CHEM01200604005 A. K. Pathak - Homi Bhabha National Institute

For open shell HF i. e. unrestricted HF (UHF) two sets of density matrix is defined, one
for α and other for β electrons.
α−occupied
β−occupied
α α α β β β
λσ
= χλiχσi , Pλσ = χλiχσi
i
i
P
∑ ∑ (7)
1.3.2. Electron Correlation
Energies calculated by the HF method are typically in error by 0.5 % to 1% of the
total energy. 38 Though an absolute basis this is not too much, it is of the order of the
chemical bond energy. So, to study the clusters having weak interaction one need to
improve on the HF energy. The motions of electrons are correlated with each other and
this is called electron correlation. The electron correlation energy is the difference
between the exact non-relativistic energy and HF energy of the system (clusters). The
wave function in HF method is single determinant, not capable of considering the
correlation of the electron motion. To include the electron correlation energy several ab
initio post HF multi-determinant methods are constructed, namely, second order Moller-
Plesset perturbation theory (MP2), Configuration interaction (CI), Coupled cluster (CC)
etc. It is well known that all these methods are costly ones and some time it is impossible
to calculate the geometry by applying these methods. Density functional theory (DFT) is
developed to improve the time requirement over the ab initio correlated methods like
MP2, CC, etc.
1.3.3. Density Functional Theory
The electronic wave function of an N electron system depends upon 3N spatial
and N spin coordinated. Since the Hamiltonian contains only one and two electron spatial
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