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11: Computational Quantum Chemistry

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    Computational chemistry is the field of chemistry that uses mathematical approximations and computer programs to solve problems of chemical interest. Quantum chemistry is a subfield that addresses the equations and approximations derived from the postulates of quantum mechanics; specifically involving solving the Schrödinger equation for molecular systems. Quantum chemistry is typically separated into ab initio, which uses methods that do not include any empirical parameters or experimental data and semi-empirical which do.

    • 11.1: Overview of Quantum Calculations
      The variational principle says an approximate energy is an upper bound to the exact energy, so the lowest energy that we calculate is the most accurate.  This limiting energy is the lowest that can be obtained with a single determinant wavefunction . This limit is called the Hartree-Fock limit, the energy is the Hartree-Fock energy, the molecular orbitals producing this limit are called Hartree-Fock orbitals, and the determinant is the Hartree-Fock wavefunction.
    • 11.2: Gaussian Basis Sets
      A minimal basis set of STOs for a molecule includes only those STOs that would be occupied by electrons in the atoms forming the molecule. A larger basis set, however, improves the accuracy of the calculations by providing more variable parameters to produce a better approximate wavefunction, but at the expense of increased computational time. STOs have the following radial part (the spherical harmonic functions are used to describe the angular part) .
    • 11.3: Extended Basis Sets
      Today, there are hundreds of basis sets composed of Gaussian Type Orbitals (GTOs). The smallest of these are called minimal basis sets, and they are typically composed of the minimum number of basis functions required to represent all of the electrons on each atom. The largest of these can contain literally dozens to hundreds of basis functions on each atom.
    • 11.4: Orbital Polarization Terms in Basis Sets
      The use of a minimal basis set with fixed zeta parameters severely limits how much the electronic charge can be changed from the atomic charge distribution to describe molecules and chemical bonds. Expanding the basis set with more flexible functions can obtain more accurate results. Such functions are called polarization functions because they allow for charge polarization away form the atomic distribution to occur.
    • 11.E: Computational Quantum Chemistry (Exercises)
      These are homework exercises to accompany Chapter 11 of McQuarrie and Simon's "Physical Chemistry: A Molecular Approach" Textmap.

    11: Computational Quantum Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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