and DMol for the diastereomers of ClCPA
E DREIDING was used with charge set The DMAREL results are uncorrected
for conformational energy di erences of the ions and using unscaled multip oles
The lattice energies for DREIDING DMAREL and DMol show large variations
they are roughly and kcal mol resp ectively This not necessarily
means that the relative lattice energies should also show large variations It do es
show however the di erence in balance b etween the electrostatic and van der
Waals contributions to the intermolecular interaction energy for these metho ds
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
Conclusions
Ab initio structure optimizations on complex mo del chains with translational and
screw symmetry yielded a go o d structural t b etween exp eriment and calcula
tion The energy di erence b eteen the mo del complexes with translational and
screw symmetry was largely conserved in the three complex mo del chains The
screw symmetric mo del chain was found to b e around kcal mol more stable p er
complex than its translationally symmetric counterpart This in agreement with
exp eriment since exp erimentally seven crystal structures of the diastereomers
of CPA with ephedrine have the screw symmetric chain and only one has the
translational symmetry
The calculated stability order of the diastereomeric salts with the DREIDING
force eld and various typ e of charges was wrong Moreover the calculated
relative energies of the diastereomeric salts are wrong by one order of a magnitude
The calculated stability order of the diastereomeric salts with the DMAREL
program is dep endent on whichmultip ole scaling factor is used and whether the
energies are corrected for the conformational energy di erences of the rigid b o d
ies The conformational energy di erences were found to b e at least of the same
magnitude as the packing energy di erences Although the calculated relative
energies are of the correct magnitude the correct stability order of the diastereo
meric salts was only once predicted correctly for the diastereomers of ClCPA E
when calculations were made with unscaled multip oles and no correction for con
formational energy di erences of the rigid b o dies However the errors in the
calculated lattice parameters are large when using unscaled multip oles up to
for the structure FIMVAY The smallest errors in the calculated lattice
parameters were found with a multip ole scaling constantof
The calculated stability order of the diastereomeric salts with the VASP SIESTA
programs at p oint in k space is in qualitative and quantitative agreement with
exp eriment The non chlorine analogue of the exp erimentally most stable di
astereomer FIMVAY was calculated to b e the least stable non chlorine diastere
omer This is probably in agreement with exp eriment since this crystal packing
was not observed exp erimentally The stability of the diastereomer FIMVAYis
probably due to an electrostatically favourable interaction b etween a chlorine con
nected to a phenyl ring and hydrogen connected to a phenyl ring With improved
Chapter
k space sampling however this agreement with exp eriment is partly destroyed
with FIMVAY b eing calculated to b e as stable as its diasteromer FIMTUQ
The calculated stability order of the diastereomeric salts FIMTUQ and FIM
VAY with the DMol program at is in qualitative and quantitative agreement
with exp eriment and with the VASP calculations at the p oint The third dia
steromer SUMWEC however is incorrectly predicted to b e the most stable of the
three We do not knowany reason for the disagreementbetween the calculations
with DMol and VASP SIESTA despite the similarity of these metho ds
Relative energy calculations on subsystems of the diastereomers FIMTUQ
and FIMVAY con rmed the higher stability of the isolated screw symmetric
chains over those with translational symmetry The relative energies of the packed
chains in the complete crystals may b e reversed as is the case with FIMTUQ and
FIMVAY due to interactions other than those considered in the mo del chains
In the cases of FIMTUQ and FIMVAY there is an electrostatic interaction b e
tween a chlorine connected to a phenyl ring and hydrogen connected to a phenyl
ring that stabilizes the translationally symmetricchain structure FIMVAYwith
resp ect to the screw symmetry chain structure FIMTUQ where this interaction
is absent
Ab initio calculations predict all diastereomers of CPA E and ClCPA Etolie
roughly within a kcal mol range Exp eriment puts this range at kcal mol for
ClCPA E This shows that the calculations are at least kcal mol in error New
exchange correlation functionals that b etter describ e the long range disp ersion
and ring ring interactions are probably required to improve the agreementbe
tween calculation and exp eriment Although disagreementbetween DMol and
VASP SIESTA also shows other sources of error
Acknowledgements
The investigations rep orted in this pap er were supp orted by the Netherlands
Organization for Chemical Research NWO CW within the framework of the
PPM CMS c crystallization pro ject This pro ject is a Dutch research collab ora
tion with academic and industrial partners fo cusing on pre comp etitive research
into mo delling packing morphology and industrial crystallization of organic com
p ounds Sp ecial thanks are due to Dr J H No ordik and Rob Meier for the
Quantum mechanical and force eld calculations on the
diastereomeric salts of cyclic phosphoric acids with ephedrine
initialization of this pro ject and to DSM for sp onsoring this pro ject and in par
ticular wewould like to thank Rob Meier and Betty Coussens for their interest
in this pro ject DSP acknowledges supp ort by Grants No DOE and
No DEFG ER and from the Basque Government Programa de
Formaci on de Investigadores The SIESTA calculations presented in this pap er
were p erformed at the NCSA computational resources
Chapter
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Louie S G Froyen S Cohen M L Phys Rev B
King Smith R D Payne M C Lin J S Phys Rev B
Kresse G unpublished
Rowland R S Taylor R J Chem Phys
Chapter
The gas phase chemistry of the methyl
carbamate radical cation
This chapter has b een repro duced with kind p ermission from Schaftenaar G Postma R Rut
tink P J A Burgers P C McGibb on G A Terlouw J K Int J Mass Sp ectrom
c
Elsevier Science
Summary
The unimolecular chemistry of the methyl carbamate radical cation H NCOOCH
has b een investigated byacombination of mass sp ectrometry based exp eri
ments metastable ion MI collisional activation CA collision induced disso
ciative ionization CIDI neutralization reionization NR sp ectrometry H C
and O isotopic lab eling app earance energy AE measurements and ab initio
molecular orbital calculations executed at the SDCI G G level of
theory and corrected for zero p oint energies
These calculations indicate that b esides ionized methyl carbamate there are
at least seven other equilibrium structures including distonic ions and hydrogen
bridged radical cations The most stable isomer is the hydrogen bridged sp ecies
H N CH O H O C H whichisbestviewed as the carb enium ion H N
CH OH interacting with the formyl dip ole The related sp ecies H N C O H
O CH in whichthehydroxyamino carb ene ion H N C OH interacts with
the formaldehyde dip ole is also a stable sp ecies This hydrogen bridged radical
cation is the key intermediate in the sp ontaneous unimolecular disso ciations of
methyl carbamate ions
Exp erimentally the metastable molecular ions form two sets of pro ducts
namely H N CH OH HCO the comp onents of the most stable isomer and
CH O H NH CO The minimum energy requirement paths have
Chapter
b een lo cated by ab initio calculations and the reactions followmultistep isomer
izations In the rst step H NCOOCH isomerizes via a hydrogen shift
which then rearranges to the hydrogen to the distonic ion H NC OH OCH
bridged radical ion H N C O H O CH The incipient formaldehyde
molecule can then donate a hydrogen to the C atom of H NCOH followed by
loss of HCO or it can accept the hydroxyl hydrogen to form a CH OH radical
this radical then migrates within the electrostatic eld of the H N C O ion
towards the N atom to form the complex H C O H NH C O This
latter sp ecies which can b e viewed as a formaldehyde and a CO molecule inter
lies in a shallow p otential well only and sheds C O to pro duce acting with NH
CH O H NH as observed exp erimentally
It is stressed that only with the aid of high level ab initio calculations could
the ab ovemechanisms b e elucidated
Intro duction
From the inception of organic mass sp ectroscopy it has b een realized that manya
molecular ion may undergo more or less complex rearrangement reactions This
is esp ecially true for reactions taking place in the microsecond time frame for
the metastable ions However rearrangement reactions may also dominate in the
submicrosecond time frame and the resulting ionic pro ducts mayleadtointense
and even to base p eaks in the conventional mass sp ectra years ago it
was stated that the o ccurrence of such rearrangements is one of the problems
which complicate exceedingly the simple interpretation of ionisation and frag
mentation pro cesses and is moreover a serious obstacle to the determination of
the constitution of the original comp ound from the mass sp ectrum However
even b efore the ab ove statementwas made Biemann wrote The formation
of rearrangement p eaks of high intensitythus requires a certain arrangementof
atoms in the molecule whichmakes such p eaks very useful for the interpretation
of mass sp ectra Biemann go es on to write A deep er knowledge of the mecha
nism of these rearrangements is extremely imp ortant for this purp ose Indeed
it has b een rep eatedly shown that a go o d understanding of ionic pro cesses such
as rearrangement reactions can lead to a more con dentinterpretation of mass
sp ectra of unknowns In this resp ect it is worthy to note that in the name of
The gas phase chemistry of the methyl carbamate radical cation
a
this very Journal was changed to include the word Pro cesses instead of Physics
Often metastable ions are chosen for mechanistic studies b ecause i their in
ternal energy although not well de ned lies in a narrow range ii the nominal
mass of the neutral exp elled can b e measured iii when in doubt the structure
of the neutral can b e assessed by collision induced disso ciative ionization CIDI
avariant of neutralization reionization mass sp ectrometry NRMS and iv
the kinetic energy release even when in the submillielectronvolt range can b e
accurately measured Even within a homologous series of small metastable ions
strikingly di erent disso ciation reactions can b e encountered Let us consider the
following methyl formate ions H C O OCH pro duce CO for a detailed
computational and exp erimental study see ref methyl acetate ions CH
C O OCH formCH OH in admixture with CH O for a recent review see
ref ionized methyl propanoate CH CH C O OCH generates CH O
but not CH OH and methyl butyrate ions CH CH CH C O OCH pro
and C H by the McLa erty rearrangement see for example ref duce CH
Ethyl acetate CH C O OCH CH amazingly pro duces water molecules
From recentwork it has b ecome clear that much can b e learned ab out reac
tion mechanisms and ion structures byintegration of results obtained from state
of the art ab initio calculations and from mass sp ectrometry based exp eriments
Previous results have shown that ab initio calculations can lead
to a prop er description of the isomerization disso ciation pathways provided that
a split valence basis set is employed for geometry optimizations and that the nal
relative energies include the e ects of p olarization functions and of correlation
energy Using this approach it has b ecome clear that many radical cations exist
for which the neutral counterpart is unknown and that such ions are key in
termediates in the rearrangement disso ciation pathways of many organic radical
cations Of particular interest are the so called distonic ions hydrogen
bridged radical cations and ion dip ole complexes Distonic ions are
those radical cations whichhave the charge and radical sites at separate heavy
atoms e g CH O H as opp osed to CH OH In larger distonic ions e g
A B C D often the charged moiety can migrate to the radical centre thereby
generating another distonic ion
a
International Journal of Mass Spectrometry and Ion Processes
Chapter
A
B C
D
which in turn can shift its ionized part to the radical site B C D A
Such a sequence can rationalize otherwise mechanistically problematic reactions
In such a rationalization it is assumed that the rearrangements o ccur stepwise as
in the Whitmore mechanism in solution carb enium ion chemistry Another
class of ions which are increasingly b eing invoked to rationalize fragmentations are
hydrogen bridged radical cations formally proton b ound molecule radical pairs
A H BH which unlike their even electron counterparts A H B
have only b een scantly studied In such radical ions a hydrogen shift can lead to
another hydrogen bridged cation HA H B which in turn can undergo a
similar reaction
Such a sequence has b een invoked to explain the seemingly complex unimolec
ular chemistry of ionized ethanediol a and propanediol b With
resp ect to the ab oveitisofinterest to note that high level ab initio calculations
have convincingly shown that formation of CH OH from ionized methyl acetate
pro ceeds via both distonic ions and hydrogen bridged radical cations as shown
below a
distonic H C C O O CH H C C OH O CH
CH C O H O CH H bridged
CH C O CH OH
In a recent computational and exp erimental study b on the CH NO
potential energy surface we provided evidence that loss of CO from ionized
methyl carbamate H NCOOCH leads to the hydrogen bridged radical cation
CH O H NH formally the ionized formaldehyde ammonia asso ciated
molecule and not the conventional sp ecies CH ONH by CO extrusion
On the basis of a variety of mass sp ectrometric exp eriments we prop osed that
the reaction pro ceeds as follows
The gas phase chemistry of the methyl carbamate radical cation
and we note here that this sequence to o includes a distonic hydrogen
bridged transformation byintramolecular hydrogen b onding chelation How
ever we stressed that without computational supp ort this prop osal must remain
sp eculative Thus weembarked up on a computational study of the methyl carba
mate rearrangement disso ciation reactions and some further exp eriments which
we rep ort here Our ab initio calculations show that loss of CO o ccurs via a
pathway completely di erentfromthatshown ab ove Also a rationale is given
for the dominant reaction in the microsecond time frame viz loss of HCO
Before presenting the evidence whichnow leads us to reject the ab ove mecha
nism it may b e useful to summarize brie y the grounds up on whichitwas based
i The daughter ions are CH O H NH and not CH ONH or
CH ONH
ii H N C O O CH sp eci cally loses C O
iii Electron capture by the rearranged molecular ions leads to complete
breakdown indicating that the neutralized sp ecies lie s in a shallowwell
only as exp ected for structures akin to and Ma jor neutral pro ducts
are CH O and CH OH not CH O consistent with structures and
iv The CH NO daughter ions also fall apart up on neutralization to among
other pro ducts CH OH not CH O the CH D NO daughter ions gener
Chapter
ated from the OCD lab elled ester form CD OH and CD OD radicals in
a ratio of
All the ab ove observations lend strong supp ort for the ab ovemechanism
Exp erimental
Metastable ion MI collisional activation CA and neutralization reionization
NR mass sp ectra were recorded on VG Analytical ZAB F and ZAB E in
struments as describ ed in ref b The NR mass sp ectra were obtained using
xenon for neutralization and O for reionization O was also used as the target
gas in the CA exp eriments IE and AE values were obtained using mono chro
matic electrons as describ ed in ref AE values for metastable p eaks were
obtained by the comparative metho d describ ed in ref using the KRATOS
MS S instrument at the University of Ottawa Professor J L Holmes The
lab elled esters were synthesized on a microscale from the appropriately lab elled
OH and CH OH isotopic purity greater than alcohols CD OH CD HOH CH
Merck Sharp and Dohme and urea using zinc acetate as a catalyst
For the synthesis of the doubly lab elled ester H N C O O CH a methanol
OH and OH CH sample Amersham U K containing CH
OH was used CH
Results and discussion
Loss of CO is among metastable ions a minor reaction path only and most of
the metastable ions disso ciate by loss of HC O Loss of HC O was
not investigated in our previous study and we deal with it here Firstly what
is the structure of the daughter ions A hydrogen shift in followed by loss
of HC O would lead to H N CH O a However formation of the isomeric
carb enium ion H N C H OH b may b e energetically more attractive since ion b
has twopowerful electron donating groups attached to the carb enium centre The
proton a nity of formamide H C O NH has b een measured a yielding
an enthalpy of formation of kcal mol for the protonated molecule but its
structure a or b has not b een determined However our theoretical calculations
The gas phase chemistry of the methyl carbamate radical cation
show that ion b is considerably more stable than ion a by kcal mol and
thus the protonation of formamide probably yields CH NO ion b
Fig CA mass sp ectrum of the CH NO ions generated by loss of HCO
from ionized methyl carbamate H NCOOCH
The CA mass sp ectrum of the CH NO ions generated bylossofHC O is
shown in Fig Sp ontaneous reactions lead to m z NH which seeTable
is by far the least energy demanding reaction There are intense p eaks at
m z and also at m z The CA mass sp ectrum is compatible with ion a
which is exp ected to disso ciate to H C O which can fragment further to CO
However there are also clear signals at m z probably HNC and to NH
indicative of structure b The NR at m z NH andat m z loss of NH
sp ectrum of the CH NO ions is shown in Fig A Two imp ortant observations
are that there is a recovery signal at m z of considerable intensity and
the NR sp ectrum is very similar to the CA mass sp ectrum m z is much
less intense in the NR sp ectrum as this p eak arises from the slow disso ciation of
the reionized sp ecies These observations indicate that the neutralized sp ecies
is stable for at least s and this argues against ions a which are not exp ected
to survive neutralization
Further evidence for this assignment comes from the NR mass sp ectrum of the
CH D NO ions generated by D C O loss no H C O loss is observed from
the OCD lab elled ester shown in Fig B If wewere dealing with typ e a ions
Chapter
Table Enthalpies from ref a of pro ducts for CH NO disso ciations
m z Pro ducts H kcal mol
f
NH HCO
CO NH
HCNH H O
HCO NH
OH HCNH
HCOH NH
these ions could b e H DN CD O and or HD N CH O However since m z
is very weak cf the intensityof m z in Fig A the latter structure can
b e discarded and so the sp ecies would havetobeH DN CD O This ion after
NR should yield CD O followed bylossofD to pro duce p eaks at m z and
but no p eak at m z is exp ected in sharp contrast with the exp erimental
ndings Fig B The m z p eak must then b e the result of HDO loss and
so ab out of m z in the unlab elled NR and CA sp ectra is not CO but
rather HNCH formed by loss of H O These ndings are compatible with the
prop osal that the daughter ions are indeed H N C H OH b which incidentally
can pro duce m z HCNH ions via a simple cleavage reaction see Table
That loss of H O is observed at all is not so surprising considering the pro ducts
enthalpies The lab elled CH D NO daughter ions are then H N CD OD as also
evidenced by the clean shift of m z to m z CDOD
It should b e noted that the CA mass sp ectrum of H N C H OH Fig
contains weak signals at m z and m z These signals could well arise
from a trace of ethanol a the corresp onding signals are absent in the CA
mass sp ectrum of the lab elled sp ecies not shown Wemention this b ecause a
trace amount of ethanol may render the interpretation of the AE m z value
The gas phase chemistry of the methyl carbamate radical cation
Fig A Xe O NR mass sp ectrum of the CH NO ions generated by
loss of HCO from ionized methyl carbamate H NCOOCH B NR mass sp ec
trum of the CH D NO ions generated bylossofDCO from the lab elled ester
H NCOOCD
questionable see b elow
To obtain more information on the mechanism of HCO and CO loss the MI
and CA sp ectra of several lab elled molecules were investigated and the results
are summarized as follows
Chapter
loses DCO and CO H N C O O CD
loses H CO and CO H N C O O CH
loses HC O and C O H N C O O CH
loses H C O and C O H N C O O CH
Both rearrangement disso ciation pro cesses loss of HCO and CO are thus
atom sp eci c and the following reactions are established
C O CH O HNH H N C O O CH
H N C H OH H C O
Energetic measurements
The IE and AE values were measured using mono chromatic electrons see exp eri
mental section IE H NCOOCH eV yielding H H NCOOCH
f
kcal mol using H H NCOOCH kcal mol AEm z was
f
measured as eV which is only eV ab ove the IE of ethanol
a Since we had noted ab ove that a trace of ethanol could well b e present
it is conceivable that the measured value is to o low Toremovethisambiguitythe
AE of the metastable p eak for loss of HCO was measured by the comparative
metho d describ ed in ref AE eV The AE of the metastable
p eak for loss of CO was also measured by this metho d AE eV The
latter AE value was found to b e identical with that obtained using mono chro
matic electrons AE eV which gives credence to the metastable
measurements Therefore we prop ose that the activation energies for loss of HCO
and CO are the same within exp erimental error
The H for H N C H OH as derived from the ab ove AE measurement
f
kcal mol ismuch higher than that of protonated formamide kcal mol
This leads to the conclusion that the loss of HCO from is asso ciated with a
signi cant energy barrier ab out eV for the reverse reaction It should b e
noted that this is not re ected in the magnitude of the kinetic energy release
hT i is only meV This p oint will b e addressed later The formation of the
too mayinvolve a barrier for hydrogen bridged sp ecies CH O H NH
The gas phase chemistry of the methyl carbamate radical cation
Fig Xe O NR mass sp ectrum of the CH DNO ions generated by loss
of CD O from the lab elled ester H NCOOCD
the reverse reaction and so the exp erimentally determined H kcal mol
f
b must b e regarded as an upp er limit
At slightly higher energies AE eV another pro cess comes into play
namely disso ciation into m z H N C O ions and m neutrals CH OH
H kcal mol a or CH O H kcal mol a
f f
Dep ending on the structure of the neutral lost the apparent H of the m z
f
H N C O ions is kcal mol for loss of CH O and kcal mol for
loss of CH OH Since H for H N C O has b een established as kcal
f
mol b it follows that at threshold the radical eliminated is CH OH and
not CH O
At still higher energies a fourth reaction loss of CH O comes into play for
which the AE is eV This pro cess could lead to the ionized carb ene H N C
OH or to the distonic ion H N C O The NR mass sp ectrum of the lab elled
daughter ion CH DNO formed from the OCD lab elled ester is shown in Fig
It is observed that the recovery signal is the base p eak and that intense
signals are presentat m z NH and m z OD Since the hyp ervalent
sp ecies H DN C O is not exp ected to survive it is prop osed that the daughter
ion is H N C OD which up on neutralization yields the stable carb ene H N C
OD The daughter ion is thus H N C OH and not H N C O in agreement
with our theoretical calculations which predict that the N C b ond strength in
Chapter
H N C O is only kcal mol see b elow H for H N C OH barring
f
a reverse term is assessed at kcal mol
The higher energy losses of CH O and CH OH or CH O giveriseto
prominent p eaks in the CA mass sp ectrum b These reactions to o app eared
atom sp eci c the H N C O O CH lab elled ester loses exclusively CH O
and CH O and or CH OH Thus for the collision induced disso ciations
the following reactions are established
H N C OH CH O H N C O O CH
H N C O CH O CH OH
It is remarkable that whereas the AE value for loss of CH OH is only slightly
higher than the AE value for loss of HCO and CO no loss of CH OH is observed
in the MI sp ectrum the signal at m z is at least a factor of less intense
than that at m z loss of HCO and in addition it maywell result from
collision induced disso ciation by residual background gas That the losses of CO
and HCO comp ete in the microsecond time frame indicates that their activation
energies are almost if not exactly the same the latter will b e so if these reactions
pro ceed via the same rate determining barrier see b elow
Theoretical methods
Standard LCAO MO SCF calculations were p erformed with the program GAMESS
employing restricted Hartree Fock RHF pro cedures The isomers transi
tion states and disso ciation pro ducts whichhave b een examined are given in
Scheme The geometries of the isomers were determined using analytical gra
dientandnumerical second derivative optimization pro cedures with the G
basis set These are displayed in Fig The calculated energies are shown in
Table The relative energies presented in Table were obtained by p erform
ing single plus double con guration interaction SD CI calculations in the G
optimized geometries using the G basis set with the help of the DIRECT
CI program The SD CI results were size consistency corrected using the
formula of Pople et al
The gas phase chemistry of the methyl carbamate radical cation
The Pople size consistency corrected results were corrected for the scaled
contribution of zero p oint vibrational energies ZPVE The ZPVEs
in Table were calculated for the G optimized geometries employing the G basis set
Chapter
Scheme C H NO isomers and transition states
studied theoretically
The gas phase chemistry of the methyl carbamate radical cation
Chapter
The gas phase chemistry of the methyl carbamate radical cation
Chapter
The unimolecular chemistry of methylcarbamate ions
Since we b elieve b that wehave indications for the participation of ion in
the loss of CO from we rst calculated its relative energy and the barrier sepa
rating it from At our highest level of theory see Table is favoured over
by kcal mol and so the ion is thermo dynamically accessible However
the barrier for its formation from turned out to b e surprisingly high
kcal mol i e kcal mol higher than the exp erimentally derived activation
energy kcal mol Considering the level of our calculations and the gen
erally go o d agreementbetween exp eriment and theory at comparable levels of
theory found for other systems we conclude that the isomerization
do es not in fact take place at least not prior to the sp ontaneous loss of CO or
that of HCO
How then do es the loss of CO and also that of HCO o ccur Previous the
oretical calculations on methyl esters indicate that a hydrogen shift to the
oxygen atom requires only kcal mol In the case of methyl carbamate
TS lies only kcal mol ab ove and isomer the distonic ion H N
C OH OCH is kcal mol more stable than Thus it is clear that the
transformation can take place b elow the minimum energy required for the
losses of CO and HCO bycontrast the transformation cannot take place
below the minimum disso ciation energy Hence we conclude that the distonic
ion is accessible That TS is much higher in energy than TS
may b e traced to the fact that the NCOO electron system in is not a ected
by the transition whereas in TS the electron delo calization do es
not extend to the N atom However for ion to servea key intermediate in
the losses of CO and HCO it must b e able to undergo rearrangement reactions
whose energy requirements are b elow that for the direct b ond cleavage reaction
H NCOH CH O An attractive pathway which satis es this
requirementinvolves isomerization into the very stable hydrogen bridged isomer
as the rst step
The gas phase chemistry of the methyl carbamate radical cation
A similar isomerization has b een prop osed to o ccur in the distonic ions H
C OH OCH generated from ionized methyl formate and CH C OH OCH
generated from ionized methyl acetate calculations a have shown
that in these ions stretching of the formaldehydecarb ene b ond do es not imme
diately lead to disso ciation but to a situation where well b elow the disso ciation
limit isomerization can o ccur to the stable hydrogen bridged isomer
R HorCH R C O H O CH
Using the SCF metho d however wewere not able to nd a saddle p oint for
the transition state TS We then p erformed a numb er of partial geometry
optimizations for xed values of the angle OOC as the reaction co ordinate
These calculations indicated that for two SCF solutions exist one which
is characterized byasingle C O b ond in the formaldehyde moiety as in ion
and one in which this b ond is a double C O b ond as in ion The two solutions
corresp ond to valleys in the p otential energy surface which are not separated by
a saddle p ointbutbyanintersecting line as indicated in Fig
Chapter
Table Calculated total energies hartree zero p oint vibrational energies kcal
mol and relative energies kcal mol for isomers and comp onents of ionized methyl
carbamate
Sp ecies Point State RHF G RHF G Pople G ZPVE E
rel
group G G G G
C A
s
C A
s
A C
C A
C A
C A
C A
s
C A
C A
s
C A
s
TS C A
TS C A
TS C A
s
TS C A
s
TS C A
TS C A
TS C A
TS C A
TS C A
TS C A
TS C A
s
TS C A
s
The gas phase chemistry of the methyl carbamate radical cation
Fig Schematic representation of the SCF
p otential energy surface of the isomerization
Additional SCF calculations were p erformed for several C O b ond lengths
between the two partial SCF minima A and B in Fig for a xed angle
These calculations show a discontinuity in the energy gradientofthe
formaldehyde C O b ond resulting in an intersecting line b etween the twovalleys
the b old broken line in Fig The discontinuity will disapp ear when the two
SCF solutions are sup erimp osed into a CASSCF wavefunction In the case of a
CASSCF calculation one selects an active orbital space which consists of o ccupied
and uno ccupied virtual orbitals Within the active space all excitations are
allowed so a full con guration interaction CI calculation is done for the active
orbital space chosen In our case we need three active orbitals for the three
electrons which are directly involved in the isomerization reaction viz one
electron on eachofthetwo C atoms and one on the O atom involved in the
isomerization Using an interp olated geometry with and R A
CO
as the starting p ointwewere thus able to lo cate the transition state TS
The calculation of the activation energy was p erformed at the CASSCF G
level of theory and the same level of theory was used for optimizing the geometries
of the ions and According to these calculations the transition state TS
corresp onds to b oth the breaking of the N C O C b ond in ion and the breaking
of one H C O b ond in ion InTS there are essentially three radical
electrons In the SCF metho d two of these electrons are forced to o ccupy the
same MO The character of the SCF wavefunction is determined by the H C O
Chapter
b ond length for intermediate CO b ond lengths there is an instability with resp ect
to lo calization of the radical electron on either of the two C atoms leading to a
discontinuity in the energy gradient of the CO b ond
Fig Theoretically derived energy diagram for the disso ciation
reactions of ionized methyl carbamate H NCOOCH
The nal results of our CASSCF calculations which b ecause of the large
computational exp ense involved had to b e restricted to the CASSCF G
level of theory are as follows ion E ion E
and TS E hartree This is equivalenttoTS b eing
kcal mol higher in energy than or kcal mol ab ove see Fig
From the results in Table it can b e seen that enlarging the basis set
with p olarization functions generally has little e ect on the activation energies
However electron correlation e ects are much more imp ortant for the transition
states than for the stable isomeric ions and their inclusion results in a decrease
in the activation energies for the isomerizations Since inclusion of the ZPVE s is
exp ected to have the same e ect we prop ose that the calculated activation energy
for the isomerization step may b e an upp er limit In any case the calculated
relative energy for TS is in satisfactory agreement with the exp erimental
The gas phase chemistry of the methyl carbamate radical cation
observations it lies b elow the disso ciation limit for H NCOH CH O
anditmaywell represent the rate determining second isomerization
step in the mechanism for the losses of CO and HCO
The fate of ions is intriguing in marked contrast with the related sp ecies
CH O O H O CH and H C O H O CH which disso ciate
by simple b ond cleavage to their comp onents our calculations indicate that ion
can undergo two rearrangement reactions b elow or close to the disso ciation
limit The energy diagram presented in Fig shows the results of our ab
initio calculations For comparison this diagram also contains the exp erimentally
derived activation energies for loss of HCO CO kcal mol CH O
kcal mol and CH O CH OH kcal mol
The rst p ossibility is that the formaldehyde molecule in attracts the hy
droxyl hydrogen The incipient CH OH radical subsequently moves within the
electrostatic eld of the H N C O ion towards the N atom to form via TS
thehydrogen bridged sp ecies H C O H NH CO
Thus in agreement with our previous prop osal b it is indeed ion
from which the loss of CO o ccurs However this ion is not formed via the simple
pathway prop osed previously but via a more complex route According to the
calculations these ions lie in a shallowwell only and they disso ciate by loss of
in CO to pro duce the hydrogen bridged pro duct ion H C O H NH
agreement with exp eriment It should b e noted that the disso ciation limit for
the reaction H N C O CH O is much higher in energy i e the N C
Chapter
b ond in is muchweaker than the O H Nhydrogen bridged ion dip ole
interaction
Alternatively instead of accepting a hydrogen atom the formaldehyde molecule
in may donate a hydrogen atom to the C atom of the NH C OH ion form
ing via TS the most stable C H NO isomer H NCHOH O C H
in which the NH C OH ion interacts with the formyl dip ole Loss of HCO
o ccurs directly therefrom
Are the results of the calculations as summarized in the energy diagram
shown in Fig in agreement with exp eriment Firstly theory predicts
that metastable ions will lose HCO and CO as is observed exp erimentally
Secondly theory predicts the correct structures for the daughter ions i e NH
CH OH and H C O H NH resp ectively Furthermore for the lab elled
sp ecies theory predicts atom sp eci c b ehaviour and it also predicts the correct
isotopic p ositions in the pro ducts see ab ove notably the observation that H N
C O O CH cleanly eliminates H C O and C O
In addition we had shown earlier b that the disso ciative neutralization
of the OCD lab elled ester generated among other pro ducts largely CD OD
together with some CD OH Disso ciative neutralization not collisional activa
tion was chosen to prevent p ost collisional isomerization b Had low energy
methyl carbamate ions rearranged to then mostly CD OH would havebeen
generated This is strong supp ort for the rearrangement after which
disso ciative neutralization to CD OD takes e ect
The small amountof CD OH formed after the neutralization indicates that
in the formaldehyde molecule may also migrate to the N atom generating
The gas phase chemistry of the methyl carbamate radical cation
CH O H NH C OH but this was not further investigated It should
b e noted that formation of CD OH cannot b e ascrib ed to the transformation
as low energy ions are sampled in the NR exp eriment The partially lab elled
ion H NC O OCD H in the microsecond time frame loses DCO and HCO in
a ratio of This is precisely what our calculations predict provided that no
isotop e e ects op erate in the steps and and so we conclude that not
these steps but the transformation is rate determining as was the case with
ionized methyl acetate a
The calculated relative energies and the exp erimental values where they over
lap compare favourably except for the energy di erence b etween and its
disso ciation pro ducts H N C O CH OH exp eriment this work
kcal mol vs theory kcal mol The reason for this large
discrepancy is not well understo o d although it should b e noted that in general
disso ciation energies are more di cult to establish accurately than the relative
energies of a set of isomeric ions
There is particularly go o d agreementbetween the exp erimentally and theo
retically derived magnitude of the reverse term for loss of HCO kcal mol
exp eriment vs kcal mol theory However the average kinetic energy re
lease hT i is small and non sp eci c hT i kcal mol and so only ab out of
the energy is released as kinetic energy Similar e ects have b een observed previ
ously in the disso ciation of other hydrogen bridged radical cations b a
Similarly the loss of CO has a calculated reverse term E of ab out kcal
rev
mol but hT i is only kcal mol ab out of E The observation
rev
daughter ions formed from the OCD lab elled that the CD O D NH
ester generate up on collisional activation a mixture of CD OH and CD OD
ions and up on disso ciative electron capture a ratio of CD OH and CD OD
radicals can b e rationalized by allowing the formaldehyde dip ole to freely ro
tate around the ammonia ion i e CD O D NH CD O H
NDH
Finally there are two questions related to the ionchemistry of ionized methyl
carbamate whichwe are currently investigating The rst question concerns the
p ossible participation of the isomeric ion H N C OH OCH a the enol
analogue of methyl acetate in the isomerization b ehaviour of H N C O OCH
This enol typ e ion which according to preliminary calculations is quite a sta
Chapter
ble sp ecies could b e formed from ion by a hydrogen shift a hydrogen
shift in ion is probably energetically prohibited d However if this iso
merization reaction o ccurs then ion a cannot isomerize backto b ecause the
sp eci cally loses DCO Ion a was exp ected lab elled ion H N C O OCD
to b e generated by a McLa erty typ e rearrangementinRCH N N H COOCH
R H CH but surprisingly
the MI CA and NR sp ectra of the abundant m z C H NO ions generated
from these precursor molecules were very close to those of the keto ion We
are currently investigating other means of generating a and also establishing
the height of the barriers for its inter conversion with ions and by ab initio
calculations
The second question concerns the following if one of the amino hydrogen
atoms of methyl carbamate is substituted byanNH group yielding methyl
carbazate H N N H COOCH an unexp ected and totally di erent disso ciation
behaviour ensues Methyl carbazate ions disso ciate among other pro ducts
to the immonium ion H N N H CH by expulsion of COOH in a one step
pro cess Based on a variety of exp eriments the following mechanism was prop osed
The gas phase chemistry of the methyl carbamate radical cation
According to this prop osal in the intermediate distonic ion whichcanbe
considered as the analogue of a methylene unit is transferred to the charged
centre In the case of ion a similar reaction would lead to the very stable immo
nium ion CH NH and COOH whose combined enthalpies H CH NH
f
COOH kcal mol a are lower than those for the observed re
action pro ducts From the start of the present study wewere in fact surprised
that methyl carbamate ions do not exp el COOH This to o is under further
investigation
Conclusions
The results of our study provide a detailed insightinto the unimolecular chemistry
of ionized methyl carbamate Although its chemistry loss of HCO and CO
would sup er cially app ear to b e totally di erent from that of ionized methyl
acetate loss of CH O and CH OH the rst two of the three isomerization
steps are in fact the same molecular ion distonic ion hydrogen bridged
ion
However in contrast with ionized methyl acetate the resulting hydrogen
can undergo two further rear bridged radical cation H N C OH O CH
rangement reactions The rst pro cess involves rearrangementtothehydrogen
bridged ion dip ole complex H C O H NH C O which leads to the
loss of CO by a simple b ond cleavage The second pro cess involves isomerization
into another hydrogen bridged ion dip ole complex the most stable C H NO
isomer H NCHOH O C H which is the immediate precursor for loss
of HCO Thus it app ears that the participation of hydrogen bridged ion dip ole
complexes in the isomerization is even more imp ortant in the unimolecular chem
istry of ionized methyl carbamate than in that of ionized methyl acetate This is
largely due to the combination of stability and exibility in these ions
Chapter
Finally we note that as was the case with methyl acetate a a coherent
description of the chemistry of solitary methyl carbamate ions could not have
b een achieved by the analysis of exp erimental data only
Acknowledgements
The authors are grateful to Dr F P Lossing for app earance energy measure
ments and to Professor J L Holmes for valuable discussions and for access to the
KRATOS MS S instrument J K T thanks the National Sciences and Engi
neering Research Council of Canada NSERC and the University of Utrechtfor nancial supp ort
The gas phase chemistry of the methyl carbamate radical cation
References and Notes
a H Budzikiewicz C Djerassi and D H Williams Mass Sp ectrometry of Or
ganic Comp ounds Holden Day London
b F W McLa erty Mass Sp ectrometry of Organic Ions Academic Press New
York
R I Reed Quart Rev
K Biemann Mass Sp ectrometry Organic Chemical Applications McGraw Hill
New York p
a R G Co oks J H Beynon R M Caprioli and G R Lester Metastable Ions
Elsevier Amsterdam
b K Levsen Fundamental Asp ects of Organic Mass Sp ectrometry Verlag
Chemie Weinheim
a C Wesdemiotis and F W McLa erty Chem Rev
b J K Terlouw and H Schwarz Angew Chem Int Ed Engl
Angew Chem
c J K Terlouw Adv Mass Sp ectrom
d J L Holmes Mass Sp ectrom Rev
e F W McLa erty Science
P C Burgers T Drewello N Heinrich W Kulik C J Morrow J Schmidt J K
Terlouw and H Schwarz in preparation
P C Burgers and J K Terlouw Sp ec Perio d Rep Vol Chem So c
London Chap
P C Burgers C E C A Hop J K Terlouw and J L Holmes Org Mass Sp ec
trom
C E Hudson T Lin and D J McAdo o Org Mass Sp ectrom
a A N H Yeo J Chem So c D
b J L Holmes P C Burgers and J K Terlouw Can J Chem
c L Freiser Monteiro M L Freiser Monteiro J L Butler and T Baer J Phys
Chem
N Heinrich and H Schwarz in J P Maier Ed Ion and Cluster Ion Sp ec
troscopy and Structure Elsevier Amsterdam p
a N Heinrich J Schmidt H Schwarz and Y Ap eloig J Am Chem So c
and references cited therein
b P C Burgers C Lifshitz P J A Ruttink G Schaftenaar and J K Terlouw Org Mass Sp ectrom
Chapter
c W Hehre L Radom P v R Schleyer and J A Pople Ab Initio Molecular
Orbital Theory John Wiley NewYork
d B Yates and L Radom J Am Chem So c
a S Hammerum Mass Sp ectrom Rev
b B F Yates W J Bouma and L Radom Tetrahedron
a P C Burgers J L Holmes C E C A Hop R Postma P J A Ruttink and
J K Terlouw J Am Chem So c
b B L M van Baar P C Burgers J L Holmes and J K Terlouw Org Mass
Sp ectrom
c P C Burgers J L Holmes J K Terlouw B L M van Baar Org Mass
Sp ectrom
a D J McAdo o Mass Sp ectrom Rev
b R Postma P J A Ruttink B L M van Baar J K Terlouw J L Holmes and
P C Burgers Chem Phys Lett
D Rethel and V Gold Carb onium Ions An Intro duction Academic Press New
York p
F P Lossing and J C Traeger Int J Mass Sp ectrom Ion Phys
A M Paquin Z Naturforsch
P C Burgers and J L Holmes Org Mass Sp ectrom
a S G Lias J E Bartmess J F Liebman J L Holmes R D Levin and W G
Mallard J Phys Chem Ref Data Suppl
b C E C A Hop J L Holmes P J A Ruttink G Schaftenaar and J K Ter
louw Chem Phys Lett note that this pap er shows that
H H NC O as quoted in ref a kcal mol is probably in error
f
M Dupuis D Spangler and J Wendolowski NRCC Software Catalog Pro
gram No QG GAMESS M F Guest and J Kendrick GAMESS User
Manual An Intro ductory Guide CCP Daresbury Lab oratory
V A Saunders and J H van Lenthe Mol Phys
J A Pople R Seeger and N R Krishan Int J Quantum Chem
J A Pople H B Schlegel R Krishan D J DeFrees J S Binkley M J Frisch
R A Whiteside R F Hout Jr and W J Hehre Int J Quantum Chem
P C Burgers T Drewello H Schwarz and J K Terlouw Int J Mass Sp ectrom Ion Pro cesses
Summary
Computational Chemistry Metho ds
Applications to racemate resolution and radical cation chemistry
This thesis deals with the application of computational mo dels to solvereal
life chemical problems Two distinct problems are tackled First the prediction
of lattice energy di erences b etween a pair of diastereomeric salts and secondly
the elucidation of the unimolecular chemistry of the methyl carbamate radical
cation
The intro ductory chapter deals with the background of racemate resolution
via the formation of diastereomeric salts The solubility di erence b etween two
salts of a diastereomeric pair is related to the lattice enthalpy di erence in a pair
A computational mo del that accurately repro duces exp erimental lattice enthalpy
di erences can b e used as a predictive to ol for the resolution of optical isomers
In addition we summarize the mass sp ectrometry techniques used for the ex
perimental elucidation of the unimolecular chemistry of the methyl carbamate
radical cation The computational metho ds applied to b oth these problems are
brie y reviewed
Chapter covers the Molden package our pre and p ost pro cessing program
of molecular and electronic structure This program has b ecome central to this
research It is used to calculate a numb er of di erenttyp es of charges in a
molecule the electrostatic p otential distributed multip oles Z matrix constructs
to imp ose translational and screw typ e of symmetry forinterfacing with the
program packages DMAREL and VASP that p erform lattice energy calculations and for manipulation of crystal structures Other features include the calculation
visualization of molecular orbitals the electron density molecular minus atomic
density and the Laplacian of the electron density
Chapter discusses the developmentoftwo new molecular p oint charge mo d
els a charges t to repro duce the Distributed Multip ole derived electrostatic
p otential and b charges t to repro duce the quantum mechanical electrostatic
p otential sampled on a numb er of surfaces with constant electron density In ad
dition weinvestigated the e ect of the numb er of expansion sites in a Distributed
Multip ole Analysis on the qualityofcharges tted to the DMA derived electro
static p otential The inclusion of b ond centers into the calculations improves
the agreementbetween the Quantum Mechanical electrostatic p otential and the
DMA derived p otential The numb er of expansion sites needed for an accurate
approximation of the QM electrostatic p otential increases with increasing qual
ity of the basis set used Sampling on constant electron density surfaces gives a
b etter t b etween the quantum mechanical p otential and the p otential derived
from the tted charges than sampling on a Van der Waals surface comp osed of
intersecting spheres
Chapter describ es Quantum Mechanical and Force Field calculations on
Diastereomeric Salts Wehave calculated the relative lattice energies of the di
astereomers of cyclic phosphoric acid and its chlorine derivative with ephedrine
with various computational mo dels and compared them with exp erimental data
All computational mo dels gave go o d structural agreement with the exp eriment
but only some mo dels repro duced the exp erimental stability order Calculations
with the DREIDING force eld in combination with several charge sets includ
ing the charge set develop ed in chapter failed to repro duce the exp erimental
stability order of the diastereomers By using distributed multip oles to mo del
the electrostatic interactions in force eld calculations the correct stability order
was repro duced in one case but the results are very sensitive to the factor used
for scaling the electrostatic interactions and to conformational energy corrections
of the rigid molecular ions Quantum mechanical calculations with the DMol
density functional package predict a correct stability order for one pair of diastere
omers but fail to p osition a third p olymorph correctly Similar calculations with
the VASP and SIESTA density functional packages predict the stability order
of all diastereomers correctly at the p oint in k space With b etter k space
sampling however the agreementbetween theory and exp eriment b ecomes less
go o d An exp erimentally unknown chlorine free analogue of the exp erimentally
most stable chlorine containing diastereomer was calculated to b e the least sta
ble Mo del systems of the twotyp es of hydrogen b onded chains observed in a
series of diastereomeric salts with screw and translational symmetry were op
timized at the Hartree Fock and density functional level The exp erimentally
most frequently o ccurring hydrogen b onded chain with screw axis symmetry was
calculated to b e the most stable
In the nal chapter the unimolecular chemistry of the methyl carbamate rad
ical cation H NCOOCH has b een investigated bya combination of mass sp ec
trometry based exp eriments and ab initio molecular orbital calculations These
calculations indicate that b esides ionized methyl carbamate there are at least
seven other equilibrium structures including distonic ions and hydrogen bridged
radical cations The most stable isomer is the hydrogen bridged sp ecies H N
CH O H O C H which is b est viewed as the carb enium ion H N CH
OH interacting with the formyl dip ole The related sp ecies H N C O H
O CH in which the hydroxyamino carb ene ion H N C OH interacts with
the formaldehyde dip ole is also a stable sp ecies This hydrogen bridged radical
cation is the key intermediate in the sp ontaneous unimolecular disso ciations of
methyl carbamate ions Exp erimentally the metastable molecular ions form two
sets of pro ducts namely H N CH OH HCO the comp onents of the most
stable isomer and CH O H NH CO The minimum energy paths
have b een lo cated by ab initio calculations The reactions followmultistep iso
merizations It is stressed that the ab ovemechanisms could only b e elucidated
with the aid of high level ab initio calculations
In conclusion the presentday computational mo dels for the calculation of
lattice energies are still not su ciently accurate to reliably predict and design
racemate resolutions The structures of the diastereomeric salts were correctly
predicted however The unimolecular chemistry of the methyl carbamate radical
cation could b e succesfully elucidated by ab initio calculations
Samenvatting
Computational Chemistry Metho den
To epassingen op racemaat splitsingen en radicaal kation chemie
Dit pro efschrift b ehandelt de to epassing van rekenmo dellenvo or het oplossen
van chemische problemen Twee verschillende problemen worden b ehandeld de
vo orsp elling van verschillen in ro osterenergie tussen een diastereomeer zoutpaar
en de opheldering van de unimoleculaire chemie van het methylcarbamaat radi
caal kation
Het eerste inleidende ho ofdstuk b ehandelt de achtergrond van racemaatsplit
sing via de vorming van diastereomere zouten Het oplosbaarheidsverschil tussen
de twee zouten van een diastereomeer paar is gerelateerd aan het verschil in
ro osterenergie tussen de zouten Een rekenmo del dat nauwkeurig verschillen in
exp erimentele ro osterenergie kan repro duceren kan gebruikt worden als gereed
schap bij de vo orsp elling van scheiding van optische isomeren Tevens wordt een
overzicht gegeven van massasp ectrometrische technieken gebruikt bij de ophelde
ring van de unimoleculaire chemie van het methylcarbamaat radicaal kation De
in b eide problemen to egepaste rekenmo dellen worden kort b ehandeld
Ho ofdstuk b elicht het Molden pakket ons vo or en na b ewerkingsprogramma
vo or moleculaire en electronische structuur Dit programma sp eelt een centrale
rol in dit onderzo ek Het wordt gebruikt voordeberekening van verschillende
typ en ladingen in een molecuul de electrostatische p otentiaal gedistribueerde
multip olen Z matrix constructies vo or het opleggen van translatie en schro efas
symmetrie voor interfacing met de programma pakketten vo or ro osterenergieb e
rekeningen DMAREL en VASP envo or het manipuleren van kristalstructuren
Andere mogelijkheden zijn de b erekening visualisatie van moleculaire orbitalen
de electronendichtheid de moleculaire minus atomaire electronendichtheid en de
Laplaciaan van de electronendichtheid
Ho ofdstuk b espreekt de ontwikkeling van twee nieuwe moleculaire punt
ladingsmo dellen a ladingen ge t ter repro ductie van de p otentiaal afgeleid van
gedistribueerde multip olen en b ladingen ge t ter repro ductie van de kwantum
mechanische electrostatische p otentiaal b emonsterd op een aantal opp ervlakken
van constante electronendichtheid Tevens werd het e ect van het aantal expan
siecentra in een gedistribueerde multip o ol analyse DMA op de kwaliteit van
de ladingen ge t aan de DMA afgeleide p otentiaal onderzo cht Het meenemen
van bindingscentra bij de b erekeningen verb etert de overeenstemming tussen de
kwantummechanische electrostatische p otentiaal en de DMA afgeleide p otenti
aal Het aantal expansiecentra no dig vo or een nauwkeurige b enadering van de
QM electrostatische p otentiaal neemt to e met de kwaliteit van de gebruikte ba
sisset Het monsteren op opp ervlakken van constante electronendichtheidgeeft
een b etere overeenkomst tussen de kwantummechanische p otentiaal en de p oten
tiaal afgeleid van de ge tte ladingen dan het monsteren op een Van der Waals
opp ervlak b estaande uit overlapp ende b ollen
Ho ofdstuk b ehandelt kwantummechanische en krachtveld b erekeningen aan
diastereomere zouten Met verschillende rekenmo dellen werden de relatieve ro os
terenergie en van de diastereomeren van een cyclisch fosforzuur en zijn chlo or
derivaat met efedrine b erekend en de resultaten worden vergeleken met de exp e
rimentele gegevens Alle rekenmo dellen gaven go ede overeenkomst tussen b erek
ende en exp erimentele structuur echter slechts enkele rekenmo dellen repro duceer
den de exp erimenteel gevonden stabiliteitsvolgorde Berekeningen met het DREIDING
krachtveld in combinatie met verschillende ladingssets inclusief de ladingsset
ontwikkeld in ho ofdstuk repro duceerden niet de exp erimenteel gevonden sta
biliteitsvolgorde van de diastereomeren Bij gebruik van gedistribueerde multi
p olen vo or het mo delleren van de electrostatische interacties in de krachtveld
berekening wordt de correcte stabiliteitsvolgorde slechts in e en geval gerepro
duceerd maar de resultaten zijn erg gevo elig vo or de factor gebruikt bij het
schalen van de electrostatische interacties en vo or de conformationele energiecor
recties van de moleculaire ionen kwantummechanische b erekeningen met het
DMol density functional pakket vo orsp ellen de correcte stabiliteitsvolgorde voor
e en paar diastereomeren maar een derde p olymorf wordt niet go ed gep osition
eerd Vergelijkbare b erekeningen met de VASP en SIESTA density functional
pakketten vo orsp ellen de correcte stabiliteitsvolgorde van alle diastereomeren bij
het punt in de k ruimte Echter met b etere b emonstering van de k ruimte
wordt de overeenkomst tussen de theorie en het exp erimentslechter Een ex
perimenteel onbekende chlo orvrije analo og van de exp erimenteel meest stabiele
chlo orb evattende diastereomeer was in de b erekening het minst stabiel Mo del
systemen van de twee typ en van waterstofgebrugde ketens die gevonden worden in
een serie van diastereomere zouten met translatie en schro efas symmetrie werden
geoptimaliseerd op het Hartree Fock en density functional niveau De exp eri
menteel meest gevonden waterstofgebrugde keten met schro efas symmetrie was
in de b erekening het meest stabiel
Het laatste ho ofdstuk b espreekt de unimoleculaire chemie van het methyl
carbamaat radicaal kation H NCOOCH onderzo chtmeteencombinatie van
massasp ectrometrie exp erimenten en ab initio moleculaire orbitaal b erekeningen
Deze b erekeningen geven aan dat b ehalvege oniseerd methylcarbamaat er ten
minste zeven andere evenwichtsstructuren zijn waaronder distonische ionen en
waterstofgebrugde radicaal kationen Het meest stabiele isomeer is het water
stofgebrugde H N CH O H O C H dat het b est gezien kan worden
als het carb enium ion H N CH OH in interactie met de formyl dip o ol Het
gerelateerde isomeer H N C O H O CH waarin het hydroxyami
no carb een ion H N C OH interactie heeft met de formaldehyde dip o ol is o ok
een stabiel ion Dit waterstofgebrugde radicaal kation is een b elangrijk interme
diair voor de spontane unimoleculaire disso ciatie reacties van methylcarbamaat
ionen Exp erimenteel vormen de metastabiele moleculaire ionen twee sets van
pro dukten namelijk H N CH OH HCO de comp onenten van het meest
stabiele isomeer en CH O H NH CO De minimumenergiepaden
zijn gevonden met b ehulp van ab initio b erekeningen Benadrukt wordt dat de
opheldering van de b ovengeno emde reactiemechanismes slechts mogelijk was met
behulp van hogekwaliteits ab initio b erekeningen
Concluderend kan gesteld worden dat de huidige rekenmo dellenvoor de bere
kening van ro osterenergie en nog steeds niet accuraat geno eg zijn om b etrouwbaar
vo orsp ellingen van racemaatsplitsingen te kunnen do en De structuren van de di
astereomere zouten werden echter wel go ed vo orsp eld De unimoleculaire chemie
van het methylcarbamaat radicaal kation kon succesvol opgelost worden met b e
hulp van hogekwaliteits ab initio b erekeningen
Dankwoord
Tot slot zou ik ieder e en willen b edanken die op de e en of andere manier aan de
totstandkoming van dit pro efschrift heeft bijgedragen Op de eerste plaats b en
ik natuurlijk dank verschuldigd aan mijn promotores Ad van der Avoird en Elias
Vlieg Zij hebb en het aangedurfd een pro ject onder hun ho ede te nemen dat al
driejaarinvolle gang was Daarnaast wil ik Jan No ordik b edanken onder wiens
leiding ik aan dit werk b egonnen b en Met name Jan s oprechte b elangstelling
vo or mij als p erso on en mijn werk en zijn gelo of in mijn kunnen zijn mij zeer tot
steun geweest Rob ert Meier mijn co promotor en Betty Coussens b eiden van
DSM Research wil ik b edanken vo or de inspirerende discussies over dit werk Prof
Gert Vriend wil ik vo oral b edanken vo or zijn inspanningen achter de schermen
zonder welke dit pro efschrift het lichtwellicht niet had gezien Mijn kamergeno ot
en CMS c collega Paul Verwer b edank ik vo or zijn immer elo quente en taalkundig
opvo edende gesprekken do orsp ekt met zijn zeer eigen humor Hens Borkent wil
ik b edanken vo or zijn go ede suggesties met b etrekking tot het Molden pakket
Daarnaast wil ik natuurlijk de rest van mijn collega s bij het CMBI b edanken
Ondanks wo elige tijden is de go ede band is gebleven De collega s binnen het
CMS c pro ject wil ik b edanken vo or een go ede samenwerking Gijs
Curriculum Vitae
Gijsb ert Schaftenaar werd op augustus in Harderwijk geb oren In juni
b ehaalde hij het diploma Atheneum B aan het Christelijk College Nas
sau Veluwe te Harderwijk Aansluitend b egon hij met de studie scheikunde aan
de Rijksuniversiteit Utrecht Het do ctoraalexamen omvatte analytische chemie
Prof Dr J van der Maas als ho ofdvak en kwantumchemie als bijvak Op
maart werd het do ctoraalexamen succesvol afgelegd Een intermezzovan
maanden vormde de vervulling van de militaire dienstplicht Op augustus
volto oide hij als assistent in opleiding een tweejarige onderzo ekersopleid
ing op het gebied van de kwantumchemievan kationen radicalen en waterstof
gebrugde complexen in de gasfase zie ho ofdstuk van dit pro efschrift Sinds
augustus is hij werkzaam bij het Centre for Molecular and Biomolecu
lar Informatics het CMBI vo orheen CAOS CAMM Center aan de Katholieke
Universiteit Nijmegen de eerste twee jaar binnen een samenwerkingspro ject van
het CAOS CAMM Center en de werkgemeenschap Quantumtheoretische Chemie
Het do el hiervan was het ontsluiten van kwantumchemische programmatuur voor
chemici in het algemeen In deze p erio de werd b egonnen met het schrijven van
het Molden software pakket Ho ofdstuk van dit pro efschrift De daaropvol
gende vier jaar werd onder leiding van Dr J A M Leunissen gewerkt aan de
ondersteuning van de bioinformatica service van het Center Dit hield in het up
to date houden van sequentiedatabanken en het programmeren van gebruikerin
terfaces Daarnaast was hij actief als p enningmeester en interim vo orzitter van
de Research and Development committeevan het EMBnet Europ ean Molecular
Biology network Van augustus tot augustus was hij werkzaam als
pro jectmedewerker in dienst van NWO Chemische Wetenschapp en in het kader
van het Kristallisatie pro ject uit het Prioriteiten Programma Materialenonder
zo ek Computational Material Science eerst onder leiding van Dr J H No ordik
en later onder leiding van Prof dr ir A van der Avoird en Prof dr E Vlieg