Abstract:

    The dipole moments, partial atomic charges, electrostatic potentials, lowest unoccupied molecular orbital (LUMO), highest occupied molecular orbital (HOMO), vibrational energies, and geometries of bromine, hydrogen sulfide, and p-dichlorobenzene were calculated using 6-21G, 6-31G, AM1, DZV, and PM3 as different levels of molecular orbit theory.  The calculated vibrational wavelengths for H₂S, p-dichlorobenzene, and Br₂ matched well with experimentally obtained IR Spectrum data. With the exception of p-dichlorobenzene, many of the levels of theory did not provide accurate energies levels and bond lengths for the studied molecules.  DZV was found to be the best level of theory to determine these characteristics of bromine, hydrogen sulfide, and p-dichlorobenzene. 

Introduction:

The molecular dipole moment, polarizability, probability of absorption of visible light, tendency to donate electrons in a reaction, and vibrational frequencies can be determined if the electronic structure of the molecule is known.  The variational principle, which states that the lowest energy version for the wavefunction is the best approximation for the actual wavefunction, is commonly used to perform molecular orbital calculations.  Thus, the energy can be found by taking the sums of trial wavefunctions.  The expectation value of the energy can be calculated through the Hamiltonian operator and by dividing by a normalization constant.  As the terms used to find the expectation value of energy increases exponentially with the amount of atoms in a molecule, these calculations can become overwhelming if done by hand.  Prior to computers, geometry optimization calculations were limited to molecules of only a few atoms due to the sheer complexity and length of the required calculations.  However, with current computer software programs, the best geometry for a larger molecule, such as p-dichlorobenzene, can be found in a matter of seconds.  There are multiple methods used to calculate the expectation value of energy.  These methods/levels of theory differ in regards to the number of integrals used to provide the calculations.  Levels of theory including AM1 and PM3 utilize empirical data for estimation of the values for two electron overlap integrals required for calculating the Hamiltonian expectation value.  AM1 and PM3 are relatively quick, as they are both significantly faster than complete ab initio calculations.  The most accurate level of theory is ab initio, in which all integrals are calculated.  The difference in ab initio methods is the size of the basis set, with 6-21G, 6-31G, and DZV being listed in increasing basis set size.     

            In this experiment, the molecules bromine, hydrogen sulfide, and p-dichlorobenzene were initially drawn and optimized using the Avagadro software.¹  The resulting .xyz file containing the geometries for the given molecule was opened in MacMolPlt.  Once the file was properly prepared and converted into an .inp file through MacMolPlt, the program Gamess was used to calculate the molecular orbitals in the form of .log files.  These orbitals, including the LUMO and HOMO, were visualized through the modeling software Jmol.  Additional runs between MacMolPlt and Gamess were used to generate a variety of optimized geometries using 6-21G, 6-31G, AM1, DZV, and PM3 as different levels of molecular orbit theory.  The resulting .log files were used to create vibrational files, UV-Vis (Single Pt. Energy) files, multiple variations of the DZV molecular orbit theory for hydrogen sulfide to identify conditions most similar to the experimental dipole, and potential energy files for graphical display on igor pro through MacMolPlt and Gamess.  These files were also used to visualize the partial atomic charges, bond lengths, and electrostatic potentials through the use of Jmol.

Links: Bromine, Hydrogen Sulfide, Para-Dichlorobenzene

Conclusion:

    6-21G, 6-31G, AM1, DZV, and PM3 all provided somewhat decent geometry approximations, with DZV being the most accurate.  Many of the levels of theory did a poor job at calculating accurate energies levels and bond lengths for the studied molecules, with the exception of p-dichlorobenzene.  Initially the H₂S calculated dipole significantly deviated from the experimental value.  However, after adding diffuse functions to the DZV run for H₂S, the calculated dipole only differed from the experimental value by ~5%.  The DZV logs showed the resulting calculation from Gamess of the vibrational energies for the molecule.  When compared to an experimentally obtained IR spectrum, the vibrational wavelengths found matched well for H₂S, p-dichlorobenzene, and Br₂.  Overall, DZV was the most accurate level, as it contained the largest basis set, and was deemed useful while the other levels of theory were not.

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