CC2 oscillator strengths within the local framework for calculating excitation energies (LoFEx)

Abstract

In a recent work [P. Baudin and K. Kristensen, J. Chem. Phys. 144, 224106 (2016)], we introduced a local framework for calculating excitation energies (LoFEx), based on second-order approximated coupled cluster (CC2) linear-response theory. LoFEx is a black-box method in which a reduced excitation orbital space (XOS) is optimized to provide coupled cluster (CC) excitation energies at a reduced computational cost. In this article, we present an extension of the LoFEx algorithm to the calculation of CC2 oscillator strengths. Two different strategies are suggested, in which the size of the XOS is determined based on the excitation energy or the oscillator strength of the targeted transitions. The two strategies are applied to a set of medium-sized organic molecules in order to assess both the accuracy and the computational cost of the methods. The results show that CC2 excitation energies and oscillator strengths can be calculated at a reduced computational cost, provided that the targeted transitions are local compared to the size of the molecule. To illustrate the potential of LoFEx for large molecules, both strategies have been successfully applied to the lowest transition of the bivalirudin molecule (4255 basis functions) and compared with time-dependent density functional theory.

Reduced-Scaling Correlation Methods for the Excited States of Large Molecules: Implementation and Benchmarks for the Second-Order Algebraic-Diagrammatic Construction Approach

“…For this purpose, a set of realistic systems containing 51–127 atoms was assembled. These widely-studied molecules were taken from the literature, ,,− ,,,, and most of them are real challenges for local excited-state methods because they have Rydberg or CT excitations, as well as conjugated or delocalized electronic structures. Our test set includes two borondipyrromethene-flavin dyads [Flv­(a) and Flv­(b)], the above dyad molecule, a perylene bisimide derivative (bisimide derivative), leupeptin, met-enkephalin, D21L6, and the pyrene-phenothiazine-isoalloxazine triad (triad) .…”

“…To demonstrate the applicability of the method, additional calculations were carried out for even larger systems including up to 400 atoms and 13000 AOs. Two of the selected compounds (C60Im-ZnP-BDP and WW-6 dye) play important roles in photovoltaics, − bivalirudin is a notable synthetic polypeptide in biochemistry, and the hydrated formamide (FA) model is an excellent system to study the effects of the explicit solvation . The structure of the molecules is depicted in the Supporting Information.…”

“…Thereafter, Korona, Schütz, Kats, and their co-workers developed various excited-state CC methods using local approaches. − In later publications, the development of local CC2 and ADC(2) methods was reported, , which were also extended to the calculation of molecular properties and improved with Laplace transform techniques. − Parallel to those efforts, further articles were published by Russ and Crawford about the calculation of excited-state properties. , Promising results were also obtained by Hättig and Helmich extending the pair NO (PNO) approach to excited-state theories. − The chain of spheres exchange and the back-transformed PNO-based − approaches developed by Izsák et al, and the state-averaged PNO-EOM-CCSD scheme of Valeev et al represent further cost reducing ideas in this category. The recent local framework for calculating excitation energies (LoFEx) − and the correlated natural transition orbital framework (CorNFLEx) approaches of Baudin and Kristensen introduce somewhat different strategies. The latter is an encouraging combination of the NO and the local approaches, where the reduced domains of the MOs are constructed by analyzing an approximate second-order density matrix and considering distance criteria for the orbitals.…”

Reduced-Scaling Approach for Configuration Interaction Singles and Time-Dependent Density Functional Theory Calculations Using Hybrid Functionals

“…The calculated excitation energies are close to those determined by experimental measurements 110 and higher-order theoretical methods. 99,111 Furthermore, in the case of the S 1 transition, the MOs involved in the excitation are located on the chromophore group (11-cisretinal protonated Schiff base, SBH + ) of the system. In contrast, at the DFT level every transition is a CT excitation with unusually low excitation energy, and the MOs of the chromophore group are not involved in the excitations in any case.…”

A simple scheme for calculating approximate transition moments within the equation of motion expectation value formalism

“…12 Transition properties for generalized coupled cluster wave functions have been implemented by Kállay and Gauss using string-based algorithms. 13 A very efficient implementation of transition dipole moments within the framework of CC2 theory has been reported by Hättig and Köhn using the densityfitting/resolution of the identity approach 14 and Baudin et al 15 as well as Schütz and co-workers 16 using the local correlation approach. The implementation of transition dipole moments for other variants of coupled cluster or related methods, such as similarity transformed EOMCC (STEOMCC), 17 Fock space multireference coupled cluster (FSMRCC), 18,19 and symmetry adapted cluster/configuration interaction (SAC-CI), 20 has also been reported.…”