A constrained Roothaan–Hartree–Fock method

Abstract

Nonperturbational and perturbation–iteration procedures for determining constrained Roothaan–Hartree–Fock wave-functions are described and compared. The perturbation–iteration procedure most rapidly converges, the secant-parameterization method requires less computation and is less sensitive to numerical errors.

Analyzing the Behavior of Spin Phases in External Magnetic Fields by Means of Spin-Constrained States

“…In order to constrain a particular wave function to a target value S z ,target for the spin expectation value ⟨S ̂z⟩ along the axis of the applied magnetic field, we can use the formalism of constraints. [67][68][69]71 In this framework, the Lagrangian…”

“…This allows us to determine the energetic costs of only partially allowing for certain spin flips and why certain spin sectors are disfavored energetically. In order to do so, we extend the theory of Li and co-workers with a constrained formalism − that allows us to target states with a particular ⟨ Ŝ z ⟩. The resulting formalism allows us to characterize the electronic structure underlying the spin behavior in magnetic fields in terms of the constrained GHF (CGHF) states and spin phase diagrams that arise from the associated Lagrange multipliers.…”

Quantifying Delocalization and Static Correlation Errors by Imposing (Spin)Population Redistributions through Constraints on Atomic Domains

“…In order to redistribute charges and spins over the open subsystem and the reservoir, we will constrain the ground state wave function of the total system to attain a particular feature of the open system (in this study, those features will be Mulliken (spin)­populations of atomic domains). The framework needed to impose such constraints was initially developed by Mukherji and Karplus in the context of observables like the dipole moment in unrestricted variational theories and has been significantly expanded upon since then, ,− culminating in modern day applications such as, among others, constrained density functional theory, electronegativity equalization, ,,, and restricted open-shell Hartree–Fock reformulated as a constrained unrestricted Hartree–Fock model . In order to make this paper self-contained, we will recall the necessary theoretical concepts needed to construct the framework that will allow us to constrain the (spin)­population of such an open subsystem.…”

A possible resurrection of the abinitio maximum overlap (MOM) method

“…Of the procedures for maximum overlap (7,8,(15)(16)(17)(18)(19)(20)(21)(22), that of Lykos and Schmeising (20) was most suitable for the present study, because their MOM wavefunctions can be directly compared with RHF (21,22) and NDDO' wavefunctions. Secondly, the secant-parameterization method used in the constrained RHF calculations (21) is easily adapted to this version of the MOM method.…”

“…Secondly, the secant-parameterization method used in the constrained RHF calculations (21) is easily adapted to this version of the MOM method. Thirdly, the MOM method of Lykos and Schmeising is similar to other approximate molecular orbital methods, and therefore the results from constrained MOM calculations are relevant to other methods: Lykos and Schmeising (20) and others (23,24) have shown the close correspondence between the maximum overlap and simple Hiickel methods (25,26).…”