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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14607 |
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| _version_ | 1866913439131107328 |
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| author | Culpitt, Tanner Tellgren, Erik I. Peters, Laurens D. M. Helgaker, Trygve |
| author_facet | Culpitt, Tanner Tellgren, Erik I. Peters, Laurens D. M. Helgaker, Trygve |
| contents | Non-adiabatic coupling matrix elements (NACMEs) are important in quantum chemistry, particularly for molecular dynamics methods such as surface hopping. However, NACMEs are gauge dependent. This presents a difficulty for their calculation in general, where there are no restrictions on the gauge function except that it be differentiable. These cases are relevant for complex-valued electronic wave functions, such as those that arise in the presence of a magnetic field or spin-orbit coupling. Additionally, the Berry curvature and Berry force play an important role in molecular dynamics in a magnetic field, and are also relevant in the context of spin-orbit coupling. For methods such as surface hopping, excited-state Berry curvatures will also be of interest. With this in mind, we have developed a scheme for the calculation of continuous, differentiable NACMEs as a function of the molecular geometry for complex-valued wave functions. We demonstrate the efficacy of the method by using the H$_2$ molecule at the full configuration-interaction (FCI) level of theory. Additionally, ground- and excited- state Berry curvatures are computed for the first time using FCI theory. Finally, Berry phases are computed directly in terms of diagonal NACMEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-adiabatic coupling matrix elements in a magnetic field: geometric gauge dependence and Berry phase Culpitt, Tanner Tellgren, Erik I. Peters, Laurens D. M. Helgaker, Trygve Chemical Physics Non-adiabatic coupling matrix elements (NACMEs) are important in quantum chemistry, particularly for molecular dynamics methods such as surface hopping. However, NACMEs are gauge dependent. This presents a difficulty for their calculation in general, where there are no restrictions on the gauge function except that it be differentiable. These cases are relevant for complex-valued electronic wave functions, such as those that arise in the presence of a magnetic field or spin-orbit coupling. Additionally, the Berry curvature and Berry force play an important role in molecular dynamics in a magnetic field, and are also relevant in the context of spin-orbit coupling. For methods such as surface hopping, excited-state Berry curvatures will also be of interest. With this in mind, we have developed a scheme for the calculation of continuous, differentiable NACMEs as a function of the molecular geometry for complex-valued wave functions. We demonstrate the efficacy of the method by using the H$_2$ molecule at the full configuration-interaction (FCI) level of theory. Additionally, ground- and excited- state Berry curvatures are computed for the first time using FCI theory. Finally, Berry phases are computed directly in terms of diagonal NACMEs. |
| title | Non-adiabatic coupling matrix elements in a magnetic field: geometric gauge dependence and Berry phase |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2407.14607 |