Spectral-product methods for electronic structure calculations

Quantum-Mechanical Definition of Atoms and Chemical Bonds in Molecules

“…Although elaborate methods have been developed for finite-subspace calculation in atomic spectral-product representations [61,[65][66][67][72][73][74], a factored version of the general development is particularly suited to calculations of the molecular and fragment energies of focus here [66,67,74]. The approach requires for its validity only the linear independence of the antisymmetrized form of the chosen finite subspace [75], providing a Hamiltonian matrix identical in appearance to Eq.…”

“…(16) employed to transform from this pair representation to the corresponding finite subspaceΦ(r : R) [66]. In more general variants of the development [72][73][74], the form of Eq.…”

“…Molecular (Born-Oppenheimer) Hamiltonian matrices take particularly simple forms in the atomic spectral-product representation as sums over universal atomic and pair-interaction Hamiltonian matrices which can be calculated once and for all and retained for repeated applications [66,67]. Total molecular energies obtained by conventional Hamiltonian matrix diagonalization are seen to take the form of sums over atomic and pairwise-interaction energies, expressed in terms of products of the universal atomic and interaction Hamiltonian matrices and the calculated molecular eigenvectors.…”

“…Atomic energy distributions obtained in this way describe the extent to which individual atoms are excited and their electrons apportioned to atomic bonding partners over the entire molecular volume, whereas the pairwise-atomic interaction energies provide corresponding chemical-bonding energies between constituent atoms. Overall electron antisymmetry of molecular eigenstates is formally achieved in the development by convergence in the limit of closure, or by ex-post-facto enforcement in finite subspaces [66,67].…”

“…(16) in the indicated finite subspace spectral-product basis to accommodate this change of representation [66,67,74]. The total electronic energy obtained from the foregoing expressions for a particular molecular eigenstate (i) is seen to be a sum of atomic energies for the constituent atoms and a sum of atomic-pair bonding energies of the form [cf., Eq.…”