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 calcu- lations can be applied to small biologic systems. 0 1993 by John Wiley & Sons, Inc. INTRODUCTION AM1 and MNDO, respectively? A thorough discus- sion 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 com- puting, 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