Cluster perturbation theory. XI. Excitation-energy series using a variational excitation-energy function

作     者：Hillers-Bendtsen, Andreas Erbs Johansen, Magnus Bukhave von Buchwald, Theo Juncker Mikkelsen, Kurt V. Olsen, Jeppe Jorgensen, Poul Helgaker, Trygve 

作者机构：Univ Copenhagen Dept Chem Univ Pk 5 DK-2100 Copenhagen O Denmark Tech Univ Denmark DTU Chem Kemitorvet Bldg 206 DK-2800 Lyngby Denmark Aarhus Univ Dept Chem Langelandsgade 140 DK-8000 Aarhus C Denmark Univ Oslo Hylleraas Ctr Quantum Mol Sci Dept Chem POB 1033 Blindern N-0315 Oslo Norway 

出 版 物：《JOURNAL OF CHEMICAL PHYSICS》 (J Chem Phys)

年 卷 期：2025年第162卷第2期

页      面：024114页

核心收录：

学科分类：081704[工学-应用化学] 07[理学] 070304[理学-物理化学(含∶化学物理)] 08[工学] 0817[工学-化学工程与技术] 0703[理学-化学] 0702[理学-物理学] 

基　　金：Danish Agency for Science and Higher Educationhttps://doi.org/10.13039/501100001825 [DFF-0136-00081B, DFF-10.46540/3103-00261B] Danish Council for Independent Research European Union Norwegian Research Council through the Hylleraas Center for Quantum Molecular Sciences 

主　　题：Eigenvalues and eigenfunctions 

摘      要：Traditionally, excitation energies in coupled-cluster (CC) theory have been calculated by solving the CC Jacobian eigenvalue equation. However, based on our recent work [J & oslash;rgensen et al., Sci. Adv. 10, eadn3454 (2024)], we propose a reformulation of the calculation of excitation energies where excitation energies are determined as a conventional molecular property. To this end, we introduce an excitation-energy function that depends on the CC Jacobian and the right and left eigenvectors for the Jacobian eigenvalue problem. This excitation-energy function is variational with respect to the right and left eigenvectors but not with respect to the cluster amplitudes. Instead, the cluster amplitudes satisfy the cluster-amplitude equations, and we set up an excitation-energy Lagrangian by adding to the excitation-energy function the cluster-amplitude equations with an undetermined multiplier for each cluster-amplitude constraint. The excitation-energy Lagrangian is variational in all its parameters. Based on the variational property of the Lagrangian, we have determined two quadratically convergent excitation-energy series: the total-order cluster-perturbation (tCP) and variational cluster-perturbation (vCP) excitation-energy series. Calculations of the excitation energies of three small molecules have shown that the vCP series is to be preferred over the tCP series. The test calculations have been carried out for CPS(D) expansions [targeting the CC singles-and-doubles (CCSD) wave function from the CC singles wave function] and the CPSD(T) expansion [targeting the CC singles-doubles-triples (CCSDT) wave function from the CCSD wave function]. For the S(D) and SD(T) orbital excitation space calculations, we obtain in the second vCP iteration excitation energies with a mean deviation from CCSD excitation energies of about 0.04 eV for the S(D) orbital spaces, and for the SD(T) orbital space calculation, we obtain a mean deviation from the CCSDT excitation energies of