Accurate Energies and Structures for Large Water Clusters Using the X3LYP Hybrid Density Functional Julius T. Su, Xin Xu, and William A. Goddard III* Materials and Process Simulation Center (139-74), DiVision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 ReceiVed: June 9, 2004; In Final Form: August 10, 2004 We predict structures and energies of water clusters containing up to 19 waters with X3LYP, an extended hybrid density functional designed to describe noncovalently bound systems as accurately as covalent systems. Our work establishes X3LYP as the most practical ab initio method today for calculating accurate water cluster structures and energies. We compare X3LYP/aug-cc-pVTZ energies to the most accurate theoretical values available (n ) 2-6, 8), MP2 with basis set superposition error (BSSE) corrections extrapolated to the complete basis set limit. Our energies match these reference energies remarkably well, with a root-mean- square difference of 0.1 kcal/mol/water. X3LYP also has ten times less BSSE than MP2 with similar basis sets, allowing one to neglect BSSE at moderate basis sizes. The net result is that X3LYP is ∼100 times faster than canonical MP2 for moderately sized water clusters. 1. Introduction We predict structures and energies of water clusters containing up to 19 waters with X3LYP, 1,2 an extended hybrid density functional designed to describe noncovalently bound systems well. Our work establishes X3LYP as the most practical ab initio method today for calculating accurate water cluster structures and energies. We compare our X3LYP results to the most accurate theory available 3-8 for modest-sized water clusters, MP2 calculations using triple--plus basis sets with basis set superposition error corrections extrapolated to the complete basis set limit. Our energies match these reference energies to a root-mean-square (rms) deviation of 0.1 kcal/mol of water. This agreement is remarkable, especially since the noncova- lent bonding in water clusters (polar, hydrogen bonded) differs greatly from the bonding in the rare neutral gas dimers used to train X3LYP. In contrast, the popular hybrid functional B3LYP 9-11 provides acceptable geometries and thermochemistry for covalent molecules, but its poor description of London dispersion (van der Waals attraction) leads to poor binding energies 4,12-15 (Table 1) for water clusters. Two consequences follow: First, the result establishes the generality of the X3LYP functional, supporting its application to more diverse van der Waals and hydrogen bonded complexes. This validation sets the stage for first principles predictions of noncovalent interac- tions of ligands to proteins and DNA, with implications for the emerging field of genome-wide structure based drug design. Second, X3LYP now represents the state of the art for practical ab initio calculations on water clusters, since (1) We can use smaller basis sets while preserVing accuracy. Post-Hartree-Fock methods such as MP2 require higher angular momentum basis functions to properly describe the correlation cusp 16 and suffer from slow and unsystematic convergence to the complete basis set limit. 17 We expect the basis set requirements for DFT methods to be greatly reduced, and our results bear this out: X3LYP/aug-cc- pVTZ agrees with MP2/aug-cc-pV5Z extrapolated to the complete basis set limit to within 0.1 kcal/mol/water, a differ- ence well within the uncertainty of both methods. (2) We can neglect BSSE at moderate basis sizes. Basis set superposition error has long plagued canonical MP2 calculations, with a correction of ∼1.1 kcal/mol for water hexamer even with the aug-cc-pV5Z basis set. 3 This is larger than the energy difference between water hexamer isomers (<0.5 kcal/mol). X3LYP has ten times less basis set superposition error than MP2 with comparable basis sets, allowing smaller basis sets to be used. Non-BSSE and BSSE energies converge quickly to the same value with increasing basis set size, so that for moderate sized bases (aug-cc-pVTZ), we can neglect BSSE. Not including BSSE in X3LYP calculations speeds up our calculations significantly, since a BSSE calculation requires N single point energies with the full system basis, where N is the number of water monomers in the complex. (3) Density functional methods are faster than MP2. For larger clusters, X3LYP is at least 100 times faster than canonical MP2 at the same basis set level, where BSSE is neglected for both calculations. The speed advantage becomes even bigger for larger clusters, since density functional methods scale as a factor of N better than canonical MP2 (formally N 4 vs N 5 , with improvements possible for both). With this superior combination of speed and accuracy, we expect X3LYP to displace MP2-corrected Hartree-Fock (HF) as the preferred method for performing ab initio calculations on water clusters. 2 Computational Details 2.1. X3LYP Functional. The details of the X3LYP hybrid density functional are described elsewhere. 1,2 The X3LYP hybrid functional was developed to describe accurately the thermo- chemistry of molecules while reproducing the properties (equi- librium distance, binding energy, and Pauli repulsion) of helium * To whom correspondence should be addressed. E-mail: wag@ wag.caltech.edu. 10518 J. Phys. Chem. A 2004, 108, 10518-10526 10.1021/jp047502+ CCC: $27.50 © 2004 American Chemical Society Published on Web 11/02/2004