Energy-Filtered Excited States and Real-Time Dynamics Served in a Contour Integral.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Spectroscopy

Background:

• The Cauchy Integral Formula (CIF) is a fundamental concept in complex analysis.
• Holomorphic functions of diagonalizable operators can be represented using CIF on finite domains.
• This provides a theoretical basis for applying operators via contour integrals.

Purpose of the Study:

• To develop an algorithm for finding eigen-pairs near a specified energy value within the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) framework.
• To apply this to calculate core excited states of molecules, relevant for X-ray absorption spectroscopy (XAS).
• To introduce a novel real-time electron dynamics (RT-EOM-CCSD) algorithm using the CIF.

Main Methods:

• Utilizing the Cauchy Integral Formula (CIF) for operator representation.
• Employing the Riesz projector (CIF form of the identity operator) to design an eigen-pair finding algorithm.
• Developing a real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF representation of the time-evolution operator.

Main Results:

• An algorithm is designed to find specific eigen-pairs in the EOM-CCSD framework.
• The method is applicable to calculating core excited states for X-ray absorption spectroscopy (XAS).
• A novel RT-EOM-CCSD algorithm is presented, allowing large time steps with preserved spectral accuracy.

Conclusions:

• The Cauchy Integral Formula provides a powerful tool for operator representation in quantum chemistry.
• The developed algorithms offer efficient methods for calculating molecular excited states and simulating real-time electron dynamics.
• This approach has significant implications for understanding molecular properties and spectroscopic phenomena.