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

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 Moller-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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4704788]