Abstract
It is known that ab initio molecular dynamics based on the electron ground-state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low compared to the first electron eigenvalue gap. This work proves that a certain weighted average of the different ab initio dynamics, corresponding to each electron eigenvalue, approximates quantum observables for any temperature. The proof uses the semiclassical Weyl law to show that canonical quantum observables of nuclei–electron systems, based on matrix-valued Hamiltonian symbols, can be approximated by ab initio molecular dynamics with the error proportional to the electron–nuclei mass ratio. The result covers observables that depend on time correlations. A combination of the Hilbert–Schmidt inner product for quantum operators and Weyl’s law shows that the error estimate holds for observables and Hamiltonian symbols that have three and five bounded derivatives, respectively, provided the electron eigenvalues are distinct for any nuclei position and the observables are in the diagonal form with respect to the electron eigenstates.
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27 June 2019
On page 2744 in [1], it is stated that the nonlinear eigenvalue problem (3.8).
27 June 2019
On page 2744 in [1], it is stated that the nonlinear eigenvalue problem (3.8).
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Communicated by Claude Alain Pillet.
The authors are grateful to Caroline Lasser for valuable help on this work. The research was supported by Swedish Research Council 621-2014-4776 and the Swedish e-Science Research Center. The research of P.P. was supported by ARO MURI Award No. W911NF-14-024.
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Kammonen, A., Plecháč, P., Sandberg, M. et al. Canonical Quantum Observables for Molecular Systems Approximated by Ab Initio Molecular Dynamics. Ann. Henri Poincaré 19, 2727–2781 (2018). https://doi.org/10.1007/s00023-018-0699-x
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DOI: https://doi.org/10.1007/s00023-018-0699-x