Quantum Calculations of Molecules:

Nitric Oxide, Ethylene, and o-Dichlorobenzene

Jordan Berget and Kelly Genskow

                Introduction

     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.  GAMESS 4 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
NO image
ethylene image
dichlorobenzene image

 

                    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).