Discrete Variable Representation Implementation of the One-Electron Polarization Model Tae Hoon Choi, † Thomas Sommerfeld, ‡ S. Levent Yilmaz, † and Kenneth D. Jordan* ,† Department of Chemistry, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260, Southeastern Louisiana UniVersity, Hammond, Louisiana 70402, and Center for Simulation and Modeling, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260 Received May 18, 2010 Abstract: A discrete variable representation (DVR) implementation of an one-electron polariza- tion model (OPEM) for characterizing (H 2 O) n - clusters is described. For the (H 2 O) 90 - cluster, evaluation of the energy and gradient using a suitable DVR basis sets is about a 2 orders of magnitude faster than corresponding calculations using a Gaussian orbital basis set. The DVR version of the code has been parallelized using OpenMP to enable molecular dynamics (MD) simulations of large (H 2 O) n - clusters. 1. Introduction The interaction of excess electrons with water clusters has been the subject of numerous experimental and theoretical studies. 1–40 A key to much of the computational work in this area has been the development of the electron-water potentials for use in one-electron model Hamiltonians. 27–40 Our group has introduced both a quantum Drude oscillator approach 33,34 and a computationally simpler one-electron polarizable model (OEPM) 39 for describing (H 2 O) n - clusters. The GTO implementation of the OEPM model, including the evaluation of analytical gradients, has been described in earlier publications. 39,41 When using Gaussian type orbital (GTO) basis sets, the construction of the matrix elements H kl ) ∫ k * (x)H l (x)dx is the major time-consuming part of the calculation of the energy and of the analytical gradients. We consider here an alternative approach involving the discrete variable repre- sentation (DVR) method. 42–56 Although the use of the DVR basis sets results in much larger Hamiltonian matrices, the matrix elements are rapid to evaluate, and the sparsity of the matrices allows for rapid diagonalization. In the following section, we describe the DVR implementation of the OEPM algorithm and compare its performance with the GTO implementation for (H 2 O) n - clusters with n as large as 90. We note that Jacobson and Herbert have also used a DVR approach for calculating the electron binding energies of their one-electron polarization model. 40 However, there are several differences between the two approaches, making a detailed examination of a DVR approach to our one-electron model instructive. Parallelization of the OEPM-DVR code using shared memory and OpenMP 57 is also described. 2. Computational Methods 2.1. DVR with the OEPM Hamiltonian. The OEPM method is built on top of the DPP water model developed in our group. 58 In this model, each water monomer carries three point charges, +Q at each H atom and -2Q at a so- called M site located 0.25 Å from the O atom on the rotational axis and displaced toward the H atoms. In the DPP model, each atom is polarizable, with Thole-type 59 damping of the charge-induced dipole and induced dipole-induced dipole interactions. Finally, there are exponential repulsive interactions between atoms of different monomers and attractive van der Waals interactions between the O atoms. In the OEPM method, the model Hamiltonian (in atomic units) for an excess electron interacting with a water cluster is * To whom correspondence should be addressed: E-mail: jordan@pitt.edu. † University of Pittsburgh. ‡ Southeastern Louisiana University. H )- 1 2 ∇ 2 - ∑ i Q i r i f pc (r i ) + ∑ j V j rep + ∑ j μ j · r j r j 3 f ind (r j ) - ∑ j R 2r j 4 f pol (r j ) (1) J. Chem. Theory Comput. 2010, 6, 2388–2394 2388 10.1021/ct100263r  2010 American Chemical Society Published on Web 07/12/2010