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Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the-identity approximation

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10.1063/1.4704788

### Abstract

We present an implementation of static and frequency-dependent polarizabilities for the approximate coupled cluster singles and doubles model CC2 and static polarizabilities for second-order Møller-Plesset perturbation theory. Both are combined with the resolution-of-the-identity approximation for electron repulsion integrals to achieve unprecedented low operation counts, input–output, and disc space demands. To avoid the storage of double excitation amplitudes during the calculation of derivatives of density matrices, we employ in addition a numerical Laplace transformation for orbital energy denominators. It is shown that the error introduced by this approximation is negligible already with a small number of sampling points. Thereby an implementation of second-order one-particle properties is realized, which avoids completely the storage of quantities scaling with the fourth power of the system size. The implementation is tested on a set of organic molecules including large fused aromatic ring systems and the C_{60} fullerene. It is demonstrated that exploiting symmetry and shared memory parallelization, second-order properties for such systems can be evaluated at the CC2 and MP2 level within a few hours of calculation time. As large scale applications, we present results for the 7-, 9-, and 11-ring helicenes.

© 2012 American Institute of Physics

Received 29 February 2012
Accepted 04 April 2012
Published online 02 May 2012

Acknowledgments: The authors acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) through Grant No. HA 2588/5-1. D.H.F also acknowledges the financial support by the Studienstiftung des Deutschen Volkes through a PhD scholarship.

Article outline:

I. INTRODUCTION

II. THEORY

A. The CC2 Lagrangian

B. Derivatives of the Lagrangian

C. Response of the amplitudes

D. First-order densities and effective Fock matrices

E. The expectation value of

F. Contraction with the cluster amplitude Hessian **F**

III. IMPLEMENTATION

A. The effective right-hand-side vector ξ^{eff}

B. First-order one-particle densities

IV. APPLICATIONS

A. Computational efficiency and large scale application

B. Accuracy of the numerical Laplace transformation

C. RI and one-electron basis set error

D. Comparison with experimental data

V. CONCLUSIONS

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/content/aip/journal/jcp/136/17/10.1063/1.4704788

2012-05-02

2014-04-19

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