where the sum runs over the
atomic orbitals with the binding energies [E.sub.i] and the filling numbers [n.sub.i].
Figure 3(a-c) shows the total density of states (DOS) with the electronic contributions of the
atomic orbitals from the Ti and O atoms in PT, PST and ST with a gap value of 3.60 eV, 3.20 eV, 3.70 eV, respectively.
• Visualization of
atomic orbitals and electron effects.
Deeper
atomic orbitals would provide a large number of additional molecular orbitals, however the expected energies of these molecular orbitals would be much larger than the maximum observed energy of 5 eV (250 nm).
Mulliken charges arising from the Mulliken population analysis provides a mean of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of
atomic orbitals molecular orbital method [28,29].
Among the topics are
atomic orbitals, the anti-symmetry of many-electron wavefunctions, valence bond theory and the chemical bond, and elements of Rayleigh-Schroedinger perturbation theory.
Just as the case with
atomic orbitals, the shape of a ground state molecular orbital is highly specific in shape and size.
Far from the surface and in the absence of a field, the
atomic orbitals of A and B hybridize into molecular orbitals which we take to be a low-lying bonding orbital and an empty antibonding orbital.
The composition (%) of
atomic orbitals in molecular frontier orbitals is analyzed by Multiwfn software.
The attractive magnetic force in the anti-parallel spin electrons accounts for the anti-parallel pairing of electrons in
atomic orbitals where the electrons are close together, this leading to the Periodic Table of elements.
The tight-binding model (7) is based upon the Linear Combination of
Atomic Orbitals (LCAO) method and is both accurate and easy to implement (8), (9).