Benchmark Calculations of Vertical Excitation Energies for Medium-Sized Molecules Using Unitary Coupled-Cluster-Based...

The unitary coupled-cluster (UCC)-based polarization propagator theory (PPT) is a novel Hermitian quantum chemical method for calculating excited states. This study benchmarks vertical excitation energies (VEEs) for medium-sized molecules using two practical schemes for UCC-PPT: UCC3 and quadratic UCCSD (qUCCSD). Their performance is evaluated and compared with the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method and the algebraic construction (ADC) family of methods (ADC(2) and ADC(3)). The qUCCSD method achieves a mean absolute deviation (MAD) of 0.21 eV and a standard deviation (SD) of 0.20 eV with respect to theoretical best estimates (TBEs), demonstrating systematic improvements over UCC3 with a 12% lower MAD and a 26% lower SD. Among the four Hermitian excited-state methods in this work, UCC-based methods excel at describing Rydberg states but tend to underestimate VEEs for both singlet and triplet excitations. Statistical analysis reveals that UCC-based approaches are competitive with ADC(3) and outperform ADC(2) in certain cases. These findings suggest that the commutator truncation scheme within the UCC framework offers a promising path for the development of UCC-based excited-state methods.