A constrained configuration interaction method

Abstract

. 61, 2552 (1983). Constrained configuration interaction (CI) wavcfunctions (CVM-CI) wcrc dctcr~nined using the modified pcrtusbationiteration (MPI) method, two approxinlate versions of thc MPI method. and the secant-paran~etcrization method. The resuIts of constrained CI calculations on CO using a 25 configuration wavefunction showed that the MPI method converged rapidly, and that the secant-parameterization nlcthod was cornputationally more economical.G. D. ZErss et M. A. WHITEHEAD. Can. J. Chem. 61, 2552Chem. 61, (1983. On a dbterminb les fonctions d'ondc (CVN-IC) d'interaction de configuration (IC) contrainte cn utilisant la mbthode modifiee de perturbation-itbration (MPI). deux versions approximatives dc la mithode MPI ainsi quc la lntthode de pararnttrisation sbquentielle. Les rksultats des calculs de IC contrainte, effcctuis sur le CO en utilisant une fonction d'ondc i 25 configurations, montrent que la mithode MPI converge rapidelnent et que la ~nithodc de para~netrisation siquentielle est, du point de vuc du temps de calcul, plus bconomique.[Traduit par le journal]

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

“…In this case the total energy of such systems directly shows the influence of the flat-plane condition, with the slope of the resulting lines dictated by the difference in ionization potential and electron affinity of the system and its associated reservoir . As we will show, the constrained configuration interaction methodology originally developed by Zeiss and Whitehead can be adapted to achieve arbitrary charge and spin redistributions in these systems by constraining full-configuration interaction wave functions to Mulliken (spin)­populations. Not only will the resulting energies obtained at each bonding distance allow us to computationally illustrate the effects of the flat-plane conditions in the limit to infinity, they will also provide useful reference data for the exact asymptotic behavior toward infinity and lead to more chemical insight into those flat-plane conditions.…”

“…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.…”

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…”

“…In order to constrain a particular wave function to a target value S z ,target for the spin expectation value ⟨ Ŝ z ⟩ along the axis of the applied magnetic field, we can use the formalism of constraints. − , In this framework, the Lagrangian is optimized, and the optimality condition for the wave function parameters p (which are the spinor rotation generators κ in the case of GHF and the ONV expansion coefficients c in the case of FCI) causes the usual molecular magnetic Hamiltonian (cf. eq ) to be replaced by the modified Hamiltonian where the term −μ Ŝ z represents an additional one-electron potential .…”

“…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.…”