## Assignments

#### Level 1

1) Read the Simplified Introduction to Ab Initio Basis Sets by Dr. Jan Labanowsy and explain how exponentials for Gaussian functions are usually determined. Use XMGrace, Mathematica, or any other data fitting program to create STO-5G basis set that approximates the radial (Slater-type) function that you obtained as a solution to hydrogen atom in the tutorial. This involves determination of optimal contraction coefficients and Gaussian exponents, possibly via numeric least squares fitting of Gaussian functions to data points that represent the true radial wave function of hydrogen atom. Examples on how to perform data fitting with Mathematica may be found in the tutorial Introduction to Mathematica.

2) Calculate the Hartree-Fock energy at the basis set limit for the Ne atom using correlation consistent basis sets cc-pVXZ up to X = 6. Provide a graph illustrating the convergence of the energy with respect to the cardinal number. Also, make a graph illustrating the time required for the calculation as a number of basis functions used. Perform basis set extrapolation to obtain value for E. Compare your basis set limit energy result with an accurate literature value; provide the literature reference. You may use a computational chemistry program of your choice. However, Firefly does not currently support cc-pV5Z and cc-pV6Z basis sets, so consider Gaussian for this task.

3) Create an image that effectively illustrates the electrostatic potential of a water molecule mapped on HF/6-31+G(d,p) electron density. Briefly discuss your findings in terms of polarity of water.

#### Level 2

1) Calculate the energy of the He atom at the Hartree-Fock (SCF), second-order perturbation theory (MP2), and fourth-order perturbation theory (MP4) levels using three different basis sets. Use 3-21G as the smallest basis set; this Pople-type basis set provides only a couple of s-type functions for helium. Use cc-pVTZ as the medium-size basis set; this correlation-consistent basis set provides a few s functions, two p functions, and one d function. Use aug-cc-pV5Z as the large basis set. This augmented correlation-consistent basis set provides several s functions, five p functions, four d functions, three f functions, and two g functions. You can perform this calculation with Firefly or with Gaussian, or with both if you want to compare the energy values and the speed of computation.

Prepare a table that shows the Hartree-Fock energy, total energy, and the correlation energy of the helium atom in these calculations. Compare your results with true (basis set limit or Hylleraas-type treatment) values from the literature; provide a reference. Discuss the importance of using a flexible basis set for obtaining accurate correlation energies. Are the high-angular momentum functions present in aug-cc-pV5Z critical for getting a accurate Hartree-Fock energy?

Prepare a table that summarizes the total number of basis functions and computational (CPU) times of these calculations. Discuss the scaling of Hartree-Fock, MP2, and MP4 calculations with respect to number of basis functions.

2) Calculate the syn rotational barrier in 1,2-dicloroethane at the basis set limit using the Hartree-Fock method. Gaussian is probably a good program to carry out this calculation. You may optimize the structures of the staggered minimum and the eclipsed saddle point at the HF/6-31+G(d,p) level. If you employ the symmetry correctly, the structure of the saddle point can be obtained by usual Newton-Rhapson minimization, otherwise the Gaussian directive Opt=(CalcAll,TS) can be used to reach the saddle point. Analyze the output of the saddle point optimization job to verify that you indeed have one negative frequency and one negative eigenvalue in the Hessian. Use cc-pVDZ, cc-pVTZ, cc-pVQZ basis sets for single point energy calculations. Calculate the Hartree-Fock limit for the minimum and the saddle point. Provide graphs illustrating the convergence of the absolute energies with respect to the cardinal number.

Obtain the rotational barrier by subtracting the energy of the minimum from the energy of the saddle point. The energies are in atomic units (Hartree); convert these to more common kcal/mol units by multiplying the energy difference with conversion factor 627.51. Compare your result with experimental data and comment on the accuracy of the HF calculations for estimating this rotational barrier. Firefly (PC GAMESS) may be a good choice for this task; the correlation consistent basis sets that you need are stored in the directory /usr/local/pcgamess/

3) Create an image that effectively illustrates the electrostatic potential of a anisole mapped on MP2/6-311+G(d,p) electron density. Please see the Gaussian manual for keywords that yield MP2 density. Briefly discuss your findings in terms of the reactivity of anisole toward electrophiles.

#### Level 3

1) Carefully read the tutorial at http://www.chem.ucsb.edu/~kalju/chem226/public/pcgamess_tutorial_A1.html that analyzes the energetic justification behind the Zaitsev rule in organic chemistry. Carry out analogues calculations and insightful analysis with two modifications: (i) the starting compound is 2-ethylcyclohexanol, and (ii) the basis set for all MP4(SDQ) energy evaluation is cc-pVTZ. You can still use 6-31+G(d,p) for Hartree-Fock geometry optimizations. When performing calculations of secondary and tertiary carbocations, maintain Cs symmetry by placing the -CH3 group of the ethyl substituent in the mirror plane that divides the carbocation into two. Feel free to copy the layout of the tutorials (HTML tables etc) when writing up your analysis. You may find that one of the two workstations in the front of the CCL lab is better suited for performing these calculations.

2) Calculate the stability of the water dimer at the basis set limit using the Hartree-Fock method. You may optimize the structures of isolated H2O and the dimer in the the HF/6-311++G(d,p) basis. If you use the Newton-Rhapson algorithm, start from a good initial structure (feel free to consult literature on how water dimer looks), then verify that your Hessian has only positive eigenvalues. Use cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-PV5Z basis sets for single point energy calculations. Calculate the Hartree-Fock limit for the isolated molecules and the dimer. Provide graphs illustrating the convergence of the absolute energies with respect to the cardinal number. Also provide a graph illustrating the convergence of the stability of the water dimer (recall that you can convert the energy difference to kcal/mol units by multiplying with 627.51) with respect to the cardinal number. Compare your result with an experimental stability of the water dimer and comment on the accuracy of the HF calculations for estimating strengths of intermolecular complexes that are dominated by electrostatic interactions.

3) Minimize the structure of carbon dioxide dimer at the HF/cc-pVTZ and MP2/cc-pVTZ levels and compare the minimized geometries in terms of carbon-carbon bond distance and oxygen-carbon-oxygen angle. Create an image that effectively illustrates the electrostatic potential of a carbon dioxide dimer mapped on MP2/cc-pVTZ electron density. Please see the Gaussian manual for keywords that yield MP2 density. Discuss what interactions are responsible for the formation of carbon dioxide dimer? Briefly discuss your findings in terms of the sublimation temperature of carbon dioxide.