Bonding Properties of the Water Dimer: A Comparative Study of Density Functional Theories

For a variety of density functional theories, we examined the ground-state properties of the water monomer (geometry, vibrational frequencies, dipole moment, polarizability) and dimer (geometry, vibrational frequencies, bond energy, and barrier heights for the transition states for the interchange of hydrogen atoms within the dimer). Thus, we considered LDA (SVWN), seven pure GGA methods (BLYP, BP86, BPW91, PWPW, mPWPW, PBEPBE, and XLYP), and eight hybrid GGA methods (BH&HLYP, B3LYP, B3P86, B3PW91, PW1PW, mPW1PW, PBE1PBE and X3LYP). We find that the best overall performance is given by X3LYP, a hybrid method using a modified GGA constructed from a linear combination of the Becke and Perdew GGAs. Comparing with the exact values, the errors in X3LYP for the water dimer are 0.05 kcal/mol (bond energy), 0.004 Å (bond distance), and 12 cm ^-1 (vibrational modes), and for the monomer, the errors are 0.002 Å (bond distance), 0.6° (bond angle), 14 cm ^-1 (vibrational modes), 0.005 D (dipole moment), and 0.008 Å ³ (polarizability). These data were not used in determining the parameters or form of X3LYP, suggesting that X3LYP should be generally useful for predicting accurate properties for systems dominated by hydrogen bonding, electrostatics, and van der Waals (dispersion) interactions, such as ligand/protein complexes.