Rank-one basis made from matrix-product states for a low-rank approximation of molecular aggregates.

Abstract

An efficient low-rank approximation to complete active space (CAS) wavefunctions for molecular aggregates is presented. Molecular aggregates usually involve two different characteristic entanglement structures: strong intramolecular entanglement and weak intermolecular entanglement. In the method, low-lying electronic states of molecular aggregates are efficiently expanded by a small number of rank-one basis states that are direct products of monomolecular wavefunctions, each of which is written as a highly entangled state such as the matrix product state (MPS). The complexities raised by strong intramolecular entanglement are therefore encapsulated by the MPS and eliminated from the degree of freedom of the effective Hamiltonian of molecular aggregates. It is demonstrated that the excitation energies of low-lying excited states of a pair of bacteriochlorophyll units with CAS(52e, 50o) are accurately reproduced by only five rank-one basis states. Because the rank-one basis states naturally have diabatic character and reproduce the low-lying spectrum of the CAS space, off-diagonal elements of the Hamiltonian are expected to give accurate diabatic couplings. It is also demonstrated that the energy splitting and the diabatic couplings in anthracene dimer systems are improved by augmenting with additional rank-one basis states.