Introduction to Molecular Modeling

Transcription

1 Introduction to Molecular Modeling As the title implies, the following dry lab is meant to be an introduction to the exciting (OK, maybe not exciting but definitely important) world of molecular modeling. Why, you might ask, is molecular modeling important? Let me answer that question (as I usually do) with another question. Look at molecules A and B. Are they the same or different? What do you think the bond angle is between the two chlorine atoms in molecule A? What about molecule B? Cl Cl Cl A B At first glance, the answer may not be obvious. The two molecules are in fact the same and the bond angles between the two chlorine atoms are identical at This example drives home an important aspect of organic chemistry: the importance of the 3- dimensional structure of organic molecules. As organic chemists, we often draw structures and reactions on paper. Although this is useful, we must never forget that molecules are 3-dimensional structures. For this reason, it is strongly recommended that a modeling kit be used when studying organic chemistry. Fortunately, chemists also have modeling programs at their disposal. In addition to viewing structures three dimensionally, modeling programs allow us to measure bond lengths, bond angles, and calculate energies. The program you will be using for this lab is called yperchem. One of the purposes of this lab is to familiarize you with the basics of yperchem by building some models and performing some basic calculations. Before we start I have to apologize. What follows in an instructional how to and there are very few ways to make how to instructions more exciting than watching paint dry. For that I m sorry. I do not, however, feel bad enough to let you not do this lab. Acyclic Aliphatic ydrocarbons Start the yperchem program by selecting Start, Programs, Class Software, yperchem Std 5.1. It is easier to work on a white background. To change the background colour select File, Preferences, Window Color, White, OK. The main tools you will be using are shown below: Cl Draw Select Rotate in Plane Rotate out of Plane Start by drawing the molecule methane (C 4 ). To draw a carbon atom, double click on the Draw Tool. A periodic table will appear. Select the element carbon and close the periodic table window. Now click anywhere on the drawing surface and a carbon atom will be seen. To add the hydrogen atoms, click on Build, Add & Model Build. 11

2 Quick Tip: Double clicking on the Select Tool icon is the same as selecting Add & Model Build provided that Explicit ydrogens in the Build menu is not checked Note that when you are building molecules in yperchem, you need only draw the carbon skeleton. The program will add the requisite number of hydrogen atoms when you click the Add & Model Build command. To obtain a different type of model, select Display, Rendering, Balls and Cylinders, OK. To vary the size of the balls select Display, Rendering, Balls and vary the Ball Radius slider. Use the Rotate in Plane and Rotate out of Plane Tools to view your molecule at different angles and positions. To use the Rotate tools, click anywhere in the main drawing window while dragging the mouse. Before proceeding, you will need to change the highlight colour. In the File menu, select Preferences, Selection Colour, Choose a colour. Any atoms or bonds you select will now be highlighted in the chosen colour. To determine the length of any bond, click on the bond you want to measure using the Select Tool. This will highlight both of the atoms attached to this bond. The value, in Angstroms (Å), will appear in the information bar at the bottom left of the screen. For the molecule methane, each C- bond distance will be 1.09Å. You can also measure the distance between any two atoms using the same procedure. When selecting atoms, make sure that you click on the centre of the atom. It is important to realize that these are unoptimized values. Later we will show how to obtain an optimized value. In order to determine a bond angle, first make sure that the Multiple Selections option in the Select menu is selected and then use the Select Tool and click on two bonds (three atoms should be highlighted). The bond angle will appear in the information bar at the bottom left of the screen. For the molecule methane, each -C- bond angle will be Quick Tip: If you left click on the background with the Select Tool the entire molecule will be selected. If you right click on the background with the Select Tool, everything will be deselected. If you accidentally select the wrong bond or atom, deselect it by right clicking on it. yperchem has the ability to optimize molecules. When we optimize a molecule we are calculating the most stable structure of the molecule. There are many different levels of calculations; some more advanced than others. For our purposes we will use basic method of calculations since the molecules we are investigating are small. In the Setup menu, select Semi-empirical, then AM1. To optimize a structure, select Geometry Optimization in the Compute menu. NOTE: BEFORE STARTING TE GEOMETRY OPTIMIZATION, YOU MUST MAKE SURE TAT EVERYTING IS DESELECTED IN TE DRAWING WINDOW. Optimize the structure of methane as described above. When the geometry optimization calculation is done, the energy of the molecule will be displayed in the information bar. The energy for methane is kcals. Note that the energy is in kilocalories (kcals) and that the value is negative. The more negative the energy, the more stable the 12

3 molecule is. This will be useful when comparing the relative stabilities of different isomers. Note that it is only useful to compare energies of molecules (or groups of molecules) with the same total molecular formula. Let us now look at molecules A and B more closely. To draw molecule A, or dichloromethane, you will need to change two of the hydrogen atoms of methane to chlorine atoms. Double click on the Draw Tool to bring up the periodic table. Select the element chlorine and then convert two hydrogen atoms into chlorine atoms by clicking them. Two chlorine atoms will be appear larger then the two hydrogen atoms. To make the atoms different colours, select Element Colour, in the Display menu. ere you can give each element a different colour. Do not select the colour green as this is the highlight colour. You should now have a carbon atom which is bonded to two hydrogen and two chlorine atoms. Optimize the molecule as described above and note its energy. Measure and record the values of the bond lengths of the C- and C-Cl bonds. Measure and record the values of the Cl-C-Cl, Cl-C-, and -C- bond angles. Use the Rotate in Plane and Rotate out of Plane Tools to generate the view depicted in molecule A. Now rotate the molecule to generate the view depicted in molecule B. opefully you are now convinced that both structures A and B represent the same molecule. Quick Tip: To delete everything in the drawing window, you can either select everything by left clicking on the background with the Select Tool and then pressing the Delete key or you can right click on the atoms with the Draw Tool. Clear the drawing window and draw a molecule of ethane. Using the Draw Tool (make sure that the element carbon is selected in the periodic table) click in the drawing window to add a carbon atom then click on this carbon atom and drag away. This will add another carbon atom bonded to the first one. Add the hydrogen atoms by selecting Add & Model Build. The program will automatically generate ethane in the staggered conformation. Optimize this structure and note its energy. Measure the C-C- and -C- bond angles. Measure the distances between the hydrogen atoms on adjacent carbon atoms. Staggered Eclipsed To make ethane in the eclipsed conformation, you must first make sure that Multiple Selections is on in the Select menu. Make sure that molecule is in an orientation where you can clearly see all the atoms. Using the Select Tool, highlight all four atoms of one methyl group. Using the Rotate out of Plane Tool, position the molecule so that both 13

4 carbon atoms are superimposed. Next, choose the Rotate in Plane Tool and right click and drag anywhere on the background. The methyl group that you highlighted will now rotate along the carbon-carbon bond. Position the hydrogen atoms so that they are eclipsed. Optimize this structure and record its energy. Measure the C-C- and -C- bond angles. Measure the distance between the hydrogen atoms on adjacent carbon atoms. Which conformer is more stable? Why? Newman projections are often used to show conformational relationships between certain atoms. Newman projections are drawn by looking down the axis of a carbon-carbon bond. Ethane has only one carbon-carbon bond so the Newman projection is drawn looking down this bond. Shown below is the Newman projection for the two conformers of ethane. The front carbon atom is represented as the point where the three lines intersect. The second carbon atom is represented as the circle. The Newman projections of staggered and eclipsed ethane clearly show the spacial relationship of the hydrogen atoms. It is important that you learn to read and draw Newman projections. staggered ethane Another useful way to look at the conformational relationships of molecules is to plot the energy of each conformer versus the angle of rotation of one carbon atom relative to the other. This is demonstrated below with ethane. Start with the higher energy eclipsed conformer. Rotation of a methyl group by 60 will generate the lower energy staggered conformation. Rotation by another 60 will regenerate an eclipsed conformer. Repeating this through 360 will alternately generate the eclipsed and staggered conformers giving a sinusoidal wave. a a a eclipsed ethane a a a a a 14

5 Clear the drawing window and build a model of propane. Optimize and record its energy. This is fully staggered propane. Using the Rotate out of Plane Tool, look down the two carbon-carbon bonds. You will notice that all of the hydrogen atoms are staggered. As you did with ethane, rotate one of the carbon atoms 60 while holding the others stationary. This will generate a propane molecule with one staggered carboncarbon bond and one eclipsed carbon-carbon bond. Optimize and note its energy. Finally, make fully eclipsed propane by rotating the other carbon-carbon bond 60. Optimize and note its energy. Which of the three propane conformers is the most stable? Which is the least? Is the stability as you expected? Build a model of butane. Optimize and record its energy. Superimpose carbon atoms 2 and 3. The two terminal methyl groups will be as far apart as possible. Measure the distance between carbon atom 1 and carbon atom 4. This is called the anti conformer of butane. Rotation of carbon 3 by 60 increments will generate six conformers. These are shown below as Newman projections. Note that there are two equivalent gauche and anticlinal eclipsed conformers. Starting with the anti conformer of butane, generate each conformer and calculate and note its energy. For each conformer, measure the distance between carbon atoms 1 and 4. C 3 C 3 C 3 C 3 C 3 C 3 C 3 C 3 syn-periplanar gauche anticlinal eclipsed anti Based on their energies, list the four conformers of butane from most stable to least stable. For all six conformers of butane, plot a graph of relative energy versus the dihedral angle between carbon atoms 2 and 3 (similar to the graph shown on the previous page for ethane). When you first start looking at the structure of organic molecules, it is important to be aware of isomers. Isomers are molecules that have the same molecular formula but different structure. There are several different types of isomers: constitutional isomers, geometric isomers, and stereoisomers. In today s lab, we will only be looking at constitutional isomers. Constitutional isomers are molecules that have the same molecular formula but differ in connectivity. Consider the two molecules dimethyl ether and ethanol: C 3 OC 3 C 3 C 2 O Both dimethyl ether and ethanol have a molecular formula of C 2 6 O but the arrangement of the atoms is different. Constitutional isomers can be divided into several subcategories. Although you should be aware of these different subcategories, it is more important that you remember that they all represent constitutional isomers. The subcategories are: 15

6 Structural (skeletal) isomers: compounds that differ in connectivity within the hydrocarbon framework only. Positional isomers: compounds in which the placement of the functional group is different. Functional isomers: compounds in which the different connectivity gives rise to different functional groups. In the above example, dimethyl ether and ethanol can be described as constitutional isomers or, more precisely, as functional isomers. It is important to realize that isomers represent different molecules and thus will have different properties. Some isomers have very different physical properties (solid and a liquid) while others have the exact same physical properties except for the direction in which they rotate plane polarized light. You will look at these properties in more detail later. Cyclic Aliphatic ydrocarbons In the first part of this lab, you looked at conformers of some small aliphatic hydrocarbons. These different conformers exist because of the possibility of rotation about the carbon-carbon bonds. The conformations of cyclic hydrocarbons are influenced differently than their acyclic analogues because of the rotation about carboncarbon bonds are restricted. Build a model of cyclopropane: Make a triangle of carbon atoms then select Add & Model Build to finish the structure. Optimize the molecule and record its energy. Measure the C-C-C bond angles. Measure the distance between hydrogen atoms on adjacent carbon atoms. Position the molecule so that any two carbon atoms are superimposed. Are the hydrogen atoms on adjacent carbons atoms eclipsed or staggered? Build a model of cyclobutane: Make a square of carbon atoms and then select Add & Model Build. Optimize the molecule and record its energy. Measure the C-C-C bond angles and measure the distance between hydrogen atoms on adjacent carbon atoms. Superimpose any two carbon atoms and note the spatial relationship between the hydrogen atoms. Are they staggered or eclipsed? As you did for cyclopropane and cyclobutane, build a model of cyclopentane. Optimize the structure and record its energy. Measure the C-C-C bond angles and measure the distance between hydrogen atoms on adjacent carbon atoms. When looking down a carbon-carbon bond, are the hydrogen atoms eclipsed or staggered? Is cyclopentane flat? Build a model for cyclohexane. Optimize the structure and record its energy. Using the Rotate out of Plane tool, look at the molecule from different angles and positions. Is cyclohexane flat? The cyclohexane molecule will be in what is called the chair conformation. 16

7 Cyclohexane Chair conformer What are the C-C-C bond angles? Superimpose any two adjacent carbon atoms. Are the hydrogen atoms staggered or eclipsed? Do this for every carbon-carbon bond, noting whether the hydrogen atoms are staggered or eclipsed. Based on their calculated energies, rank the four cyclic hydrocarbons that you just looked at from least to most stable. Give one good reason why the most stable cyclic hydrocarbon is lower in energy than the least stable one. We can also draw Newman projections for cyclohexane rings. The Newman projection shown below is drawn looking down both the C 2 -C 1 and C 4 -C 5 bonds. The Newman projection clearly shows how the hydrogen atoms are staggered with respect to each other. Also note that all the carbon-carbon bonds are gauche with respect to bonds emanating from adjacent carbon atoms. For example, sighting down the C 2 -C 1 bond a gauche interaction can be seen between the C 3 -C 2 bond and the C 6 -C 1 bond. This interaction is shown in the Newman projection with highlighted bonds. C 5 C 1 C 6 C 3 chair cyclohexane It is very important that you learn how to draw cyclohexane in the chair conformation. Your textbook (Sorrell, 1 st Ed. page 136; 2 nd Ed. page 85) has an excellent description on how to properly draw cyclohexane in its chair conformation. You will also notice that there are two different types of atoms or bonds attached to a cyclohexane ring. They are described as axial and equatorial. These are shown on the diagram below. Since studies in organic and biological chemistry frequently encompass six-membered rings, mastery of drawing chair cyclohexane rings with properly placed hydrogen atoms is essential to understanding their energetics and reactivity. It would be wise to practice drawing cyclohexane in the chair form until you can draw the ring with appropriately placed hydrogen atoms without difficulty. e e a a e a a e a a = e e C 5 C 4 C 6 C 3 C 2 a = axial hydrogen e = equatorial hydrogen Newman projection of chair cyclohexane C 1 17

8 Although cyclohexane has restricted rotation about its carbon-carbon bonds, it is still a flexible molecule. Cyclohexane undergoes rapid ring-flips in which one end moves down and the other end moves up. As a consequence of this ring-flip, the axial atoms become equatorial and the equatorial bonds become axial. This is illustrated below (for clarity, only four of the twelve hydrogen atoms are shown). a a e C 4 C 1 e e 4 C C 1 e a a Another important conformer of cyclohexane is the boat conformer. The boat conformer has a higher energy then the chair conformer. Prove this by building a model of the boat conformer of cyclohexane. To make the boat conformer you will need to start with an optimized model of the chair conformer. ighlight the four carbon atoms that make up the seat of the chair (see Figure A). In the Select menu, choose Name Selection and Plane. Deselect all atoms and then select one of the two out-ofplane methylene groups (C 2 ). In the Edit menu, select Reflect. This will reflect the chosen atoms about the defined plane (Figure B). Optimize this structure and record its energy. Rotate the Boat conformer molecule and look down each carbon-carbon bond. Are the hydrogen atoms staggered or eclipsed? Provide one good reason why you think the boat conformer of cyclohexane is higher in energy than the chair conformer. C C C C Fig. A. Four carbon seat. Fig. B. Reflection of the methylene group about the defined plane. The chair and boat form of cyclohexane are the two most common conformers. There are other conformers but we will not be looking at these at this time. For more information on these other conformers, refer to your textbook. 18

9 Let us now look at what happens when we substitute a hydrogen atom on cyclohexane for some other group. Suppose we were to substitute a hydrogen atom for a methyl group. This would give rise to two different chair conformers; one where the methyl group is in the axial position (Figure C) and one where the methyl group is in the equatorial position (Figure D). Me What difference, if any, is there between the two structures? What is the relative stability of these two molecules? The key to answering these questions is to look at the gauche interactions between the methyl group and neighboring carbon atoms. For the conformer with the axial methyl group, two gauche interactions, indicated by arrows (Figure E), are shown in the chair conformation of methylcyclohexane. In the corresponding Newman projection (Figure F), which is looking down the C 2 -C 1 and C 4 -C 5 bonds, one gauche interaction between the C 3 -C 2 bond and the axial methyl group is highlighted in bold. To see the second gauche interaction, draw the Newman projection looking along the C 1 -C 6 and C 3 -C 4 bonds. When the methyl group is in the equatorial position, there are no gauche interactions (Figure G). As the Newman projection clearly shows, the methyl group is anti (180 ) to the C 2 -C 3 bond. The anti arrangement places the methyl group as far away as possible from the neighbouring carbon atoms (Figure ). C 5 C 1 C 6 C 3 C 5 C 1 C 6 C 3 Fig. C. Fig. D. C 3 C 3 Me C 3 C 3 C 6 Fig. E. Fig. F. Fig. G. C 3 C 6 Fig.. C 3 19

10 Another factor to consider are the 1,3-diaxial interactions. When the methyl group in methylcyclohexane is in the axial position, there are steric interactions between it and the hydrogen atoms attached to carbon atoms 3 and 5 (Figure I). When the methyl group is in the equatorial position, it is pointing away from the ring and these steric interactions are absent (Figure J). C 5 C 1 C 6 C 3 Fig. I. C 5 C 1 C 6 C 3 Fig. J. Methylcyclohexane illustrates an important point. The most stable position for any group on a cyclohexane ring larger than hydrogen is the equatorial position. Thus, although methylcyclohexane exists as both conformers, the equilibrium lies further on the side where the methyl group is in the equatorial position. C 3 C 3 Convince yourself that the conformer with the methyl group in the equatorial position is more stable. Build optimized models of both conformers and calculate and record their energies and their energy difference. For each optimized model, use the Rotate out of Plane and Rotate in Plane tools to position the molecule like the Newman projections depicted in Figures F and G respectively. You should be able to see one of the gauche interactions. Rotate the molecule to generate the second Newman projection which shows the other equivalent gauche interaction. Finally, for each conformer, change the rendering to Overlapping Spheres. This gives a better idea as to how much space each atom occupies. If you press the F2 key, you can toggle back and forth between the last two renderings (Balls and Cylinders and Overlapping Spheres). In the Overlapping Spheres rendering, you will see that when the methyl group is axial it is much closer to the hydrogen atoms attached to carbon atoms 3 and 5 (1,3-diaxial interactions, Fig I) then when it is equatorial (no 1,3-diaxial interactions, Fig J). What happens if cyclohexane is substituted with a group larger than methyl? As the group increases in size, the equilibrium will lie further and further to the side with the group in the equatorial position. This is exemplified with tert-butylcyclohexane. The tert-butyl group is so large that the equilibrium lies almost completely on the side of the equatorial conformer. 20

11 Build optimized models for both conformers of tert-butylcylcohexane. When optimizing the conformer with the tert-butyl group in the axial position, watch the tert-butyl group. You should see the carbon-carbon bond that attaches it to the ring elongate as well as the tert-butyl group itself move away from the top of the ring. Essentially, the molecule undergoes a major distortion in order to accommodate the size of the substituent. Record the energies of both conformers and calculate the energy difference. Is the difference between the two tert-butylcyclohexane conformers bigger or smaller then the difference between the two methylcyclohexane conformers? Why? Toggle between the Balls and Cylinders and Overlapping Spheres renderings to get a better sense of the size of the tert-butyl group relative to a methyl group. So far, we have only looked at monosubstituted cyclohexane rings. With monosubstituted cyclohexane rings, we looked at the relationship of the substituent between conformers. As we turn our attention to disubstituted cyclohexane rings, you will see that not only do we need to look at the relationship between conformers, but we also need to look at the relationship of the two substituents within a certain conformer. This relationship is refered to as its configuration. Consider the three molecules (A, B, and C) of 1,2-dimethylcyclohexane shown below. 3 C C 3 C 3 C 3 C 3 A B C What different is there between these structures? The first thing to look at is the relationship between the two methyl groups. They are either both in the axial position, both in the equatorial position, or one in the axial and one in the equatorial position. The second thing to look at is the relationship of the substituents relative to a plane defined by the six carbon atoms of the ring. The methyl substituents are either above or below this plane. When two substituents are on the same side of the plane of the ring, they are said to be in the cis configuration. When the two substituents are on opposite sides of the ring, they are said to be in the trans configuration. Therefore, compound A is in the trans configuration because one methyl group is above the plane of the ring and the other methyl group is below it. When naming compounds, the cis/trans descriptor is placed in front of the name and is italicized. The proper IUPAC name for compound A is thus trans-1,2-dimethylcyclohexane. Look at compound B. Although the two methyl groups C 3 C 3 C 3 C 3 C 3 C 3 C 3 21

12 are both in the equatorial position, they are still trans to each other. One methyl group is above the plane of the ring and the other is below it. Therefore, compound B is also trans-1,2-dimethylcyclohexane. Compound C, where both methyl groups are above the plane of the ring, represents the cis configuration. The full IUPAC name for compound C is cis-1,2-dimethylcyclohexane. Although we looked at three different molecules, disubstituted cyclohexanes can only have two different configurations: cis or trans. Build a model for each of the three dimethylcyclohexane molecules (A, B, and C) and calculate their energies. Place them in order of increasing stability and provide a rationale for this order. Cis and trans isomers can also be drawn for 1,3-dimethylcyclohexane and 1,4- dimethylcyclohexane. For each of these two molecules, draw the isomers and decide which is most stable. Build models for each isomer and calculate their energies. Are the relative stabilities what you expected? Provide a rationale for the order of their relative stabilities. 22