The dipole moments, partial atomic
charges, electrostatic potentials, lowest unoccupied molecular orbital (LUMO),
highest occupied molecular orbital (HOMO), vibrational energies, and geometries
of bromine, hydrogen sulfide, and p-dichlorobenzene were calculated using 6-21G,
6-31G, AM1, DZV, and PM3 as different levels of molecular orbit theory. DZV was found to be the best level of theory
to determine these characteristics of bromine, hydrogen sulfide, and
p-dichlorobenzene.
The molecular dipole
moment, polarizability, probability of absorption of visible light, tendency to
donate electrons in a reaction, and vibrational frequencies can be determined
if the electronic structure of the molecule is known. The variational principle, which states that
the lowest energy version for the wavefunction is the best approximation for
the actual wavefunction, is commonly used to perform molecular orbital
calculations. Thus, the energy can be
found by taking the sums of trial wavefunctions. The expectation value of the energy can be
calculated through the Hamiltonian operator and by dividing by a normalization
constant. As the terms used to find the
expectation value of energy increases exponentially with the amount of atoms in
a molecule, these calculations can become overwhelming if done by hand. Prior to computers, geometry optimization
calculations were limited to molecules of only a few atoms due to the sheer
complexity and length of the required calculations. However, with current computer software
programs, the best geometry for a larger molecule, such as p-dichlorobenzene,
can be found in a matter of seconds. There
are multiple methods used to calculate the expectation value of energy. These methods/levels of theory differ in
regards to the number of integrals used to provide the calculations. Levels of theory including AM1 and PM3
utilize empirical data for estimation of the values for two electron overlap
integrals required for calculating the Hamiltonian expectation value. AM1 and PM3 are relatively quick, as they are
both significantly faster than complete ab
initio calculations. The most
accurate level of theory is ab initio,
in which all integrals are calculated.
The difference in ab initio methods
is the size of the basis set, with 6-21G, 6-31G, and DZV being listed in
increasing basis set size.
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