Question

1. Why are Gaussian type functions preferred to the Slater type orbitals for actual numerical Hartree Fock Calculation of molecular systems?

2. Explain the difference between Unrestricted Hartree Fock and Open Shell Restricted Hartree Fock (ORHF), and the benefit of each method.

Answer 1

1. In the early days of quantum chemistry so-called Slater type orbitals (STOs)
were used as basis functions due to their similarity with the eigenfunctions of
the hydrogen atom.

a. STOs have an advantage in that they have direct physical
interpretation and thus are naturally good basis for molecular orbitals.
b. From a computational point of view the STOs have the severe
shortcoming that most of the required integrals needed in the course of
the SCF procedure must be calculated numerically which drastically
decreases the speed of a computation.

STOs can be approximated as linear combinations of Gaussian orbitals.
GTOs are not really orbitals.
They are simpler functions and are frequently called gaussian primitives

a. Gaussian primitives are usually obtained from quantum calculations on
atoms (i.e. Hartree-Fock or Hartree-Fock plus some correlated
calculations, e.g. CI).
b. Typically, the exponents are varied until the lowest total energy of the
atom is achieved.
c. For molecular calculations, these gaussian primitives have to be
contracted, i.e., certain linear combinations of them will be used as
basis functions.
d. Such a basis function will have its coefficients and exponents fixed.

The main difference to the STOs is that the variable r in the exponential
function is squared. Generally the inaccuracy at the center nor the
qualitatively different behaviour at long distances from the center have a
marked influence on the results.

2. Restricted open-shell Hartree–Fock (ROHF) is a variant of Hartree–Fock method for open shell molecules. It uses doubly occupied molecular orbitals as far as possible and then singly occupied orbitals for the unpaired electrons. This is the simple picture for open shell molecules but it is difficult to implement.In contrast to unrestricted Hartree–Fock (UHF), the ROHF wave function is a satisfactory eigenfunction of the total spin operator (i.e. no Spin contamination).