Similarities and differences of the Lagrange formalism and the intermediate state representation in the treatment of molecular properties

Abstract

When dealing with approximate wave functions, molecular properties can be computed either as expectation values or as derivatives of the energy with respect to a corresponding perturbation. In this work, the intermediate state representation (ISR) formalism for the computation of expectation values is compared to the Lagrange formalism following a derivative ansatz, which are two alternative approaches of which neither one can be considered superior in general. Within the ISR formalism, terms are included up to a given order of perturbation theory only, while in the Lagrange formalism, all terms are accounted for arising through the differentiation. Similarities and differences of the Lagrange and ISR formalism are illustrated using explicit working equations for selected methods and analyzing numerical results for a range of coupled-cluster as well as algebraic-diagrammatic construction (ADC) methods for excited states. The analysis explains why the ADC(3/2) method is able to yield a large amount of the orbital-relaxation effects for p-h states in contrast to ADC(2) although the same second-order ISR is used to represent the corresponding operator.

Complex Excited State Polarizabilities in the ADC/ISR Framework

“…the anisotropy of the polarizability (∆α = 1 2 (α yy + α xx ) − α zz ) is reported as 5.4 and 45.2 au for the ground state and the lowest singlet state, respectively. 42 For the pyrimidine molecule, a similar trend is observed for the agreement between computational results, which are shown in 26 This explains the trends observed for the employed ADC schemes.…”

Complex excited state polarizabilities in the ADC/ISR framework

“…In a recent study, it has been demonstrated that ADC(3) yields orbital relaxation effects for p − h excited states through higher order of perturbation theory by including 2p − 2h states. 26 This explains the trends observed for the employed ADC schemes.…”

“…34,35 In all ADC calculations, the second-order ISR was employed. 4,6,26 In combination with third-order ADC, this results in the ADC(3/2) approximation which is referred to as ADC(3) throughout this paper. For consistency, the calculations using the EOM-CCSD derivative and expectation-value approaches were repeated from Ref.…”

“…A comparative analysis of these approaches has recently been conducted for ADC methods. 26 For excited state polarizabilities, both approaches have been reported for equation-of-motion coupled-cluster with singles and doubles (EOM-CCSD). 12,21,27,28 The ISRbased ansatz described in this work is comparable to the expectation-value coupled-cluster approach to molecular properties, and both methods will be analyzed and compared to experimental Complex Excited State Polarizabilities using ADC data where available.…”

QUESTDB: A database of highly accurate excitation energies for the electronic structure community

“…Regarding future improvements and extensions, we would like to mention that although our present goal is to produce chemically accurate vertical excitation energies, we are currently devoting great efforts to obtain highly accurate excited‐state properties 225, 226 such as dipoles and oscillator strengths for molecules of small and medium sizes, 227, 228 so as to complete previous efforts aiming at determining accurate excited‐state geometries 172, 229 . In this context, methods for which one has access to analytic nuclear gradients (e.g., ADC(2), CC2, and EOM‐CCSD) and frequencies (e.g., TD‐DFT) have an indisputable edge.…”