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Springer eBooks

Many-Electron Wavefunctions, Density Matrices, Reduced Density Matrices and Variational Principles

Eugene S. Kryachko, Eduardo V. Ludeña

Published Jan 1, 1990• 0 citations
Publisher
DOI
10.1007/978-94-009-1970-9_2

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Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.
Nuclear dynamics is incorporated into an efficient density matrix formalism of electronic dynamics which has been applied to molecular systems containing thousands of atoms. The formalism for the combined dynamics of electrons and nuclei is derived from the Dirac–Frenkel variational principle. The single electron reduced density matrices and the Glauber coherent states are used for the electronic and nuclear degrees of freedom, respectively. The new formalism is applicable to simulate the dynamics of large molecular systems. As an illustration of its validity, the formalism is employed to calculate the electron and nuclei dynamics of hydrogen molecules.