Canonical quantum observables for molecular systems approximated by ab initio molecular dynamics

• It is known that ab initio molecular dynamics based on the electron ground state eigenvaluecan be used to approximate quantum observables in the canonical ensemble when the temperature is low compared tothe 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 semi-classical Weyl law to show thatcanonical 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 resultincludes observables that depend on correlations in time. A combination of the Hilbert-Schmidt inner product for quantum operators and Weyl's lawshows 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 positionand the observables are in diagonal form with respect to the electron eigenstates.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Numerical Analysis

Numerisk analys

Publication and Content Type

ref (subject category)

art (subject category)