Molecular Orbital calculations of Dinitrogen, Hydrogen Cyanide, and Phenol
Ryan Bednarski and Larry Vue
Abstract:
Quantum mechanic
calculations become very complicated when the number of electrons and
atoms get bigger than one. Computational approximation methods have been
developed to reduce the time spent calculating and give rough estimates
of large molecules. The geometry optimization used come from the Ab
Initio theory. The Ab Initio levels of theory include: 621G, 631G, and
DZV. Using these optimization methods were use on the molecules,
Dinitrogen, Hydrogen Cyanide, and Phenol. The best optimization for each
molecule had their own level of theory that work the best. For
dinitrogen, 621G was the best for the best bond length, but DZV gave the
more negative potential. HCN used DZV for the bond lengths and 621G for
the dipole moment. Phenol used DZV for the bond lengths and 621G for
the dipole moment.
Introduction:
The
electronic activity, especially the valence electrons, is what gives a molecule
or an atom its reactive properties. The dipole moment, polarizability,
vibrational frequencies, probability of absorption of visible light, and
tendency to donate electrons in a reaction, can be determined if the structure
of the molecule and the location of its electrons are known. To determine the
structure of a molecule and where its electrons can be found, a wavefunction
can be used to represent the electrons which are known as molecular orbitals. Unfortunately,
this model of assigning a wavefunction to electrons or group of electrons can
only give an exact value for a single atom with one electron. As the number of
atoms and electrons increase, the more complicated the potential energy
(eigenvalue) portion of the Hamiltonian operator becomes. No exact solutions
can be found for two or more atoms and electrons.
With this problem of not being able
to obtain an exact value, an approximation method was implemented. The
variational principle allows us to approximate wavefunctions with a sum of
simpler wavefunctions. To put it in other words, a linear combination of atomic
orbitals (LCAO).The wavefunctions found
with the lowest energy, or the most negative, have been proven to be the best
approximation to the actual wavefunction. This energy found is the expectation
value of the Hamiltonian wavefunction divided by the normalized wavefunction.
First, a little background on the computation geometry optimization methods is needed. MOPAC3 or molecular
orbital package combines these semi-empirical methods that provide estimation
of two electrons overlap integrals needed for calculating Hamiltonians.
The ab initio molecular orbital theory
first states that nuclei are stationary relative to electrons due to the Borne-Oppenheimer approximation, which are
equilibrated to the molecular geometry. Electrons also move independently of
each other, and how it is affected by the average electric field created by all
other electrons and nuclei in the molecule. The molecular orbital will then be
constructed as a linear combination of atomic orbitals and calculated. The
smallest calculation in the basis set is 621G. Then increasing in geometry
theory is 631G, and DZV. Delta Zeta Valence (DZV) being the high level of
theory for geometry optimization.
First, the program Avogadro was used to construct
each molecule to be optimized. Then the progam MacMolPlt was utilized to
perform the MOPAC3 AM1 and PM3 optimizations. Those
optimized files were then optimized again in MacMolPlt using the Ab
Initio daisy chain of 621G to 631G to DZV. After the optimizations of
all three molecules were complete, the molecules were ran through the
GamessQ package to be able to view the .log files of each molecule.
These .log files of each molecule were then search for dipole moments,
UV-Vis wavelengths, and IR-speectrum data. All other values for each
molecule were determined through the Jmol software. These values
include, bond length, bond angles, electrostatic potential, partial
atomic charge, and HOMO and LUMO orbitals.
Results:
The results from the experiment for each molecule can be found within
these hyperlinks. These hyperlinks contain interactive diagrams along
with figures and tables to represent all data
collected: DinitrogenHydrogen CyanidePhenol
Conclusion:
Overall, Quantum Mechanical geometry optimizations
gave a rough estimate of values for molecules. The levels of theory used
for the calculations were 621G, 631G, and DZV. Generally, the smaller
the molecule is, the close the calculated values will be to the
literature values. Dinitrogen was a simple diatomic molecule and it did
not require a high level of theory to calculate the bond lengths. 631G
was best for the bond lengths. However, DZV gave the lowest potential
energy versus bond length which has been proven to be the best
optimization according to the Hardtree-Fock self consistent field
theory. For the smallest polar molecule, hydrogen cyanide, the opposite
was true compared to dinitrogen. The best optimization for the bond
length used DZV level of theory, where as the best optimization for the
dipole moment only needed to use the 621G level of theory. Phenol was
the last molecule to be optimized. Phenol used the highest level of
geometry optimization for calculating the bond length, but only required
the 621G theory for the dipole moment. HCN and phenol were similar with
the theories used to obtain values. This might have to do with them
being polar molecules.
Since the quantum mechanical calculations of large
molecules get increasingly complex to the point that it would take days
to solve, computer programs and approximation methods have been
implemented. Using these geometry optimization methods, HF-SCF, MOPAC3 and
Ab Initio, can be very useful when determine the values or data of
structures that are enormous, for example proteins, virus structures,
and ribosomes. These approximations do have their draw backs. For
example, over approximating for IR spectrum values, dipole moments, and
UV-Vis wavelengths. This was shown for the molecules.
References:
1. Mohrig R. Jerry, Hammond Noring Christina, Schatz F. Paul, Techniques in Organic Chemistry, Third Edition.; W.H. Freeman and Company: New York 2010; pp IR index.
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http://cccbdb.nist.gov/exp2.asp?casno=7727379 accessed March 10, 2015.
3. Listing experimental Data for HCN (Hydrogen Cyianide), http://cccbdb.nist.gov/exp2.asp?casno=74908 accessed March 10, 2015.
4. Listing experimental Data for C6H5OH (Phenol), http://cccbdb.nist.gov/exp2.asp?casno=108952 accessed March 10, 2015.
5. McClellan L. A., Table of Experimental Dipole Moments, W.H. Freeman and Company: San Francisco and London 1963. pp 38.
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