Department of Chemistry, Rice University, Houston, Texas 77005, USA.
J Chem Phys. 2011 Sep 28;135(12):124108. doi: 10.1063/1.3643338.
We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.
我们推导出并实现了对称投影 Hartree-Fock-Bogoliubov（HFB）方程，并将其应用于分子电子结构问题。所有对称性（粒子数、自旋、空间和复共轭）都在自洽的变分后投影方法中被故意打破和恢复。我们表明，所得到的方法以有效的单电子（平均场）计算成本对静态相关进行全面的黑盒处理。由此产生的波函数具有多参考特征，并贯穿问题的整个 Hilbert 空间。能量表达式与常规 HFB 理论不同，但仍然是独立准粒子密度矩阵的泛函。所有约化密度矩阵都可以表示为在规范网格上对跃迁密度矩阵的积分。我们提出了几个原理验证示例，展示了投影准粒子理论在量子化学中的强大功能。
