Martin Head-Gordon and David Chandler, University of California, Berkeley,
and Lawrence Berkeley National Laboratory

Research Objectives

(1) Exploration of density functional theory for simulation of ground and excited states of radicals. (2) Computational studies of unsaturated hydrocarbon radicals and ions. (3) Parallel electronic structure software code development. (4) Application of transition path sampling to weak acid dissociation in an aqueous environment. (5) Test of Car-Parrinello ab initio molecular dynamics (CPMD) force field for physically relevant nuclear configurations. (6) Development of large time step algorithms for transition path sampling.

Computational Approach

(1) We are exploring whether ground states and low-lying excited states of radicals can be adequately described using time-dependent density functional theory (TDDFT) with existing functionals. (2) We are applying TDDFT to the problem of the excited states of unsaturated hydrocarbon radicals and ions. (3) We have pioneered a new method we call the Energy Renormalization Group (ERG) for obtaining a small number of judiciously chosen collective variables for describing long-range density matrix correlations in small-gap systems. (4) We use transition path sampling along with CPMD to simulate representative trajectories of H₂O dissociation. (5) We have created a formulation of transition path sampling that can be interfaced with any trajectory algorithm, and have used this formulation to combine transition path sampling with CPMD. (6) We apply coarse-grained methods that are consistent with principles of detailed balance and microscopic reversibility.

Transition states for water auto-dissociation involve the coincidence of two events. First, there must be a solvent fluctuation in local potential energy propelling the proton away from a nascent hydroxide ion. Second, this fluctuation must be accompanied by breaking of a hydrogen bond along the proton wire connecting the hydroxide and hydronium ions. The two illustrations show 32 water molecules shortly before (left) and after (right) crossing the auto-dissociation transition state surface. The oxygen atoms colored yellow and blue highlight the hydronium and hydroxide ions, respectively. The dotted lines show hydrogen bonding proton wires along which ionic species move relatively quickly.

Accomplishments

(1) We have formulated and implemented a quasidegenerate single-reference second-order perturbation theory of electronic excitation energies. We have applied this method to evaluate excited states in large unsaturated organic species. (2) We have nearly completed a joint theoretical and experimental study of the reaction of H2S with atomic carbon. (3) For several one- and two-dimensional model problems involving tight-binding Hamiltonians, we have been able to demonstrate near-linear scaling for the first time, using a parallel code on the Cray T3E. (4) We have demonstrated the applicability of transition path sampling to weak acid dissociation in an aqueous environment through preliminary studies of water dissociation in water, the basic kinetic step of pH. (5) We have shown that the CPMD force field for dynamically accessed configurations for proton transfer in the protonated water trimer is in excellent agreement with that predicted by higher level ab initio techniques. (6) We have devised a set of statistical methods for interpreting the behavior of transition paths in complex systems.

Significance

Developing techniques that can reliably treat excited states, reliably break chemical bonds, and feasibly simulate molecules containing very large numbers of electrons will permit better simulations of mechanisms relevant to combustion chemistry and soot formation, structural biology, and nanocluster technology.

Publications

S. Hirata and M. Head-Gordon, "Time-dependent density functional theory for radicals: An improved description of excited states with substantial double excitation character," Chem. Phys. Lett. 302, 375 (1999).

M. Head-Gordon, M. Oumi, and D. Maurice, "Quasidegenerate second order perturbation corrections to single excitation configuration interaction for excitation energies," Mol. Phys. 96, 593 (1999).

P. L. Geissler, C. Dellago, and D. Chandler, "Kinetic pathways of ion dissociation in water," J. Phys. Chem. 103, 3706 (1999).

http://www.cchem.berkeley.edu/~mhggrp
http://gold.cchem.berkeley.edu