Molecular Orbital calculations of Nitric oxide, Bromobenzene, and Difluoromethane

Andrew Gassner and Nick Cirricione
Abstract
    The geometries, highest occupied molecular orbital, lowest unoccupied molecular orbital, electrostatic potentials, dipole moments, partial atomic charges and vibrational energies were calculated for Nitric Oxide, Difluoromethane, and Bromobenzene using different levels of molecular orbital theory.  They included 3-21G, 6-21G, 6-31G, and DZV.  The best level of theory to determine these characteristics for the molecules was not always the same as geometry was best found by using 6-31G theory, vibrational frequency DZV and dipole moments by AM1 theory.

Introduction
    The useful properties of a molecule may be predicted if its electronic structure is known because it determines much of a molecules reactivity.  Some of these useful properties include molecular dipole moment, polarizability, vibrational frequencies, probability of absorption of visible light, and tendency to donate electrons in a reaction.  The molecular orbital calculations were based off the relationship that the lowest possible energy of a molecule was were it was most stable and at this point it would have the optimum geometry.  The energy therefore could be found using the variational principle which allows the true wavefunctions to be approximated with sums of trial wavefunctions.  The expectation value of the energy can then be found by taking the expectation value of the Hamiltonian and dividing by a normalization constant.  Both of these terms are composed of integrals that increase exponentially as the amount of atoms in a molecule increase.  The calculations needed in order to determine the electronic structure are massive and in the early days of science they were accomplished using a paper and pencil.  This became almost impossible if the molecule being examined were larger than a few atoms due to all the interactions.  With the proliferation of computers with high processing capabilities and software designed to calculate molecular orbitals, the heart of a molecules electronic structure, it has become capable to determine the structures of larger molecules easier and faster.
    There are different ways to calculate the expectation value of the energy depending on the amount of integrals a level of theory uses.  Some use empirical data to provide estimates of the values for two electron overlap integrals needed for calculating the expectation value of the Hamiltonian.  These methods include AM1 and PM3 and are some of the quickest because they just use these two.  The best level of theory is Ab initio in which all integrals are calculated.  The difference between these is the size of the basis sets, number of trial wavefunctions, used to determine the energy.  These methods in order of increasing basis set size are 3-21G, 6-21G, 6-31G, and DZV.1
     In this experiment the program Gamess was used to calculate the molecular orbitals of nitric oxide, bromobenzene, and difluoromethane.  The first step used in performing the calculations was to find the geometries of the molecules.  The initial guess of the geometries for Nitric Oxide, Difluoromethane, and Bromobenzene was generated using the software program Avogadro. Using the initial geometries generated by Avogadro an AM1.inp file (to optimize geometry) was generated using the software program macmolplt, which further refined the geometries. The .inp file was then run using GamessQ, the interface for Gamess at the lowest level of molecular orbital calculations, AM1. The AM1.log file obtained from GamessQ was then used to generate a 6-21G.inp file, which in turn was used to generate a 6-31G.inp file followed by a DZV.inp file.  The exception to this process was for bromobenzene where a 3-21G file was used in place of the 6-21G. Jmol, modeling software, was then used to visualize various aspects of these molecule for each level of theory as well as to display some physical constants for each molecule that were calculated by Gamess.

Use the following hyperlinks to see the calculated values: Nitric Oxide    Difluoromethane  Bromobenzene
  
Conclusion
    Each level of theory generated fairly decent geometries with 6-31G being the best.  All levels of theory did not do a great job of generating energies that gave good bond lengths.  All the levels gave lengths that deviated from experimental values and seeing that the greater the basis sets the longer the computing time it would not be recommended going past 6-31G. 
     The calculated dipole moments for NO and difluoromethane were useful and had percentage errors of 10.6 and 3.6% respectively.  The interesting part is that the best value for NO used DZV and difluoromethane used AM1.  For bromobenze an error of 97.0% was obtained which calls into question the usefulness of using these theories to calculate dipoles.
    For vibrational energies the DZV theory was used to calculate at which wavelengths the vibrational levels would absorb energy.  When compared to a IR spectrum for the molecules the vibrational wavelengths found matched up well with the peaks in the spectrum.  This can be seen on the individual pages.
    The different levels of theory were sometimes useful and sometimes not depending on the value being calculated.  DZV would have been expected to be the most accurate level as it contained the largest basis set but sometimes was not. Because of the inconsistency of the data sets it is beneficial to generate data from several levels of theory however it may not be wise to base additional calculations off any of these levels of theory.  

References
    1.  Gutow, J. Molecular Orbital (MO) Calculations 2014, p 1-3.   

    2.  Listing of experimental data for CH2F2 (Methane, difluoro-) 2014, http://cccbdb.nist.gov/exp2.asp accessed Mar. 7, 2014.

    3.  Listing of experimental data for NO (Nitric Oxide) 2014, http://cccbdb.nist.gov/exp2.asp accessed Mar. 7, 2014.

    4.  CRC HANDBOOK of CHEMISTRY and PHYSICS; 68TH ed; Weast, Robert C., Ed.; CRC Press, Inc.: Boca Raton 1987; p F-160 thru            F-162.
   
    5.  Benzene, Bromo 2014, http://webbook.nist.gov/cgi/cbook.cgi?ID=C108861&Units=SI&Type=IR-SPEC&Index=2#IR-SPEC                              accessed Mar. 7, 2014.
   
    6.   Dimitriu, Mihaela; Ivan, Liliana-Mihaela; Dorohoi, Dana Ortansa. Analele Stiintifice ale Universitatii "Al. I. Cuza" 2007, 3, 21-26. 

    7.  McClellan, A. L. Tables of Experimental Dipole Moments; W.H. Freeman and Co.: San Francisco, 1963.