B. L. Hammond

Monte Carlo methods in Ab Initio quantum chemistry

Review of ab initio quantum chemistry introduction to Monte Carlo methods the variational Monte Carlo method quantum Monte Carlo exact Greens function methods released node methods excited states properties other than energy determination of interaction potentials, stationary geometries, energy derivatives valence-electron and acceleration methods.

Valence quantum Monte Carlo with ab initio effective core potentials

Effective‐core potentials (ECP’s) obtained from ab initio methods are implemented in molecular quantum Monte Carlo (QMC). The theory is presented, and applied to the calculation of electron affinities (EA) of Li and Na, the ionization potential (IP) of Mg, the binding energies (De) of NaH and Na2, and the potential energy curve of Na2. In all cases ECP–QMC results are found to be as accurate as previous all‐electron results. In particular, the calculated quantities (vs experimental values) are (in eV): EA(Li)=0.611±0.020 (0.620), EA(Na)=0.555±0.021 (0.546), IP(Mg)=7.637±0.026 (7.646), De (NaH) =1.954±0.073 (1.971), and De (Na2)=0.746±0.020 (0.747). In addition, the statistical precision obtained surpasses that which can be readily achieved in all‐electron QMC calculations on these systems.

Theoretical study of the H+O3↔OH+O2↔O+HO2 system

The key features of the H+O3 potential energy surface have been determined using ab initio quantum mechanical methods. The electronic wave function used is a multiconfiguration Hartree–Fock wave function which provides a qualitatively correct description of various reactive channels. It is found that the H+O3→HO+O2 reaction proceeds along a nonplanar pathway in which the H atom descends vertically to the plane containing the ozone molecule to form an HO3 intermediate which then undergoes fragmentation. No planar transition state for a direct O‐atom abstraction could be located. The radical–radical O+HO2 reaction was found to have no energy barrier to formation of HO3 which was determined to subsequently decompose to HO+O2. The H‐atom abstraction reaction O+HO2→OH+O2 was found to have a small activation energy. The dynamical implications of these findings are discussed. The results are consistent with the observed vibrational excitation of the OH product in the H+O3 reaction. The key features of the H+O3 p...

Molecular physics and chemistry applications of quantum Monte Carlo

We discuss recent work with the diffusion quantum Monte Carlo (QMC) method in its application to molecular systems. The formal correspondence of the imaginary-time Schrödinger equation to a diffusion equation allows one to calculate quantum mechanical expectation values as Monte Carlo averages over an ensemble of random walks. We report work on atomic and molecular total energies, as well as properties including electron affinities, binding energies, reaction barriers, and moments of the electronic charge distribution. A brief discussion is given on how standard QMC must be modified for calculating properties. Calculated energies and properties are presented for a number of molecular systems, including He, F, F−, H2, N, and N2. Recent progress in extending the basic QMC approach to the calculation of “analytic” (as opposed to finite-difference) derivatives of the energy is presented, together with an H2 potential-energy curve obtained using analytic derivatives.

Quantum Monte Carlo approach to electronically excited molecules

Quantum Monte Carlo (QMC) is used to compute the electronic energies of H2(B 1Σ+u) and H2(E 1Σ+g). The E state calculation represents the first application of QMC to a molecular excited state with the same symmetry as a lower state. In this QMC approach a trial function specifies the nodes of the QMC distribution. The role of these nodes in excited state calculations is discussed. QMC energies that contain over 95% of the correlation energy are computed using MCSCF wave functions as trial functions.

On quantum Monte Carlo for the electronic structure of molecules

Abstract We present recent advances in the quantum Monte Carlo (QMC) method for the electronic structure of atoms and molecules. The QMC method used here is a procedure for solving the Schrodinger equation stochastically based on the formal similarity between the Schrodinger equation and the classical diffusion equation. Quantum mechanical expectation values are obtained as Monte Carlo averages over an ensemble of random walkers undergoing diffusion, drift (from importance sampling), and branching. The power of the QMC method is that it is inherently an N-body method which can capture all of the dynamic correlation of the electrons. The approach yields highly accurate energies and has been used to determine other properties, including dipole moments and molecular geometry energy gradients. Here we present a description of the QMC method that we employ and give representative results. In addition we discuss recent progress on the calculation of transition dipole moments and developments with the “damped-core” QMC method which enables studies of molecular systems containing heavy atoms without reliance on Pseudopotentials.