Updated: 2016-02-25
WORKSHOP Institut de Química Computacional i Catàlisi
AA newnew perspectiveperspective onon quantifyingquantifying electronelectron localizationlocalization andand delocalizationdelocalization inin molecularmolecular systemssystems
TheoreticalTheoretical foundationsfoundations ofof thethe bond-orbitalbond-orbital projectionprojection formalismformalism
dr Dariusz Szczepanik GIRONA JAGIELLONIAN UNIVERSITY January 21st, 2016 Department of Theoretical Chemistry Theoretical foundations of the bond-orbital projection formalism 2/33
Presentation plan
1. Electron density, atoms in molecules, chemical bonds.
2. Localization and delocalization components of the electron density
3. Electron delocalization between atoms.
4. Electron delocalization between bonds.
5. The effectiveness of bond conjugation as an aromaticity criterion. Theoretical foundations of the bond-orbital projection formalism 3/33
Electron density, atoms in molecules, chemical bonds
I Hohenberg–Kohn theorem: the ground-state electron density (ED) uniquely determines the potential and thus all physicochemical properties of the molecular system.
What about traditional concepts such as atom and chemical bond? Theoretical foundations of the bond-orbital projection formalism 4/33
Electron density, atoms in molecules, chemical bonds
Partitioning of the electron density into atomic contributions (charges):
● Bader's charges (QTAIM approach),
● Hirshfeld's charges,
● Politzer's charges,
● Voronoi charges,
● Coulson's charges,
● Mulliken's charges,
● Löwdin's charges,
● Weinhold's (natural) charges,
● Merz-Kollman's charges,
● Breneman's charges,
● Szigeti charges, and many others...
A difficult choice! Theoretical foundations of the bond-orbital projection formalism 5/33
Electron density, atoms in molecules, chemical bonds
Delocalization of atomic charges – chemical bonding analyses:
● Bond critical points (QTAIM by Bader),
● Coulson's, Wiberg's, Mayer's and Gopinathan-Jug's bond orders,
● Localized molecular orbitals (Boys, Edmiston-Ruedenberg, Pipek-Mezey schemes)
● Natural bond orbitals (NBO),
● Natural orbitals for chemical valence (NOCV),
● Localized orbitals of bond orders (LOBO),
● Iterative double-atom partitioning by orthogonal projectors (IDAP),
● Electron localization function (ELF),
● Localized orbital locator (LOL),
● Single exponential decay detector (SEDD),
● Reduced density gradient (RDG), and many others...
A difficult choice! Theoretical foundations of the bond-orbital projection formalism 6/33
Electron density, atoms in molecules, chemical bonds
Delocalization of chemical bonds – a multicenter electron-sharing analyses:
● Scanning for multicenter bonding within the framework of the NBO analysis,
● Adaptive natural density partitioning (AdNDP) analysis,
● Multicenter delocalization descriptors (MCI,DI,ESI),
● Bridgeman-Empson's three-center bonding analysis,
● Electron density of delocalized bonds approach (EDDB), and others...
Is it possible to probe electron localization and delocalization within one theoretical paradigm? Theoretical foundations of the bond-orbital projection formalism 7/33
Localization and delocalization components of the electron density
.. electrons electrons electrons
ED(r) EDLA(r) EDLB(r) EDDB(r)
EDDA(r)
ED(r) – electron density,
EDLA(r) – density of electrons localized on atoms, EDDA(r) – density of electrons delocalized between atoms, ! EDLB(r) – electron density of localized bonds, EDDB(r) – electron density of delocalized bonds, Theoretical foundations of the bond-orbital projection formalism 8/33
Electron delocalization between atoms (EDDA)
Electron density layer representing the population of electrons delocalized between atoms, EDDA(r), is crucial for the whole ED-decomposition procedure. It involves the Hilbert-space partitioning scheme and is defined through the following steps:
Definition of the matrix
1.Transformation of non-orthogonal atomic orbitals (AOs) into the represe- ntation of natural atomic orbitals (NAOs). 2.Solving the eigenproblems of a set of Jug's matrices, representing all possible bonds (interactions) in a molecule, to obtain two-center bond- order orbitals (2cBO) and their occupations. 3.Projection of the 2cBO metric onto the subspace of occupied MOs. Theoretical foundations of the bond-orbital projection formalism 9/33
Electron delocalization between atoms (EDDA)
1. The occupancy-weighted symmetric orthogonalization (OWSO) of atomic orbitals (AOs) to natural atomic orbitals (NAOs): A). Transformation from cartesian to pure AOs. B). Partitioning and symmetrization of intra-atomic blocks of the overlap and the Coulson's density matrix (D). C). Löwdin orthogonalization of the intra-atomic blocks of the DM. D). Solving the eigenproblems for intra-atomic blocks of the DM. E). Division of eigenfunctions into the (pre-orthogonalized) natural minimal basis (NMB) and the complementary natural Rydberg's basis (NRB). F). Interatomic Gramm-Schmidt orthogonalization of NRB to NMB. G). Repeating the B,C and D steps, but only for the NRB 'orbitals'. H). A separate interatomic occupancy-weighted orthogonalization of both subsets, I). Re-orthogonalization of both subspaces by repeating the B,C and D steps. Features of NAOs: – The effective dimensionality of the AO space is reduced to that of the formal NMB subspace. – For isolated atoms NAOs coincide with natural orbitals (NO). – NAOs mostly retain a well-localized one-center character. – NAOs are intrinsically stable toward basis set extensions. Theoretical foundations of the bond-orbital projection formalism 10/33
Electron delocalization between atoms (EDDA)
2. Construction of a set of two-center bond orbitals.
– electron density in the NAO basis reads
– the Jug's matrix is a (α,β)-diatomic block matrix of type: =
– the eigenvectors of represent the two-center bond orbitals of three different types: bonding >0, non-bonding =0, and antibonding <0
, and both subsets of 2cBOs form a paired-orbital basis.
– for duodemponent density matrices, the Wiberg's bond-order (covalency) index reads: Theoretical foundations of the bond-orbital projection formalism 11/33
Electron delocalization between atoms (EDDA)
2. Construction of a set of two-center bond orbitals.
– bonding 2cBOs CCbond Acetylene – antibonding 2cBOs
For typical molecular systems with well defined Lewis-like electronic structures the highest-occupied 2cBOs form a set of nearly orthogonal bond orbitals and, consequen- tly, twice the sum of Wiberg's indices between all pairs of covalently bonded atoms approximates the population of electrons delicalized between all atoms (EPDA). Theoretical foundations of the bond-orbital projection formalism 12/33
Electron delocalization between atoms (EDDA)
3. Projection of 2cBOs onto the subspace of occupied MOs Obviously, for accurate calculations as well as in the case of large molecular systems with non-typical bonds and weak interactions, twice the sum of Wiberg's covalencies n sometimes exceeds the exact EPDA due to nonorthogonal all = overcounting. In such situations we have two choices: ( 2 ) I. Restore orthogonality of the highest-occupied 2cBOs within the iterative double-atom partitioning procedure using orthogonal projectors or, more familiar, by transformation to the subset of bonding NBOs.
II. Remove the nonorthogonal electron overcounting by the following projection cascade: NAO → MO(occupied) → 2cBO(bonding) → MO(occupied) → NAO , which is fully equivalent to the following orthogonal similarity transformation: Theoretical foundations of the bond-orbital projection formalism 13/33
Electron delocalization between atoms (EDDA)
3. Projection of 2cBOs onto the subspace of occupied MOs 8 25% 14%
6
π-electrons 4
2 Number of of Number 0 4.800 4.311 6.000 4.889 6.857 4.903 7.500 4.768 - + 2+ C5H5 C6H6 C7H7 C8H8
Projections through the subspace of occupied MOs remove π-electron overcounting...… a little too much! So where is the problem? Theoretical foundations of the bond-orbital projection formalism 14/33
Electron delocalization between atoms (EDDA)
3. Projection of 2cBOs onto the subspace of occupied MOs Due to nonorthogonalities both bonding and antibonding 2cBOs are linear combinations of MOocc and MOvir. Therefore, the projection cascade MUST involve both 2cBO subspaces. ! c o m p l e m e n t a r y
+
NAO → MO(occupied) → 2cBO(all) → MO(occupied) → NAO Theoretical foundations of the bond-orbital projection formalism 15/33
Electron delocalization between atoms (EDDA)
3. Projection of 2cBOs onto the subspace of occupied MOs 25% 8 14%
6
π-electrons 4
2 Number of of Number 4.800 4.311 6.000 5.760 4.889 6.000 6.857 4.903 5.877 7.500 4.768 0 5.625 - + 2+ C5H5 C6H6 C7H7 C8H8
NAO → MO(occupied) → 2cBO(all) → MO(occupied) → NAO Theoretical foundations of the bond-orbital projection formalism 16/33
Electron delocalization between atoms (EDDA)
ED(r) EDLA(r) EDDA(r)
30.0 2.3 27.7 (1.7) Theoretical foundations of the bond-orbital projection formalism 17/33
Electron delocalization between atoms (EDDA)
ED(r)
30.0 30.0 30.0
EDDA(r)
29.3 24.2 23.4
EDLA(r)
0.7 5.8 6.6 Theoretical foundations of the bond-orbital projection formalism 18/33
Electron delocalization between bonds
The EDDA component of the electron density can be further partitioned:
EDDA(r) = EDLB(r) + EDDB(r)
EDLB(r) – electron density of localized (two-center) bonds, EPLB EDDB(r) – electron density of delocalized (multi-center) bonds, EPDB
0 – localized 2cBO 1 – delocalized 2cBO Theoretical foundations of the bond-orbital projection formalism 19/33
Electron delocalization between bonds
Construction of the matrix
1. Forming two sets of 2cBOs for adjacent bonds Xα–Xβ and Xβ–Xγ, ie. and , respectively. 2. Forming a set of three-center bond orbitals (3cBO), . 3. Expanding bonding 3cBOs in the basis of orthogonalized bonding 2cBOs. 4. Canceling of the phase-opposite 3cBOs. 5. Determining scaling factors . 6. Removing the nonorthogonal electron overcounting. Theoretical foundations of the bond-orbital projection formalism 20/33
Electron delocalization between bonds
1. Forming two sets of 2cBOs for adjacent bonds Xα–Xβ and Xβ–Xγ:
2. Forming a set of three-center bond orbitals (3cBO), representing
the bonding between Xα and Xγ through the conjugation center Xβ :
We do not take into account the through-space (direct) interactions
between Xα–Xβ and Xβ–Xγ,and hence . Theoretical foundations of the bond-orbital projection formalism 21/33
Electron delocalization between bonds 3cBO 2cBO 2cBO
= –
3. Expanding bonding 3cBOs in the basis of orthogonalized bonding 2cBOs.
Orthogonalization: OWSO Theoretical foundations of the bond-orbital projection formalism 22/33
Electron delocalization between bonds
4. Canceling out the phase-opposite 3cBOs.
If two 2cBOs do not form effectively a 3cBO they do not Effective Effective ! contribute to bond delocalization. 3cBO 2cBO If two linear combinations of 2cBOs are in opposite pha- ses and have nearly degenerated occupation numbers, ! they do not contribute to bond delocalization. Phase-opposite To determine if and to what extent both conditions are satisfied we can use an auxiliary vector with the elements defined as follows (we assume that 3cBOs are ordered from the highest to lowest occupied):
where ,
= 1 (effective 3cBO) = 0 (effective 2cBO) = –1 (effective 3cBO but in opposite phase with other 3cBO) Theoretical foundations of the bond-orbital projection formalism 23/33
Electron delocalization between bonds
4. Canceling out the phase-opposite 3cBOs.
Benzene 3cBOs:
2 0.980 0.979 0.887 0.032 0.002
1.000 –0.999 1.000 0.999 –0.998
2 0.980 –0.978 0.887 0.032 –0.002
2 0.002 0.000 0.887 0.030 0.000
If < 0 then the mth 3cBO cancels out the pth 3cBO for which Theoretical foundations of the bond-orbital projection formalism 24/33
Electron delocalization between bonds
5. Determining scaling factors .
To determine the scaling factor for the ith 2cBO of the Xα–Xβ bond we have to consider conjugations with 2cBOs of all possible adjacent bonds.
6. Removing the nonorthogonal electron overcounting.
*
order– reversed , assuming that: Theoretical foundations of the bond-orbital projection formalism 25/33
Localization and delocalization components of the electron density Theoretical foundations of the bond-orbital projection formalism 26/33
Localization and delocalization components of the electron density Theoretical foundations of the bond-orbital projection formalism 27/33
Localization and delocalization components of the electron density
65%
35% Theoretical foundations of the bond-orbital projection formalism 28/33
The effectiveness of bond conjugation as an aromaticity criterion
HÜCKEL's AROMATICITY GLOBAL/LOCAL AROMATICITY Theoretical foundations of the bond-orbital projection formalism 29/33
The effectiveness of bond conjugation as an aromaticity criterion
HOMOAROMATICITY MÖBIUS AROMATICITY
+ + Homotropylium cation C8H9 Cyclononatetraenyl cation C9H9
METALLOAROMATICITY 3D-AROMATICITY SPHERICAL AROMATICITY
closo-borane 2- [B7H7] 9.633
19.645 25.650 49.118 2- 10+ Co(Por) Fuzed closo-borane [B17H13] Fullerene C60 Theoretical foundations of the bond-orbital projection formalism 30/33
The effectiveness of bond conjugation as an aromaticity criterion
k Theoretical foundations of the bond-orbital projection formalism 31/33
The effectiveness of bond conjugation as an aromaticity criterion
Comparative analysis of selected aromaticity indices Theoretical foundations of the bond-orbital projection formalism 32/33
The effectiveness of bond conjugation as an aromaticity criterion*
Comparative analysis of selected aromaticity indices
*By courtesy of dr Justyna Dominikowska Theoretical foundations of the bond-orbital projection formalism 33/33
What distinguishes the EDDB as an aromaticity measure?
✔ Intuitiveness and simplicity
✔ No reference molecule is needed
✔ Ring-size independence
✔ σ/π dissection for planar and non-planar aromatic species
✔ Low computational cost
✔ Small method/basis-set dependence
✔ Wide applicability
This presentation is available at
www2.chemia.uj.edu.pl/~szczepad/UdG.Workshop.pdf Updated: 2016-02-25
WORKSHOP Institut de Química Computacional i Catàlisi
AA newnew perspectiveperspective onon quantifyingquantifying electronelectron localizationlocalization andand delocalizationdelocalization inin molecularmolecular systemssystems
AA practicalpractical guideguide toto thethe useuse ofof thethe EDDBEDDB methodmethod
dr Dariusz Szczepanik GIRONA JAGIELLONIAN UNIVERSITY January 28st, 2016 Department of Theoretical Chemistry A practical guide to the use of the EDDB method 2/40
Presentation plan
1. Electron density of delocalized bonds.
2. Installation, configuration and execution of the RunEDDB program
3. Visualization of EDDB and related functions.
4. Selected examples:
4.1. Relative aromaticity along different conjugation paths. 4.2. Multifold aromaticity in all-metal clusters. 4.3. Local and global aromaticity in polycyclic aromatic species.
5. Plans for future development. A practical guide to the use of the EDDB method 3/40
Electron density of delocalized bonds
ED(r) EDLA(r) EDLB(r) EDDB(r) .. aromatic stabilization
ED(r) – electron density,
EDLA(r) – density of electrons localized on atoms,
EDLB(r) – electron density of localized bonds, ! EDDB(r) – electron density of delocalized bonds. A practical guide to the use of the EDDB method 4/40
Electron density of delocalized bonds
EPDB Closed-shell One-determinant is defined as twice the sum
DB – one-electron density matrix within the NAO basis D – off-diagonal (α,β)-diatomic block of – two-center bond orbital (2cBO) – diagonal matrix of the 2cBO occupations – diagonal matrix of scaling factors for each 2cBO
(localized 2cBO) (delocalized 2cBO) of the corresponding components spin For For open-shell systems A practical guide to the use of the EDDB method 5/40
Electron density of delocalized bonds
What distinguishes the EDDB as an aromaticity measure?
✔ Intuitiveness and interpretational simplicity ✔ No parametrization and reference molecule is needed ✔ Ring-size independence ✔ σ/π dissection for planar and non-planar aromatic species ✔ Low computational cost ✔ Small method/basis-set dependence ✔ Wide applicability
References (1) Electron delocalization index based on bond order orbitals D.W. Szczepanik, E. Żak, K. Dyduch, J. Mrozek, Chem. Phys. Lett. 593 (2014) 154-159. (2) A uniform approach to the description of multicenter bonding D.W. Szczepanik, M. Andrzejak, K. Dyduch, E. Żak, M. Makowski, G. Mazur, J. Mrozek, Phys. Chem. Chem. Phys. 16 (2014) 20514-20523. (3) A new perspective on quantifying electron localization and delocalization in molecular systems D.W. Szczepanik, Comput. Theor. Chem. 1080 (2016) 33-37. A practical guide to the use of the EDDB method 6/40
Installation, configuration and execution of the RunEDDB program
The current version of the RunEDDB program is available for Linux systems as a script written in R, and as such it requires the R-package (www.r-project.org). An up to date version of the script can be downloaded from:
www2.chemia.uj.edu.pl/~szczepad/RunEDDB (program) www2.chemia.uj.edu.pl/~szczepad/RunEDDBman.pdf (manual)
To generate the cube files, the original Gaussian (www.gaussian.com) cubegen utility is required as well as the dat2cube bash script available at: www2.chemia.uj.edu.pl/~szczepad/dat2cube The method is based on the the NAO representation, which is provided by the NBO software (http://nbo6.chem.wisc.edu). To generate the FILE.49 file (containing the AO→NAO and NAO→MO matrices), an input file to the RunEDDB program, the following NBO keywords have to be used:
$NBO SKIPBO AONAO=W49 NAOMO=W49 $END
If you already have the .chk file you can generate the .49 file using this script: www2.chemia.uj.edu.pl/~szczepad/chk249 A practical guide to the use of the EDDB method 7/40
Installation, configuration and execution of the RunEDDB program
Configuration... 1. Download the RunEDDB script:
wget -P $HOME www2.chemia.uj.edu.pl/~szczepad/RunEDDB
2. If necessary, edit the first line to provide correct path to the Rscript interpreter. E.g., if the R-package is installed in /aplic/R/3.0.0/ then copy and paste this command: sed -i "1s/.*/\#\!\/aplic\/R\/3.0.0\/bin\/Rscript/" $HOME/RunEDDB 3. Make the script executable:
chmod a+x $HOME/RunEDDB
4. Create an alias to the script in the .bashrc file:
echo "alias runeddb=©$HOME/RunEDDB©" >> $HOME/.bashrc
5. Repeat steps 1, 3 and 4 for scripts dat2cube and chk249. A practical guide to the use of the EDDB method 8/40
Installation, configuration and execution of the RunEDDB program
Execution... If the SGE queue system is used... 1. Open an interactive session, e.g. :
qlogin -clear -q compilar.q
2. Load the R module, e.g.:
module load R/R-3.0.0_ICS-11.1.072
3. To support the cube files load also the appropriate Gaussian module,e.g.:
module load g09d01_pgi-10.1_NBO6
4. To get FILE.49 from the Gaussian checkpoint file run the chk249 script:
chk249 FILE.chk 4. To perform the EDDB analysis (e.g. benzene / RHF) simply run:
runeddb FILE.49 1:21
What is the general syntax of the command line options for RunEDDB? A practical guide to the use of the EDDB method 9/40
Installation, configuration and execution of the RunEDDB program
Syntax... the order is very important!
runeddb FILE.49 MOspec BONDspec OtherOpts
required optional
FILE.49 - file generated by the NBO module and containing the AO→NAO and NAO→MO transformation matrices. MOspec – a list of occupied molecular orbitals, separated by commas; the range operator (:) is allowed (e.g. benzene / RHF, σ-MOs):
runeddb FILE.49 7:15,17,18,19 For UHF calculations MOspec lists have to be specified separately for alpha and beta molecular spinorbitals (e.g. benzene / UHF, π-MSOs):
runeddb FILE.49 16,20:22 16,20 A practical guide to the use of the EDDB method 10/40
Installation, configuration and execution of the RunEDDB program
Syntax... the order is very important!
runeddb FILE.49 MOspec BONDspec OtherOpts
required optional
BONDspec – a list of atoms and chemical bonds taken into account in the bond-orbital projection procedure. If does not specify or contains the lowercase a character, the program considers all possible bond-conjugation paths in a molecule, according to the bond-order threshold set to 0.001 (the parameter in the 3rd line of the RunEDDB script):
runeddb FILE.49 1:21 equivalent to runeddb FILE.49 1:21 a
The uppercase A sets the bond-order threshold to 0:
runeddb FILE.49 1:21 A A practical guide to the use of the EDDB method 11/40
Installation, configuration and execution of the RunEDDB program
Syntax… examples the order is very important!
runeddb FILE.49 MOspec BONDspec OtherOpts
required optional
Global aromaticity of naphthalene: (all possible bond conjugations) 7.5e BONDspec:
a
A
1:18
1:10,11,12,13:18
For medium/large species it is easier to specify atoms and fragments rather than bonds. A practical guide to the use of the EDDB method 12/40
Installation, configuration and execution of the RunEDDB program
Syntax… examples the order is very important!
runeddb FILE.49 MOspec BONDspec OtherOpts
required optional
Local aromaticity of a selected ring in naphthalene: (only kekulean CC conjugations) BONDspec:
1-2,1-9,2-3,9-10,3-4,4-10 3.5e 1-2-3-4-10-9-1
9-1-2-3-4,4-10,9-10
1:4,9-10 wrong!
The last case specify in total six conjugations centers, but does not restrict possible bond- conjugations only to one ring (and even to carbon backbone!). A practical guide to the use of the EDDB method 13/40
Installation, configuration and execution of the RunEDDB program
Syntax… examples the order is very important!
runeddb FILE.49 MOspec BONDspec OtherOpts
required optional
Local aromaticity of a selected ring in naphthalene: (kekulean + cross-ring CC conjugations) BONDspec:
1-2-3-4-10-9-1,1-3,1-4,1-1 0,2-4,2-10,2-9,3-10,3-9,4-9 3.6e 1:2:3:4:10:9 4:1:9:2:3:10 1,2,3,4,10,9 wrong!
The 3rd bond specification list is identical to the 2nd one. This notation allows one to restrict bond conjugations to particular molecular fragment only. A practical guide to the use of the EDDB method 14/40
Installation, configuration and execution of the RunEDDB program
Syntax… the order is very important!
runeddb FILE.49 MOspec BONDspec OtherOpts
required optional
OtherOpts:
EDED – save the ED(r) function into the ED.dat file. In the case of spin-unrestric- ted open-shell calculations EDLA – save the EDLA(r) function into the EDLA.dat file. the corresponding spin-den- sities are saved into the EDLB – save the EDLB(r) function into the EDLB.dat file. SDXX.dat files in the same directory. EDDB – save the EDDB(r) function into the EDDB.dat file. POFF – skip the orthogonal similarity transformation step. NMB – restrict the EDDB analysis to the Natural Minimal Basis subspace only; it significantly reduces computational time. These keywords can appear in the command line in any order. A practical guide to the use of the EDDB method 15/40
Installation, configuration and execution of the RunEDDB program
Results (benzene [singlet] / RHF) … B3LYP/6-311+G(d,p)
runeddb FILE.49 7:21 A ------Atom ED EDLA EDLB EDDB ------1 4.208 0.074 3.138 0.996 2 4.208 0.074 3.138 0.996 3 4.208 0.074 3.138 0.996 4 4.208 0.074 3.138 0.996 5 4.208 0.074 3.138 0.996 6 4.208 0.074 3.138 0.996 7 0.792 0.036 0.735 0.021 8 0.792 0.036 0.735 0.021 9 0.792 0.036 0.735 0.021 10 0.792 0.036 0.735 0.021 11 0.792 0.036 0.735 0.021 12 0.792 0.036 0.735 0.021 ------Total: 30.000 0.656 23.242 6.101 ------Computational cost: 00:00:01 (660x3cBO) A practical guide to the use of the EDDB method 16/40
Installation, configuration and execution of the RunEDDB program
Results (benzene [triplet] / UHF) … B3LYP/6-311+G(d,p)
runeddb FILE.49 7:22 7:20 A ------Atom ED SD EDLA SDLA EDLB SDLB EDDB SDDB ------1 4.264 -0.178 0.232 -0.014 3.390 -0.074 0.642 -0.091 2 4.169 0.605 0.306 0.184 3.331 0.203 0.533 0.219 3 4.169 0.605 0.306 0.184 3.331 0.203 0.533 0.218 4 4.264 -0.178 0.232 -0.014 3.390 -0.074 0.642 -0.091 5 4.169 0.605 0.306 0.184 3.331 0.203 0.533 0.218 6 4.169 0.605 0.306 0.184 3.331 0.203 0.533 0.218 7 0.789 0.004 0.036 -0.001 0.731 0.005 0.021 -0.000 8 0.804 -0.018 0.032 0.005 0.758 -0.022 0.015 -0.001 9 0.804 -0.018 0.032 0.005 0.758 -0.022 0.015 -0.001 10 0.789 0.004 0.036 -0.001 0.731 0.005 0.021 -0.000 11 0.804 -0.018 0.032 0.005 0.758 -0.022 0.015 -0.001 12 0.804 -0.018 0.032 0.005 0.758 -0.022 0.015 -0.001 ------Total: 30.000 2.000 1.887 0.725 24.596 0.586 3.518 0.689 ------Computational cost: 00:00:02 (1320x3cBO) A practical guide to the use of the EDDB method 17/40
Visualization of EDDB and related functions
Syntax… the order is very important!
dat2cube FILE.fchk EDXX.dat ngrid nproc
required optional
In the current implementation, the dat2cube script requires a formatted check- point file (FILE.fchk) from Gaussian and the EDXX.dat file obtained from the RunEDDB program. By default, dat2cube uses 1 CPU to generate a cube file with the number of points per side equal to 803=512k. It can be changed by specifying parameters nroc and ngrid, respectivety. E.g.
dat2cube FILE.fchk EDDB.dat 100 4
uses 4 CPUs to convert EDDB.dat into the cube file, EDDB.cube, containing 1003 points distributed evenly over a rectangular grid.
Which programs support the Gaussian cube format? GaussView, (g)Molden, Molekel, VMD, Gabedit, Avogadro, ... A practical guide to the use of the EDDB method 18/40
Relative aromaticity along different conjugation paths.
Along which Bis-palladium(II)? [36]octaphyrin(1.1.1.1.1.1.1.1) conjugation path the electron delocalization is the most effective? B3LYP/SDD
wget www2.chemia.uj.edu.pl/~szczepad/octaphyrin.tar.gz
tar -xzf octaphyrin.tar.gz
qlogin -clear -q compilar.q
module load R/R-3.0.0_ICS-11.1.072
module load g09d01_pgi-10.1_NBO6 A practical guide to the use of the EDDB method 19/40
Relative aromaticity along different conjugation paths.
All possible bond conjugations
runeddb FILE.49 1:178 a eddb > EDDB.all.log
mv EDDB.dat EDDB.all.dat
dat2cube molecule.fchk EDDB.all.dat 80 1 A practical guide to the use of the EDDB method 20/40
Relative aromaticity along different conjugation paths.
65 66 28 61 29 24 68 69 36 63 26 34 56 1 37 19 38 55 43 2 18 42 6 53 5 15 49 41 47 4 12 46 9 10
The conjugated 32 π-electronic (iner) circuit
runeddb FILE.49 1:178 1-2-6-5-4-9-10-12-15-18-19-26-24-28- 29-36-34-37-38-43-42-41-46-47-49-53-55-56-63-61-65-66-68-69-1 eddb > EDDB.in.log
mv EDDB.dat EDDB.in.dat
dat2cube molecule.fchk EDDB.in.dat 80 1 A practical guide to the use of the EDDB method 21/40
Relative aromaticity along different conjugation paths.
61 65 28 24 59 66 29 22 58 68 69 36 21 34 56 1 37 19 38 55 43 2 18 42 6 53 5 15 49 41 4 12 47 46 10
The conjugated 36 π-electronic (mediate) circuit
runeddb FILE.49 1:178 1-2-6-5-4-9-10-12-15-18-19-21-22-24- 28-29-36-34-37-38-43-42-41-46-47-49-53-55-56-58-59-61-65-66- 68-69-1 eddb > EDDB.med.log
mv EDDB.dat EDDB.med.dat
dat2cube molecule.fchk EDDB.med.dat 80 1 A practical guide to the use of the EDDB method 22/40
Relative aromaticity along different conjugation paths.
66 71 29 61 65 31 28 24 59 70 32 22 58 21 69 34 56 1 37 19 55 18 38 2 53 40 3 15 51 14 50 46 41 4 9 47 10 13 The conjugated 36 π-electronic (outer) circuit
runeddb FILE.49 1:178 1-2-3-4-9-10-13-14-15-18-19-21-22-24- 28-29-31-32-34-37-38-40-41-46-47-50-51-53-55-56-58-59-61-65- 66-71-70-69-1 eddb > EDDB.out.log
mv EDDB.dat EDDB.out.dat
dat2cube molecule.fchk EDDB.out.dat 80 1 A practical guide to the use of the EDDB method 23/40
Relative aromaticity along different conjugation paths. EDDB.all.cube
All possible bond conjugations
------Atom ED EDLA EDLB EDDB ------
------...... Total: 356.000 140.207 167.939 47.854 48.389 ------EDDB.all.log Computational cost: 00:00:37 (23022x3cBO) without threshold: 00:07:45 (194472x3cBO) A practical guide to the use of the EDDB method 24/40
Relative aromaticity along different conjugation paths. EDDB.in.cube
The conjugated 32 π-electronic (iner) circuit
------Atom ED EDLA EDLB EDDB ------
------...... Total: 356.000 NA 68.771 20.419 (43%)
EDDB.in.log ------Computational cost: 00:00:01 (34x3cBO) A practical guide to the use of the EDDB method 25/40
Relative aromaticity along different conjugation paths. EDDB.med.cube
The conjugated 36 π-electronic (mediate) circuit
------Atom ED EDLA EDLB EDDB ------
------...... Total: 356.000 NA 76.380 18.510 (39%) ------EDDB.med.log Computational cost: 00:00:01 (36x3cBO) A practical guide to the use of the EDDB method 26/40
Relative aromaticity along different conjugation paths. EDDB.out.cube
The conjugated 36 π-electronic (outer) circuit
------Atom ED EDLA EDLB EDDB ------
------...... Total: 356.000 NA 85.511 14.674 (31%) ------EDDB.out.log Computational cost: 00:00:01 (38x3cBO) A practical guide to the use of the EDDB method 27/40
Relative aromaticity along different conjugation paths.
Along which conjugation path the electron delocalization is the most effective?
All possible bond conjugations 32 π-electronic (iner) circuit 47.9e (100%) 20.4e (43%)
36 π-electronic (mediate) circuit 36 π-electronic (outer) circuit 18.5e (39%) 14.7e (31%) A practical guide to the use of the EDDB method 28/40
Multifold aromaticity in all-metal clusters.
Cu Cu Al + Y Y Cu Al 2- Al -
Al Hf Hf Y Single, double or triple Hf B3LYP/6-311+G(d) aromaticity? B3LYP/X/Stuttgart+2f
wget www2.chemia.uj.edu.pl/~szczepad/allmetaroma.tar.gz
tar -xzf allmetaroma.tar.gz
qlogin -clear -q compilar.q
module load R/R-3.0.0_ICS-11.1.072
module load g09d01_pgi-10.1_NBO6 A practical guide to the use of the EDDB method 29/40
Multifold aromaticity in all-metal clusters.
21 22 23 24 25 Al
Al 2- Al 26 27
Al
runeddb Al42-.49 21:27 A > Al42-.all.log
runeddb Al42-.49 21:26 A > Al42-.sigma.log
runeddb Al42-.49 27 A > Al42-.pi.log A practical guide to the use of the EDDB method 30/40
Multifold aromaticity in all-metal clusters.
13 14 15 16 17 18
Cu Cu 19 20 21 22 23 24 +
Cu 25 26 27 28
runeddb Cu3+.49 13:28 A > Cu3+.all.log
runeddb Cu3+.49 13:15,17,20,21,23,24,27,28 A > Cu3+.sigma.log
runeddb Cu3+.49 16,18,19,22,25,26 A > Cu3+.pi.log A practical guide to the use of the EDDB method 31/40
Multifold aromaticity in all-metal clusters.
Y 13 14 15 16 17
- Y Y
runeddb Y3-.49 13:17 A > Y3-.all.log
runeddb Y3-.49 13:16 A > Y3-.sigma.log
runeddb Y3-.49 17 A > Y3-.pi.log
Hf Hf 13 14 15 16 17 18
Hf
runeddb Hf3.49 13:18 A > Hf3.all.log
runeddb Hf3.49 13:16 A > Hf3.sigma.log
runeddb Hf3.49 17 A > Hf3.pi.log
runeddb Hf3.49 18 A > Hf3.delta.log A practical guide to the use of the EDDB method 32/40
Multifold aromaticity in all-metal clusters. 2- + - Al 4 Cu 3 Y3 Hf3
EDDB 3.42 1.98 5.78 6.16 (3.43) (1.98) (5.89) (6.26) EDDB ( σ ) 1.92 1.95 4.00 2.60 EDDB ( π ) 1.50 0.02 1.78 1.78 EDDB ( δ ) 0.00 0.00 0.00 1.78 MCI* 3.56 1.89 7.54 10.37 MCI* ( σ ) 1.69 1.88 4.58 4.45 MCI* ( π ) 1.87 0.01 2.96 2.96 MCI* ( ) 0.00 0.00 0.00 2.95
* multiplied by 10 δ
Aromaticity: σ+π σ σ+π σ+π+δ double single double triple A practical guide to the use of the EDDB method 33/40
Global and local π-aromaticity in polycyclic aromatic species.
What is the influence of non-local conjugation effects on local aromaticity? Does (and to what extent) the orthogonal similarity transformation affects local aromaticity? B3LYP/6-311+G(d,p)
wget www2.chemia.uj.edu.pl/~szczepad/glolocaroma.tar.gz
tar -xzf glolocaroma.tar.gz
qlogin -clear -q compilar.q
module load R/R-3.0.0_ICS-11.1.072
module load g09d01_pgi-10.1_NBO6 A practical guide to the use of the EDDB method 34/40
Global and local π-aromaticity in polycyclic aromatic species.
1 6 2 runeddb C6H6.49 17,20,21 1:2:3:4:5:6 > 5 3 C6H6.global.log 4 Benzene
6 1 5 2 runeddb C10H8.49 27,30,32:34 5:6:1:2:7:8:9:10:4:3 > C10H8.global.log 4 3
runeddb C10H8.49 27,30,32:34 1:2:3:4:5:6
Naphthalene 10 7 9 8 > C10H8.local.log A practical guide to the use of the EDDB method 35/40
Global and local π-aromaticity in polycyclic aromatic species.
C runeddb C16H10.49 17 18 39,43,46,49:53 16 11 1 1:2:3:4:5:6:11:12:13:14:15:1 2 6 6:17:18:22:23 > 14 13 D A 3 5 C16H10.global.log 4 15 B 12 runeddb C16H10.49 Fluoranthene 22 23 39,43,46,49:53 1:2:3:4:5:6 > C16H10.local.A.log
runeddb C16H10.49 39,43,46,49:53 12:13:14:15:22:23 > C16H10.local.B.log
runeddb C16H10.49 39,43,46,49:53 11:12:13:14:15:16:17:18:22:23 > C16H10.local.C.log
runeddb C16H10.49 39,43,46,49:53 2:3:11:12:13 > C16H10.local.D.log A practical guide to the use of the EDDB method 36/40
Global and local π-aromaticity in polycyclic aromatic species.
e en nz be to ed ar mp co 0% -4 3.139 3.211 (-2%) 4.828 5.327 0.910 (-9%) 3.139 3.211 (-2%)
6.501 6.414 (-1%) 11.828 12.387 (+5%)
Numbers inside rings stand for the (total) local EDDB populations. The outermost numbers are the (total) global EDDB populations Percentages in brackets refer to the effect of linking of benzene ring to naphthalene. A practical guide to the use of the EDDB method 37/40
Global and local π-aromaticity in polycyclic aromatic species.
3.994 4.290 (+24%) (+37%) 4.004 5.367 5.327 (+11%) (0%) +340% 3.994 4.290 (+24%) (+37%)
7.018 (+10%)
Numbers inside rings indicate the sum of the corresponding atomic contri- butions to the global EDDB population. Percentages in brackets show the effect of non-local conjugations on local aromaticity of particular ring..
The non-local conjugation effects are especially important in the cases of fused aromatic rings. But the the global EDDB populations should be used with a special caution due to overlap overcounting. A practical guide to the use of the EDDB method 38/40
Global and local π-aromaticity in polycyclic aromatic species.
4.828 3.139 6.3%
0.197 (0.000) 4.672 0.061 (4.832) (0.000) 0.156 2.881 (0.000) (3.153)
96.8% 1.9% 3.2% 91.8%
Numbers above structures are (total) local EDDB populations. Numbers inside rings stand for the sum of the selected (coloured) atomic contributions to the local EDDB population. Numbers in brackets refer to the corresponding populations before orthogonal similarity transformation. The more effective conjugation between cyclic subunits, the higher „diffusion” of local EDDB populations due to orthogonal similarity transformation. A practical guide to the use of the EDDB method 39/40
Plans for future
Method
(1) Energy decomposition based on the EDDB method. (2) Post-HF correlated wavefunctions generalization.
Program
(1) A new Fortran 90 implementation of the method. (2) Support for other quantum-chemical programs (3) Different representations of the minimal-basis AOs (4) Automatic dissection into σ- and π-components. (5) Built-in cube generating module. (6) New functionalities (e.g. detection of hydrogen bonds) A practical guide to the use of the EDDB method 40/40
A complete presentation of the EDDB method is available at
www2.chemia.uj.edu.pl/~szczepad/UdG.Workshop.pdf