Previous attempts to combine Hartree–Fock theory with local density‐functional theory have been unsuccessful in applications to molecular bonding. We derive a new coupling of these two theories that maintains their simplicity and computational efficiency, and yet greatly improves their predictive power. Very encouraging results of tests on atomization energies, ionization potentials, and proton affinities are reported, and the potential for future development is discussed.

A New Mixing of Hartree-Fock and Local Density-Functional Theories

https://www.lct.jussieu.fr/pagesperso/savin/papers/lyp/MieSavStoPre-89.pdf

Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Ψ(r1,r2,r3,...). Having been widely used for over 30 years by physicists working on the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications:  the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.

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Density Functional Theory of Electronic Structure

A new dynamical correlation functional is constructed subject to a small number of simple, yet key, requirements not all satisfied by existing functionals in the literature. The new functional gives good atomic correlation energies, and, in conjunction with previous gradient‐corrected exchange functionals and exact‐exchange mixing, excellent thermochemistry in the G2 benchmarks of Pople and co‐workers.

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Density‐functional thermochemistry. IV. A new dynamical correlation functional and implications for exact‐exchange mixing

A formula is derived for the approximate calculation of the correlation energy, starting from knowledge of the one-electron and two-electron density matrices, calculated by the Hartree-Fock method.

Approximate calculation of the correlation energy for the closed shells

A formula is derived for the approximate calculation of the correlation energy of both open and closed shell systems. The formula integrates a functional of the one- and two-electron density matrices, obtained from a wavefunction built up by one or several Slater determinants.

Approximate calculation of the correlation energy for the closed and open shells

A detailed analysis of a method proposed earlier for calculating a good approximation to the electronic correlation energy is presented here The principal advantages of this method compared to the usual CI techniques are discussed

A general method for approximating the electronic correlation energy in molecules and solids

SCF‐MO's of the CH4 molecule have been calculated for the experimental geometry by using bases of up to 39 STO's. The best molecular energy obtained is −40.20452 a.u. The ground‐state wavefunctions have been utilized to compute some one‐electron properties, viz., the electric octupole moment, the electric field gradient at the protons, and the diamagnetic susceptibility. In addition, the electric polarizability and the paramagnetic susceptibility have been evaluated using a perturbed H–F calculation.

SCF-MO's and Molecular Properties of Methane

SCF MO's of H2O molecule have been calculated for a geometry very close to the experimental one, using a basis set of 29 STO's. The evaluated HF energy is −76.0384 a.u. Several ground‐state one‐electron properties have also been computed, viz., the first three electric multipole moments, electric field and gradient field at the nuclei, electric polarizability, and magnetic susceptibility.

Oriano Salvetti

Papers

Approximate calculation of the correlation energy for the closed shells

Approximate calculation of the correlation energy for the closed and open shells

A general method for approximating the electronic correlation energy in molecules and solids

SCF-MO's and Molecular Properties of Methane

SCF MO's and Molecular Properties of H2O