Previous Up

Assignments

Level 1

1) Read the paper Accuracy of spectroscopic constants of diatomic molecules from ab initio calculations . Carry out the frequency analysis using the Hartree Fock method with cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. Answer the following questions.

  1. Summarize what you learned from Figure 1 in this paper.
  2. Why didn't the authors show SCF results on Figure 2 even though they have made plots for this data?
  3. Create a series of graphs showing the convergence of harmonic frequency with increasing basis set for each molecule and visually estimate the frequency at the HF limit.
  4. Discuss fundamental reasons why HF harmonic frequencies differ from experimental harmonic frequencies. Is there a quick fix if one wishes to use HF frequencies for the purpose of identification of large organic molecules based on their IR spectra?

2. a) Calculate the syn (Cl-C–C-Cl = 0°) rotational barrier in 1,2-dichloroethane in the gas phase based on MP3 single point energies at HF/6-31+G(d,p) geometries to treat electron correlation. Make sure to use an appropriate basis set in the MP3 calculation. Make a statement about the effect of electron correlation in this case.

2. b) Calculate the syn rotational barrier in 1,2-dichroroethane in water. You may use HF/6-31+G(d,p) calculations with an appropriate implicit solvent model. Rationalize the observed direction of the solvent effect.

Level 2

1) Read the paper "Accuracy of spectroscopic constants of diatomic molecules from ab initio calculations" and a paper "Coupled-cluster connected quadruples and quintuples corrections to the harmonic vibrational frequencies and equilibrium bond distances of HF, N2, F2, and CO". Carry out geometry optimization and harmonic frequency analysis of F2 at the MP3 level using aug-cc-pVDZ, aug-cc-pVTZ, and aug-cc-pVQZ basis sets with a program of your choice. The last of these is a rather challenging calculation and you should expolore ways to carry it out with a minimal amount of CPU time spent. Some things to consider include:

  1. 1) Gaussian 03 offers analytic second derivatives at the MP2 level but not at the MP3 level. However, Hessian calculated at the MP2 level is an excellent starting point for the BFGS algorithm
  2. 2) Gaussian offers analytic first derivatives at the MP3 level. Second derivatives at the MP3 level in Gaussian are evaluated by numeric differentiation of analytic first derivatives.
  3. 3) PC GAMESS does not allow automated geometry optimization or frequency analysis at the MP3 level but offers extremely fast single point MP3 energies.
  4. 4) Numeric differentiation requires rather accurate energy values. With PC GAMESS / Firefly, the following performance and accuracy-related options are recommended:
    $contrl icut=10 inttyp=hondo $end
    $system mwords=60 $end $scf nconv=7 $end $mp3 cutoff=1E-14 $end
  5. 5) Speed of electron correlation calculations with PC GAMESS depends on the choice between the the conventional ($scf direct=.f. $end) and direct ($scf direct=.t. $end) method for the SCF part. If you have a very fast disk, it is better to write the atomic integrals to the disk before starting SCF, these integrals will be read in also before the MP3 stage. If the disk is slow, it is better to recalculate AO interals at each SCF cycle as well as during the MP3 stage.
  6. 6) With PC GAMESS, specify the basis set on the command line, e.g. -b /usr/local/pcgamess/acc-pvqz.lib

Provide the following with your answer:

  1. Discussion about the most efficient (in terms of CPU time) strategy to obtain the desired results.
  2. Discussion about the geometry of F2 with MP2, MP3, CCSD, CCSD(T), and CCSDTQ methods near the basis set limit. Specifically, discuss one fundamental reason why the MP2 bond length is far off from the experimental value
  3. Discussion about the harmonic frequency of F2 with HF, MP2, MP3, CCSD, CCSD(T), and CCSDTQ methods near the basis set limit. Specifically, why would authors expect that "all high-order connected contributions to the harmonic frequencies are negative".
  4. Evaluate the suggestion that "the harmonic frequency at the MP3 basis set limit can be readily obtained by exponential extrapolation of aug-cc-pVDZ, aug-cc-pTZ, and aug-cc-pVQZ frequency values."

2) Consider the stereoselective synthesis of a methyl ester of 2-[(1S)-1,2,2-trimethylpropyl]-4-pentene(dithioic) acid from (S)-3,4,4-trimethyl-1-(methylthio)-1-(2-propenylthio-(Z)-1-pentene. One of the predictions of the semiempirical PM3 method was that this reaction is thermodynamically unfavorable. Reinvestigate this reaction using correlated ab initio or density functional theory. Each student should individually decide on the appropriate way to generate one conformer for the reactant, and one conformer for the product, and optimize these structures with their method of choice. Calculate the reaction energy and reaction free energy in the gas phase as accurately as you possibly could, given the requirement that none of your calculations should take more than 16 hrs on our local workstations. Then calculate the reaction energy, and reaction free energy in the water using an appropriate implicit solvent model. Note that the free energy calculation in water does not require a frequency calculation. The statistical thermodynamics formulas that allow the calculation of the enthalpy and entropy from vibrational frequencies are strictly valid for isolated molecules.

Level 3

1) Discuss what is the main difference between the MP4(SDQ) and MP4(SDTQ) methods. Determine the minimum energy structure of F2 at MP4(SDQ)/aug-cc-pVTZ and MP4(SDTQ)/aug-cc-pVTZ levels. Calculate energies on 5-point stencil centered at these structures. Write a computer program that will perform the following tasks:

  1. Numerically calculates the first, second, third, and fourth derivative of the potential energy with respect to displacement based on user-supplied energy values via centered finite difference formulas. Notice that if you work with units of Å and Hartrees, the derivatives have units of Hartree*Å-1, Hartree*Å-2, Hartree*Å-3, Hartree*Å-4, respectively.
  2. Calculates the harmonic frequency (waven), the equilibrium rotational constant Be (via the moment of inertia), the quartic centrifugal distortion constant, and the vibration-rotation coupling constant; express these in cm-1 units. The quartic centrifugal distortion coefficient for diatomics is given as 4*Be**3 / waven**2 and the vibration-rotation coupling constant for diatomics is given as -(2*Be**2 / waven )*( (2*Be*r**3*cubic_k ) / (hp*c*waven**2 ) + 3)
  3. Creates a plot that shows the first five vibrational energy levels for F2 at the MP4(SDTQ)/aug-cc-pVTZ level. The y-axis of this plot should be in cm-1 units, the x-axis could be either in meter or angstroms, you are allowed to consider the minimum energy distance as the origin in this graph.
  4. Creates a plot that shows the first five vibratioal wave functions for F2 at the MP4(SDTQ)/aug-cc-pVTZ level. You may scale these wave functions and show them on the same plot together with the vibrational energy levels.

Compare your MP4(SDQ) and MP4(SDTQ) minimum energy structures, harmonic frequencies, centrifugal distortion constants, and vibration-rotation coupling constants with experimental data. Discuss relative merits of MP4(SDTQ) over MP4(SDQ) for spectroscopic description of fluorine.

2) Do one of the following projects:

  1. Calculate the visible spectrum of 2-(4'-hydroxystyryl)-N-methyl-quinolinium-betaine in the gas phase with CIS and TDDFT methods using an appropriate basis set. Repeat the calculations in water with a suitable implicit solvent model. Then construct an explicitly solvated structure for 2-(4'-hydroxystyryl)-N-methyl-quinolinium-betaine that contains at least three appropriately placed water molecules. Calculate CIS and TDDFT spectra of this model using the same basis set as earlier. Discuss the performance of CIS vs. TDDFT. Discuss the ability of explicit and implicit solvent models to predict solvatochromic shifts in this case
  2. Study the effect of solvation on the Menschutkin reaction between methyl chloride and N,N-dimethylamine or quinuclidine using an appropriate implicit solvent model. Reoptimize the reactants, products, and the transition state with a suitable polarizable continuum model at the HF level using a basis set that you think is appropriate for the description of his reaction. Perform a frequency calculation to verify that the optimized transition state is indeed the first order saddle point. Provide a rationale for the observed solvent effect.
Previous Up

Materials by Dr. Kalju Kahn, Department of Chemistry and Biochemistry, UC Santa Barbara. ©2008.