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引用次数: 0
摘要
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约束为正交,从而导致轨道参数化和优化算法复杂化。这项研究表明,如果在 DFT 能量函数中增加一个惩罚线性相关状态的项,就可以用非正交轨道进行轨道优化。这种方法被称为可变参数自洽场(VM SCF)优化,它允许我们在直接、无约束的最小化过程中使用分子轨道系数(单电子轨道的自然描述符)作为独立变量,从而得到非常简单的电子梯度和赫塞斯闭式表达式。研究表明,对于各种系统,包括具有挑战性的窄间隙系统和单二元化合物的自旋纯二决定态,可以通过基本的预处理共轭梯度算法实现 VM SCF 程序的高效收敛。这种变分过程的简单重述可以很容易地扩展到多构型态的电子相关方法和激发态轨道的优化。
Direct Unconstrained Optimization of Molecular Orbital Coefficients in Density Functional Theory
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.
期刊介绍:
The Journal of Chemical Theory and Computation invites new and original contributions with the understanding that, if accepted, they will not be published elsewhere. Papers reporting new theories, methodology, and/or important applications in quantum electronic structure, molecular dynamics, and statistical mechanics are appropriate for submission to this Journal. Specific topics include advances in or applications of ab initio quantum mechanics, density functional theory, design and properties of new materials, surface science, Monte Carlo simulations, solvation models, QM/MM calculations, biomolecular structure prediction, and molecular dynamics in the broadest sense including gas-phase dynamics, ab initio dynamics, biomolecular dynamics, and protein folding. The Journal does not consider papers that are straightforward applications of known methods including DFT and molecular dynamics. The Journal favors submissions that include advances in theory or methodology with applications to compelling problems.