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Typical Questions for Final Exam Describe the difference between the MCSCF and CISD methods. Imagine that you carried out HF calculations of a certain molecule and found that the orbital energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied MO (LUMO) are very close to each other. Now you need to improve your calculation by including electron correlation. What type of electron correlation, dynamical or nondynamical, will be more important for this case and why? Choose one of the following three methods for electron correlation calculations, MP2, CISD, or MCSCF, and explain your choice. Outline the Kohn-Sham Self Consistent Field method. In this outline, describe the main ideas of density functional theory, two Hohenberg-Kohn theorems, and draw a flow chart of the KS SCF procedure. Describe the difference between LDA, GGA, and hybrid density functionals. Explain the classification of partial atomic charges into Class I, Class II, Class III, and Class IV. How the charges are calculated in the Mulliken population analysis? Match the following calculations with the best method for them. Each method can be used only once. Give a very brief reason for each choice. [Note: While the highest-level method could be a good choice for any of the calculations, there is one superior combination when each method has to be used once.] Calculation Method Refine (optimize) the X-ray crystallographic geometry of a protein PM3 Electron affinity of ClO4 INDO/S Electronic excitation energy for a transition metal complex HF/6-31G(d) Energy difference between the boat and chair conformation of hexane HF/6-31+G(d) Barrier for the interconversion of the cis and trans isomers of C2H2Cl2 CHARMM force field Describe Hückel theory. Illustrate application of this theory to the allyl system – write the secular determinant and secular equations for this molecule. What is Molecular Mechanics (MM)? What are the four main kinds of terms used in the molecular mechanics force field? What are some advantages and disadvantages of MM? Describe the difference between the MCSCF, configuration interaction, and MöllerPlesset perturbation theory methods. How would you decide which method would be most appropriate for calculations of a particular molecule? What molecular properties can be computed using the GAUSSIAN program and with what kind of experimental data can they be compared? Take 1,2-dichlorobenzene as an example and write GAUSSIAN input files for calculations of these properties (for input files, you may write z-matrix only once and give different command lines for calculations of various properties. You need to calculate the standard heat of formation of chloroethane, C2H5Cl. Describe how would you do these calculations if you know: a) experimental heats of formation of C, H, and Cl atoms; b) experimental heats of formation of ethane C2H6, methane CH4, and chloromethane CH3Cl. What theoretical methods would you use for the cases a) and b)? Describe the Gaussian-2 (G2) method. What is its expected accuracy for energy calculations? What is the main idea of G2? What is the difference between trajectories and Monte-Carlo calculations in Molecular Dynamics? You study a bimolecular chemical reaction leading to a unimolecular product, A + B → TS → C, and, using GAUSSIAN, have managed to calculate enthalpies and entropies of the reactants, HA, HB, SA, and SB and the product, HC and SC, and the transition state, HTS and STS. Write expressions for the equilibrium constant between A + B and C, and for the reaction rate constant. Also, based on the available data, predict the activation energy and pre-exponential factor in the Arrhenius expression for this reaction. Match the following calculations with the best method for them. Each method can be used only once. Give a very brief reason for each choice. [Note: While the highest-level method could be a good choice for any of the calculations, there is one superior combination when each method has to be used once.] Calculation Method Average dipole moment of a water molecules in solution Hybrid QM/MM Accurate atomization energy and heat of formation of melamine INDO/S Geometric structure and frequencies of a medium-size organometallic molecule G3 ‘model chemistry’ Energy difference between different conformers of a medium-size organic molecule CCSD(T)/CBS Epoxidation reaction mechanism of a small molecule on the active site of chloroperoxidase MD simulation 13 B3LYP Barrier height in a small reaction system like CH4 + H → CH3 + H2 MP2 Electronic excitation energies of Fe(CO)6 HF C NMR chemical shifts for melamine