Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs

Abstract

An implementation of scaled opposite-spin CC2 (SOS-CC2) for ground and excited state energies is presented that requires only fourth order scaling computational costs. The SOS-CC2 method yields results with an accuracy comparable to the unscaled method. Furthermore the time-determining fifth order scaling steps in the algorithm can be replaced by only fourth order scaling computational costs using a "resolution of the identity" approximation for the electron repulsion integrals and a Laplace transformation of the orbital energy denominators. This leads to a significant reduction of computational costs especially for large systems. Timings for ground and excited state calculations are shown and the error of the Laplace transformation is investigated. An application to a chlorophyll molecule with 134 atoms results in a speed-up by a factor of five and demonstrates how the new implementation extends the applicability of the method. A SOS variant of the algebraic diagrammatic construction through second order ADC(2), which arises from a simplification of the SOS-CC2 model, is also presented. The SOS-ADC(2) model is a cost-efficient alternative in particular for future extensions to spectral intensities and excited state structure optimizations.

Performance of SOPPA-based methods in the calculation of vertical excitation energies and oscillator strengths

“…SCS-CIS(D) [58,59] and SOS-CIS(D) [59], SCS-CC2 and SOS-CC2 [60] or SOS-ADC(2) [12,60,61]. A comparison between ADC(2) and SOS-ADC(2) for a subset of the benchmark set employed in this study showed significant differences in the mean errors between ADC(2) and two different versions of SOS-ADC(2) [12].…”

Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2

“…It is worth noting that Algorithms I and II could be modified slightly to evaluate scaled opposite-spin CC2 (SOS-CC2). 15 Under the THC approximation, the cost of each SOS-CC2 iteration would be reduced to O(N 3 ) operations. The final contributions to the CC2 energy and singles amplitudes include exchange-like integrals and represent the rate limiting limiting step of the entire THC-CC2 computation.…”

“…12,13 In particular, a) Electronic mail: toddjmartinez@gmail.com CC2 has proven useful in the study of chromophores with extended π -conjugated systems and for excited states with significant charge-transfer character. [14][15][16] In recent years, the density fitting (DF) approximation, also called the resolution of the identity (RI) approximation, has become a popular means of improving the efficiency of many methods in electronic structure theory. [17][18][19][20][21] In particular, DF has been applied to MP2 with great success.…”

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

“…There are highly efficient CC2 and scaled opposite-spin (SOS) CC2 implementations using this approach for excited states. [24][25][26][27][28][29] However, DF reduces only the prefactor, but not the scaling: DF-CC2 still scales as O(N 5 ), the approximate DF-SOS-CC2 method as O(N 4 ).…”