Ability of the PM3 Quantum-Mechanical Method to Model Intermolecular Hydrogen Bonding Between Neutral Molecules

Ability of the PM3 Quantum-Mechanical Method to Model Intermolecular Hydrogen Bonding between Neutral Molecules

Marcus W. Jurema and George C. Shields* Department of Chemistry, Lake Forest College, Lake Forest, Illinois 60045

Received 31 March 1992; accepted 23 July 1992

The PM3 semiempirical quantum-mechanical method was found to systematically describe intermolecular hydrogen bonding in small polar molecules. PM3 shows charge transfer from the donor to acceptor molecules on the order of 0.02-0.06 units of charge when strong hydrogen bonds are formed. The PM3 method is predictive; calculated hydrogen bond energies with an absolute magnitude greater than 2 kcal mol-' suggest that the global minimum is a hydrogen bonded complex; absolute energies less than 2 kcal mol-' imply that other van der Waals complexes are more stable. The geometries of the PM3 hydrogen bonded complexes agree with high-resolution spectroscopic observations, gas electron diffraction data, and high-level ab initio calculations. The main limitations in the PM3 method are the underestimation of hydrogen bond lengths by 0.1-0.2 for some systems and the underestimation of reliable experimental hydrogen bond energies by approximately 1-2 kcal mol-l. The PM3 method predicts that ammonia is a good hydrogen bond acceptor and a poor hydrogen donor when interacting with neutral molecules. Electronegativity differences between F, N, and 0 predict that donor strength follows the order F > 0 > N and acceptor strength follows the order N > 0 > F. In the calculations presented in this article, the PM3 method mirrors these electronegativity differences, predicting the F-H- - -N bond to be the strongest and the N-H- - -F bond the weakest. It appears that the PM3 Hamiltonian is able to model hydrogen bonding because of the reduction of two-center repulsive forces brought about by the parameterization of the Gaussian core-core interactions. The ability of the PM3 method to model intermolecular hydrogen bonding means reasonably accurate quantum-mechanical calculations can be applied to small biologic systems. 0 1993 by John Wiley & Sons, Inc.

INTRODUCTION AM1 and MNDO, respectively? A thorough discussion of the modified INDO and NDDO methods can The semiempirical quantum-mechanical methods de- be found in ref. 6. veloped by Dewar and coworkers'-4 have been suc- Because ub initio methods give quantitative re- cessful at reproducing molecular energies, replicat- sults only for relatively small molecules, semiempir- ing molecular structures, and interpreting chemical ical pr~ceduresl-~are used to study larger organic reaction^.^^^ These methods have been combined into systems6 MIND0/3, MNDO, and AM1 have limited one molecular orbital package, MOPAC.7MOPAC al- application to biologic systems because the MIND01 lows for the calculation of wave functions by a self- 3 and MNDO methods can not model hydrogen consistent field method using the Hartree-Fock for- bonds and AM1 does not always reproduce inter- malism. MOPAC contains one Hamiltonian based molecular hydrogen bonds. AM1 calculations in gen- upon the modified method of intermediate neglect eral predict bifurcated intermolecular hydrogen of differential overlap approximation (MIND0/3) Buemi et aLZ4reported AM1 intermolec- and three Hamiltonians based upon the modified ne- ular hydrogen bonding energies for small molecule glect of diatomic differential overlap approximation dimers but did not report the geometric results. (MNDO, AM1, and PM3). The PM3 model was de- Many authors have cautioned against the uncritical veloped using a new optimization procedure for use of AM1 for calculations of intermolecular quickly determining atomic parameters from exper- hydrogen bonded specie^^^^^^^^^^^^^^^^^^^^^^^ The AM1 imental reference data: With this method, the av- method is useful for calculating intermolecular hy- erage difference between calculated heats of for- drogen bonds of many charged speciesF6J7 mation and experimental values for 713 compounds One of the best understood hydrogen bonded spe- is 8.2 kcal mol-', as compared with 13.8 and 22.5 for cies is the water dimer. The structure of the water dimer has been established as a truns-linear C, equi- librium geometry by microwave spectroscopy ex- *Author to whom all correspondence should be addressed. periment~?~-~~The experimental structure is repli-

Journal of Computational Chemistry, Vol. 14, No. 1, 89-104 (1993) 0 1993 by John Wiley & Sons, Inc. CCC 0 192-8651 193 / 010089- 16 90 JUREMA AND SHIELDS cated by high-level ab initio res~lts?~-~~Yet, AM1 molecular hydrogen bonding by a semiempirical calculations fail to match experimental and ab initio method should be useful. In this article, results of results, predicting the bifurcated structure. This fail- calculations with the PM3 semiempirical method are ure of AM1 theory to describe this fundamental sys- presented for 32 intermolecular hydrogen bonding tem has been discussed by Smith et al?5Rzepa and systems composed of neutral molecules. Yi have concluded that the tendency of AM1 to in- correctly favor bifurcated arrangements of water METHOD molecules arises when two or more hydrogen bond- Fourteen polar molecules and 32 neutral intermo- ing sites are a~ailable.2~ lecular hydrogen bonded systems were built with AM1 calculations have been useful in describing Alchemy I1 (Tripos Associates, St. Louis, MO) or intramolecular hydrogen as well as pro- Chem 3D Plus software (Cambridge Scientific Com- ton affinities for a large series of aromatic computing, Inc., Cambridge, MA) on a Macintosh I1 com- po~nds.4~-~~The AM1 method reproduces experi- puter (Apple Computer, Inc., Cupertino, CA). The 14 mental values for proton affinities of substituted monomers were fully geometry optimized with the pyridines better than the PM3 method.50 Both the AM1 and PM3 methods. Complexes were created AM1 and PM3 methods have been shown to accu- from the monomers with initial hydrogen bond an- rately predict gas-phase acidities and singlet-triplet gles of 180" and hydrogen bond distances of 1.7 gaps for a large number of molecule^.^^^^^ In an AM1 A. These structures were input coordinates for AM1 study of the hydration of small anions, heats of hy- and PM3 calculations of geometries, heats of dration agreed with available experimental data but formation (AH; 298 K), and atomic charges using the AM1 structures did not always agree well with MOPAC 5.0 ~oftware.~Additional configurations available ab initio calculations of these ~lusters.2~ were used to explore the potential energy surfaces Stewart's PM3 method describes the intermolec- of selected complexes. ular hydrogen bonding geometry of water dimers and The criterion for terminating all optimizations was intramolecular hydrogen bonding distances in sali- increased 100-fold over normal MOPAC limits using cylaldoxime~.~Juranic et al.lg demonstrated that the the PRECISE option. Unrestricted Hartree-Fock cal- PM3 method realistically describes the geometries culations were performed for exploration of the hy- of ammonia-oxygen complexes solvated with water. drogen bonded potential energy surfaces. All struc- In addition, Rzepa and Yi9 calculated hydrogen tures were characterized as stationary points and bonded structures of ammonia and water, a water true minima on the potential energy surfaces using trimer, and a water tetramer; their results are su- the keyword FORCE. A stationary point is described perior to those from calculations. The PM3 AM1 if the first derivatives of the energy with respect to method has also been used to help investigate a changes in the geometry are zero. The criterion for uniquely strong OH- - -N intramolecular hydrogen a minimum is that all eigenvalues of the Hessian bond.53Ventura et alF4 performed a comparison of matrix are positive! The FORCE calculation is es- AM1, PM3, and MQller-Plesset ab initio calculations sential for characterization of these weak intermo- corrected for the basis set superposition error lecular interactions, the potential energy surface (BSSE) for the direct addition of water to formal- as for a hydrogen bonded complex is fairly flat, with dehyde. The authors conclude that the PM3 method minima separated by a few kilocalories per mole is preferable to ab initio calculations with a 4-31G from each other and the separated monomers. basis set corrected for BSSE and to AM1 calculations Energy partitioning of the one- and two-center for this reaction.54Both PM3 and AM1 calculations terms was performed for different geometries of predict vibrational frequencies with greater accu- six water dimers using the keywords ENPART and ISCF. racy than MNDO or MIND0/3, and the best method For each geometry, the calculation was repeated us- to use depends upon the type of vibrational mode ing the PM3, AMl, and MNDO Hamiltonians. being inve~tigated.~~,~~ The enthalpies of association (heat liberated) for Accurate ab initio calculations replicating hydro- the hydrogen bonded complexes were determined gen bonding systems are expensive, and the correct at 298 K by determining the difference between the kind of ab initio calculation is not heats of formation for the unassociated monomers The difficulty of calculating the interaction energy and those for the complexes. The hydrogen bond of two weakly bound molecules originates from the geometries were checked by inspection and calcu- small magnitude of the quantity sought relative to lated PM3 hydrogen bond energies determined by the BSSE.63 Applications of quantum-mechanical dividing the enthalpy of association by the number methods to biologic systems will be largely confined of hydrogen bonds present in the system. All cal- to the faster semiempirical methods in the near fu- culations were performed on a microVAX 3400. ture provided that these methods adequately describe hydrogen bonding. While high-level ab initio RESULTS calculations will remain the method of choice to study hydrogen bonding of small molecules, for bio- The AM1 and PM3 calculated heats of formation for logic molecules a successful description of inter- 14 polar molecules, and available experimental val- PM3 AND INTERMOLECULAR HYDROGEN BONDING 91

Table I. Calculated and experimental heats of formation kcal mol-’ with a standard deviation of 0.74 kcal for 14 molecules that participate in hydrogen bonding. mol-’. The methods of Dewar and have AH; 2988 (kcal mol-’) been successful because of their general applicabil- Molecule PM3 AM1 Experiment ity to a wide variety of molecular systems, with each new model improving the overall ability to replicate H2O - 53.4 - 59.2 - 57.8 diverse systems. For the molecules listed in Table CH3OH - 51.9 - 57.0 - 48.2 I, HCOOH - 94.4 - 97.4 - 90.5 the PM3 calculations for C3H4N2and C02are notably CH3COOH - 101.9 - 103.0 - 103 more accurate than are the AM1 results. C,jH&OOH - 66.2 - 68.0 - 66.2 Thirty-two neutral complexes built from the spe- CH20 - 34.1 -31.5 - 26 cies in Table I were fully geometry optimized with COZ - 85.0 - 79.8 - 94.0 the AM1 and PM3 methods; the results of the PM3 NH3 -- 3.1 - 7.3 - 11 C2H;N -- 7.9 - 5.6 - 4.4 calculations are presented in Table 11. Table I1 lists C3H4N2 48.8 65.6 44 the heats of formation for these hydrogen bonded C5H5N 30.4 32.0 33 complexes and the calculated heats of association NHZCHO - 41.8 - 44.8 - 44 for these hydrogen bonded systems. A bold number CSHjNO - 15.6 - 11.3 - 18 is listed for each system to facilitate comparison of HF - 62.7 - 74.3 -65.1 energies with complexes presented in the figures. All experimental values are from ref. 64 except COZ, Table I11 organizes information into different cat- taken from ref. 65. egories, including types of hydrogen bonds, the iden- tity of the donor/acceptor pair, the distance between ues,@~~~are presented in Table I. The average differ- donor and acceptor atoms, the charge transfer be- ence between AM1 enthalpies and experimental en- tween the donor and acceptor molecules in the com- thalpies is 4.5 kcal mol-’ with a standard deviation plex, and the calculated PM3 hydrogen bond energy. of 1.22 kcal mol-’. PM3 has an average error of 4 Also included in Table I11 are available experimental

Table 11. Calculated PM3 heats of formation and enthalpies of association for hydrogen bonded complexes. Enthalpy of association for complex relative to the PM3 AH/”2988 separated monomers (kcal

System (donor/ acceptor) Complex (kcal mol- l) mol ~ l)

HZO/CHZO lb - 90.25 - 2.75 HZO/HZO 2 - 110.35 - 3.55 (HZ0)3 3 - 169.24 - 9.04 (H20)3cyclic 4 - 170.35 - 10.14 (HzO), 1 donor 5 - 166.26 - 6.06 (H,O), 1 acceptor 6 - 166.96 - 6.76 (H2015 7 - 284.93 - 17.93 HZO / CH3OH 8 - 108.23 - 2.93 HZO/COZ 9 - 139.37 - 0.97 CH30H/CHROH 10 - 106.35 - 2.55 CH3OH/HZO 11 - 108.51 -3.21 HCOOH/HCOOH 12 - 197.47 - 8.68 CH3COOH/CH;&OOH 13 - 212.84 - 9.05 CGH&OOH/CCH&OOH 14 - 141.16 - 8.76 NH3/NH3 15 - 6.01 0.19 CZH7N/NH3 16 - 11.07 - 0.07 (C:,H,N,), cyclic 17 131.65 - 14.76 HZO/CSHSN 18 - 25.15 - 2.50 CH30H/CsHSN 19 - 23.55 - 2.05 HZO/NH, 20 - 59.53 - 3.03 CH30H/NHo 21 - 57.83 - 2.83 HCOOH/ NH3 22 - 98.29 - 0.79 CH3COOHINH3 23 - 107.50 - 2.50 NHZCHO/NH&HO 24 - 88.29 - 4.69 CSH,NO/CSH5NO 25 -41.03 - 9.83 NH3/H20 26 - 57.37 - 0.87 NH3/CH3OH 27 - 55.21 - 0.21 NH,/HCOOH 28 - 97.93 - 0.43 H,O/HF 29 - 120.12 - 4.02 HF/H20 30 - 121.61 - 5.51 HF/NH3 31 - 71.72 - 5.92 NH3/HF 32 - 67.30 - 1.50 ~______~ Enthalpies of association were obtained by difference from the AHf”,,,, of the hydrogen bonded complexes and the sums of AH; zgaK for the monomers (given in Table 1). 92 JUREMA AND SHIELDS

Table 111. Types of hydrogen bonds, distance between donor and acceptor atoms, charge transferred from donor molecule to acceptor molecule upon complex formation, and calculated and experimental hydrogen bond energies for the 32 hydrogen bonded complexes investigated with the PM3 quantum mechanical method. H bond energy (kcal mo1-l’) Type Donor (D) Acceptor (A) Complex R(D-A) (A) Charge transfer PM3 Em. Ref.

~~ 0-H-0 HzO 2 2.77 0.0221 -3.55 -4.4 to -5.4 66-69 HzO (2 D) 3 2.74 - 0.0292 (D) - 4.52 (open trimerj 0.0014 (D;A) 2.71 0.0278 4 2.67 0.0009 (D,A) - 3.38 2.67 0.0006 (D,A) 2.67 - 0.0015 (D,A) 5 2.77 0.0214 - 3.03 - 0.0430 (D) 2.77 0.0214 6 2.76 -0.0171 (Dj - 3.38 0.0344 2.76 -0.0171 (D) HzO (3 D) 7 2.71 0.0301 - 4.48 (open pentamerj 2.71 0.0301 - 0.0007 (D,Aj 2.74 - 0.0298 (D) 2.74 -0.0298 (D) H20 8 2.78 0.0224 - 2.93 H2O lb 2.78 0.0246 - 2.75 H20 9 2.79 0.0151 - 0.97 CH30H 10 2.78 0.0219 - 2,55 - 3.2 to - 7.3 66,70 CH30H 11 2.76 0.0219 - 3.21 HCOOH 12 2.74 0.0001 (D,A) - 4.34 - 5.85 71 CH3COOH 13 2.74 0.0000 (D,A) -4.52 -6.4 to -8.4 66,67,72 CsHSCOOH 14 2.74 0.0001 (D,Aj - 4.38 - 7.3 73 N-H-N NH3 15 2.92 0.0295 0.19 C2H7N 16 2.91 0.0345 - 0.07 C3H4N2 17 2.81 0.0015 (D,Aj - 4.92 (trimerj 2.80 - 0.0002 (D,A) 2.80 - 0.0015 (D,A) 0-H-N HPO 18 2.80 0.0381 - 2.15 CH30H 19 2.80 0.0379 - 2,05 - 4.4 74 H2O 20 2.79 0.0446 - 3.03 CH30H 21 2.79 0.0455 - 2.83 HCOOH 22 2.77 0.0559 - 0.79 CH3COOH 23 2.77 0.0544 - 2.50 N-H-0 NHeCHO 24 2.83 0.0004 - 2.34 - 7 (solid) 67 CSHSNO 25 2.80 0.0001 - 4.92 NH3 26 2.87 0.0130 - 0.87 NH3 27 2.88 0.0137 - 0.21 NH3 28 2.88 0.0178 - 0.43 0-H-F HZ0 29 2.72 0.0230 - 4.02 F-H-0 HF 30 2.68 0.0272 - 5.51 - 7.2 69 F-H-N HF 31 2.74 0.0588 - 5.92 N-H-F NH3 32 2.81 0.0166 - 1.50

hydrogen bond energies and appropriate refer- evant bond distances, bond angles, and atomic ence~.~~-~~Table IV contains a detailed comparison charges are included in these diagrams. To under- of e~perimental?~ab initio, 76 and PM3 results for stand the parameters associated with the success of the formic acid dimer. the PM3 method in reproducing hydrogen bonds, six Fully optimized hydrogen bonded structures of the complexes of water molecules were calculated and water-formaldehyde complexes, where the water results are presented in Figure 3. Figure 4 displays molecule donates a hydrogen to the oxygen in for- the PM3 results for other complexes with 0-H- - -0, maldehyde, are shown in Figure 1. Figure 2 displays N-H- - -N, 0-H- - -N, and N-H- - -0 hydrogen bonds. the results of a reaction path calculation for the Figure 4 also contains the results for systems in- water dimer. These two figures illustrate the general volving a fluorine atom and the global minimum for differences between the AM1 and PM3 models. Rel- the ammonia dimer system. PM3 AND INTERMOLECULAR HYDROGEN BONDING 93

Table IV. Comparison of PM3, experimental (ref. 75), and DZ + P ab initio (ref. 76) bond distances and bond angles for the formic acid dimer. Geometrical parameter PM3 Exp. DZ + P r(C=O) I! .22 1 1.220 ? ,003 1.199 riC--O) 1.328 1.323 ? .003 1.300 0.1781 (.) r(C-H) 1.095 1.082 ? .021 1.087 r(0--HI 0.969 1.036 * .017 0.966 ~(0-H-- -0) 2.74 2.703 ? .007 2.779 r(0-- -0) 2.193 2.268 * ,004 2.227 <(C-0-H)- - - 113.4 108.5 ? .4 111.0 <(O=C-0) 118.6 126.2 * .48 125.9 w- <(H-CzO) 127.9 115.4 k 3.1 122.2 <(O-H- - -0) 177.4 180" 172.7 Bond lengths in A, bond angles in degrees. Geometric parameter assumed in the refinement of the 0 1932 electron diffraction data. 0.1934 102156) 10.1830J H

4.3403 PM3 charge rnrfa; 0.0611 (0.1W7J (437SJJ [MIAIi~=-lO1.11 chnrgc nonrfer=O.O03lIkdmol A label is used for each complex in the figures for 1.5h -0.4615 H .. . . -...... % ease in correlating the energies in Tables I1 and I11 (4.1527)& with the appropriate hydrogen bonded complexes. O.ZD04 o~zz48 0.2007 (02156) The Chem 3D Plus and Chemdraw software pack- 102611J (0.1566) ages (Cambridge Scientific Computing) were used Figure 2. Selected geometries of the water dimer rein conjunction with an Apple Laserwriter to produce action coordinate as calculated by PM3. Atomic charges and print the final geometry-optimized structures. are given next to each atom; the overall charge transfer and heat of formation for each complex are listed to the right of each structure. The AM1 values, in parentheses, DISCUSSION result from an AM1 reaction coordinate calculation where the angle of approach is constrained to the PM3 minimum structure 2. Hydrogen bonding was recognized by hug gin^^^ in 1919 and Latimer and Rodebush in 1920?8 The general features of hydrogen bonding interactions have

"OM,.. .. 108 4 '~,, h i: 0 .. 03071 108 8 '- 1.110

(J ,979

1.111 AM1 la 0 0769

03274 .->1.091 00139 PM3

lb 00197 6 7

Figure 1. Geometries of the waterlformaldehyde hydro- Figure 3. PM3 geometries for selectet hydrogen bonded gen bonded complex. Bond distances in A, bond angles in water complexes. Bond distances in A, bond angles in degrees, and atomic charges presented in italics. degrees. 94 JUREMA AND SHIELDS

10 11

12 13

&174.8 ----.912 6 N n &nCn 180.01.889-_ & 15 16 17

178.0 176.7 _-

18 19 20 21 175.7 w

Figure 4. PM3 geometries for selected 0-H- - -0,N-H- - -N, 0-H- - -N, and N-H- - -0 hydrogen bonded systems and for systems involving the fluorine atom. At the bottom right is the PM3 geometry for the global minimum of the ammonia dimer. Hydrogen bond distances in A, hydrogen bond angles in degrees.

been thoroughly studied and are well kn0wn,6~J~yet Comparison of the PM3 and AM1 Methods detailed knowledge of specific systematic differences is an area of active research.@' Precise values Figure 1 displays the hydrogen bonding geometries for the energetics of hydrogen bond formation are and atomic charges for the intermolecular system difficult to measure experimentally. Valuable in- where water donates a hydrogen to formaldehyde. sights into the detailed structure of hydrogen bonded The AM1 minimum energy structure la has two hy- systems have been obtained by high-resolution in- drogen bond angles of 108" and two hydrogen to frared and microwave spectroscopy experiments. In acceptor distances of approximately 2.24 A. The ox- the following discussion, results of PM3 and AM1 ygen-oxygen distance is 2.706 A. The PM3 structure calculations of hydrogen bonded structures and hy- lb has a hydrogen bond distance of 1.817 A, a bond drogen bond energies are compared with experi- angle of 177.2", and an oxygen-oxygen separation mental and theoretical values. Comparisons with distance of 2.78 A. This structure has been previously recent experimental and high-level ab initio in- reported." The association energy of the AM1 com- vestigations are emphasized. plex is -4.0 kcal mol-'; the PM3 energy of associ- PM3 AND INTERMOLECULAR HYDROGEN BONDING 95 ation is -2.75 kcal mol-' (Table 11). Although the but with the 0-- -H separation distance set at 99 A. absolute value of the energy of interaction is greater Unrestricted Hartree-Fock calculations were per- for the AM1 complex la, Figure 1 illustrates that formed with PM3. In this reaction path calculation, only the PM3 complex lb assumes a classic hydro- the 0-- -H separation distance was reduced and the gen bond configuration, that is, with a hydrogen geometry was optimized after each step. At 99 A, bond angle between 140 and 180", and where the there is no charge difference between the two hy- distance between the hydrogen and acceptor atoms drogens on the donating molecule (charge on each is significantly less than the sum of their van der hydrogen equals 0.1793). At 4.0 A, the hydrogen in- Waals radii. The distance between the hydrogen and volved in hydrogen bonding has a charge of 0.1839. donor atom is lengthened for the PM3 complex as In contrast, the donor water's remaining hydrogen expected upon hydrogen bond formation. The has a charge of 0.1787. Charge transfer between do- charges on the atoms, in italics in the figure, are nor and acceptor begins when the 0-- -H separation more negative for the donor and acceptor oxygen, distance reaches 3 A. This charge transfer increases and the carbon atom is more positive, when calcu- as intermolecular distance is reduced; when the lated by the PM3 method. The nonsymmetrical PM3 global minimum structure 2 is reached, 0.0221 of charge distribution is critical for formation of hy- charge is transferred from the donor water to the drogen bonds. acceptor water. As the separation distance is de- In the AM1 calculation, a bifurcated conformation creased below 1.809 A, charge transfer increases but is favored with each hydrogen of the water approx- repulsion drives up the overall energy of the system. imately 2.24 A from the oxygen acceptor atom in This same reaction path calculation was repeated formaldehyde. The AM1 calculation produces a with the AM1 method but with the PM3 hydrogen nearly symmetrical charge distribution about the bond angle of 178.5" held constant as the 0- - -H dis- water molecule. Bifurcated structures are typical re- tance was varied from 99 to 1A (Fig. 2). The complex sults predicted by AM1 calc~lations.~-~"There are was geometry optimized at each step with the ex- many experimental bifurcated structures reported in ception of the hydrogen bond angle, which was fixed the literature, such as the helical conformation of at the PM3 global minimum (structure 2, Fig. 3), and cyclic oxyphosphoranes" and DNA double helicesF2 the 0-- -H step distance. In this calculation, a small The problem with the AM1 bifurcated structure is amount of charge is transferred between the accep- the hydrogen bond angle of 108", indicating that both tor and donor water molecules. At the PM3 minimum lone pairs of electrons on the formaldehyde oxygen geometry 2, the AM1 calculation shows a charge are involved in bonding. transfer of 0.0041 but in the opposite direction One critical parameter responsible for structural (A -+ D) from the PM3 result (D -+ A), that is, the differences calculated by PM3 and AM1 is the charge donor water has a charge of +0.0041 and the ac- transfer from donor to acceptor molecules upon hy- ceptor water has a charge of -0.0041, opposite in drogen bond formation. The symmetrical AM1 global sign from the charge transfer that occurs in the PM3 minimum la has a charge of -0.0023 on the donor and AM1 minimum structures. If the PM3 global min- water molecule and a charge of + 0.0023 on the ac- imum 2 is used as the input geometry for an AM1 ceptor formaldehyde molecule; a charge transfer of calculation, a bifurcated complex similar to the 0.0023 occurs from the donor molecule to the ac- water-formaldehyde complex la is the AM1 geom- ceptor molecule upon formation of the global min- etry-optimized result. These results suggest that the imum la. In the PM3 structure lb, a charge transfer AM1 method does not reproduce classic hydrogen of 0.0246 from donor molecule to acceptor molecule bonds because charge is transferred from the ac- occurs, an order of magnitude greater than occurs ceptor molecule to the donor molecule for dimers for the AM1 structure la. If structure la is used as constrained to classic hydrogen bonding geometry. the input geometry for a PM3 calculation, a local When hydrogen bond angle and bond distance con- minimum with similar geometry to the AM1 structure straints are relaxed in full AM1 optimizations of neu- results. This PM3 local minimum has two H- - -0 dis- tral complexes, bifurcated structures are inevitable tances of 2.65 and 2.77 A and two O-H- - -0 angles of results. We suggest the AM1 method is deficient in 110.73 and 102.42". The dissociation energy is - 1.5 transferring charge both within the donor molecule kcal mol- ' and 0.0022 of charge is transferred from and from the donor to the acceptor. the donor molecule to the acceptor molecule, similar Our AM1 computed structures are the same as the to the AM1 result for this symmetrical complex. structures reported by Dannenberg (1),13 Ventura et When lbis used as the input coordinates for an AM1 al. (WW7),14 Rzepa and Yi (lb)? and Smith et al. (7)?5 calculation, the AM1 global minimum la is the result. There is virtually no charge transfer for the AM1 To understand the differences between AM1 and global minima, with just 0.0005 of the charge trans- PM3 hydrogen bonding geometries, the potential en- ferred from the donor to the acceptor. The AM1 ergy surface of the water dimer was explored with structure is a transition state point on the high-level both methods. Two water molecules were oriented at, initio potential energy surfa~e?~?~~The AM1 min- with the geometry shown by structure 2 in Figure 3 imum is actually a trifurcated structure, with three 96 JUREMA AND SHIELDS weak hydrogen bonds involving three lone pairs. that AM1 calculations are not reliable for determin- This result led to the preliminary conclusion that ing intermolecular hydrogen bonded structures be- AM1 overemphasizes hydrogen bond ability in such tween neutral molec~les.~~"~'~~'~~'~~~~~~~~~ a way that the maximum number of lone pairs is PM3 and AM1 calculations differ by the magnitude involved in these bonds.I4 Our results for 32 com- of charge transfer between donor and acceptor mol- plexes confiim this conclusion for neutral species. ecules in the complex. The global minima in AM1 One other structure for AM1 that is closest to the calculations are bifurcated structures with symmet- PM3 structure has an 0-- -H distance of 2.1 A but is rical charge distributions. The AM1 global minima a second-order saddle point on the AM1 energy sur- are local minima on the PM3 potential energy surface. faces. The PM3 global minima are characterized by When the reaction path calculation is repeated charge transfer of 0.02-0.06 units of charge for asym- with the PM3 method with the geometry fixed in the metric hydrogen bonded complexes. For cyclic hy- AM1 minimum, charge transfer occurs, although it drogen bonded complexes, such as the carboxylic is an order of magnitude less than occurs for the acid dimers 12-14, PM3 charge transfer is zero. PM3 fully-optimized reaction path calculation. When Charge transfer occurs for these symmetric systems, the AM1 global minimum geometry is used as the but because each molecule is an acceptor and a do- input coordinates for a full optimization with PM3, nor the overall charge remains unchanged for the a PM3 local minimum structure similar to the AM1 system. The ability of the PM3 method to predict result is produced. This PM3 local minimum is sym- hydrogen bonds is not correlated with the change in metric, with H- - -0 distances of 2.61 A, 0-H- - -0 an- charge on the individual acceptor, donor, and hy- gles of 104", no charge transfer between the donor drogen atoms upon formation of a complex. Rather, and acceptor molecules, and an association energy charge transfer between donor and acceptor mole- of - 2.0 kcal mol-'. cules, or electron redistribution from the acceptor The water/ water system and the water/formal- to the donor, is linked to the PM3 hydrogen bonded dehyde system illustrate that PM3 calculates hydro- structures displayed in Figures 1-4. gen bonded complexes with charge transfer, or electron redistribution, between acceptor and donor Differences between the MNDO Hamiltonians molecules. AM1 calculations starting from the PM3 hydrogen bonded minima produce symmetrical bi- Why does the PM3 Hamiltonian treat hydrogen bond- furcated complexes with little if any charge transfer. ing better than the AM1 Hamiltonian? It is useful to PM3 calculations starting from the AM1 minima pro- examine the evolution of the semiempirical Hamil- duce local minima similar to the symmetrical AM1 tonians pioneered by De~ar.'-~MNDO overesti- complexes; there is little charge transfer in these van mates repulsions between atoms separated by van der Waals complexes, which are local minima on the der Waals distances. Thus, the MNDO minimized PM3 potential energy surfaces. These results reveal water dimer geometry reveals the underestimation that if the calculated PM3 hydrogen bond energy has of intermolecular forces by separating the waters by an absolute magnitude less than 2.0 kcal mol~care over 3.4 A. In an attempt to overcome this problem, should be taken to explore the potential energy sur- Dewar et al. modified the core repulsion function face of the system in search of van der Waals com- (CRF) by adding two to four parameterized Gaussian plexes that are not hydrogen bonded. If a careful terms for each atom? The Gaussian parameters in- search is not made, then the location of the global troduced into the AM1 Hamiltonian to modify the minima is uncertain. core-core repulsion between pairs of atoms are K, The MNDO/H method shows the same pattern of L, and M. The parameter K determines the magnitude charge transfer as the PM3 method does for its suc- of the Gaussian term and whether the Gaussian is cessful description of hydrogen bonding between attractive or repulsive. The parameter L determines water dimer~.~~The most stable, linear MNDO/H di- the width of the Gaussian term and parameter M mer has a charge transfer of 0.02. For the less stable, determines the location of the Gaussian term. In bifurcated structure, only 0.002 units of charge are AMl, a common value of L was used for most atom transferred. types and this parameter was not optimized. Two AM1 calculations of the hydrogen bonded com- strategies were used to modify the CRF and reduce plexes displayed in Figures 3 and 4 reveal that AM1 excessive interatomic repulsions at large separa- predicts bifurcated complexes similar to la (Fig. 1). tions: (1) One or more attractive Gaussians were Only cyclic hydrogen bonded systems, such as the added, centered in the region where the repulsions carboxylic acid dimers 12,13,and 14, have angular were excessive; (2) repulsive Gaussians were cen- geometries similar to PM3 results. Yet, the 0-H tered at smaller internuclear separations to reduce distances are greater than 2.2 A. These AM1 hydro- the main term in the expression for core repulsion gen bond lengths for carboxylic acids are approxi- and reduce repulsion at larger internuclear dis- mately 0.5 A greater than experimental and theoret- tances. In the case of hydrogen and nitrogen, one ical values.75276 Our results confirm previous work attractive and two repulsive Gaussians were in- PM3 AND INTERMOLECULAR HYDROGEN BONDING 97

cluded. Two repulsive Gaussians were used for ox- of 1.72 A. Success of the PM3 method in replicating ygen, with no attractive terms. geometries of hydrogen bonded complexes does not In the PM3 Hamiltonian, only two Gaussians are necessarily mean that other nonhydrogen bonded added per element. All three of the parameters K,L, van der Waals complexes will be accurately repro- and M (a,b, and c in Stewart's nomenclature4) are duced by PM3 computations. optimized within the PM3 framework. The elements Stewart stated that the Gaussian core-core inter- hydrogen, nitrogen, and oxygen each have one at- actions that correct for long-range repulsion in AM1 tractive and one repulsive Gaussian term. and PM3 are operator equivalents to the van der Energy partitioning was used to assess the differ- Waals attraction or dispersion effects and can there- ences in the two-center terms for MNDO, AM1, and fore behave as if they were dispersion forces oper- PM3 calculations on the water dimer. The two-center ators. This allows correlation effects to be approx- terms are the resonance energy (J),exchange energy imated by simple Gaussian functions at the MNDO (K),electron-electron repulsion (E-E), electron-nu- level! Rzepa and Yi noted that the close agreement clear attraction (E-N), and nuclear-nuclear repul- between PM3 and ab initio correlated methods for sion (N-N). The Coulombic interaction is the sum hydrogen bonded complexes does suggest that the of the repulsive and attractive terms (C = E-E + PM3 Hamiltonian must allow for certain types of E-N + N-N). PM3, AM1, and MNDO lSCF calcu- correlation effects via the parameters? Further im- lations were performed on six different geometries: provements in hydrogen bonding within the MNDO (1) the PM3 minimum geometry, structure 2; (2) the series of programs can be expected with the incor- AM1 second-order saddle point with an O- - -H dis- poration of high-resolution hydrogen bonded micro- tance of 2.1 A; (3) the bifurcated minimum AM1 wave structures and accurate heats of association structure; (4) the MNDO minimum structure; and (5) for hydrogen bonded complexes in future parame- two transition state structures from AM1 and MNDO terizations. calculations. In every case, the sum of the E-E repulsion terms and the sum of the N-N repulsion terms, as well as the sum of the E-N attraction terms, Water Complexes and the PM3 Method had the greatest magnitudes for the PM3 calculations and the least magnitudes for AM1 calculations. Upon Figure 3 includes the results of calculations for four summing these terms to get the total electrostatic water trimers, a pentamer, and a dimer. The dimer interaction C, PM3 had the lowest value, followed 2 has a hydrogen bond distance of 1.809 A and a by AM1 and MNDO. For the six water structures hydrogen bond energy of - 3.55 kcal mol-'. The tri- examined, the value for C ranged from 23.3-24.4 eV mer 3 is an open trimer with the middle water serv- for PM3, 27.0-28.5 eV for AM1, and 32.8-34.2 eV for ing both as an acceptor and donor. The open trimer MNDO. Only the E--E, E-N, and N-N terms varied 3 has bond angles near 160" and a charge transfer in these calculations; the values for J,K, and C were of 0.0278 to the acceptor molecule. The charge on approximately the same for a given Hamiltonian for the middle water only changes by 0.0014 upon com- all six different dimer geometries. plex formation (Table 111). This charge redistribution These two-center results reveal that while the AM1 pattern suggests the donor molecule has transferred Hamiltonian reduces the overall repulsive forces be- most of its charge through the open complex to the tween atoms compared to MNDO the PM3 Hamil- acceptor molecule. Two hydrogen bonds are formed tonian further reduces the overall repulsive forces. in the open trimer; the distance between the closest The addition of parameterized Gaussian forces to hydrogen on the acceptor water and the oxygen on the CRF was responsible for the reduction of re- the original donor water is 2.6 A. pulsive forces within the AM1 frame~ork:~It is likely Trimer 4 differs from 3 as each water in the cyclic that the parameterization of the PM3 Hamiltonian, trimer 4 is an acceptor and a donor; the cyclic trimer including the K, L, and M parameters, is the reason 4 has three bond angles of 145-149"; the hydrogen why the PM3 Hamiltonian treats hydrogen bonding bond energy for the three bonds formed is -3.38 better than the AM1 Hamiltonian. kcal mol-'. The cyclic trimer 4 is more stable than While the AM1 Hamiltonian appears to still over- the open trimer 3, with a heat of association of estimate repulsive forces, the PM3 Hamiltonian may - 10.14 kcal mol-' compared with -9.04 kcal mol-' reduce repulsive forces too much. This is evidenced for 3. by the PM3 predicted hydrogen bond lengths being To assess the relationship between hydrogen bond 0.1-0.2 A shorter than the best high-resolution spec- strength and charge transfer, trimers 5 and 6 were troscopy results in some cases. Additional evidence calculated and a pentamer 7 configured similar to for this reasoning has appeared in a QCPE Bulletin the structure of ice. The trimer 5 has the central [V. pub, J. Messinger, and N. Heuser, QCPE Bull., water donating to two different acceptors; 6 has one 11(1), (1991)], where two methane monomers ori- acceptor and two donor molecules. The energy per ented with the two nearest C-H bonds in a straight hydrogen bond is 0.35 kcal mol-I greater for 6 than line reach a minimum at an H,H separation distance for 5, indicating that two donors and one acceptor 98 JUREMA AND SHIELDS

is energetically more favorable than is one water not report the AM1 energetic results in Tables I1 and donating its two hydrogens to two different accep- 111. tors. The most stable water trimer is the cyclic trimer (Table II), a result of formation of three bent hydro- Types of Hydrogen Bonds gen bonds. The sequential trimer 3, with two bent hydrogen bonds, is more stable than either of the 0-H-- -0 complexes 5 or 6, a result attributable to the greater Complexes lb, 2-7, and 8-14 are displayed in polarizability of 3, that is, in the open chain trimer Figures 1, 3, and 4. Pertinent information for the 3 the interaction of the central water with an ac- 0-H---0 hydrogen bond type appears in Table 111. ceptor water leads to a redistribution of electron The PM3 results for the water complexes 2-7 were density that enhances the strength of the hydrogen discussed in the previous section. Comparison of bond with the third water molecule. these PM3 results with experimental and ab initio In the ice-like structure 7, a central water mole- work is discussed here. cule bonds to two different waters like 5 and accepts Rzepa and Yi previously reported the PM3 struc- two different donors like 6. The resulting structure tures for a water dimer, trimer, and tetramer? Their is best described as the combination of two open dimer and trimer are identical to our dimer 2 and trimers 3, with the central water in one trimer do- cyclic trimer 4. The trans-linear structure of the di- nating to an additional water with a bond angle of mer 2 agrees with previous calculati~ns~~~~~~~~~and 156" and accepting an additional water donor with molecular beam resonance and microwave spec- a bond angle of 167". The central water in the pen- troscopy experiment^?^-^^ Rigorous ab initio cal- tamer 7 has very little change in charge, with the culations replicate the details of the water dimer charge transferred from the two outermost donors geometry with greater Ab initio to the two outermost acceptors in the same manner calculations6g and simulated annealing compu- as complex 3. An important point concerning water tationsa5predict that the cyclic water trimer is the structures is that the charge transfer in the pentamer most stable triplex, followed by the open sequen- 7 increases for outer water molecules compared tial trimer 3, and then by the double donor and ac- with isolated trimers 5 and 6. The symmetrical con- ceptor complexes, in agreement with our results (Ta- figuration of the pentamer allows for more effective ble 11). The ab initio results were explained by the charge transfer, as more charge is available to be effects of stabilizing and destabilizing three-body in- transferred among the molecules. The increase in teractions. Polarization makes 3 the strongest of the polarity around the outermost waters in this small open dimers, but polarization of the double donor 5 cluster 7 is quite likely the reason water clusters are and double acceptor 6 complexes leads to mutual favored; symmetrical clusters yield more and weakening of the hydrogen bonds.6yThis argument stronger hydrogen bonds. The hydrogen bond energy is supported by the PM3 calculations as explained is greatest for the water systems described here in the preceding section. when the charge is transferred across a central mol- Rzepa and Yi also observed this polarization effect ecule that is both an acceptor and donor. in their PM3 calculations of a water dimer, cyclic The charge transfer results for the water dimer trimer, and cyclic tet~-amer.~In their system, the hy- and the ice-like structure 7 are very similar to the drogen bond strength increases as waters are added results obtained with the MNDO/H meth0d.8~The to the cluster, which they trace to the increased po- experimental enthalpy of formation for the hydrogen larization of the water molecule upon hydrogen bond bond in water ranges from - 4.4 to - 5.4 kcal mol-' formation. Structural evidence for a cyclic hydrogen (Table 111). The PM3 result that the hydrogen bond bonded trimer comes from the measured rotational energy is -4.5 kcal mol-' for complexes 3 and 7 constants of 1-naphthol-(water), The in- agrees with experiment. The results of the PM3 cal- frared spectra of several isotopomers of the water culations on these small water clusters illustrate that trimer have been studied in argon and krypton matri- the PM3 method is capable of predicting both linear ~es.8~The results indicate the trimer is cyclic. Thus, and bent hydrogen bonds. the PM3 calculations successfully predict the correct Two previous evaluations of water cluster geom- geometries for the experimentally determined water etries from AM1 calculations reveal that AM1 retains dimeP8-32and trimer.86,*7 the incorrect features of the bifurcated dimer in In the ice-like structure 7, all three kinds of trimer cyclic oligomers of ~ater.~,'~These authors mention substructures are present, resulting in partial com- that AM1 calculations can yield hydrogen bond ener- pensation of repulsive three-body interactions; con- gies close to known values for geometries where a sequently, PM3 predicts hydrogen bond energies as semblance of the hydrogen bond is difficult to dis- strong as the open trimer for the cluster 7. Structure Cern.9JzJ8 our AM1 results for 32 intermolecular 7 is one of many possible minima on the water pen- structures confirm this view, as AMl-calculated tamer potential energy surface. The choice of this energies appear reasonable yet geometries do not. structure was based upon the desire to better understand factors involved in PM3 Calculations-There Because the geometries are not reasonable, we do PM3 AND INTERMOLECULAR HYDROGEN BONDING 99

are many possible configurations of water penta- 1.338,and 1.098A, respectively, well within one stan- mers. A theoretical study of water clusters, from dard deviation of the experimental values. The dimers to hexamers, was done with the QPEN/BB C-C=O and C-C-0 experimentally determined bond potential function.88Eleven local minima were found angles of 123.6 and 113.0"compare well with the PM3 on the pentamer potential energy surface; the global results of 126.8 and 115.7'. The acceptor oxygen/ minimum was a cyclic pentamer containing five hy- donor oxygen separation distance is 2.68A from the drogen bonds. In contrast, the simulated annealing gas diffraction work, and the present calculation method produces a structure with four other mole- yields a value of 2.74 A for this parameter. The ben- cules arranged tetrahedrally around the central zoic acid dimer 14 is another symmetrical carboxylic water?5 Our PM3 results for water trimers support acid complex, with a calculated hydrogen bond en- the predictionsRthat the cyclic cluster with five hy- ergy of - 4.38 kcal mol-'. The experimental value73 drogen bonds is the most stable pentamer. obtained from electron diffraction work in 1969 is The waterimethanol complex 8, methanol dimer -7.3 kcal mol-', and in general experimental hy- 10,and the methanol/water complex 11 have similar drogen bond energies for carboxylic acids range hydrogen bond energies, charge transfer properties, from -6 to -7 kcal mol-'?o All three of the car- and hydrogen bond angles. The methanol dimer has boxylic acid dimers exhibit symmetrical charge the weakest hydrogen bond, followed by the water/ transfer, as each molecule is both a hydrogen donor methanol complex and the methanol/water com- and hydrogen acceptor, and the hydrogen bonds that plex. These results, along with those for the water form are quite strong. dimer, indicate that the water molecule is superior The water/carbon dioxide complex 9 has a small to methanol both as an acceptor and donor. association energy of -0.97 kcal mol-' and a rela- The formic acid dimer 12, acetic acid dimer 13, tively small amount of charge transfer, with 0.0151 and benzoic acid dimer 14 are cyclic structures in- units of charge transferred from water to carbon corporating two hydrogen bonds. Each hydrogen dioxide upon complex formation. The complex 9 is bond contributes approximately 4.5 kcal mol- ' to not experimentally observed. High-resolution spec- stabilization of these carboxylic acid complexes. The troscopy results show that the waterlcarbon dioxide formic acid dimer is symmetric, with hydrogen complex is a planar, Cz, structure, with the oxygen bonds of 1.776A and hydrogen bond angles of 177.4'. atom 2.836 A from the carbon and the water hydro- The PM3 hydrogen bond energy is - 4.34kcal mol-', gens pointing away from C02?1,g2The 0-H- - -0 bond in reasonable agreement with a recent Fourier trans- in the water/formaldehyde complex lb is stronger form infrared (FI'IR) experiment" that yielded a than in the symmetrical COz molecule, with 0.0246 bond energy of - 5.85 kcal mol- '. The structure of charge transferred to water and a calculated energy the formic acid dimer has been investigated with gas of -2.75 kcal mol-'. The PM3 structure lb differs electron diffraction techniq~es.7~Numerous ab in- from the strongly bent structure calculated by SCF, itio calculations have been performed, with a com- MPZ, and CEPA-1 ab initio calculation^.^^ High-res- putation at the double-i plus polarization level olution spectroscopy experiments for the water/for- (DZ + P) in excellent agreement with experimental maldehyde system would be useful for comparing results.'" Table IV compares experimental DZ + P, these theoretical results. and present results for the formic acid dimer. The Because the water/ carbon dioxide complex global PM3 geometry agrees with the experimental and minimaY'.Y2 is' a van der Waals complex with no hy- high-level ab initio results. The authors of the DZ drogen bonding, the PM3 structure, with a hydrogen + P ab initio calculation assert that the experi- bond energy of approximately 1 kcal mol- ', is only mental 0-H single bond distance and the H-C=O a local minima. Therefore, when PM3 predicts a hy- bond angle values are in error by an amount greater drogen bond energy with an absolute magnitude less than the estimated experimental ~ncertainty.~~The than 2 kcal mol-' other van der Waals complexes PM3 results listed in Table IV support the argument should be examined to ensure determination of the that the experimental 0-H bond distance and H- global minimum. C=O bond angle are outside the range of uncertainty reported in the gas diffraction experiment. The acetic acid dimer 13 (Fig. 4) is similar to the N-H- - -N formic acid complex. The calculated PM3 hydrogen bond energy of - 4.52 kcal mol- ' is approximately Ammonia is the only frst-row hydride that does not the same as the hydrogen bond energy of formic acid donate a hydrogen to form a hydrogen bonded com- (Table 111). The structures of the acetic acid mono- plex with ammonia.g3 High-resolution microwave mer and dimer have been determined by gas electron spectroscopy experimentsg3of van der Waals com- diffraction." The experimental values for C-C, plexes of NH3 isotopomers reveal that the gas-phase C=O, C-0, and C--H bond distances in the dimer ammonia dimer complex has a distance of 3.337 A are 1.506,1.231, 1.334, and 1.102 A,respectively. The separating the nitrogen atoms. Although the posi- PM3 structure has bond distances of 1.500,1.228, tions of the six hydrogen atoms are not exactly 100 JUREMA AND SHIELDS

known, none of the allowed structures may be de- metrical complex containing three strong hydrogen scribed as hydrogen bonded. The dissociation energy bonds, with an energy of - 4.92 kcal mol- ' per bond. of this complex is less than 2.8 kcal mol-' according to microwave-infrared double resonance studies?' O-H- - -N The calculated PM3 ammonia dimer 15, displayed in Figure 4, is unique among investigated complexes The water/pyridine complex 18 and the methanol/ because a positive energy is required for the for- pyridine complex 19 have similar donor-acceptor mation of the classic ammonia dimer hydrogen bond. distances, charge transfer properties, and hydrogen Eigenvalue calculations show that 15 is a local min- bond energies. These structures are displayed in Fig- imum even though the complex requires 0.19 kcal ure 4 and results are presented in Tables I1 and 111. mol-' more energy than two monomers separated The water/ pyridine dimer has a stronger calculated by infinite distance. Therefore, the ammonia dimer hydrogen bond and a shorter hydrogen bond length 15 is not held together by a hydrogen bond. than the methanol/pyridine dimer. Unrestricted Hartree-Fock calculations of the Ammonia is an excellent hydrogen bond acceptor. NH,/NH, system reveal that the potential energy hy- The complexes of water 20 and methanol 21 with persurface is extremely flat with numerous local ammonia have similar bond strengths, charge trans- minima. The lowest-energy PM3 structure is dis- fer properties, and hydrogen bond lengths. Structural played at the bottom right in Figure 4. This van der analysis of a molecular beam electric resonance Waals complex is not hydrogen bonded, with an en- spectroscopy e~periment~~yielded a geometry for thalpy of association of -0.93 kcal mol-' and a the H,O/NH, complex similar to the PM3 structure N---N separation distance of 3.5 A. The molecular 20, with a linear O-H- - -N bond. The PM3 calculated mechanics for clusters approach has been applied hydrogen bond energy of 3.03 kcal mol-' is lower to complexes of ammonia, yielding a dimer structure than the 5.6 kcal mol-' energy calculated with a consistent with our results.g4 Determination of the modified 6-31G"* basis set.'" The experimental do- exact structure of the ammonia dimer is the subject nor atom/acceptor atom distance is 2.983 A, 0.19 A of ongoing research in high-resolution spectros- longer than the result from the PM3 calculation; the copy?5396 experimental H- - -N distance is 1.97 A and the PM3 Calculation of the NH,/NH, dimer using the value is 1.825 A. Ab initio calculations agree better 6-31 + G(d) basis set, followed by evaluation of the with the experimental hydrogen bond length?7-gg energetics of the stationary points using fully polar- The methanol/ammonia complex 21 has been ized 6-31 + G(dp) basis sets, predicts the traditional studied experimentally with a pulsed-nozzle Fourier- ammonia hydrogen bond?7 This ab initio calcula- transform microwave spectrometer.lol Data analysis tion, which included electron correlation using yields a hydrogen bond length of 2,015 A and a bond fourth-order Mdler-Plesset perturbation theory angle of 179.93", with the experimental w~rk~~,'~'for (MP4), yields a structure similar to the water dimer, 20 and 21 agreeing closely just as the present PM3 with a dimerization energy of - 3.3 kcal mol- '.Reop- results agree closely for these similar systems. It is timizing the geometries at the MP2/6-311 + G(dp) apparent that a weakness in the PM3 method is the level does not change the ab initio prediction of the underestimation of the hydrogen bond length in ammonia dirner.g8 Ab initio calculations at the 6- these complexes, on the order of 0.1-0.2 A. The ex- 31G(d) levelggand modified 6-31G**levelloo predict perimental work indicates that the water/ammonia a cyclic structure with CZhsymmetry and an enthalpy complex 20 has a slightly stronger interaction than of association of -1.6 kcal mol-'. The separation the methanol/ammonia complex 21. This trend is distance between the nitrogens is 3.271 A in this also indicated by the present results, with the PM3 calculation and the structure is not hydrogen hydrogen bond energy 0.2 kcal mol-' greater and the bonded. No ammonia dimer structure calculated by hydrogen bond length 0.002 A shorter for 20. Com- quantum-mechanical techniques is consistent with plexes 18-21 reinforce the idea stated previously: the experimental results, and only some ab initio The water molecule is a better donor than methanol. structures99,'00and the PM3 structure are close. The complexes of formic acid 22 and acetic acid The dimethylamine/ammonia complex 16 was 23 with ammonia, although having similar charge calculated to help assess the effects of electron do- transfer and bond lengths, differ greatly in bond nating groups on N-H- - -N hydrogen bonds. The strength. The HCOOH/NH3 complex 22 has a hy- C,H7N molecule is slightly better than NH3 as a do- drogen bond energy of -0.79 kcal mol-' and the nor, but the effect is small, with a PM3-calculated CH,COOH/NH, complex 23 has a bond energy of hydrogen bond energy of -0.07 kcal mol-'. A hy- -2.5 kcal mol-'. Based on the low calculated hydrogen bonded complex would not be expected to drogen bond energy, other van der Waals complexes predominate over other van der Waals complexes in of HCOOH/NH3 are expected to predominate in the the gas phase. Although the ammonia nitrogen is not gas phase, It is clear from the analysis of PM3 hy- a donor, nitrogens in rings are capable of donating drogen bonded complexes that although charge hydrogen bonds. The pyrazole trimer 17 is a SYm- transfer from the donor to the acceptor molecule is PM3 AND INTERMOLECULAR HYDROGEN BONDING 101 a general indicator of hydrogen bond strength there factor in hydrogen bonding as PM3 is far superior are other factors involved in the subleties of the PM3 to AM1 in predicting hydrogen bonding complexes calculation. Complex 22 has one of the highest val- involving nitrogen. Rzepa and Yi noted that a parti- ues for charge transfer yet one of the weakest cal- tioning of the two-center energies reveals that the culated hydrogen bonds. total 0-- -H term for ammonia donating a hydrogen to formaldehyde is significantly less than for the complexes where water is the donor mole~ule.~This N-H- - -0 result is additional evidence that the PM3 parame- Complexes 24-28 are displayed in Figure 4 and re- terization of the Gaussian core-core interactions are sults are presented in Tables I1 and 111. The fairly adequate dispersion forces operators because PM3 symmetrical formamide dimer 24 has a hydrogen calculations correctly predict that ammonia is a poor bond energy of -2.34 kcal mol-' per bond, as cal- hydrogen bond donor. culated with the PM3 method, and the experimental value derived from sublimation energies is - 7 kcal Hydrogen Bonds Involving Fluorine mol-'. The pyridone dimer 25 has two strong calculated hydrogen bonds with an energy of -4.92 The complexes involved in hydrogen bonding with kcal mol- ' per bond. The ammonialwater complex HF are displayed in Figure 4 and results summarized 26 and the ammorda/methanol complex 27 have a in Tables I1 and 111. The H,O/HF complex 29 and charge transfer of 0.0130 and 0.0137 units of charge, the HF/H20complex 30 illustrate that HF is a better respectively, to the water and methanol. These com- donor to oxygen (- 5.51 kcal mol-') than OH is to plexes form weak hydrogen bonds of -0.87 and fluorine ( - 4.02 kcal mol- I), in accordance with - 0.21 kcal mol- ', respectively. These results rein- standard discussions of hydrogen bond ~trengths.~~f'~ force the notion that water is a better hydrogen bond The experimental value is -7.2 kcal mol-' for the acceptor than methanol. HF/H,O complex and the experimental donor/ac- The NH,/HCOOH complex 28 transfers 0.0178 ceptor distance is 2.662 A; the PM3 values are - 5.51 units of charge from ammonia to formic acid and kcal mol-' and 2.68 A. Both the experimental'"2 and forms a weak hydrogen bond (-0.43 kcal mol-'). PM3 geometries have C, symmetry. The HF/NH3 These calculations illustrate a fundamental result; complex 31 has a hydrogen bond energy of -5.92 PM3 predicts ammonia is a poor hydrogen donor kcal mol-', and the NH3/HF complex 32 has a hy- (structures 15,26-28, and 32; see Table 111). These drogen bond energy of - 1.50 kcal mol-'. The PM3 results agree with the conclusions of Nelson et al.,"4 results predict complex 31 should be observed in that NH:, is a strong acceptor and poor donor, con- the gas phase, and we would expect only to observe trary to the traditional picture of NH3 as a strong HF donating to ammonia. These four structures 29- donor. None of the ammonia complexes where NH3 32 follow the traditionally recognized principle is a donor (15, 26-28, 32) should predominate that the acceptor strength follows the order N > among the possible van der Waals complexes based 0 > F and the donor strength follows the order upon their small calculated PM3 hydrogen bond F>O>N. energies. A previous PM3 study of the ammonia/formaldehyde system resulted in two unusual structures, with CONCLUSIONS association energies of - 0.08 and - 1.0 kcal mol-'? These structures did not agree with those from ub The PM3 semiempirical quantum-mechanical initio calculations (MP2/6-31G**level) and the au- method successfully predicts intermolecular hydro- thors cite a specific error in the PM3 method; namely, gen bonding between neutral molecules. One main the interaction between N-H a-bonds and an oxy- difference between AMl, which does not describe gen lone pair of electrons? These authors point out intermolecular hydrogen bonding between neutral that the reported4PM3 values for the atomic valence molecules, and PM3 is that in the PM3 calculations ionization potentials Us, and U, for nitrogen are significant charge transfer occurs from donor to ac- approximately 12 and 14 eV less negative than ex- ceptor molecules. The magnitude of charge transfer pected from a smooth interpolation of the parame- is on the order of 0.02-0.06 units of charge when ters from boron to fluorine. This potential error in strong hydrogen bonds are formed. Other van der Us, and Up, for nitrogen would lead to a less elec- Waals complexes computed with PM3, and all com- tronegative nitrogen center than expected and could plexes calculated with AM1, do not show such a large affect properties where the s/p orbital mixing at ni- redistribution of electronic charge. trogen changes (such as the inversion barrier in am- PM3 is predictive; calculated hydrogen bond ener- monia and the rotational barrier for the C-N pep- gies greater than an absolute magnitude of 2 kcal tide bond).gWhile the Us, and Up,values may affect mol-' suggest that the global minima is a hydrogen some aspects of PM3 calculations on nitrogen-con- bonded complex; energies less than an absolute mag- taining compounds,50they do not appear to be a nitude of 2 kcal mol-' imply that other van der Waals 102 JUREMA AND SHIELDS complexes will be observed experimentally. The ticipate additional results pertinent to biochemistry waterlcarbon dioxide system 9, ammonia/ammonia from PM3 computations and expect that future pa- system 15, ammonia/water system 26, ammonia/ rameterizations of the modified NDDO method will methanol system 27, and the ammonia/hydrogen improve the accuracy of hydrogen bond calculations. fluoride system 32 have PM3 energies less than an absolute magnitude of 1.6 kcal mol-' and are not This work was supported by Lake Forest College experimentally observed. The dimethylaminelam- (M.W.J.) and a Bristol-Meyers Company Grant of Research monia complex 16, formic acid/ammonia complex Corporation (G.C.S.). The research reported here was com- 22, and ammonia/formic acid complex 28 are pre- pleted as part of the Honors Senior Thesis in Chemistry dicted to be less stable than other van der Waals for M.W.J., which won the 1991 Phi Beta Kappa Senior complexes, as the PM3 hydrogen bond energies are Thesis Award at Lake Forest College. The authors thank David Pilkington and Tricia Lively for technical assistance less than an absolute magnitude of 0.8 kcal mol-'. and the referees for helpful comments. Compared with experimental heats of association, PM3 calculations underestimate reliable experimental information by approximately 1-2 kcal mol-'. References Accurate experimental heats of association are difficult to obtain, and further work in this area is en- 1. R.C. Bingham, M.J.S. Dewar, and D.H. Lo, J. Am. couraged. Chem. SOC.,97, 1285, 1294, 1302, 1307 (1975). 2. M.J.S. Dewar and W. Thiel, J. Am. Chem. SOC.,99, The geometries of the PM3 hydrogen bonded com- 4899,4907 (1977). plexes agree with high-resolution spectroscopy and 3. M.J.S. Dewar, E.G. Zoebisch, E.F Healy, and J.J.P. gas electron diffraction data, as well as with high- Stewart, J. Am. Chem. SOC.,107, 3902 (1985). level ab initio calculations. Agreement between ex- 4. J.J.P. Stewart, J. Comp. Chem., 10, 209, 221 (1989). perimental hydrogen bond geometries and PM3 hy- 5. F.L. Pilar, Elementary Quantum Chemistry, Mc- Graw-Hill, New York, 1990. drogen bond geometries is excellent for the cyclic 6. D.M. Hirst, A Computational Approach to Chemistry, carboxylic acid systems. A weakness in the PM3 Blackwell Scientific Publications, Oxford, UK, 1990. method is the underestimation of hydrogen bond 7. J.J.P.Stewart, QCPE 455, Department of Chemistry, lengths by 0.1-0.2 for some systems. This problem Indiana University, Bloomington, IN. causes the acceptor/donor distances to be under- 8. J.J.P. Stewart, J. Comp. Chem., 11, 543 (1990). 9. H.S. Rzepa and M. Yi, J. Chem. SOC.,Perkins Trans. estimated by an equal amount. 2, 943 (1990). The PM3 calculations are sensitive to the shallow 10. I.H. Williams, J. Am. Chem. SOC.,109, 6299 (1987). potential energy surfaces of these weak interactions. 11. A.A. Bliznyuk and A.A. Voityuk, J. Mol. Struct. Both PM3 and experimental results agree that am- (THEOCHEM), 164,343 (1988). monia is an excellent hydrogen bond acceptor and 12. W.C. Herndon and T.P. Radhakrishnan, Chem. Phys. Lett., 148, 492 (1988). a terrible hydrogen bond donor. Electronegativity 13. J.J. Dannenberg, J. Phys. Chem., 92, 6869 (1988). differences between F, N, and 0 predict that donor 14. O.N. Ventura, E.L. Coitiiio, A. Lledos, and J. Bertran, strength follows the order F > 0 > N; acceptor J. Mol. Struct. (THEOCHEM), 187, 55 (1989). strength follows the order N > 0 > F. PM3 mirrors 15. J.Y. Choi, E.R. Davidson, and I. Lee, J. Comp. Chem., 10, 163 (1989). these electronegativity differences in the calcula- 16. J.J. Dannenberg and L.K. Vinson, J. Phys. Chem., 92, tions, predicting the F-H- - -N bond to be the strong- 5635 (1988). est and the N-H- - -F bond the weakest. PM3 results 17. L.K. Vinson and J.J. Dannenberg, J. Am. Chem. SOC., predict water is a better hydrogen bond donor and 111, 2777 (1989). acceptor than is methanol. 18. S. Galera, J.M. Lluch, A. Oliva, and J. Bertrh, J. Mol. Struct. (THEOCHEM), 163, 101 (1988). The PM3 Hamiltonian treats intermolecular hy- 19. 1. Juranic, H.S. Rzepa, and M. Yi, J. Chem. SOC.,Perkin drogen bonding between neutral molecules better Trans. 2, 877 (1990). than the AM1 Hamiltonian, in part because the PM3 20. C.H. Reynolds, J. Am. Chem. SOC.,112, 7903 (1990). parameterization results in a reduction of two-center 21. M. Khalil, R.J. Woods, D.F. Weaver, and V.H. Smith, J. Comp. Chem., 12, 584 (1991). repulsive forces in the CRF. The ability of the PM3 22. T. Katagi, J. Comp. Chem., 11, 1094 (1990). method to model intermolecular hydrogen bonding 23. L.P. Davis, L.W. Burggraf, and D.M. Storch, J. Comp. means reasonably accurate quantum-mechanical cal- Chem., 12,350 (1991). culations can be applied to small biologic systems. 24. G. Buemi, F. Zuccarello, and A. Raudino, J. Mol. In fact, since the completion of this work Kollman Struct. (THEOCHEM), 164, 379 (1988). 25. H.S. Rzepa and M. Yi, J. Chem. SOC.,Faraday Trans. and coworkers reported that PM3 is superior to AM1 2, 531 (1991). for modeling compounds pertinent to the serine pro- 26. P.L. Cummins and J.E. Gready, J. Comp. Chem., 11, tease catalyzed hydrolysis of amides and esters.'"3 791 (1990). These same researchers used the PM3 method to 27. G.P. Ford and B. Wang, J. Comp. Chem., 13, 229 (1992). show that the attack of the substrate by the active 28. T.R. Dyke, J. Chem. Phys., 66, 492 (1977). site serine to form a tetrahedral intermediate was 29. T.R. Dyke, K.M. Mack, and J.S. Muenter, J. Chem. the rate-limiting step with both substrate^.'"^ We an- Phys., 66, 498 (1977). PM3 AND INTERMOLECUM HYDROGEN BONDING 103

30. J.A. Odutola and T.R. Dyke, J. Chem. Phys., 72,5062 63. D. Feller and E.R. Davidson, in Reviews in Compu- (1980). tational Chemistry, K.B. Lipkowitz and D.B. Boyd, 31. L.H. Coudert, F.J. Lovas, R.D. Suenram, and J.T. Eds., VCH, New York, 1990. Hougen, J. Chem. Phys., 87, 6290 (1987). 64. S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, 32. J.A. Odutola, T.A. Hu, D. Prinslow, S.E. O’detl, and R.D. Levin, and W.G. Mallard, Gas-Phase Ion and Neu- T.R. Dyke, J. Chmn. Phys., 88, 5352 (1988). tral Thermochemistry; J. Phys. Chem. Re$ Llata, vol. 33. Z. Latajka, H. Ratajczak, and W.B. Person, J. Mol. 17, suppl. 1,American Chemical Society, Washington, Stmct.. 194, 89 (1989). DC, 1988. 34. P. Herbine and T.R. Dyke, J. Chem. Phys., 83, 3768 65. D.R. Stull, and H. Prophet, in JANAF Thermochemical ( 1985). Tables, National Bureau of Standards, Washington, 35. B.J. Smith, D.J. Swanton, J.A. Pople, H.F. Schaefer, DC, 1971. and L. Radom, J. Chem. Phys., 92, 1240 (1990). 66. G.C. Pimentel and A.L. McClellan, The Hydrogen 36. C.J. Marsden, B.J. Smith, J.A. Pople, H.F. Schaefer, Bond, W.H. Freeman, San Francisco, CA, 1960. and L. Radom, J. Chem. Phys., 95, 1825 (1991). 67. P. Schuster, G. Zundel, and C. Sandorfy, The Hydrogen 37. E.S. Marcos, J.J. Maraver, J.L. Chiara, and A. Gomez- Bond, North-Holland Publishing Company, New York, Sanchez,J. Chem. Soc., Perkin Trans. II, 2059 (1988). 1976. 38. G. Buemi and C. Gandolfo, J. Chem. SOC.,Faraday 68. L.A. Curtiss, D.J. Frurip, and M. Blander, J. Chem. Trans. 2, 85, 215 (1989). Phys., 71, 2703 (1979). 39. G. Buemi, J. Chm.Soc., Faraday Trans. 2, 85,1771 69. A. Beyer, A. Karpten, and P. Schuster, Topics Cum: (1989). Chem., 120 (1984). 40. S. Millefiori and .A. Millefiori, J. Chem. Soc., Faraday 70. J. Snir, R.A. Nemenoff, and H.A. Scheraga, J. Phys. Trans. 2, 85, 1465 (1989). Chem., 82, 2497 (1978). 41. G. Buemi, J. Chem. Soc., Faraday Trans. 2, 86,2813 71. G. Henderson, J. Chem. Educ., 64, 88 (1987). (1990). 72. A.D.H. Clagne and H.J. Bernstein, Spectroch.im. Acta, 42. G. Buemi, J. McJ. Struct. (THEOCHEM), 201, 193 22A, 807 (1966). (1989). 73. A.D.H. Clagne and H.J. Bernstein, Spectrochim. Acta, 43. W.M.F. Fabian, J. Phys. Org. Chem., 3, 332 (1990). 25A, 593 (1969). 44. G. Buemi and F. Zuccarello, J. Mol. Struct. (THEO- 74. T. Kitao and C.H. Jarboe, J. Org. Chem., 32, 407 CHEM), 209, 89 (1990). (1967). 45. R.J. Woods, W.A. Szarek, and V.H. Smith, J. Am. 75. A. Almenningen, 0. Bastiansen, and T. Motzfeldt, Acta Chem. Soc., 112, 4732 (1990). Chim. Scand., 23, 2849 (1969). 46. .J.J. Novoa and M.-H. Whangbo, J. Am. Chem. Soc., 76. Y.-T. Chang, Y. Yamaguchi, W.H. Miller, and H.F. 113, 9017 (1991). Schaefer, J. Am. Chem. Soc., 109, 7245 (1987). 47. G. Buemi, J. Mol. Struct. (THEOCHEM), 208, 253 77. M.L. Huggins, Science, 55, 679 (1922); thesis, Univer- (1990). sity of California, 1919. 48. R. Voets, J.-P. Francois, J.M.L. Martin, J. Mullens, J. 78. W.M. Latimer and W.H. Rodebush, J. Am. Chem. Soc., Yperman, and L.C. Van Pouke, J. Comp. Chem., 10, 42, 1419 (1920). 449 (1989). 79. S.N. Vinogradov and R.H. Linnell, Hydrogen Bonding, 49. R. Voets, J.-P. Francois, J.M.L. Martin, J. Mullens, J. Van Nostrand Reinhold, New York, 1971. Yperman, and L.C. Van Pouke, J. Comp. Chem., 11, 80. J.E. Griffin, Ed., The Hydrogen Bond: New lnsights 269 (1990). on an Old Story, vol. 22, The American Ctystallo- 50. M. Szafran and J. Koput, J. Comp. Chem., 12, 675 graphic Association, New York, 1986. (1991). 81. R.O. Day, K.C. Kumara Swamy, L. Fairchild, J.M. 51. R. Karaman, J.-T.L. Huang, and J.L. Fry, J. Comp. Holmes, and R.R. Holmes, J. Am. Chem. SOC.,113, Chon., 11, 1009 (1990). 1627 (1991). 52. R. Karaman, J.-T.L. Huang, and J.L. Fry, J. Comp. 82. A.D. DiGabrielle, M.R. Sanderson and T.A. Steitz, Chm., 12, 536 (1991). Proc. Natl. Acad. Sci. USA, 86, 1816 (1989). 53. P. Camilleri, C.A. Marby, B. Odell, H.S. Rzepa, R.N. 83. A. Goldblum, J. Comp. Chem., 8, 835 (1987). Sheppard, J.J.P. Stewart, and D.J. Williams, J. Chem. 84. R.J. Vos, R. Hendriks, and F.B. van Duijneveldt, J. Soc., Chm. Commun., 1772 (1989). Comp. Chem., 11, l(l990). 54. O.N. Ventura, E.L. Coitino, K. Irving, A. Iglesias, and 85. S.H. Nilar,J. Comp. Chem., 12, 1008 (1991). A. Lledos, J. Mol. Struct. (THEOCHEM), 210, 427 86. L.L. Connell, S.M. Ohline, P.W. Joireman, T.C. Cor- (1990). coran, and P.M. Felker, J. Chem. Phys., 94, 4668 55. D.M. Seeger, C. Korzeniewski, and W. Kowalchyk, J. (1991). Phys. Chem., 95, 6871 (1991). 87. A. Engdahl and B. Nelander, J. Chem. Phys., 86,4831 56. M.B. Coolidge, J.E. Marlin, and J.J.P. Stewart, J. (1987). Comp. Chmn., 12, 948 (1991). 88. K.-P. Schroder, Chem. Phys., 123, 91 (1988). 57. P.-O. Astrand, A. Wallquist, and G.J. Karlstrom, J. 89. J.L. Derissen, J. Mol. Stmct., 7, 67 (1971). Phys. Chem., 95, 6395 (1991); J.J. Dannenberg and 90. Y. Marechal, in Vibrational Spectra and Structure, M. Mezei. J. Phys. Chem., 95,6396 (1991). vol. 16, J.R. Durig, Ed., Elsevier, New York, 1987. 58. S. Tolosa, J.J. Esperilla, and F.J. Olivares del Valle, J. 91. K.I. Peterson, G.T. Fraser, D.D. Nelson, and W. Klem- Comp. Chem., 11, 576 (1990). perer, in Comparison of Ab Initio Quantum Chem- 59. S.K. Loushin and C.E. Dykstra, J. Comp. Chem., 8, istry WithExperiment for Small Molecules, R.J. Bar- 81 (1987). tlett, Ed., D. Reidel Publishing Company, Boston, MA, 60. S.K. Loushin, S.-Y. Liu, and C.E. Dykstra, J. Chem. 1985. Phys., 84, 2720 (1986). 92. S.E. Novick, K.R. Leopold, and W. Klemperer, in 61. Z. Latajka and S. Scheiner, J. Comp. Chem., 8, 663 Atomic and Molecular Clusters, E.R. Bernstein, Ed., (1987). Elsevier, New York, 1990. 62. C. Kozmutza and IS. Kapuy, J. Comp. Chem., 12,953 93. D.D. Nelson, G.T. Fraser, and W. Klemperer, Science, (1991). 238, 1670 (1987). 104 JUREMA AND SHIELDS

94. C.E. Dykstra and L. Andrews, J. Chem. Phys., 92, 99. J.E. Del Bene, J. Cornp. Chem., 10, 603 (1989). 6043 (1990). 100. Z. Latajka and S. Scheiner, J. Cornp. Chem., 8, 674 95. M. Havenith, R.C. Cohen, K.L. Busarow, D.-H. Gwo, (1987). Y.T. Lee, and R.J. Saykally, J. Chem.Phys., 94, 4776 101. G.T. Fraser, R.D. Suenram, F.J. Lovas, and W.J. Ste- (1991). vens, Chem. Phys., 125, 31 (1988). 96. J.-P. Perchard, R.B. Bohn, and L. Andrews, J. Phys. 102. A.C. Legon and D.J. Millen, Chem. SOC.Rev., 21, 71 Chem.,95,2707 (1991). (1992). 97. M.J. Frisch, J.A. Pople, and J.E. Del Bene, J. Phys. 103. S. Schroder, V. Daggett, and P. Kollman,J. Am. Chem. Chem.,89, 3664 (1985). SOC.,113, 8922 (1991). 98. M.J. Frisch, J.E. Del Bene, J.S. Binkley, and H.F. 104. V. Daggett, S. Schroder, and P. Kollman,J. Am. Chem. Schaefer, J. Chem. Phys., 84,2279 (1986). SOC.,113, 8926 (1991).