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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2409.07354 |
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| _version_ | 1866913930889134080 |
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| author | Liao, Ke |
| author_facet | Liao, Ke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy-filtered excited states and real-time dynamics served in a contour integral Liao, Ke Chemical Physics Quantum Physics 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. |
| title | Energy-filtered excited states and real-time dynamics served in a contour integral |
| topic | Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2409.07354 |