Direct Unconstrained Optimization of Molecular Orbital Coefficients in Density Functional Theory,Journal of Chemical Theory and Computation

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Direct Unconstrained Optimization of Molecular Orbital Coefficients in Density Functional Theory
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2024-09-11 , DOI: 10.1021/acs.jctc.4c00696
Hanh D M Pham ₁ , Rustam Z Khaliullin ₁

Affiliation

One-electron orbitals in Kohn–Sham density functional theory (DFT) are typically constrained to be orthogonal during their variational optimization, leading to elaborate parameterization of the orbitals and complicated optimization algorithms. This work shows that orbital optimization can be performed with nonorthogonal orbitals if the DFT energy functional is augmented with a term that penalizes linearly dependent states. This approach, called variable-metric self-consistent field (VM SCF) optimization, allows us to use molecular orbital coefficients, natural descriptors of one-electron orbitals, as independent variables in a direct, unconstrained minimization, leading to very simple closed-form expressions for the electronic gradient and Hessian. It is demonstrated that efficient convergence of the VM SCF procedure can be achieved with a basic preconditioned conjugate gradient algorithm for a variety of systems, including challenging narrow-gap systems and spin-pure two-determinant states of singlet diradicals. This simple reformulation of the variational procedure can be readily extended to electron correlation methods with multiconfiguration states and to the optimization of excited-state orbitals.

中文翻译：

密度泛函理论中分子轨道系数的直接无约束优化

Kohn-Sham 密度泛函理论 (DFT) 中的单电子轨道在变分优化过程中通常被限制为正交，从而导致轨道的复杂参数化和复杂的优化算法。这项工作表明，如果用惩罚线性相关态的项来增强 DFT 能量泛函，则可以使用非正交轨道执行轨道优化。这种方法称为可变度量自洽场（VM SCF）优化，允许我们使用分子轨道系数（单电子轨道的自然描述符）作为直接、无约束最小化中的自变量，从而得到非常简单的封闭形式电子梯度和 Hessian 的表达式。结果表明，对于各种系统，包括具有挑战性的窄带隙系统和单重态双自由基的自旋纯二行列式状态，可以通过基本的预处理共轭梯度算法实现 VM SCF 过程的有效收敛。这种变分过程的简单重新表述可以很容易地扩展到具有多配置态的电子相关方法以及激发态轨道的优化。

更新日期：2024-09-11

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