Perturbation Theory for the Fock-Dirac Density Matrix

1962/05/01 by R. McWeeny · 35 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Density matrix #Eigenvalues and eigenvectors #Fock matrix #Fock space #Hamiltonian (control theory) #Hamiltonian matrix #Magnetism in coordination complexes #Mathematical physics #Mathematics #Perturbation (astronomy) #Physics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Symmetric matrix

paper · doi:10.1103/physrev.126.1028

openalex publication_date 1962/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In Hartree-Fock theory and its various generalizations, it is customary to solve an eigenvalue problem involving an effective one-body Hamiltonian. The eigenvectors determine the Fock-Dirac density matrix, which also appears in the effective Hamiltonian, and solution proceeds iteratively until self-consistency is achieved.An alternative (necessary and sufficient) condition for a solution is that the density matrix (\ensuremathρ) is idempotent and commutes with the Hamiltonian (h). The change in \ensuremathρ, accompanying a change \ensuremathΔ in h, can then be expressed as a perturbation series. Formulas for the perturbation, to all orders, are obtained in terms of the unperturbed Hamiltonian and density matrix. It is also shown that the whole perturbation may be obtained directly, without separating the orders, and that the approach is related to earlier steepest-descent methods.

Cited by

• Reactivity of Pnictaalumenes Towards 1,3‐Dipole Molecules
• Cyclo ‐P 5 − Revisited: The Surprisingly Stable Uncoordinated Pentaphospholide Anion
• A scalable route to first-order response properties with correlated sampling phaseless auxiliary-field quantum Monte Carlo
• Functionalized Calix[4]Nanocones
• Self-Consistent Perturbation Theory. II. Extension to Open Shells
• A theoretical study of the 77Se NMR and vibrational spectroscopic properties of SenS8n ring molecules
• Aromaticity and Ring Currents
• Ambient-Temperature Isolation of a Compound with a Boron-Boron Triple Bond
• Density Matrix Perturbation Theory
• Ab Initio Prediction of Boron Compounds Arising from Borozene: Structural and Electronic Properties
• Intermolecular shielding contributions studied by modeling the (13)C chemical-shift tensors of organic single crystals with plane waves. [europepmc]
• Ab Initio Prediction of Boron Compounds Arising from Borozene: Structural and Electronic Properties. [europepmc]
• Quantum mechanical studies of lincosamides. [europepmc]
• Experimental and quantum chemical studies of a novel synthetic prenylated chalcone. [europepmc]
• Size variation of infrared vibrational spectra from molecules to hydrogenated diamond nanocrystals: a density functional theory study. [europepmc]
• Application of Computational Chemical Shift Prediction Techniques to the Cereoanhydride Structure Problem-Carboxylate Complications. [europepmc]
• Association of aescin with β- and γ-cyclodextrins studied by DFT calculations and spectroscopic methods. [europepmc]
• The protonation states of GTP and GppNHp in Ras proteins. [europepmc]
• Stability of a Series of BODIPYs in Acidic Conditions: An Experimental and Computational Study into the Role of the Substituents at Boron. [europepmc]
• Benchmarking the Fluxional Processes of Organometallic Piano-Stool Complexes. [europepmc]
• Pd-Catalyzed Heteroannulation Using N -Arylureas as a Sterically Undemanding Ligand Platform. [europepmc]
• The hidden aromaticity in borazine. [europepmc]
• Theoretical insights into the effect of halogenated substituent on the electronic structure and spectroscopic properties of the favipiravir tautomeric forms and its implications for the treatment of COVID-19. [europepmc]
• MISPR: an open-source package for high-throughput multiscale molecular simulations. [europepmc]
• Five new secondary metabolites from an endophytic fungus Phomopsis sp. SZSJ-7B. [europepmc]
• DELTA50: A Highly Accurate Database of Experimental 1 H and 13 C NMR Chemical Shifts Applied to DFT Benchmarking. [europepmc]
• A Comprehensive Computational NMR Analysis of Organic Polyarsenicals including the Marine Sponge-Derived Arsenicins A-D and Their Synthetic Analogs. [europepmc]
• Koningipyridines A and B, two nitrogen-containing polyketides from the fungus Trichoderma koningiopsis SC-5. [europepmc]
• Chiral Jahn-Teller Distortion in Quasi-Planar Boron Clusters. [europepmc]
• Unexpected discovery: "A new 3,3'-bipyrazolo[3,4- b ]pyridine scaffold and its comprehensive analysis". [europepmc]
• Influence of Selective Deoxyfluorination on the Molecular Structure of Type-2 N -Acetyllactosamine. [europepmc]
• Use of Factorial Design for Calculation of Second Hyperpolarizabilities. [europepmc]
• ⁠Reversible C─H Insertion in Bulky Unsaturated NHCs: A Carbon-Based Analogue of Oxidative Addition/Reductive Elimination. [europepmc]
• Synthesis of Enantiopure [3]Cyclorubicenes. [europepmc]
• Ligand-Assisted Formation of Heterobimetallic Adducts of AlMe 3 and ZnMe 2 with Zr and Hf Salan Catalysts for Olefin Polymerization. [europepmc]

Related

• On the Hartree-Fock dynamics in wave-matrix picture
• Alternative dimensional reduction via the density matrix: A test
• Coefficients of almost-degenerate density matrix perturbation theory for eigenvalue problems
• Density Matrix Renormalization: A Review of the Method and its Applications
• Adaptive Perturbation Theory I: Quantum Mechanics