Critical point search and linear response theory for computing electronic excitation energies of molecular systems. Part II. CASSCF
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arXiv
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| Format: | Preprint |
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2026
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| author | Grazioli, Laura Hu, Yukuan Nottoli, Tommaso Lipparini, Filippo Cancès, Eric |
| author_facet | Grazioli, Laura Hu, Yukuan Nottoli, Tommaso Lipparini, Filippo Cancès, Eric |
| contents | The computation of excited states within the Complete Active Space Self-Consistent Field (CASSCF) framework remains a significant challenge in quantum chemistry, both theoretically and algorithmically. In this work, we extend the Kähler manifold formalism introduced in Part I of this series to the CASSCF theory, and draw a geometrical connection from the time-dependent CASSCF equations to state-specific and linear response methodologies for excited states. This is achieved by first investigating the underlying CASSCF manifold and identifying its Kähler structure, which is complicated by the nontrivial coupling of CI and orbital degrees of freedom. Building on these theoretical findings, we derive the CASSCF linear response equations in a straightforward manner, and develop a robust state-specific method that relies solely on first-order derivatives of the CASSCF energy functional. Numerical results on representative molecular systems-water, formaldehyde, and ethylene-demonstrate the effectiveness of the proposed state-specific method, while revealing the difficulty of reliable identification of excited states due to nonlinearity induced by the CASSCF theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical point search and linear response theory for computing electronic excitation energies of molecular systems. Part II. CASSCF Grazioli, Laura Hu, Yukuan Nottoli, Tommaso Lipparini, Filippo Cancès, Eric Chemical Physics The computation of excited states within the Complete Active Space Self-Consistent Field (CASSCF) framework remains a significant challenge in quantum chemistry, both theoretically and algorithmically. In this work, we extend the Kähler manifold formalism introduced in Part I of this series to the CASSCF theory, and draw a geometrical connection from the time-dependent CASSCF equations to state-specific and linear response methodologies for excited states. This is achieved by first investigating the underlying CASSCF manifold and identifying its Kähler structure, which is complicated by the nontrivial coupling of CI and orbital degrees of freedom. Building on these theoretical findings, we derive the CASSCF linear response equations in a straightforward manner, and develop a robust state-specific method that relies solely on first-order derivatives of the CASSCF energy functional. Numerical results on representative molecular systems-water, formaldehyde, and ethylene-demonstrate the effectiveness of the proposed state-specific method, while revealing the difficulty of reliable identification of excited states due to nonlinearity induced by the CASSCF theory. |
| title | Critical point search and linear response theory for computing electronic excitation energies of molecular systems. Part II. CASSCF |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2604.13753 |