Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry

DOI10.1016/j.na.2011.08.038zbMath1229.81346OpenAlexW2069095457MaRDI QIDQ644209

Michael Melgaard, Carlos Argáez

Publication date: 3 November 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.08.038

zbMATH Keywords

semilinear elliptic equationsmultiple solutionsPalais-Smale sequencesabstract critical point theorydensity operator techniques

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics (70H40) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Molecular physics (81V55)

Related Items (11)

Normalized ground states for the critical fractional Choquard equation with a local perturbation ⋮ On fractional Schrödinger equations with Hartree type nonlinearities ⋮ The compatible Grassmannian ⋮ On some qualitative aspects for doubly nonlocal equations ⋮ Comment on `Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry', by C. Argaez and M. Melgaard ⋮ Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity ⋮ Normalized solutions for the Schrödinger-Poisson system with doubly critical growth ⋮ Asymptotic decay of solutions for sublinear fractional Choquard equations ⋮ Stiefel and Grassmann manifolds in quantum chemistry ⋮ MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE ⋮ Addendum and erratum to ``Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry [Nonlinear Anal. TMA 75 (2012) 384-404]

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stiefel and Grassmann manifolds in quantum chemistry
• Proof of the ionization conjecture in a reduced Hartree-Fock model
• Hartree-Fock theory for pseudorelativistic atoms
• Existence of a solution to Hartree-Fock equations with decreasing magnetic fields
• Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations
• Spectral theory of the operator \((p^2+m^2)^{1/2}-Ze^2/r\)
• Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations
• The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions
• Perturbation theory for linear operators.
• Solutions of Hartree-Fock equations for Coulomb systems
• Solutions of the multiconfiguration equations in quantum chemistry
• A general approach for multiconfiguration methods in quantum molecular chemistry
• Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds
• On the existence of entire solutions to a class of semilinear elliptic equations on noncompact Riemannian manifolds
• Finite Morse index solutions of exponential problems
• On the Hartree-Fock equations of the electron-positron field
• NON-RADIALLY SYMMETRIC SOLUTIONS FOR A SUPERLINEAR AMBROSETTI–PRODI TYPE PROBLEM IN A BALL
• A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
• Nontrivial solutions of operator equations and Morse indices of critical points of min-max type
• Morse indices at critical points related to the symmetric mountain pass theorem and applications
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• Morse‐type information on palais‐smale sequences obtained by min‐max principles
• On the infinitude of non–zero eigenvalues of the single–electron density matrix for atoms and molecules
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• On the discrete spectrum of Hamiltonians for pseudo-relativistic electrons
• Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction
• Higher energy solutions in the theory of phase transitions: A variational approach

This page was built for publication: Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry