Multi-referenced Excited States and Intermolecular Forces from the Anti-Hermitian Contracted Schrodinger Equation

Strong correlation due to multi-referenced electronic states of quantum chemical systems are crucial for a proper understanding of important phenomena including excited states, bond breakage and formation, singlet fission and biological transport. By solving for the 2-electron reduced density matrix (2-RDM) directly via the anti-Hermitian contracted Schrödinger equation (ACSE) we provide a balanced treatment of single and multi-referenced correlation effects without utilizing the N-electron wave function. This significantly reduces the computational expense while still maintaining near full configuration interaction accuracy when available. When provided with an initial 2-RDM guess from an active-space multi-configuration self consistent field wave function the ACSE scales as $r^2_a r^4_e$ where $r_a$ is the number of active molecular orbitals (MOs) and $r_a$ is the number of external MOs. This work demonstrates the energetic accuracy of ACSE calculations with several small multi-referenced systems and presents a novel approach for investigating intermolecular interactions, using a simple dimer test case. In this monomer-optimized basis set approach we compute each monomer's properties in isolation and obtain a set of natural orbitals that best describe the monomer. We then remove or truncate orbitals deemed excessive as a function of occupation number, defining a monomer molecular orbital basis uniquely suited to that monomer. Combining two such monomers yields a super-system expressed in the monomer basis which we then rotate to a dimer basis at a desired geometry before creating a new initial 2-RDM for the final optimization by an ACSE calculation. It is found that the intermolecular properties calculated in this fashion from larger atomic basis sets maintain their high accuracy but at a fraction of the computational cost. Furthermore this basis set optimization is free of basis set superposition error, circumventing the need for an expensive counterpoise correction.