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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2501.10907 |
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| _version_ | 1866910789725585408 |
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| author | Pham, Hanh D. M. Khaliullin, Rustam Z. |
| author_facet | Pham, Hanh D. M. Khaliullin, Rustam Z. |
| contents | Orbital-optimized density functional theory (DFT) has emerged as an alternative to time-dependent (TD) DFT capable of describing difficult excited states with significant electron density redistribution, such as charge-transfer, Rydberg, and double-electron excitations. Here, a simple method is developed to solve the main problem of the excited-state optimization -- the variational collapse of the excited states onto the ground state. In this method, called variable-metric time-independent DFT (VM TIDFT), the electronic states are allowed to be nonorthogonal during the optimization but their orthogonality is gradually enforced with a continuous penalty function. With nonorthogonal electronic states, VM TIDFT can use molecular orbital coefficients as independent variables, which results in a closed-form analytical expression for the gradient and allows to employ any of the multiple unconstrained optimization algorithms that guarantees convergence of the excited-state optimization. Numerical tests on multiple molecular systems show that the variable-metric optimization of excited states performed with a preconditioned conjugate gradient algorithm is robust and produces accurate energies for well-behaved excitations and, unlike TDDFT, for more challenging charge-transfer and double-electron excitations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Direct unconstrained optimization of excited states in density functional theory Pham, Hanh D. M. Khaliullin, Rustam Z. Chemical Physics Computational Physics Orbital-optimized density functional theory (DFT) has emerged as an alternative to time-dependent (TD) DFT capable of describing difficult excited states with significant electron density redistribution, such as charge-transfer, Rydberg, and double-electron excitations. Here, a simple method is developed to solve the main problem of the excited-state optimization -- the variational collapse of the excited states onto the ground state. In this method, called variable-metric time-independent DFT (VM TIDFT), the electronic states are allowed to be nonorthogonal during the optimization but their orthogonality is gradually enforced with a continuous penalty function. With nonorthogonal electronic states, VM TIDFT can use molecular orbital coefficients as independent variables, which results in a closed-form analytical expression for the gradient and allows to employ any of the multiple unconstrained optimization algorithms that guarantees convergence of the excited-state optimization. Numerical tests on multiple molecular systems show that the variable-metric optimization of excited states performed with a preconditioned conjugate gradient algorithm is robust and produces accurate energies for well-behaved excitations and, unlike TDDFT, for more challenging charge-transfer and double-electron excitations. |
| title | Direct unconstrained optimization of excited states in density functional theory |
| topic | Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2501.10907 |