Jorgensen zyxwvutsrqpo 1 Intermolecular Potential Functions zyxwvuts for the Water Dimer 201 1 Deriving Intermolecular Potential Functions for the Water Dimer from ab Initio Calculations’ William L. Jorgensen Contribution from the Department of Chemistry, Purdue University, West Lafayette, Indiana 47907. Received September 21, 1978 Abstract: An intermolecular potential function for the water dimer is developed from ab initio molecular orbital calculations with a minimal basis set. This allows the thorough study of the basis set dependence of Monte Carlo simulations of liquid water. General techniques for generating intermolecular potential functions are presented. A procedure for increasing the oc- currence of dimer configurations with low energy when they are selected in a random fashion is discussed and utilized. A care- ful analysis of the forms of potential functions for the water dimer reveals several interesting observations. First, it is found that the quality of fits using 12-6-3-1 potentials is the same as for functions with exponentials (cue-”) for the short-range interac- tions. However, the 12-6-3-1 functic zyxwvutsrqp 7s reduce the computation times for condensed-phase simulations by 11%. It is further es- tablished that models for a water monomer with four point charges are preferable to alternatives with three charges. Distinct improvement in the predicted geometry and dimerization energy for the linear water dimer are obtained in this way. Testing procedures including searches for unwanted minima in potential functions are applied. The final four point charge 12-6-3-1 potential is found to provide an excellent representation of the potential surface for the water dimer from STO-3G calculations. In all, 291 points on the surface were considered. The standard deviations for the fit of the 12-6-3-1 function are ca. 0.3 kcall mol In view of the chemical and biological importance of water, it has been the focus of theoretical studies of molecular liquid^.^ A key component in the research is the use of inter- molecular potential functions for the water dimer. Numerous functions have been developed either from empirical or quantum mechanical origins. In the empirical approach, sums of standard functions, such as Coulomb and Lennard-Jones 6: 12, are parametrized to reproduce experimental properties of water, e.g., multipole moments, geometries, hydrogen bond energies, lattice energy, etc. Some famous examples are the Ro~linson,~~ Ben-Naim and Stillinger (BNS),4b and ST2 potential^.^^ A new series of “central force” potentials has appeared which also permits vibrational m ~ t i o n . ~ Quantum mechanical potentials are derived by using ab initio molecular orbital methods to compute dimerization energies for many orientations Qf the dimer. The results are then fit to functional forms similar to those in the empirical potentials. An obvious advantage of the quantum mechanical approach is that systems can be treated for which there is little or no experimental data. A complication is that the potentials depend on the basis set quality and methods for correlation energy corrections in the a b initio calculations. Consequently, Clementi and co-workers have developed potentials for the water dimer at several levels of theory.6 Their first effort in- volved a large polarization basis set which yielded a potential function representative of near Hartree-Fock (HF) level calculations.6a This function was subsequently modified by a variety of empirical corrections for the correlation energy.6b However, Monte Carlo simulations with these potentials predicted too little structure for liquid water beyond the first solvation shell. The problem was remedied by a potential function derived from ab initio calculations including explicit corrections for the correlation energy via configuration in- teraction (CI).6c Several important issues remain to be resolved with regard to generating the quantum mechanical potentials. First, if it is essential to perform calculations at the CI level to obtain reasonable results, the approach will be restricted to small systems with limited study of their potential surfaces owing to the costliness of the computations. The HF results for liquid water were discouraging; however, there is no reason to expect a smooth enhancement of the results with increasing sophis- tication in the a b initio calculations. In fact, the problems with the HF potential could largely be attributable to the function’s high estimate of the dimerization energy for the water dimer 0002-7863/79/1501-2011$01.00/0 (-4.55 kcal/mol) in comparison to the CI value (-5.84 kcal/mol). This made it particularly intriguing to note that minimal basis set ab initio calculations without CI also yield dimerization energies of ca. -6 kcal/mol.’ Consequently, it seemed worthwhile to generate a potential function from minimal basis set calculations and use it in simulations of liquid water. At least a more complete picture of the basis set de- pendence of the simulations could then be obtained. The results of such studies are presented here and in the accompanying paper. The findings are encouraging because the structural and thermodynamic results are in far better agreement with ex- periment than from the HF potential and are in fact compa- rable in quality to the data from the best empirical functions. The CI potential still provides the closest agreement with ex- periment for the structure of liquid water. Nevertheless, it is established that reasonable intermolecular potential functions for hydrogen-bonded molecules containing second-row atoms can be obtained from minimal basis set calculations. Extension to larger systems and the development of a preliminary trimer potential for water at reasonable cost are possible directions for future research. During the course of this work, numerous issues of general interest arose concerning the formulation of quantum me- chanical potentials. Topics that receive attention below include the selection and number of dimer geometries, proper and ef- ficient forms for the potentials, choice of point-charge models, and unwanted minima. Selection of Dimer Geometries The genesis of a quantum mechanical potential (QMP) requires four main elements: selecting the geometries for the dimers, performing the ab initio calculations, fitting the computed dimerization energies to a functional form, and testing the function. The process is often iterative. Since a series of such undertakings is planned in this laboratory, careful consideration has gone into establishing general procedures. The application of the techniques is described here for each step in the development of an intermolecular potential for the water dimer. Until now there have been two principal ways to obtain the dimer geometries. A grid search can be performed in which the range of each geometric variable is broken into increments and each combination of values for the variables then yields one geometry. The problems here are that the number of resultant geometries increases exponentially with the number of vari- 0 1979 American Chemical Society