Global solutions of Hartree-Fock theory and their consequences for strongly correlated quantum systems
Global solutions of Hartree-Fock theory and their consequences for strongly correlated quantum systems
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Hartree-Fock 理论的全局解及其对强相关量子系统的影响
DOI：
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发表时间：
2013
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通讯作者：
D. Mazziotti
中科院分区：
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作者：
S. Veeraraghavan;D. Mazziotti
我们提出了一种基于半定规划（SDP）的密度矩阵方法，用于计算 Hartree-Fock 理论的全局解，该方法给出了量子系统 Hartree-Fock 能量的上限和下限。上下界能量相等保证了计算的解是Hartree-Fock理论的全局最优解。对于强相关系统，SDP 方法提供了欧拉-拉格朗日方程标准解中局部优化的 Hartree-Fock 能量和密度的替代方案。应用于H4二聚体和N2分子的势能曲线。
We present a density matrix approach for computing global solutions of Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. Equality of the upper-and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities from the standard solution of the Euler-Lagrange equations. Applications are made to the potential energy curves of the H4 dimer and the N2 molecule.