Similarity transformed coupled cluster response (ST-CCR) theory - A time-dependent similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach

Abstract

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

A local similarity transformed equation of motion approach for calculating excited states

“…[45] However, there are other options available, including the original proposal of Nooijen and Bartlett [6] that involves transforming the STEOM singles into the space of singles and doubles and computing EOM-CCSD densities using these vectors. Landau has also worked out the linear response equations for STEOM, [46] and a simple expectation value variant of these formulae could be easily implemented with DLPNO-STEOM. As for second derivatives, these are not currently available for STEOM, but TDDFT frequencies often provide a reasonable substitute and are used together with DLPNO-STEOM within the time-dependent framework to reproduce vibrational effects.…”

A new density for transition properties within the similarity transformed equation of motion approach

“…Analytic gradients for various flavours of STEOM-CCSD have also been implemented by Nooijen and co-workers [53,54]. Landau has developed [55] a general theoretical framework for the calculation of response properties within STEOM-CC but no numerical results were reported.…”

“…It should be noted that the formulation we propose here is aimed mainly at transition properties, and to the extent it is developed here, it yields no improvement over the CIS formula for excited state rather than transition properties, such as the excited state dipole moment. The formulation of Nooijen and Bartlett [29] and Landau [55] offers a better description of these and may serve as the basis of more efficient implementations in the future.…”

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements

“…The methods belonging to category B are clearly advantageous on two counts: they provide a natural way of cancellation of common terms in the energy differences and only one N 5 transformation. These theories include Equation Of Motion Coupled Cluster (EOMCC), [13][14][15][16][17][18][19][20][21][22] Coupled Cluster Linear Response Theory (CC-LRT), 8,[23][24][25][26][27][28][29][30][31][32] Similarity-Transformed EOMCC (STEOMCC), [33][34][35][36] Symmetry Adapted Cluster Configuration Interaction (SAC-CI), [37][38][39] propagator methods with orbital relaxation, 40 Algebraic Diagrammatic Construction (ADC), 41,42 and other response-based theories. In almost all these methods, the orbitals used are those for the closed shell ground state.…”