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Canonical Quantum Observables for Molecular Systems Approximated by Ab Initio Molecular Dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-2669-359X
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2018 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 19, no 9, p. 2727-2781Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Birkhauser Verlag AG , 2018. Vol. 19, no 9, p. 2727-2781
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-236721DOI: 10.1007/s00023-018-0699-xISI: 000441905800007Scopus ID: 2-s2.0-85049569877OAI: oai:DiVA.org:kth-236721DiVA, id: diva2:1257917
Note

QC 20181023

Correction in: Annales Henri Poincare, vol. 20, issue. 8, page. 2873-2875. Doi: 10.1007/s00023-019-00819-x, WOS: 000475516100010; Scopus:2-s2.0-85068153037

Available from: 2018-10-23 Created: 2018-10-23 Last updated: 2019-10-30Bibliographically approved

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Sandberg, Mattias

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