Energy-filtered excited states and real-time dynamics served in a contour integral

TL;DR

This paper introduces a contour integral-based approach for energy-filtered excited states and real-time dynamics, enabling efficient eigenstate targeting and large time steps in quantum chemistry calculations.

Contribution

It develops a novel contour integral framework for eigenstate filtering and real-time electron dynamics within the EOM-CCSD method, enhancing computational efficiency and spectral accuracy.

Findings

Effective eigenstate filtering using contour integrals.

Large time steps in real-time electron dynamics simulations.

Accurate calculation of core excited states for X-ray spectroscopy.

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 an 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.