Choose the difficulty level for your homework. For each level, you have two tasks to accomplish. One of the tasks pertains to conformational analysis with existing molecular modeling programs. The second task pertains to the Monte Carlo or Molecular Dynamics method.
1. a) Build axial and equatorial conformers of methylcyclohexane and minimize each using TINKER MM3 force field. Analyze the energy components of the two minimized structures with TINKER. Calculate the energy difference between the axial and equatorial conformers. Assuming that entropies and molar volumes of the two conformers are identical, calculate the percentage of each conformer in vacuum at 273 K and 373 K. Discuss why one of the conformers is more stable than the other.
1. b) Perform literature search to get experimental or computational (e.g. at MP2 or CCSD(T) level) relative conformational energies for methylcyclohexane. Create a figure showing the structure of each of the two conformers (structures can be saved as images by clicking on the camera icon in MOLDEN). Assuming that the QM results are correct, discuss the accuracy of TINKER MM3 result for this molecule.
2. Based on examples covered in the Monte Carlo tutorial, write a program that performs Monte Carlo simulation of carbon monoxide in the Kratzer potential. Perform a Monte Carlo simulations of this system at 298 K. Calculate the mean distance, mean squared distance, and mean energy. Start the simulation at 1.4 angstroms, and determine the approximate number of steps that is needed to obtain converged results (i.e. the results should not significantly depend on the number of steps). Repeat the analysis with the same number of steps at 700K, and 1900 K. Analyze how the mean distance, mean squared distance, and mean energy change with temperature. Discuss your findings in relation to suitability of using minimum-energy structures for description of interactions between diatomic gases and the space shuttle during the re-entry phase where temperatures reach 1900 K.
1. a) Perform conformational analysis of methoxycyclohexane using TINKER MM3 force field, and identify all minimum energy structures. Analyze the energy components of the minimized structures with TINKER. Calculate the relative energies of conformers with respect to the global minimum. Assuming that entropies and molar volumes of the two conformers are identical, calculate the percentage of each conformer in vacuum at 273 K and 373 K. Discuss your findings.
1. b) Minimize each of the structures found in part a) with AMBFOR/GAFF force field in MOLDEN. Perform energy decomposition analysis (E q button in the Atom Attribute Window, the results go to the Unix Shell from where you started MOLDEN). Compare TINKER-MM3 and AMBER/GAFF results.
1. c) Perform literature search to learn about conformational preferences of substituted cyclohexanes and get experimental or high level QM (MP2 or CCSD(T)) relative energies for methoxycyclohexane. Create a figure showing the structure of each conformer (structures can be saved as images by clicking on the camera icon in MOLDEN), and its energy relative to the global minimum. List relative energies with the TINKER MM3, AMBFOR/GAFF, and high-level QM methods. Assuming that the QM results are correct, discuss the accuracy of TINKER MM3 and AMBFOR/GAFF for these two molecules.
2. a) Based on examples covered in the Monte Carlo tutorial, write a program that performs Monte Carlo simulation of a particle in a symmetrical double well potential given by E = r^4 - 4*r^2. Such potentials are sometimes found in H-bonded systems such as [F---H---F]-where the hydrogen can jump between the two electronegative atoms. Plot this potential from r = -2 to +2 (r = 0 corresponds to the symmetric placement of the particle). Then start the simulation from one of the wells and study how many Monte Carlo steps are required to obtain converged results at 298 K. Ideally, the population ratio should be 50:50, but consider that a good convergence is achieved when the population ratio in two wells is better than 45:55. Analyze the same system also at 700 K, 1300 K, and 6000 K and create histograms reflecting the probability distribution at each temperature. Create plots showing the mean distance, mean squared distance, and mean energy from each simulation against temperature.
2. b) Researchers frequently run such calculations on large macromolecules and collect structural information, such as distances during the simulation. The average distances from these simulations are sometimes used to describe the structure or reactivity of a molecule (e.g. "The Linear Dependence of Log(kcat/KM) for Reduction of NAD+ by PhCH2OH on the Distance between Reactants when Catalyzed by Horse Liver Alcohol Dehydrogenase and 203 Single Point Mutants". Discuss the usefulness of characterising the system by its average distance in case of single-well and double-well potentials.
1. a) Carefully read the Introduction and Results sections of a paper by Felice Lightstone and Prof. T. C. Bruice titled "Ground State Conformations and Entropic and Enthalpic Factors in the Efficiency of Intramolecular and Enzymatic Reactions. 1. Cyclic Anhydride Formation by Substituted Glutarates, Succinate, and 3,6-Endoxo-4-tetrahydrophthalate Monophenyl Esters". In this work, authors used MM3 force field to analyze minima for some monophenyl esters of succinic and glutaric acid.
1. b) Build structures for molecule I (if your PERM ends with odd digit) or IV (if your PERM ends with even digit) in this paper, and perform conformational analysis for your molecule. Set up your structure (as anion) with MOLDEN using TINKER MM3 force field but notice that the optimization fails because the TINKER MM3 implementation lacks parameters for phenol esters. To run the conformational analysis with TINKER, use a modified MM3 force field available here as your parameter file. Specify a larger number (e.g. 25) of search directions and limit the search for structures within 7 kcal/mol of the lowest energy structure. Compare the number of conformers found with the results of Lightsone and Bruice.
1. c) Identify the lowest energy conformer. This is an example of a typical tedious task that computational chemists face. To identify the lowest energy structure, one needs:
This is what computer programs such as Python excel at doing! However, writing such a program from scratch may be challenging to the beginners (it took me couple of hours). You may use the program I wrote after you fix three errors that I intentionally created so that you can think how this program works.
1. d) Visualize each structure with MOLDEN and identify structures where the carboxylate is within 3.2 angstroms from the ester carbonyl. Calculate the energy difference between this structure and the lowest energy structure after minimizing each with AMBFOR/GAFF force field. Compare this energy difference with TINKER-MM3 energy difference. Do your results agree with energies (or enthalpies) given buy Lightsone and Bruice?
2. Isopropanol has two low energy structures in the gas phase but the conformational preference in water is not well understood in this system. Do one of the following:
a) Perform molecular dynamics simulation of a single isopropanol molecule in a cubic box of water molecules using TINKER's dynamic program for a duration of 100 ps at 298 K. Use MM3 force field with TINKER. Write our structure files every two picoseconds. Determine the torsion angle in each structure either using MOLDEN or a program you wrote for this purpose (see the discussion for relevant math). Create an histogram showing the torsion angle distribution in aqueous isopropanol at room temperature.
b) Perform a Monte Carlo simulation of single isopropanol molecule in a cubic box of 512 water molecules with BOSS. Run the simulation at 75 centigrades for for at least 16 million configurations to get well-converged results. Use OPLS-AA force field; you need to assign appropriate parameters yourself this time based on the full oplsaa.par and oplsaa.sb files. Create an histogram showing the torsion angle distribution in aqueous isopropanol at room temperature. Estimate the population percentage of the symmetrical anti conformer from the solution simulation data. Find from the literature accurate relative energy of the anti conformer in the gas phase, estimate the population percentage of the symmetrical anti conformer in the gas phase. Discuss if the solvent changes the population of conformers significantly.
You will face several technical hurdles in either approach, but the hints here might be helpful.