The integral-direct coupled cluster singles and doubles model

Abstract

An efficient and highly vectorized implementation of the coupled cluster singles and doubles ͑CCSD͒ model using a direct atomic integral technique is presented. The minimal number of n 6 processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral prescreening.

Large-scale calculations of excitation energies in coupled cluster theory: The singlet excited states of benzene

“…Concerning the vectorization, we rely on our previous experience with the implementation of the CCSD amplitude equations. 26,27 We now manipulate the formulas in Table I to obtain the linearly transformed vector in accordance with the above discussion. The results are given in Tables II and III.…”

“…We describe in detail the integral-direct implementation and especially the connection to the integral-direct algorithm for the ground-state energy described in Ref. 27.…”

“…88,89 A similar development has recently taken place in CC theory, where atomic-integral direct CCSD techniques have been presented based on a strategy where integrals are generated in distributions with one fixed and three free atomic indices. 26,27 Thus, ground-state CCSD total energies have been calculated with more than 500 basis functions. 27 We present in this paper the extension of such techniques to the calculation of CCSD excitation energies.…”

“…26,27 Thus, ground-state CCSD total energies have been calculated with more than 500 basis functions. 27 We present in this paper the extension of such techniques to the calculation of CCSD excitation energies. We have briefly described elsewhere the techniques for integraldirect calculations of CC2 excitation energies.…”

“…17 The coupled cluster approach has since its introduction in quantum chemistry gained increasing popularity, providing an efficient method for treating the dynamical correlation as evident from many recent applications. [18][19][20] Several different implementations of the CCSD model have been presented [21][22][23][24][25][26][27] and a variety of molecular properties have been calculated-molecular gradients [28][29][30] and molecular Hessians, 31 polarizabilities, [32][33][34] nuclear magnetic shielding constants, [35][36][37][38] as well as other spectroscopic constants. 39,40,41 The CCSD͑T͒ approach 42 -which includes perturbative corrections for the effect of triple excitations-has provided highly accurate results for a wide range of frequency-independent molecular properties and remains the most popular method for high-accuracy calculations.…”