Compact sum-of-products form of the molecular electronic Hamiltonian based on canonical polyadic decomposition

Abstract

We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition (CPD) of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin orbitals. The algorithm for obtaining the canonical polyadic form starts from an exact sum-of-products, which is then optimally compactified using an alternating least-squares procedure. We discuss the relation of this specific SOP with related forms, namely the Tucker format and the matrix product operator often used in conjunction with matrix product states. We benchmark the method on the electronic dynamics of an excited water molecule, trans-polyenes, and the charge migration in glycine upon inner-valence ionization. The quantum dynamics are performed with the multilayer multi-configuration time-dependent Hartree method in second quantization representation (MCTDH-SQR). Other methods based on tree-tensor Ans\"atze may profit from this general approach.