Theory of Separability of Many-Electron Systems

Abstract

Atomic and molecular systems are often intuitively separated into almost independent subsystems as, for example, the core and valence parts of an atom. Consequently, if this separation provides a good approximation, one can obtain the states of the system from the states of the subsystems which best represent the entire system. In the light of the work of McWeeny, in which one assumes strong orthogonality among subsystem wavefunctions, we determine an effective Hamiltonian for a given subsystem which should properly describe the states of that subsystem. Previous work is shown to have dealt with an improper effective Hamiltonian.

Embedding Fragment ab Initio Model Potentials in CASSCF/CASPT2 Calculations of Doped Solids: Implementation and Applications

“…They can be applied following the procedure by Huzinaga and Cantu. 6,8 As most solutions of the many-electron Hamiltonian are based on orbital expansions, we assume for simplicity that we are dealing with a closed shell Hartree-Fock calculation. In this case, the orbitals are solutions of the following Fock equation:…”

“…Then, if we choose the frozen environment orbitals to be eigenfunctions of F tot , we obtain a Huzinaga-Cantu-like equation: 6,8 ( )…”

Quantum chemical study of the lanthanide bond length contraction on Ln3+-doped Cs2NaYCl6 crystals (Ln=Ce to Lu)

“…͑3͒ is the full ion projection operator, which prevents the cluster wave functions from collapsing onto this particular lattice ion. 32 The ingredients of the embedding potentials are obtained by performing preparatory Hartree-Fock self-consistent embedded ions calculations on Cs 2 NaYCl 6 :X (XϭCs ϩ , Na ϩ , Y 3ϩ , and Cl Ϫ ). The corresponding atomic basis sets ( j ), occupied orbitals ( c ) and orbital energies are used to produce the AIMP representations described above, following the AIMP recipes for representation of operators ͑see Refs.…”

Structure and spectroscopy of Pa4+ defects in Cs2ZrCl6. An ab initio theoretical study

“…Each total-ion potential is made of ͑1͒ a long-range Coulomb potential, which is a point-charge potential, so that ͚ V lrϪCoul is the Madelung potential created by the host lattice within the cluster volume, ͑2͒ a short-range Coulomb potential, which corrects the latter taking into account the spatial distribution of the electron charge density of the ions; ͑3͒ an exchange term, which stems from the fact that the generalized antisymmetric product of the cluster and the external ion wave functions fulfill the first-principles requirement of antisymmetry with respect to interchange of electrons between cluster and host, and ͑4͒ a total-ion projection term, which prevents the cluster wave function from becoming linearly dependent with the host wave function; 24 this term actually prevents variational collapse of the cluster wave function on the host ions. The total-ion potentials were obtained in a self-consistent embedded-ions Hartree-Fock calculation 12 on a Cs 2 ZrCl 6 (O h 5 -F m3m ) lattice with a ϭ10.407 Å, x Cl ϭ0.235.…”