Scheme for time-determining steps in the construction of the RHS vectors ξ x .
Algorithm for the computation of the doubles contributions to the virtual/virtual and occupied/virtual block of the one-particle density D η(t x ) with a Laplace transformation for . The doubles contribution to the occupied/occupied block is evaluated in a similar loop over virtual orbitals a, b. For this, the intermediates B and K are resorted such that the virtual index is outermost.
Parallelization of orbital-unrelaxed CC2 polarizability calculations on C60, Naphthacene, and Naphthalene with and without symmetry. All calculations were done in the aug-cc-pVTZ basis and with frozen core approximation.
Change of the Laplace and convergence error in αmax of naphthacene upon variation of T LRE and . For , the points for T LRE = 10−7 and 10−8 are on top of each other.
Relative errors to the experimental values for the results in Table VIII. The numbers of the molecules are the same as in Table VIII.
Polarizability dispersion in cyclohexane, benzene, fluorobenzene, and allene. Dots and solid lines denote calculated values from CC2, while squares and dotted lines denote experimental values. Note that the two lines for allene are on top of each other and they also cover the solid line for fluorobenzene.
Expressions for the one-particle density D F, η. The expressions for and are the same as those given for the unrelaxed case in Ref. 21.
Intermediates needed for the contraction of the matrix F with the response of the amplitudes. denote two-electron integrals transformed with the response of the singles cluster amplitudes. All ERIs are calculated within the RI approximation.
Wall-clock timings for several aromatic hydrocarbons and C60. In all calculations except for C60, the full tensor was computed using the aug-cc-pVTZ basis32,33 with the corresponding auxiliary basis34 and the frozen core for approximation for the 1s orbitals of the carbon atoms. N m is the number of sampling points for the numerical Laplace transformation.
Results for polarizability calculations on helicene molecules. N m denotes the number of Laplace sampling points, while α is the isotropic average of the dipole polarizability. All calculations were carried out on 12 Intel(R) Xeon(R) X5670 CPUs with 2.93 GHz. The CPHF equations for the MP2 calculations were solved with exact four-index ERIs after a preoptimization using the RI approximation.
Relative errors in the polarizabilities due to limited convergence of the response equations and the numerical Laplace transformations for different thresholds T LRE and .
Mean absolute deviations due to the RI approximation in the MP2 part and the solution of the CPHF equations. The total RI error was calculated as mean absolute deviation between RI-CPHF/RI-MP2 and CPHF/MP2 and the RI-CPHF error as the mean absolute deviation between calculations using four-index ERIs and RI-CPHF for the solution of the CPHF equations. The RI-MP2 error was determined as mean absolute deviation between calculations using MP2 and RI-MP2 for the correlation part, respectively. The listed deviations in the errors are the sample-based standard deviations of the mean absolute deviations.
Average one-electron basis set errors in dipole-dipole polarizabilities. The errors in the given values are standard deviations.
Static polarizability data from calculation and experiment. All values are given in atomic units.
Frequency-dependent polarizabilities (in a.u.) for some organic molecules from unrelaxed CC2 calculations, from a combination of relaxed MP2 with the unrelaxed CC2 dispersion (αComb) and experiment (Expt.). Experimental data are from Ref. 47 if not stated otherwise. Apart from C60, which was measured by a light force technique, all experimental data are from refractive index measurements. 48
Ratios between frequency-dependent polarizabilities for cyclopropane, but-2-yne, and hexafluorobenzene.
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