J. Phys. Chem. 1994,98, 10089-10094
10089
Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer K. Kim and K. D. Jordan' Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Received: May 12, 1994@
The geometries and vibrational frequencies of the water monomer and dimer are calculated using the MP2 method and density functional theory (DFT). The DFT calculations are carried out using both the BeckePerdew and B3LYP nonlocal exchange-correlation functionals, with the latter being comprised of Becke's three-parameter exchange functional [J. Chem. Phys. 1993, 98, 56481 and the Lee-Yang-Pam correlation functional [Phys. Rev. B 1993, 37, 7851. DFT calculations with the B3LYP functional, in contrast to those with the Becke-Perdew functional, are found to give geometries and frequencies in close agreement with the MP2 and experimental results. The B3LYP calculations with the largest basis set employed give a dimer binding energy of -4.56 kcdmol, about 0.5 kcal/mol smaller in magnitude than the binding energy obtained from MP2 calculations with similar basis sets.
I. Introduction The elucidation of the structure of water in various environments continues to be an extremely challenging problem. Monte Carlo and molecular dynamics simulation methods have played a pivotal role in the theoretical effect in this area.' However, to a large extent, the success of such simulations depends on the quality of the model potentials that are employed, and efforts to develop improved potentials continue ~ n a b a t e d . ~Much , ~ of the recent effort in this area has focused on the including polarization effects and relaxing the constraint of rigid monomers. High-quality ab initio calculations on small water clusters, including the dimer, play an important role for testing and parametrizing model potentials. This fact, together with the inherent interest in the properties of small water clusters, has spurred a large number of recent ab initio studies of the dimer and other small water cluster^.^-'^ It is now well established that inclusion of electron correlation is essential for describing the bonding in water clusters and, moreover, that second-order many-body perturbation theory (MP2) ~alculations'~ closely reproduce the binding energies obtained from higher order ( e g . , fourth order or MP4) cal~ulations.6~~ For a wide range of systems density functionaltheory (DFT)18 has been found to yield properties (geometries, vibrational frequencies, and binding energies) comparable in quality to those from MP2 calculations. For large systems, DFT calculations are much less computationally demanding than MP2 calculations. It is not surprising, therefore, that several papers have recently appeared in which DFT has been applied to small water cluster^.^^-'^ In a most exciting application, DFT has recently been used in conjunction with the molecular dynamics method to carry out a simulation of liquid water (actually, 32 water molecules with periodic boundary conditions), thereby avoiding the use of empirical potential^.'^ Prior studies have revealed that it is essential to employ an exchange-correlation functional which allows for nonlocal corrections in order to obtain a reasonable description of the water dimer in the DFT method.14J5 The DFT calculations on the dimer and larger clusters of water that have included nonlocal corrections have used the Becke-Perdew (BP) functional, which consists of Becke's 1988 exchange functionalz0 and Perdew's correlation functional.z' However, judging from the results available in the literature,14J5DFT calculations with @Abstractpublished in Advance ACS Absrracts, September 1,
1994.
0022-3654/94/2098-10089$04.50/0
the BP functional provide a poorer description of the water monomer and dimer than do MP2 calculations. Thus, it is of interest to determine whether other functionalswould fare better in describing these species. In this work we present for the water monomer and dimer the results of DFT calculations using the B3LYP functional, formed by combining Becke's recent three-parameter exchange functionalzz and the nonlocal correlation functional of Lee, Yang, and Parr.23 The three parameters in Becke's new exchange functional determine the relative weights of the exact, local, and gradient-correctedz0nonlocal contributions to the exchange. DFT calculations with this functional have been found to yield accurate reaction energies for a wide range of processes,z4 but it is not known how well suited it is for describing hydrogen-bonded systems. In testing the B3LYP functional, we examine the geometries, dipole moments, and harmonic vibrational frequencies of the monomer and dimer, as well as the polarizability of the monomer and the binding energy of the dimer. Comparison is made with the results of MP2 calculations, DFT calculations with the S-VWN and BP functionals, and, when available, experimentalresults. The S-VWN functional, used for carrying out local-spin density (LSD) functional calculations, combines Slater's exchange functionalz5and the correlation functional of Vosko, Wilk, and Although large basis sets can be employed in calculations on the water monomer and dimer, their use in calculations on much larger water clusters would be computationally prohibitive. Therefore, it is of interest to establish the utility of moderate size basis sets for describing the bonding in the dimer, and for this reason, MP2 and B3LYP calculations on the water monomer and dimer are carried out using basis sets of varying flexibility.
11. Computational Methodology It has been established in prior studies that use of basis sets including diffuse functions is important for describing the bonding in the water dimer and in other hydrogen-bonded system^.^-^ The basis sets used in this study-the aug-ccpVDZ*, aug-cc-pVDZ, aug-cc-pVTZ*, aug-cc-pVTZ', aug-ccpVTZ, aug-cc-pVQZ*, and aug-cc-pVQZ' contracted Gaussian basis sets-all include diffuse functions on the 0 and H atoms. The [4s3p2d3s2pl aug-cc-pVDZ and [5~4p3d2f/4~3p2d] augcc-pVTZ basis sets were formed by Kendall et al.z7 by adding diffuse functions to the [3s2pld/2slp] cc-pVDZ and [4s3p2dlf/
0 1994 American Chemical Society
10090 J. Phys. Chem., Vol. 98, No. 40, 1994
Kim and Jordan
TABLE 1: Equilibrium Geometries, Total Energies, Harmonic Vibrational Frequencies, Dipole Moments, and Polarizabilitiesa of the Water Monomer MP2b
expt
aug-cc-pVDZ*
0.957' 104.5'
0.965 104.2 -0.2591 1630 3818 395 1 1.986 1.197 1.307 1.186
1648' 3832' 3943' 1.854d 1.372e 1.483' 1.426'
aug-cc-pVDZ 0.966 103.9 -0.2609 1622 3806 3940 1.879 1.300 1.475 1.359
aug-cc-pVTZ* aug-cc-pVTZ'
(0.965) ( 103.9)
(-0.2634) (1623) (3805) (3940) (1.880) (1.300) (1.474) (1.358)
0.961 104.3 -0.3029 1640 3829 3953 1.900 1.326 1.403 1.320
DFT-BP86
aug-cc-pVDZ* 0.974 104.1 -0.4438 1588 3677 3788 1.929 1.312 1.394 1.275
aug-cc-pVTZ
0.961 104.2 -0.3034 1641 3829 3952 1.866 1.370 1.485 1.406
0.961 104.1 -0.3290 1629 3823 3948 1.860 1.370 1.484 1.416
(0.959) (104.3) (-0.3441) (1624) (3848) (3969) (1.859) (1.366) (1.476) (1.408)
aug-cc-pVQZ' 0.958 104.2 -0.3438 1638 3843 3968 1.857 1.394 1.477 1.429
(0.957) (104.3) (-0.3740) (1639) (3846) (3970) (1.860) (1.390) (1.472) ( 1.424)
DFT-B3LYP
aug-cc-pVDZ*
aug-cc-pVDZ
aug-cc-pVTZ*
aug-cc-pVTZ'
aug-cc-pVTZ
aug-cc-pVQZ'
0.965 105.0 -0.4435 1623 3797 3905 1.959 1.229 1.343 1.218
0.965 104.7 -0.4446 1619 3194 3904 1.854 1.319 1.507 1.385
0.962 105.1 -0.4646 1635 3800 3899 1.891 1.348 1.429 1.342
0.962 105.0 -0.4648 1635 3800 3900 1.854 1.392 1.520 1.434
0.962 105.1 -0.4662 1627 3796 3898 1.847 1.394 1.522 1.444
0.961 105.1 -0.4721 1629 3804 3905 1.845 1.424 1.522 1.464
a The water monomer was oriented in the yz plane with the z axis chosen as the principal axis. Quantities in parentheses are obtained from calculations including correlation of the 0 1 , electrons. Other MP2 results are from calculations with the 0 1 , electrons frozen. Reference 31. Slightly different experimental parameters are given in refs 32 and 33. Reference 34. e Reference 35. A second set of experimental polarizability values, about 3% lower than those reported in ref 35, is given in ref 36.
pVDZ*, aug-cc-pVDZ, aug-cc-pVTZ*, aug-cc-pVTZ', aug-cc3s2pldI cc-pVTZ correlation-consistent basis sets of Dunning.28 VTZ, and aug-cc-pVQZ' basis sets, at both the MP2 and B3LYP The aug-cc-pVDZ* basis set is formed from the aug-cc-pVDZ levels of theory, as well as at the LSD/aug-cc-pVDZ* and BP/ basis set by deleting the diffuse p function from the H basis aug-cc-pVDZ* levels of theory. The calculated and experiset. The aug-cc-pVTZ' basis set retains only the [5s4p3d/4s3p] mental results for the various properties of the water monomer portion of the aug-cc-pVTZ basis set, and the aug-cc-pVTZ* are summarized in Table 1. The results obtained from LSD/ basis set deletes also the diffuse p function from the hydrogen aug-cc-pVDZ* calculations have not been included in the table basis set. The [6s5p4d/5s3p] aug-cc-pVQZ* and [6s5p4d3f/ but will be discussed in the text. 5s4p3dI aug-cc-pVQZ' basis sets are formed by deleting higher angular momentum functions from the [ 6 ~ 5 ~ 4 d 3 f 2 g / 5 ~ 4 ~ 3 d 2 f l I . MP2 Calculations. With all basis sets used the MP2 aug-cc-pVQZ basis set of Kendall et al. The aug-cc-pVQZ* calculations give geometries in excellent agreement with experibasis set also excludes the diffuse p function on the H atoms. ment. The deviation of the MP2 value of the OH bond length The MP2 and DFT calculations were carried out using the from the experimental value decreases with increasing basis set Gaussian 92 program.29 The geometries were optimized by flexibility; the OH bond length is overestimated by 0.008-0.009 means of analytical gradients, and the vibrational frequencies A in the calculations using the aug-cc-pVDZ* and aug-cc-pVDZ were calculated in the harmonic approximation, making use of basis sets, by about 0.004 A in those using the aug-cc-pVTZ*, analytical second derivatives. Unless noted otherwise, the core aug-cc-pVTZ', and aug-cc-pVTZ basis sets, and by only 0.001 (Le., 01,) orbitals were frozen in the MP2 calculations. MP2/ 8, in those using the aug-cc-pVQZ' basis set. With all six basis aug-cc-pVDZ and MP2/aug-cc-pVTZ calculations on the water sets the MP2 calculations give an HOH angle within 0.6" of monomer and dimer, in which all electrons were correlated, have the experimental value reported in ref 31. Comparison of our been reported recently by Xantheas and Dunning.8a For the results with those of Xantheas and Dunning reveals that dimer, the MP2 calculations of these authors also differ from correlation of the 01, electrons leads to a slight (0.001-0.002 presented here in that a linear hydrogen bond was imposed. A) shortening of the OH bonds and small (
