通过施加精确条件改进近似优化的有效势：电子静力学和动力学的理论和应用
Improving approximate-optimized effective potentials by imposing exact conditions: Theory and applications to electronic statics and dynamics
摘要：
我们发展了一种方法，可以限制任何局部交换相关势，以保持基本的精确条件。使用拉格朗日乘子的方法，我们计算的每一组给定的Kohn-Sham轨道，约束保持的潜力，这是最接近给定的交换相关势。该方法适用于时间相关（TD）和独立的情况。对于时间无关的情况，强制执行的确切条件是：伽利略协方差，零净力和力矩，Levy-Perdew维里定理。对于TD的情况下，我们强制平移协方差，零净力，Levy-Perdew维里定理和能量平衡。我们测试我们的方法上交换Krieger-Li-Iafrate（xKLI）近似优化的有效电位（AOEP），这两种情况下。在与时间无关的情况下，我们计算了一些氢链和小钠团簇的基态性质，考虑了xKLI势和HF交换的约束。结果表明，强制执行的确切条件是不重要的，这些情况下。另一方面，在这种情况下，约束能量平衡和零净力产生改进的结果相对于TDHF计算。研究了连续激光脉冲驱动下钠原子团簇中的电子动力学。对于每个激光脉冲，我们比较了TD约束xKLI，TD部分约束xKLI和TDHF的计算。我们发现，电子动力学，如电子电离和转动惯量动力学的约束xKLI是最相似的TDHF的结果。此外，能量守恒相对于无约束的xKLI至少好一个数量级。我们还讨论了在非CW驱动力的TD情况下满足约束时出现的问题。
英文摘要：
We develop a method that can constrain any local exchange-correlation potential to preserve ba-sic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals, a constraint-preserving potential which is closest to the given exchange-correlation potential. The method is applicable to both the time-dependent (TD) and independent cases. The exact conditions that are enforced for the time-independent case are: Galilean covariance, zero net force and torque, and Levy-Perdew virial theorem. For the TD case we enforce translational covariance, zero net force, the Levy-Perdew virial theorem and energy balance. We test our method on the exchange Krieger-Li-Iafrate (xKLI) approximate-optimized effective potential (AOEP), for both cases. For the time-independent case, we calculated the ground state properties of some hydrogen chains and small sodium clusters, for some constrained xKLI potentials and Hartree-Fock (HF) exchange. The results indicate that enforcing the exact conditions is not important for these cases. On the other hand, in the case, constraining both energy balance and zero net force yields improved results relative to TDHF calculations. We explored the electron dynamics in small sodium clusters driven by CW laser pulses. For each laser pulse we compared calculations from TD constrained xKLI, TD partially constrained xKLI and TDHF. We found that electron dynamics like elec-tron ionization and moment of inertia dynamics for the constrained xKLI are most similar to the TDHF results. Also, energy conservation is better by at least an order of magnitude with respect to the unconstrained xKLI. We also discuss the problems that arise in satisfying constraints in the TD case with a non CW driving force.
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