Expt MM 1 MOLECULAR MODELING AND PREDICTIONS OF EQUILIBRIUM CONSTANT FOR MENTHONE (trans) AND ISOMENTHONE (cis) ISOMERS (MM) Important Modification Note the software in use may be changed in 2008 to Scigress. Scigress is a new version of CAChe with slight modifications so as you read directions if a step doesn t work exactly as written then you will need to try a logical alternative or alternatives - please record any variations on these pages and share with instructor. Please consider any trial and error as part of the fun and challenge of the experiment. Also, following these directions are another set of instructions Evaluations of Conformations of Menthone and Isomenthone that have many detailed steps indicated. You should read and refer to these instructions as well as the ones below to carry out this computational experiment. OBJECTIVE The objective of this experiment is to use molecular modeling software to predict the relative amounts of menthone and isomenthone in equilibrium under acidic conditions. These two molecules are diastereomers (configurational stereoisomers that are not enantiomers). They both have methyl and propyl substituents on a cyclohexane ring. The menthone has methyl and propyl substituents on opposite sides of the ring and so is referred to as being in a trans geometry. The isomenthone has methyl and propyl substituents on the same side of the ring and so is referred to as being in a cis geometry. Menthone is trans-1-methyl-4-isopropyl-3- cyclohexanone, and isomenthone is cis-1-methyl-4-isopropyl-3-cyclohexanone. A comparison will be made of the relative amounts of these cis and trans geometries as expressed in the equilibrium constant K where K = [menthone]/[isomenthone]. The molecular modeling based result will be compared to available experimental data on the relative amounts of each. INTRODUCTION TO CONFORMATION AND ENERGY Conformation As we examine rotation around the middle C-C bond for a molecule such as butane, we find that there are staggered and eclipsed conformations. The staggered conformations have lower torsional energies and are more stable than the eclipsed conformations. There are two principle staggered conformations anti and gauche. The anti conformation exists when the two end methyl groups are as far apart as possible and the dihedral angle is 180 o. The gauche conformation exists when the two end methyl groups are at a dihedral angle of 60 o or - 60 o. If there are other side groups on the butane molecule the gauche conformations may be at lower energies at angles other than at exactly 60 o angles.
Expt MM 2 Energy For butane the anti from is more stable than the gauche by 0.8 kcal. As the methyl groups come closer to hydrogens or closer to each other in the eclipsed conformations, the potential energy increases by up to 6 kcal. The proximity of the methyl groups causes an increase in energy due to repulsive van der Waals forces (steric hindrance). Since these energy differences are low relative to thermal energy at room temperature, a given molecule moves continuously from one conformation to the next due to molecular collisions. We say there is free rotation around the carbon-carbon single bond. However, the energy differences are large enough so that at any given time there may be a larger population of molecules in the lower energy conformations. As a result of this population difference, there may be differences in the relative amounts of product molecules formed from two different conformations of an intermediate molecule. Menthone and Isomenthone In this experiment we are not dealing with rotation around a single bond but rather dealing with methyl and propyl groups in axial and equatorial positions around a cyclohexane ring. The isopropyl group remains in the equatorial position while the ring flips (under acidic conditions) to place the methyl in an equatorial (trans, menthone) or axial (cis, isomenthone) position. See drawing in CAChe directions that follow for clarification. Because there are two arrangements in equilibrium with each other then the relative amounts can be expressed by an equilibrium constant, K. Molecular modeling with molecular mechanics calculations allows us to calculate difference in steric energy in the menthone and isomenthone molecules, determine the corresponding equilbirium constant K, and then find the mole fraction of menthone. This calculated mole fraction of menthone can be compared to the value determined from experiment. EXPERIMENTAL RESULTS We will NOT be doing the laboratory portion of this experiment but we will use results that have been obtained previously. Under acidic conditions menthone was allowed to isomerize to isomenthone and an equilibrium mixture established. For purposes of our calculations we will consider the equilibirium to be written as isomenthone menthone (1) with menthone considered to be on the product side. The corresponding equilibrium constant K is given by K = [menthone]/[isomenthone] (2) or K = X m /X i (3) where X m and X i are the mole fractions of menthone and isomenthone, respectively. And if we consider the special case of a binary mixture, since the sum of the mole fractions is equal to 1, one can write X m + X i = 1. (4)
Expt MM 3 Given the equilibrium constant K and Eq. (3) and Eq. (4) then one can find the value of X m. When the experiment was done (see following CAChe directions for details) it involved refluxing menthone in a mixture of glacial acetic acid and 1.0M hydrochloric acid. After the equilbirium was established where menthone and isomenthone are both present, these molecules were extracted and the mixture isolated so the optical rotation of the mixture could be measured. The experimental optical rotation was measured and found to be -3.0 degrees. The specific rotation of the isomenthone is A i = +92 and menthone is A m = 30 degrees, and the measured angle of rotation, A, for a mixture is given by A = (A m ) ( X m ) + ( A i ) ( X i ) (5) or combining with Eq. (4), the above can be written as A = (A m ) X m + ( A i ) (1- X m ) (6) Use the information above to calculate the experimental mole fraction of menthone, X m, and isomenthone, X i. Next calculate the experimental equilibrium constant K. *Please note the angles discussed in this experimental section pertain to the rotation of plane polarized light by molecules that contain chiral carbons. These angles have nothing to do with dihedral angles discussed in all the other parts of this computational experiment. COMPUTATIONAL THEORY Consider again the following equilibrium isomenthone menthone (7) and corresponding equilbirium constant K= [menthone]/[isomenthone] (8) The Gibbs free energy, G, for this reaction is related to the equilibrium constant, K, by G = RT ln(k) (9) Recall that changes in Gibbs free energy, enthalpy, and entropy are related by G = H T S (10) and that if the change in entropy is small during the isomerization equilibration then the Gibbs free energy change is dominated by the change in enthalpy which can be estimated from the difference in steric energy in the two isomers G ~ H ~ E steric (11) Therefore combining the equations above, we may write the approximation
Expt MM 4 E steric = R T ln(k) (12) or K = e ( Esteric /R T) (13) The difference in steric energy is given by E steric = (E m E i ) (14) where E m is the calculated steric energy of menthone and E i is the calcualterd steric energy of isomenthone. Recall that any thermodynamic difference or change is always expressed as (final initial) or (product reactant) and that an equilibrium constant is always ( products / reactants ). For the purpose of using the equations above, we assume the equilibrium is at the boiling temperature of glacial acetic acid 118 o C or 391K and use a value of R= 1.987 (cal/mol K) and appropriate conversion factor since the CAChe calculations of energy are expressed in kcal/mol. After completing CAChe modeling and calculations you will report E i, E m, E steric, K, and X m values and compute the percent error comparing computed and experimental values of X m. Assume the experimental value is the accepted value and determine the percent error of the molecular modeling X m relative to this accepted value. Answer sheets are provided to guide your calculations and indicate what to report. GENERAL INTRODUCTION to CAChe (C-omputer A-ided Che-mistry) Molecular mechanics and computational chemistry visualization is an essential tool in a many research areas. There are many different commercial software packages that do molecular modeling calculations. The software we are using is called CAChe and is marketed by Fujitsu company. CAChe Scientific's Chemist's Guide to CAChe states, "Computer aided chemistry includes all the ways computers help a chemist, both for calculations and visualization. Early evolutions of computational chemistry required high powered computers and typically lacked an intuitive or interactive interface. Quality visualization is more recent. Computer aided chemistry, as developed by CAChe Scientific, effectively marries calculations and visualization in a complete chemistry workstation." In other words, with this software it is possible to visualize (to see) the molecule of interest. The results of mathematical equations that calculate the positions of atomic nuclei and the electron clouds that surround them are there to be seen. Until recent years there was no link between the powerful mathematical equations that had to run on mainframe computers and a visual result. You got numbers, but nothing to visualize. Now we can do the math and see the molecular result. Molecular modeling such as the CAChe WorkSystem has opened up a whole new world of possibilities that you can explore. In the classical approach, molecules are considered to be a collection of atoms and bonds holding the atoms together. Information on atomic radii and bond strengths, lengths, and angles are used to find the best (minimum energy) position of atoms. This classical approach can be used to determine a molecule's size and three-dimensional geometry.
Expt MM 5 Quantum mechanical models are based on the Schrodinger equation that treats electrons as waves and seeks to find the energy and spatial probability of these electron waves. MOPAC quantum mechanical models are based on semi-empirical solutions to the Schrodinger wave equation. These calculations can give estimations of spectroscopic properties, distribution of charges within a molecule, and estimations of surface area, and molecular volume based on electron orbitals (clouds of negative charge). Molecular orbital calculations are more sophisticated than molecular mechanics calculations and require more computational time on the computer. In this computational experiment, you will be using molecular mechanics calculations to estimate relative energies of the two molecules. These comparisons of relative steric energy are only valid if the molecules are the same formula and nearly identical (isomeric forms). Steric energy does not have an absolute meaning in the way that, for example, heats of formation H f do. MOLECULAR MODELING EXPERIMENT AND ANALYSIS ALTHOUGH YOU ARE WELCOME TO DISCUSS THE PROCESS OR ANY PROBLEMS YOU HAVE, EACH PARTNER MUST DO ALL COMPUTER WORK AND CALCULATIONS INDIVIDUALLY. Getting Started If using a computer in the chemistry computer lab, move the mouse to start. The computer should already be turned on. Enter your Username and password for your OneNet Account and click OK. When you are done at the end of the lab, be sure to choose Log Off option from Shut Down, but do not turn off computer. Open My Documents Folder (located on the desktop) and create a new folder with your name. Under File choose Open and choose New Folder. Anything you save must be placed in your folder only. Do not save any CAChe file in any other place than in your named folder! Expect files to be purged at the end of each semester. If you need a permanent copy beyond that time you need to save to your OneNet account or on a flash drive or other storage device. Using CAChe You can think of CAChe as a three-step process that includes: drawing a molecule, carrying out a calculation, and observing the results of the calculation. Double click on the CAChe Workspace to open it. Enlarge workspace window. Drawing a Molecule Refer to the CAChe tutorial that you previously completed for additional assistance if you need help. As you draw, make sure that you select not only appropriate atom, but also correct hybridization, charge, and bond. The box with charge specified for a neutral atom will be 0 or simply blank. You can use Select Tool to draw a box around items or click on item to highlight. You can then remove the highlighted item by use of delete key on keyboard. You can immediately correct
Expt MM 6 mistakes by choosing Undo under Edit on menu bar. The Select Tool (on Tool palette) can be used to click on a single atom or bond or to draw a box around a collection of atoms that can then be removed by striking the delete key or using the Cut or Clear choices under Edit menu. Draw the menthone and save. Draw the isomenthone and save. Be sure to get the cyclohexane from the fragment library to begin your structures. However, do not save anything in the fragment library files. Always save in a separate folder with your name. After you draw a new molecule, hold down Ctrl key and strike f key to center and size molecule. Choose Rotate from Tool palette and rotate molecule to observe from various angles. Every time you draw a new molecule you should do Ctrl f and rotate to carefully observe the three-dimensional structure of the molecule. Be sure to do Comprehensive Beautify prior to saving structures. To save the molecular structure, under the File Menu select Save. When box of places to save appears, go to the desktop and open My Documents folder and then open your named folder. You must save your files only in your own named folder. Please name file with appropriate molecules name and save. CAChe will use this file in later calculations. You can use the full name of molecules for their files but not more than 31 characters. Carrying out Molecular Mechanics Calculation and Observing Results The CAChe pages that follow beginning with Evaluations of Conformations of Menthone and Isomenthone will guide you through the CAChe procedure that you need to use, but there are some additional comments below and if needed refer to the CAChe tutorial pages that discuss generating Energy Maps for additional help. The Mechanics calculation is a classical calculation. The program considers the molecule to be a collection of spherical atoms connected by spring-like forces. The program finds the minimum energy confirmation (optimal structure) by minimizing the energy associated with the stretching, bending, and twisting forces of the forces holding the atoms together. An energy map will provide you with a graphical representation of the relationship between molecular energy and conformation or geometry of the molecule. To generate an energy map, you must add a geometry label (called the search label). There are several types of search labels that can be placed on a molecule, but in your work you will use a Dihedral Angle label. 1. Can refer to the Tutorial on Energy Maps if needed but details for this specific experiment are given in the procedure indicated in Evaluations of Conformations of Menthone and Isomenthone which follows this section. General procedure is also outlined below. 2. Rotate molecule so all four atoms can be easily seen. From Tool palette, choose Select Tool. Highlight four atoms in order for dihedral angle and then set up search range. Click on the number 1 atom, then hold the shift key and click in order on atoms number 2, 3, and 4. The first atom you clicked on to select is the one that moves when dihedral angle is varied. The dihedral angle represents rotation around the bond between the second and third atoms.
Expt MM 7 3. Under Adjust select Dihedral Angle. In the small window that appears click on Define Geometry Label. Select search range. These settings will allow us to search the full range of dihedral angle conformations. Click OK. Choose Experiment and then select New. Select options chemical sample, optimize geometry, and MM2 in dialog window. See item 5 in separate set of instruction pages that follow these pages. 4. If message appears indicating some files will be overwritten by additional files then click OK. Observe output until calculation complete and then review how Final E (total energy) varies as (dihedral angle) is changed. 5. You should observe the results on two windows: the first is a graph of molecular energy versus dihedral angle and the second is a model of the molecule. Set left window to calc_energy and set right window to dihedral_angle. You can point and click on the mouse to make either window active and you can rotate the molecule when its window is active. If the graph window is active, you can click on the graph to move the small gray ball that marks a spot on the graph. Move the ball on the energy diagram or click on a spot on the energy curve on left, or click the arrow at bottom of right window to change angle settings on molecule box. As you do so, the dihedral angle of the molecule will change and you can see the change in the model and read the corresponding energy value from the bar above the molecular model. You can click on angle setting at bottom and watch how both graph and molecule change. Use the angle box and step quickly through angles to observe energy change. Step through the graph changing the dihedral angle and observe how energy values change. Record the lowest energy from graph and angle of lowest energy. Record these values for the menthone and repeat for the isomenthone. While still in lab show the instructor your results sheet with recorded values so you can be advised if there are problems. As you observe rotation of either of the two molecules you have modeled, it may not be obvious why there should be steric hindrance since atoms seem far apart when observed in the ball and stick model. To get a better feel for steric hindrance try observing both of your molecules as space filling models and step through rotation angles around dihedral angle. Second Computational Experiment After you have completed the menthone and isomenthone CAChe calculations above, do the following second computational experiment to apply what you have learned. Draw a molecule of methylcyclohexane-equatorial and methylcyclohexane-axial and find the energies for the two isomeric molecules with the methyl group in the equatorial and axial positions, respectively. You can draw each of the isomers and run a geometry optimization using MM2 parameters. You do not have to do dihedral angle search. Use the differences in energy to calculate the relative amounts at 298K of K = [equatorial]/[axial] and then find the percent of the molecule that would be in the equatorial conformation. For comparison the accepted experimental value is K = 18 for methylcyclohexane. REFERENCES 1) A Chemist s Guide to CAChe (Fujitsu Inc. 2004). 2) Organic Chemistry 3rd edition, Paula Yurkanis Bruice (Prentice Hall, Upper Saddle River, NJ, 2001) pp. 96-103.
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Expt MM 12 MM EXPERIMENT Results and Analysis Sheet for Molecular Modeling of Conformations of Menthone (trans) and Isomenthone (cis) Isomers Reported Experimental Results Mole fraction of menthone (show calculation below) X m = Name Equilbirium constant (show calculation below) K = Computational Results Highest energy and lowest energy in energy versus dihedral angle plot for menthone. Highest energy and lowest energy in energy versus dihedral angle plot for isomenthone. Isomer Angle of Lowest Energy Energy Menthone E m = Isomenthone E i = Energy difference (kcal/mol) E steric = E m -E i =
Expt MM 13 Equilbirium constant (show calculation below) K = Mole fraction of menthone (show calculation below) X m = Percent error in mole fraction %error = Show calculation below: Mechanics Results for each isomer in its lowest energy conformations Menthone Isomenthone Energies (kcal/mol) stretch stretch bend improper torsion electrostatics angle dihedral van der Waals hydrogen bond Total Energy Locate the major sources of strain in each structure. Which of the two structures is favored and briefly discuss the reason why.
Expt MM 14 Second Computational Experiment - Equatorial or Axial for Methylcyclohexane Conformation Energy (kcal/mol) Equatorial E EQ = Axial E AX = Energy difference (kcal/mol) E steric = E EQ E AX = Equilbirium constant at 298K (show calculation below) K = Percentage in equatorial conformation (show calculation below 3 sig fig)) = For experimental equilibrium constant at 298K where K=18, the percentage in the equatorial conformation is (show calculation below 3 sig fig)