Analytic second derivatives for the spin-free exact two-component theory

Cheng, Lan; Gauss, Jürgen

doi:doi:10.1063/1.3667202

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Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

Stochastic reaction-diffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-diffusion simulation algorithm that samples realizations from the exact solution of the reaction-diffusion master equation. The present algorithm, called partial-propensity stochastic reaction-diffusion (PSRD) method, uses an on-lattice discretization of th...

Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In th...

The formulation and implementation of the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c-1e scheme, the four-component one-electron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting “electrons-only” two-component Hamiltonian is then used together with untransformed two-electron interactions. The derivatives of the two-component Hamiltonian can thus be obtained by means of simple manipulations of the parent four-component Hamiltonian integrals and derivative integrals. The SF version of X2c-1e can furthermore exploit available nonrelativistic quantum-chemical codes in a straightforward manner. As a first application of analytic SFX2c-1e second derivatives, we report a systematic study of the equilibrium geometry and vibrational frequencies for the bent ground state of the copper hydroxide (CuOH) molecule. Scalar-relativistic, electron-correlation, and basis-set effects on these properties are carefully assessed.

Article Outline

INTRODUCTION
THEORY
IMPLEMENTATION AND COMPUTATIONAL DETAILS
RESULTS AND DISCUSSIONS
1. Scalar-relativistic and electron-correlation effects
2. Basis-set effects
3. Comparison of computations to experiments
SUMMARY

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KEYWORDS and PACS

Keywords

copper compounds, electron correlations, ground states, molecular configurations, quantum chemistry, relativistic corrections, vibrational states

PACS

31.15.vq

Electron correlation calculations for polyatomic molecules
31.30.J-

Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
33.15.Bh

General molecular conformation and symmetry; stereochemistry
33.20.Tp

Vibrational analysis

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http://dx.doi.org/10.1063/1.3667202

PUBLICATION DATA

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0021-9606 (print)

1089-7690 (online)

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American Institute of Physics

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