Speeding up equation of motion coupled cluster theory with the chain of spheres approximation

Abstract

In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm(-1) (59 μHartree) for excitation energies and 6.799 cm(-1) (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.

Systematic High‐Accuracy Prediction of Electron Affinities for Biological Quinones

“…However, the O(N 5 ) scaling of the iterative process and O(N 6 ) scaling of the ground state CCSD step, as well as the huge storage requirements of canonical EA‐EOM‐CCSD makes it difficult to use on the molecules included in our test set. The bt‐PNO‐EOM‐CCSD scheme of Izsák and coworkers, which involves the use of back‐transformed pair natural orbitals, has lower scaling for the ground state calculation as well as for the most expensive EA‐EOM term, much smaller storage requirements, and gives almost identical electron affinity as that of the canonical EA‐EOM‐CCSD. Here, to obtain adiabatic EA values for comparison to experiment, two separate calculations need to be performed, one at the optimized geometry of the anion and the other at the optimized geometry of the neutral species.…”

Low rank factorization of the Coulomb integrals for periodic coupled cluster theory

“…A related acceleration scheme for coupled cluster theory is the chain of spheres exchange (COSX) method as described in Ref. 44.…”

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

“…For RI–EOM, the RI errors is reported to be about 1 meV, while RI–CC2 is shown to reproduce the CC2 EE within a MAE of 1.3 meV even when augmented basis sets are used . For COSX, the error depends on the grid and it is somewhat larger using standardized setups, but it is still lower than 0.01 eV on average . TCH–CC2 is also known to yield errors lower than 0.02 eV .…”

“…Canonical EOM–CCSD implementations usually cannot handle systems containing more than a few tens of atoms using common computer architectures although the use of RI and COS can make the treatment of 20–30 atoms more comfortable . On architectures with less than 16 cores, it seems that the limit of canonical calculations is about 700 basis functions, although the use of RI and NTOs can make systems with around 1,000 basis functions tractable by lowering the number of active orbitals .…”