投影Hartree-Fock理论
Projected Hartree-Fock Theory
摘要：
投影哈特里-福克理论（PHF）在量子化学中有着悠久的历史。PHF在这里被理解为N电子对称性破缺斯莱特行列式的变分确定，其使具有正确量子数的投影态的能量最小化。这种方法被积极地推行了几十年，但似乎已经被放弃了。在这里，我们推导并实现了“投影后的变化”PHF理论使用的技术不同于那些以前在量子化学。我们的PHF方法具有适度的平均场计算成本，产生相对简单的表达式，可以应用于共线和非共线自旋的情况下，并可以与故意的对称性破缺和恢复其他分子的对称性，如复共轭和点群。我们提出了几个基准应用程序的解离曲线和单重态-三重态能量分裂，表明所得到的PHF波函数是高质量的多参考字符。我们还提供了数值证据表明，在热力学极限，在PHF的能量不低于对称性破缺HF，一个简单的后果，缺乏大小的一致性和扩展性的PHF。
英文摘要：
Projected Hartree-Fock theory (PHF) has a long history in quantum chemistry. PHF is here understood as the variational determination of an N-electron broken symmetry Slater determinant that minimizes the energy of a projected state with the correct quantum numbers. The method was actively pursued for several decades but seems to have been abandoned. We here derive and implement a "variation after projection" PHF theory using techniques different from those previously employed in quantum chemistry. Our PHF methodology has modest mean-field computational cost, yields relatively simple expressions, can be applied to both collinear and non-collinear spin cases, and can be used in conjunction with deliberate symmetry breaking and restoration of other molecular symmetries like complex conjugation and point group. We present several benchmark applications to dissociation curves and singlet-triplet energy splittings, showing that the resulting PHF wavefunctions are of high quality multireference character. We also provide numerical evidence that in the thermodynamic limit, the energy in PHF is not lower than that of broken-symmetry HF, a simple consequence of the lack of size consistency and extensivity of PHF.
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