Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions

Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born–Oppenheimer electron–nuclear interactions in molecules, electron–hole interactions in electronically excited nanoparticles, and electron–positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron–electron) but also between particles of different types (electron–nuclear and electron–hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle–particle correlation in multicomponent systems are presented. This method provides a balanced treatment of many-particle correlation effects in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is an extension of the electronic structure CCSD formulation for multicomponent systems and is defined as |ΨmcCC⟩ = e T 1 I+T 2 I+T 1 II+T 2 II+T 11 I,II+T 12 I,II+T 21 I,II+T 22 I,II |0I0II⟩. The cluster amplitudes in the mcCC wave function were obtained by projecting the mcCC Schrödinger equation onto a direct product space of singly and doubly excited states of type I and II particles and then solving the resulting mcCC equations iteratively. These equations were derived using an automated application of the generalized Wick’s theorem and were implemented using a computer-assisted source code generation approach. The applicability of the mcCC method was demonstrated by calculating ground state energies of multicomponent Hooke’s atom and positronium hydride systems as well as by calculating exciton and biexciton binding energies in multiexcitonic systems. For each case, the mcCC results were benchmarked against full configuration interaction (FCI) calculations and were found to be in excellent agreement with the FCI results. The effect of neglecting certain classes of multicomponent connected excitation terms from the mcCC wave function was also investigated. The results from this study demonstrate that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron–hole correlation in multiexcitonic systems.