Analytic Gradients\nfor Equation-of-Motion Coupled\nCluster with Single, Double, and Perturbative Triple Excitations

Understanding the process of molecular photoexcitation\nis crucial\nin various fields, including drug development, materials science,\nphotovoltaics, and more. The electronic vertical excitation energy\nis a critical property, for example in determining the singlet–triplet\ngap of chromophores. However, a full understanding of excited-state\nprocesses requires additional explorations of the excited-state potential\nenergy surface and electronic properties, which is greatly aided by\nthe availability of analytic energy gradients. Owing to its robust\nhigh accuracy over a wide range of chemical problems, equation-of-motion\ncoupled cluster with single and double excitations (EOM-CCSD) is a\npowerful method for predicting excited-state properties, and the implementation\nof analytic gradients of many EOM-CCSD variants (excitation energies,\nionization potentials, electron attachment energies, etc.) along with\nnumerous successful applications highlights the flexibility of the\nmethod. In specific cases where a higher level of accuracy is needed\nor in more complex electronic structures, the inclusion of triple\nexcitations becomes essential, for example, in the EOM-CCSD* approach\nof Saeh and Stanton. In this work, we derive and implement for the\nfirst time the analytic gradients of EOMEE-CCSD*, which also provides\na template for analytic gradients of related excited-state methods\nwith perturbative triple excitations. The capabilities of analytic\nEOMEE-CCSD* gradients are illustrated by several representative examples.