Automatic generation of coupled cluster algorithms with application to transcorrelated Hamiltonians

Abstract

We have used automatic code generation techniques to derive and implement full transcorrelated coupled and distinguishable cluster methods for accelerated basis set convergence and wave function compactification, leading to increased accuracy with manageable cost. The methods were benchmarked on thermochemical properties and two integral approximations based on normal ordering have been explored. The integral approximations have been shown to reduce the cost of the calculations without significant sacrifices in accuracy. They have paved the way for the very versatile transcorrelated method via exclusion of explicit three-body components (xTC). It has been demonstrated that the distinguishable cluster approximation improves the accuracy of transcorrelated coupled cluster methods. The transcorrelated coupled and distinguishable cluster methods with single and double excitations have been shown to outperform their F12 counterparts and approach the accuracy of CCSD(T)-F12. A two determinant distinguishable cluster method, alongside the traditional version, has been implemented in a new Julia package for electronic structure methods, called ElemCo.jl. The methods have been benchmarked on singlet and triplet excited states of closed-shell molecules and singlet-triplet gaps of diradicals using state-specific orbitals in the delta coupled cluster framework. The distinguishable cluster approximation improved the accuracy of the two determinant coupled cluster method considerably and the two determinant distinguishable cluster method has been shown to provide comparable and sometimes better accuracy than the equation-of-motion coupled cluster methods.