Energy-filtered excited states and real-time dynamics served in a contour integral
- URL: http://arxiv.org/abs/2409.07354v1
- Date: Wed, 11 Sep 2024 15:39:50 GMT
- Title: Energy-filtered excited states and real-time dynamics served in a contour integral
- Authors: Ke Liao,
- Abstract summary: The Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain.
I showcase a novel real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF form of the exponential time-evolution operator.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: It is observed that the Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain. This forms the theoretical foundation for applying various operators in the form of a contour integral to a state, while filtering away eigen-components that are not included by the contour. As a special case, the identity operator in the integral form--the Riesz projector--is used to design a black-box algorithm for finding a given number of eigen-pairs whose energies are close to a specified value in the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) framework, with applications to calculate core excited states of molecules which is relevant for the X-ray absorption spectroscopy (XAS). As a generalization, I showcase a novel real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF form of the exponential time-evolution operator, which admits extremely large time steps while preserving accurate spectral information.
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