Molecular Orbital Calculations of Water, Diboron, and Chlorobenzene
Jelinek, Lauren and Yang, Dasan
Abstract
Computers
can be used to calculate the structure of a molecule and display said structure
in three dimensions. In order to determine the geometry of the molecule, the
computer uses molecular mechanics or quantum mechanics and common assumptions.
Within quantum mechanics there are many methods that use different combinations
of simplifications to the molecular model. The result with the lowest energy
using the least assumptions is commonly the most accurate method of calculation.
In this experiment the molecules diboron, water, and chlorobenzene were
analyzed. Avagadro was used for an initial guess, which was then put into
MacMolPlt and GamessQ to further improve the model. Jmol was then used to
display the molecules in 3D and Igor was used to display potential energies. The
quantum method with the least assumptions and the most accurate was DZV,
however, this method still deviated from the results gathered through reported
experimental values.
Introduction
The locations of electrons and
their energies may be used to predict useful properties such as the molecular
dipole moment, polarizability, vibrational frequencies, probability of
absorption of visible light, and tendency to donate electrons in a reaction, if
their electronic structure is known. Quantum mechanical molecular orbits use
wavefunctions to describe the electrons in a molecule. Using the variational
principle, we were able to approximate true wavefunctions by adjusting
parameters to find the lowest energy version of the wavefunction, which is the
best approximation. The lowest energy wavefunction is represented by the coefficients
that produce the lowest energy for the electron, which can be calculated by
calculating the expectation value of the energy. While the individual wavefunctions
used in the approximation are normalized, the approximated wavefuction itself
must still be normalized, putting additional constraints on the coefficients.
The bigger the basis set, the better the accuracy for the energy prediction.
The geometry
of the molecule must be adjusted as well to accurately predict the electronic
energy. The geometry of the electrons and nuclei are related to the potential
energy of the system. By rearranging the geometry to find the lowest energy
value, the calculation is then optimized once the minimum has been found.
Computer software and quantum
mechanics are combined to create 3d images and 2d projections of chemical
structures. These structures are interactive and can be used to display the
properties mentioned above through optimization. Once a basis set method is
chosen, the computer calculates an accurate molecular geometry to predict the
electronic energy of the system. Each method includes a different amount of
approximation, affecting the accuracy of the calculations. However with more
approximations, less time is needed for the computer to complete the calculations.
The ab initio methods are the quantum mechanical MO models with the
least approximations and the largest basis sets, therefore the most accurate. Even
so, the ab initio methods use common
assumptions: the Born-Oppenhiemer approximation stating the nuclei are
stationary relative to the electrons, the Hartree-Fock approximation saying the
electrons move independently of each other but their motion is affected by the
electron field created by the other electrons and nuclei in the molecule, and
the linear combination of atomic orbitals (LCAO) approximations to construct
the molecular orbital2. The methods used in the experiment were the
6-21G, 6-31G, and the DZV(Double Zeta Valence) in order of lowest to highest
optimization accuracy.
The semi-empirical method MOPAC
(molecular orbital package) is comprised of four choices of Hamiltonian
equations used to estimate the values for the expected value. Common assumptions
for the MOPAC in addition to those of ab
initio: only valence electrons ore considered, inner shell electrons are
not included in calculations, selected interactions involving two atoms at most
are considered (called the neglect of diatomic differential overlap, or NDDO),
parameter sets (calculated data fitted with experimental data) calculate iterations
between orbitals. The MOPAC methods used in the experiment were the Austin
method 1 (AM1) and the parameterized model 3 (PM3), where PM3 has been
parameterized for more chemical elements2.
An initial guess to the molecular
structure was used prior to the ab intio
or MOPAC methods using the software Avogadro. The software uses the molecular
mechanics method instead of quantum mechanics to estimate the geometry of the
molecule1. In molecular mechanics the molecule is treated classically
with atoms as balls and bonds as springs connecting the balls. Using harmonic oscillation
calculations, the method optimizes the geometry so that the bonds are under the
least amount of strain. This method depends on the number of atoms instead of electrons
and is better for larger molecules. Once the molecular mechanics method was
optimized in Avagadro, the result was then imported into MacMolPlt and GamessQ
to optimize the structure using the quantum mechanical MO methods.
These molecules were then displayed
in Jmol.
Results
The following are links to the calculations completed using Avagadro, MacMolPlt, GamessQ, Jmol and IGOR: Water Chlorobenzene Diboron IR Spectra
1.
(1) Mihalick, J; Gutow, J. Moleculare Orbital (MO) Calculations. 2015.
2.
(2) Mohrig, J; Hammond, C; Schatz, P. Techniques in Organic Chemistry: Miniscale,
Standard Taper Microscale, and Williamson Microscale. 3rd ed.
W.H. Freeman and Company: New York. 2010.
3.
(3) Lide, D. CRC
Handbook of Chemistry and Physics. 73rd ed. CRC Press, Inc.:
Boca Raton, US. 1993.
4.
(4) NIST.
NIST Standard Reference Database Number 69. 2011. Web. http://webbook.nist.gov/chemistry/