Sverrisdóttir Svala, Faulstich Fabian M
Department of Mathematics, The University of California, Berkeley, California 94720, United States.
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York 12180, United States.
J Chem Theory Comput. 2024 Oct 8;20(19):8517-8528. doi: 10.1021/acs.jctc.4c00644. Epub 2024 Sep 17.
The exploration of the root structure of coupled cluster (CC) equations holds both foundational and practical significance for computational quantum chemistry. This study provides insight into the intricate root structures of these nonlinear equations at both the CCD and CCSD level of theory. We utilize computational techniques from algebraic geometry, specifically the monodromy and parametric homotopy continuation methods, to calculate the full solution set. We compare the computed CC roots against various established theoretical upper bounds, shedding light on the accuracy and efficiency of these bounds. We hereby focus on the dissociation processes of four-electron systems such as (H) in both D and D configurations, H symmetrically distorted on a circle, and lithium hydride. We moreover investigate the ability of single-reference CC solutions to approximate excited state energies. We find that multiple CC roots describe energies of excited states with high accuracy. Our investigations reveal that for systems like lithium hydride, CC not only provides high-accuracy approximations to several excited state energies but also to the states themselves.
耦合簇（CC）方程根结构的探索对于计算量子化学具有基础和实际意义。本研究深入了解了这些非线性方程在CCD和CCSD理论水平上的复杂根结构。我们利用代数几何中的计算技术，特别是单值性和参数同伦延拓方法，来计算完整的解集。我们将计算得到的CC根与各种已建立的理论上限进行比较，从而揭示这些上限的准确性和效率。在此，我们专注于四电子体系的解离过程，如处于D和D构型的（H）、在圆上对称扭曲的H以及氢化锂。此外，我们还研究了单参考CC解近似激发态能量的能力。我们发现多个CC根能够高精度地描述激发态的能量。我们的研究表明，对于氢化锂这样的体系，CC不仅能对几个激发态能量提供高精度近似，还能对这些态本身提供高精度近似。
