Local CC2 electronic excitation energies for large molecules with density fitting

Abstract

A new local method for the computation of electronic excitation energies of singlet states in extended molecular systems is presented. It is based on the CC2 model and local approximations to the wave functions. In the proposed method the singles excitations are treated nonlocally and local restrictions are imposed on doubles amplitudes only. The accuracy of the new method was tested by calculating several lowest excited states for 14 molecules and comparing them with canonical CC2 values. Deviations of the local excitation energies from the canonical reference values do not exceed 0.05 eV for all test molecules and all states in the lower energy range investigated in this work. The method uses the density-fitting approximation for all two-electron integrals, which considerably simplifies the computational complexity of the individual diagrams. A combination of the local approximations and the powerful density-fitting technique leads to a low-scaling method, capable to treat molecular systems comprised of 100 atoms and more in a basis of a polarized double zeta quality. A test calculation for a system consisting of 127 atoms and 370 active electrons without symmetry is presented to show the efficiency of the new method.

An efficient local coupled cluster method for accurate thermochemistry of large systems

“…For this purpose, an initial LMP2 calculation is performed for all (except very distant) pairs, and the pair energies for the close, weak, and distant pairs are added to the LCCSD energy in Eq. (20). One can also solve the LMP2 equations with fixed strong-pair amplitudes from the converged LCCSD, but we found that this makes virtually no difference for the accuracy of the results.…”

“…By default, only the strong pairs are included in the LCCSD, i.e., the summations over ij are restricted as indicated in Eqs. (5) and (20). The close, weak, and distant pair amplitudes are optimized at the LMP2 level and kept fixed thereafter.…”

“…If a local orbital basis is used, approximations that exploit the short-range character can be introduced, as first proposed and implemented by Pulay and Saebø, [2][3][4][5][6] and later generalized and extended in our groups. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] These methods are based on two distinct approximations: first, excitations from a given pair of localized molecular orbitals (LMOs) are restricted to a subspace (domain) of non-orthogonal projected atomic orbitals (PAOs), which are spatially close to the two LMOs. Second, the pairs of LMOs can be classified according to their distance.…”

“…Originating from density functional theory (DFT) (Refs. [41][42][43] their usage spreads today from HF, [44][45][46] MP2, 14,[47][48][49][50] CC2, 20,51 MP2-F12, [52][53][54][55] up to CCSD. 16,56 Furthermore, for correlated calculations of periodic systems DF is indispensable for an efficient method.…”

Local CC2 response method based on the Laplace transform: Orbital-relaxed first-order properties for excited states

“…[30][31][32][33][34] The idea is to take advantage of the short-range nature of dynamic correlation in nonmetallic systems. To this end a basis of spatially localized orbitals, e.g., localized molecular orbitals (LMOs) and projected atomic orbitals (PAOs) is used to span occupied and virtual space, respectively.…”