Analytic Gradients for Equation-of-Motion Coupled Cluster with Single, Double, and Perturbative Triple Excitations

Understanding the process of molecular photoexcitation
is crucial
in various fields, including drug development, materials science,
photovoltaics, and more. The electronic vertical excitation energy
is a critical property, for example in determining the singlet–triplet
gap of chromophores. However, a full understanding of excited-state
processes requires additional explorations of the excited-state potential
energy surface and electronic properties, which is greatly aided by
the availability of analytic energy gradients. Owing to its robust
high accuracy over a wide range of chemical problems, equation-of-motion
coupled cluster with single and double excitations (EOM-CCSD) is a
powerful method for predicting excited-state properties, and the implementation
of analytic gradients of many EOM-CCSD variants (excitation energies,
ionization potentials, electron attachment energies, etc.) along with
numerous successful applications highlights the flexibility of the
method. In specific cases where a higher level of accuracy is needed
or in more complex electronic structures, the inclusion of triple
excitations becomes essential, for example, in the EOM-CCSD* approach
of Saeh and Stanton. In this work, we derive and implement for the
first time the analytic gradients of EOMEE-CCSD*, which also provides
a template for analytic gradients of related excited-state methods
with perturbative triple excitations. The capabilities of analytic
EOMEE-CCSD* gradients are illustrated by several representative examples.