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17: Higher Order Corrections to Electronic Structure

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    Electrons interact via pairwise Coulomb forces; within the "orbital picture" these interactions are modelled by less difficult to treat "averaged" potentials. The difference between the true Coulombic interactions and the averaged potential is not small, so to achieve reasonable (ca. 1 kcal/mol) chemical accuracy, high-order corrections to the orbital picture are needed.

    • 17.1: Orbitals, Configurations, and the Mean-Field Potential
      ab initio quantum chemistry methods typically use, as a starting point from which improvements are made, a picture in which the electrons interact via a one-electron additive potential. Their predicted atomic and molecular structure from these "mean-field" potentials are approximate and must be improved to achieve accurate solutions to the true electronic Schrödinger equation. To do so, three constructs  are employed typically employed: orbitals, configurations, and electron correlation.
    • 17.2: Electron Correlation Requires Moving Beyond a Mean-Field Model
      To improve upon the mean-field picture of electronic structure, one move beyond the single-configuration approximation. It is essential to do so to achieve higher accuracy, but it is also important to do so to achieve a conceptually correct view of chemical electronic structure. The inclusion of instantaneous spatial correlations among electrons is necessary to achieve a more accurate description. No single spin-orbital product wavefunction is capable of treating electron correlation.
    • 17.3: Moving from Qualitative to Quantitative Models
      Section 6 addresses the quantitative and computational implementation of many of the above ideas. It is not designed to address all of the state-of-the-art methods which have been, and are still being, developed to calculate orbitals and state wavefunctions.
    • 17.4: Atomic Units
      Atomic unites are used to remove all \(\hbar \text{, e, and m}_e\) factors from the equations.

    Thumbnail: Mean field approximation with a single configuration accounts for 99% of the energy of the ground-state the rest can be computed/approximated by addressing other "excited-state" configurations with electrons in virtual (unoccupied) orbitals expected for the ground-state configuration alone.

    This page titled 17: Higher Order Corrections to Electronic Structure is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jack Simons via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.