A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential

Abstract

A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.

Application of the finite-field coupled-cluster method to calculate molecular properties relevant to electron electric-dipole-moment searches

“…Since the expression for the correlation energy terminates (due to the Hamiltonian having only one and two body terms), the energy derivative in FFCC approach requires no approximation to be made for a given level of particle-hole excitation, unlike the LECC approximation. Later in this work, we also apply the finite field version of the relativistic CCSD(T) method [23], the gold standard of electronic structure calculations [24], which also includes partial triples to 5 th order, besides single and double excitations.…”

Stability analysis of a double similarity transformed coupled cluster theory

“…Recently, a new iterative scheme, which takes care of the fully connected triple excitations at a computational cost less than that of CCSD(T). The said method, known as the iterative n-body excitation inclusive CCSD, (iCCSDn) [8,9] parametrizes the wavefunction as a double exponential waveoperator Ω acting on a reference zeroth-order wavefunction, usually taken to be the Hartree-Fock (HF) determinant. Ω = {exp(S)} exp(T 1 + T 2 )…”

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions

“…Szakács and Surján 5,6 , for the first time, demonstrated that the CC iteration scheme under an input perturbation shows chaotic dynamics. Some of the present authors had shown that the dynamics associated with a double similarity transformed CC [7][8][9] iterations follows the universality of time-discrete map of one-parameter family. The authors analysed the phase space trajectory under an input perturbation and demonstrated a full period-doubling bifurcation cascade that precedes the onset of the chaos.…”