Molecular Orbital Calculations

The electronic structure of molecules determines how a certain molecule interacts during reactions. A description of the molecular orbitals predicts useful properties such as, dipole moments. Quantum mechanics creates the quantized probability of finding electrons in a given orbital, by wave functions described as molecular orbitals. The wavefunctions are then integrated to predict the total energy in an orbital. Potential energy becomes more complicated for systems with more that two charged particles.

The variation principle allows for the approximation of wavefunctions with linear combinations of trial wavefunctions. Since the trial wavefuntions aren’t eigenfunctions or Hamiltonian, the expectation values can be calculated by:

〈Ĥ〉=〈E 〉=∫Ψ*Ĥ Ψd τ /∫Ψ*Ψd τ

where Ψ is the wavefunction of the electron, Ĥ is the energy operator or Hamiltonian.

In geometry optimization calculations, the given experiment searches different arrangement of atoms until their energy is minimized. While the first calculations were manually done, computers were necessary to calculate the theoretical energies for large molecules. Software like GAMESS can be used to integrate the wavefunctions effectively and within a timely matter for large sets of calculations. The approximations can be made at different levels of theory depending on what the property of interest is. Another essential piece of software which can be used to show the data given by GAMESS in a 3-D display is Jmol. Jmol provides the user with an easy to use interface which allows a visual representation of the molecules optimization data.

Molecular properties can be calculated using both ab initio and MOPAC methods. Ab initio is considered the best level of theory, all the integrals are included but some approximations are made because self-consisted field model and finite sized basis set are used. MOPAC estimates uses the electron over lap to estimate properties like grounds state geometry, dipole moments, etc. but its restricted to only certain elements. MOPAC is mostly used to create a broad picture of the properties being studied to better approximate the basis set used during Ab initio calculations. Although Ab intio can be used to calculate very complex orbitals, within it it contains approximations, such as the Huckel approximation which assumes which states that non neighboring atomic orbitals contribute 0 to the orbital overlap energy. Another approximation which can be used during the experiments is the restriction of forming radical molecules, by using the value of RHF during the SCF type step of the process. This assumes all electrons are paired, therefore its used only in even numbered electron systems.

Experimental

Three unique molecules were studied. Different properties were studied for each molecule depending on their polarity, molecular structure, as well as their vibrational and rotational excited states . The following links (1) correspond to the data gathered during this experiment as well as experimental reference data.

HCl

Ozone

Phenol

Each data set was done using Ab initio integrals in GAMESS, with the exception of an AM1 calculation preformed on HCl with the MOPAC level of theory. Each molecule was drawn using MacMolPtl then transferred to Jmol to set up the calculation set. Each molecule was systematically done using 6-21G data set follwed by 6-31G and DZV to attain the optimal configuration giving the lowest energy. Additionally for the diatomic a potential v. bond length plot was done using the results from the DZV approximations. An approximated UV-Vis spectra of phenol was also attained using the vibrational data from the DZV log file.

    Conclusion
    The overall data contained energies that were underestimated compared to their reference values. The genereal trend in further levels of calculations form AM1 to DZV increased the accuracy of the results. Further as seen on HCl, as diffuse functions were added to calculations closer values to references were obtained. Another cause for the over stabilization of ozone was the restricted Hatree-Fock approximation or RHF. Since the electrons were always paired there was no unpairing of electrons to create changes in dipole moments.


    References

    1. Library of 3-D Molecules. A to Z Index of Molecules: HCl, Ozone, Phenol. (Accessed March 4, 2013)
    2. General Atomic and Molecular Electronic Structure System" 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.Su, T.L.Windus, M.Dupuis,         J.A.Montgomery J. Comput. Chem., 14, 1347-1363(1993).((Accessed February 12, 19 and 26 2013)
    3. Advances in electronic structure theory: GAMESS a decade later" M.S.Gordon, M.W.Schmidt pp. 1167-1189, in "Theory and Applications of Computational Chemistry: the first forty years" C.E.Dykstra,                 G.Frenking, K.S.Kim, G.E.Scuseria (editors), Elsevier, Amsterdam, 2005. (Accessed February 12, 19 and 26 2013)
    4. Jmol: an open-source Java viewer for chemical structures in 3D. http://www.jmol.org/ (Accessed February 12, 19 and 26 2013)