Richer Michelle, Kim Taewon D, Ayers Paul W
Department of Chemistry Queen's University Ontario Canada.
Department of Chemistry & Chemical Biology McMaster University Ontario Canada.
Int J Quantum Chem. 2025 Jan 5;125(1):e70000. doi: 10.1002/qua.70000. Epub 2024 Dec 20.
We consider wavefunctions built from antisymmetrized products of two-electron wavefunctions (geminals), which is arguably the simplest extension of the antisymmetrized product of one-electron wavefunctions (orbitals) (i.e., a Slater determinant). Extensive use of geminals in wavefunctions has been limited by their high cost stemming from the many combinations of the two-electron basis functions (orbital pairs) used to build the geminals. When evaluating the overlap of the APG wavefunction with an orthogonal Slater determinant, this cost can be interpreted as the cost of evaluating the permanent, resulting from the symmetry with respect to the interchange of orbital pairs, and the cost of assigning the occupied orbitals to the orbital pairs of the wavefunction. Focusing on the latter, we present a graphical interpretation of the Slater determinant and utilize the maximum weighted matching algorithm to estimate the combination of orbital pairs with the largest contribution to the overlap. Then, the cost due to partitioning the occupied orbitals in the overlap is reduced from to . Computational results show that many of these combinations are not necessary to obtain an accurate solution to the wavefunction. Because the APG wavefunction is the most general of the geminal wavefunctions, this approach can be applied to any of the simpler geminal wavefunction ansätze. In fact, this approach may even be extended to generalized quasiparticle wavefunctions, opening the door to tractable wavefunctions built using components of arbitrary numbers of electrons, not just two electrons.
我们考虑由双电子波函数（双粒子态）的反对称化乘积构建的波函数，这可以说是单电子波函数（轨道）的反对称化乘积（即斯莱特行列式）最简单的扩展。双粒子态在波函数中的广泛应用受到其高成本的限制，这种高成本源于用于构建双粒子态的双电子基函数（轨道对）的多种组合。在评估反对称化乘积波函数与正交斯莱特行列式的重叠时，这种成本可以解释为评估永久式的成本，这是由于轨道对交换的对称性以及将占据轨道分配给波函数的轨道对的成本导致的。着眼于后者，我们给出了斯莱特行列式的图形解释，并利用最大加权匹配算法来估计对重叠贡献最大的轨道对组合。然后，重叠中由于划分占据轨道而产生的成本从 降低到 。计算结果表明，获得波函数的精确解并不需要许多这些组合。由于反对称化乘积波函数是双粒子态波函数中最一般的，这种方法可以应用于任何更简单的双粒子态波函数假设。实际上，这种方法甚至可以扩展到广义准粒子波函数，为使用任意数量电子（不仅仅是两个电子）的组件构建易于处理的波函数打开了大门。
