Molecular orbitals are the wavefunctions
for electrons in molecules, and eigenvalues are numerical solutions
to these wavefunctions that provide the energies of electrons.
While information about molecular orbitals is important to know for
studying many chemical processes, particularly reactivity, it is not
possible to find eigenfunctions and eigenvalues for systems larger
than a single atom with one electron. However, it is possible
to make approximations using quantum calculations. These
calculations were originally very difficult to do by hand, and were
therefore limited to simple molecules. With the development of
computer processing speed and specialized software packages, it has
become possible to perform calculations on complicated molecules,
and even chemistry students are able to participate in the
process. Because these calculatons can provide information on
reactivity, they are useful for determining the likelihood of a
chemical reaction proceeding, and therefore can help laboratories
save money.
Because there are no eigenfunctions, a
superposition of many trial wavefuntions (the basis set) are used to
calculate a good approximation, or expectation value. In order
to calculate expectation values for the energies, geometry
optimizations are first made for the molecules. To do this,
the software program repeatedly repositions all of the electrons in
the system until the change in energy from repositioning is below a
set parameter. The goal is to find the lowest energy
configuration for the electrons. It should also be noted that
the size of the basis set used can vary, and larger basis sets (more
wavefunctions) will give more accurate energy values.
There are also different levels of theory that
can be used in computational chemistry. These levels represent
different sorts of assumptions and information used to make the
final calculations. For the calculations presented in this
project there were two levels of theory used: semi-empirical
and ab initio. The
semi-empirical method uses some experimental data such as
spectroscopic data or ionization energies to simplify the
integrals. In contrast, no experimental data is used for the ab initio theory, and all of
the results are based on solutions to the Schrodinger
equation. Ab initio is
the best level of theory. Within each level of theory, the
size of the basis set can be increased to improve output
values. For the molecules on this page AM1 and PM3 were the
basis sets used in the semi-empirical level, while 621-G, 631-G, DZV
were the basis sets used from the ab
initio level. These five basis sets are given in
order of increasing size.
For the experiment presented below, calculations
were performed on the following molecules: nitric oxide, ethylene,
and o-dichlorbenzene. Several different software programs were
also used. wxMacMolPlt² was first used to build the
molecules and create input files for GamessQ. Geometries for
the molecules built in wxMacMolPlt were originally optimized in Jmol
before the input files were built. Jmol³ was also used to view the
models that were created and to export the information and images
to a webpage. GamessQ is a program which allows the
calculations to be queued on a local desktop and checked for
completion, while GAMESS is the actual package that performs the
calculations. GAMESS4
is an acronym for General Atomic and Molecular Electronic
Structure System. By using a combination of these three
software packages, a large amount of information about each of the
highlighted molecules was calculated and is displayed on the
molecules' web pages which can be viewed below. This
information includes 3-D geometries, images of molecular orbitals,
electrostatic potential maps, partial atomic charges, dipole
moments, potential energies of bond stretching, and data about IR
and UV-Vis spectra.
To View the Results of the
Quantum Calculations Click the Molecules Below
Nitric
Oxide
Ethylene
o-Dichlorobenzene
Conclusion
As can be seen in the previous pages, using
computer programs for molecular calculations can be very
useful. In particular, geometries that are relatively close to
experimental values can be produced, as well as good 3D models of
molecules and their orbitals. However, one must also be
cautious when using these methods and calculations. Many of
the calculated results, including dipole moments and vibrational
frequencies, vary significantly from the experimental values.
In the past, only scientists familiar with the what the results
should be were able to work with these calculations, and so were
able to find errors. Now as the software packages become more
accessible and user friendly, people who do not fully understand the
process may report false results. In the end, the key to
successfully using computational chemistry is to always question the
accuracy of the results and use them more as an initial guide.
References 1) Mihalick, J.; Gutow, J. Molecular Orbital Calculations. Oshkosh, WI,
2011.
2) Bode, B. M. and Gordon, M. S. J. Mol. Graphics Mod., 16,
1998, 133-138.
3) Jmol: an open source Java viewer for chemical
structures in 3D. http://www.jmol.org/
4) M.W.Schmidt; K.K.Baldridge; J.A.Boatz; S.T.Elbert;
M.S.Gordon; J.H.Jensen; S.Koseki; N.Matsunaga; K.A.Nguyen; S.J.Su;
T.L.Windus; M.Dupuis;
J.A.Montgomery.
J.Comput.Chem. 14, 1347-1363(1993).