Molecular Orbital Calculations of Water, Diboron, and Chlorobenzene
Jelinek, Lauren and Yang, Dasan

Abstract

            Computers can be used to calculate the structure of a molecule and display said structure in three dimensions. In order to determine the geometry of the molecule, the computer uses molecular mechanics or quantum mechanics and common assumptions. Within quantum mechanics there are many methods that use different combinations of simplifications to the molecular model. The result with the lowest energy using the least assumptions is commonly the most accurate method of calculation. In this experiment the molecules diboron, water, and chlorobenzene were analyzed. Avagadro was used for an initial guess, which was then put into MacMolPlt and GamessQ to further improve the model. Jmol was then used to display the molecules in 3D and Igor was used to display potential energies. The quantum method with the least assumptions and the most accurate was DZV, however, this method still deviated from the results gathered through reported experimental values.


Introduction

 

The locations of electrons and their energies may be used to predict useful properties such as the molecular dipole moment, polarizability, vibrational frequencies, probability of absorption of visible light, and tendency to donate electrons in a reaction, if their electronic structure is known. Quantum mechanical molecular orbits use wavefunctions to describe the electrons in a molecule. Using the variational principle, we were able to approximate true wavefunctions by adjusting parameters to find the lowest energy version of the wavefunction, which is the best approximation. The lowest energy wavefunction is represented by the coefficients that produce the lowest energy for the electron, which can be calculated by calculating the expectation value of the energy. While the individual wavefunctions used in the approximation are normalized, the approximated wavefuction itself must still be normalized, putting additional constraints on the coefficients. The bigger the basis set, the better the accuracy for the energy prediction.

            The geometry of the molecule must be adjusted as well to accurately predict the electronic energy. The geometry of the electrons and nuclei are related to the potential energy of the system. By rearranging the geometry to find the lowest energy value, the calculation is then optimized once the minimum has been found.

Computer software and quantum mechanics are combined to create 3d images and 2d projections of chemical structures. These structures are interactive and can be used to display the properties mentioned above through optimization. Once a basis set method is chosen, the computer calculates an accurate molecular geometry to predict the electronic energy of the system. Each method includes a different amount of approximation, affecting the accuracy of the calculations. However with more approximations, less time is needed for the computer to complete the calculations.

The ab initio methods are the quantum mechanical MO models with the least approximations and the largest basis sets, therefore the most accurate. Even so, the ab initio methods use common assumptions: the Born-Oppenhiemer approximation stating the nuclei are stationary relative to the electrons, the Hartree-Fock approximation saying the electrons move independently of each other but their motion is affected by the electron field created by the other electrons and nuclei in the molecule, and the linear combination of atomic orbitals (LCAO) approximations to construct the molecular orbital2. The methods used in the experiment were the 6-21G, 6-31G, and the DZV(Double Zeta Valence) in order of lowest to highest optimization accuracy.

The semi-empirical method MOPAC (molecular orbital package) is comprised of four choices of Hamiltonian equations used to estimate the values for the expected value. Common assumptions for the MOPAC in addition to those of ab initio: only valence electrons ore considered, inner shell electrons are not included in calculations, selected interactions involving two atoms at most are considered (called the neglect of diatomic differential overlap, or NDDO), parameter sets (calculated data fitted with experimental data) calculate iterations between orbitals. The MOPAC methods used in the experiment were the Austin method 1 (AM1) and the parameterized model 3 (PM3), where PM3 has been parameterized for more chemical elements2.

An initial guess to the molecular structure was used prior to the ab intio or MOPAC methods using the software Avogadro. The software uses the molecular mechanics method instead of quantum mechanics to estimate the geometry of the molecule1. In molecular mechanics the molecule is treated classically with atoms as balls and bonds as springs connecting the balls. Using harmonic oscillation calculations, the method optimizes the geometry so that the bonds are under the least amount of strain. This method depends on the number of atoms instead of electrons and is better for larger molecules. Once the molecular mechanics method was optimized in Avagadro, the result was then imported into MacMolPlt and GamessQ to optimize the structure using the quantum mechanical MO methods. These molecules were then displayed in Jmol.


Results
The following are links to the calculations completed using Avagadro, MacMolPlt, GamessQ, Jmol and IGOR:     Water    Chlorobenzene    Diboron    IR Spectra

 

 

Conclusion
            Overall the DZV method was supposed to be the most accurate method because its basis set was the largest and it used the least assumptions. While this held in some cases, when calculating the bond angles and lengths, AM1 was a better comparison most likely due to the mechanical method being better for smaller molecules. In the case of the bond lengths and bond angles, all the methods were close each other in the values they provided. For chlorobenzene AM1 was found to be the most accurate optimized geometry out of all of our theories used for calculating bond lengths and 6-31G was found to be the most accurate optimized geometry for the bond angles. The percent error found between the calculated bond lengths and the experimental literature was found to be 0.71% for C=C, 2.13% for C-Cl, and 1.57% C-H. For water AM1 was found to be the most accurate optimized geometry out of all of our theories used in calculating bond length and bond angle. The percent error between the calculated bond length and the experimental was 0.26%. The percent error between the experimental bond angles and the calculated was 0.96%. The molecule diboron had no literature information due to its rarity and synthetic nature. DZV’s accuracy can be most clearly seen in the potential energy of bond stretching graph of diboron where DZV's energy is the lowest of the methods, following the variation principle. However even using the DZV method, the UV-vis values gathered were over 200% away from the literature values for the aromatic molecule chlorobenzene and showed no correlation to each other. Overall one can conclude that the use of computers to simulate a molecule's geometry produces extremely close results, however some deviation still arises due to the assumptions made during the calculation process.

 

 

References

 

1.     (1) Mihalick, J; Gutow, J. Moleculare Orbital (MO) Calculations. 2015.

2.     (2) Mohrig, J; Hammond, C; Schatz, P. Techniques in Organic Chemistry: Miniscale, Standard Taper             Microscale, and Williamson Microscale. 3rd ed. W.H. Freeman and Company: New York. 2010.

3.     (3) Lide, D. CRC Handbook of Chemistry and Physics. 73rd ed. CRC Press, Inc.: Boca Raton, US. 1993.

4.     (4) NIST. NIST Standard Reference Database Number 69. 2011. Web. http://webbook.nist.gov/chemistry/