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Excited state polarizabilities for CC2 using the resolution-of-the-identity approximation

Nora K. Graf^{a}, Daniel H. Friese^{b}, Nina O. C. Winter^{c} and
Christof Hättig^{a}
^{a}
Lehrstuhl für Theoretische Chemie,
Ruhr-Universität Bochum,
D-44801 Bochum, Germany

^{b}
Centre for Theoretical and Computational Chemistry CTCC,
Department of Chemistry, University of Tromsø
N-9037 Tromsø Norway

^{c}
Cluster of Excellence RESOLV,
Ruhr-Universität Bochum,
D-44801 Bochum, Germany

*J. Chem. Phys.*, **143**, 244108 (2015)

(Received 13 October 2015; accepted 2 December 2015)

We report an implementation of static and frequency-dependent excited state polarizabilities for the
approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an
excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and
the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations
in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations
can be solved without storage of the double excitation part of the eigenvectors. By exploiting
the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic
scaling of the main memory demands of RI-CC2 with the system size could be preserved. This
enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes
up to decacene with almost 2500 basis functions on a single compute node within a few days.
For a test set of molecules where measurements are available as reference data, we compare the
orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach
can be easily extended to other response methods, in particular CIS(D_{∞}). The latter gives results
which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster
singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference
data.

(c) 2015 American Institute of Physics. [doi:/10.1063/1.4937944]

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