revised 11/3/04 mtm

Visualizing Molecular Shape and PolarityUsing SPARTAN

I. Introduction

After completing this exercise you should be able to:i) Use VSEPR to predict the electron pair geometry and molecular geometry for a given molecule based on its Lewis Structure, and sketch its 3D shape

ii) Use computer modeling software to calculate the optimal 3D shape of a moleculeiii) Classify a molecule as either “polar” or “non-polar” according to its shape and the polarity of its individual bondsiv) Use MacSpartan computer modeling to help you visualize charge distribution in a molecule

We will investigate these issues using a powerful piece of molecular modeling software (SPARTAN). The field of molecular modeling, or more broadly, computational chemistry, refers to investigating molecules strictly through calculations. It has grown rapidly in the past two decades, primarily because advances in computing speed have enabled the use of very sophisticated (quantum mechanical) models to simulate the electron distributions of molecules. The field has had such a broad impact on chemistry that the 1998 Nobel Prize in Chemistry was awarded to a pair of individuals who were instrumental in developing efficient numerical procedures to execute such calculations. Today, a substantial fraction of chemists are exploiting computational methods for their research, and such methods are even making their way into biochemistry courses…

The plan for this lab exercise is to learn the basics of the program by “building” and simulating a few simple molecules that you are quite familiar with. At the same time, you will be drawing Lewis Structures and predicting the geometries of these molecules using VSEPR (Valence Shell Electron Pair Repulsion) Theory. The basis of VSEPR theory is that the electron pairs about a given atom move away from each other as far as possible to minimize the repulsive forces between them (all are negatively charged). As a result, for a given number of electron pairs about a given atom (either bonds or lone pairs), there is a standard arrangement called the electron pair geometry. This dictates the overall shape. The actual shape of the molecule is called the molecular geometry. At the end of this document there are some appendices that describe electron pair geometry, molecular geometry, and guidelines for drawing Lewis Structures. Our investigation of shapes will conclude with an examination of molecules with more than 8 electrons about the central atom.

After investigating shape, we will then exploit the graphical capabilities of SPARTAN to illustrate “polar” bonds. Then, we will combine this insight with that that we have gained regarding shape and learn to predict whether or not a given molecule (as a whole) is polar - that is, has a dipole moment.

You will need some scratch paper for sketching some Lewis structures and VSEPR geometries. Questions to be answered are in bold, and are separated from the body of the text. Others embedded in the text (and usually in italics) are to provoke thought.

II. Outline of the process for running SPARTAN

The process for modeling molecules in SPARTAN follows the same general outline:a. Build a molecule - the program makes a “best guess” as to how the atoms are arranged,

but the shape at this point is just the initial guess.b. Calculate and minimize molecule energy - SPARTAN next adjusts atom positions and

the electron distribution in the molecule to find the lowest energy shape and electron distribution. This is the real power of this program - sophisticated models for atom bonding determine a refined view of what the molecule “looks like”.

c. Calculate surfaces - electron density surfaces (to better envision shape) and charge distribution in the molecule (to better envision molecular polarity).

SPARTAN allows for a wide range of molecule shapes and bonding, but just because the program will let you build it doesn’t mean that your molecule is stable. Step “b.” is therefore crucial to the process. During step “b.”, three different things could happen -

i. The program returns a structure with the same general shape (the bond lengths and angles may have changed a bit). But it is not necessarily the best structure. You will need to examine the energy values for all stable structures to determine which is “best”. (More on this below)

ii. The program returns a structure with a completely different shape , which means that your starting structure was something of a poor guess.

iii. The calculation takes a long time, and the structure it returns is not bonded at all – the distances are very long, and there is no definite shape (i.e. the molecule “exploded”), which means that your initial guess was extraordinarily bad.

Controls for moving and rotating molecules on canvas -“Free-form” rotate Click and drag the mouse on the canvasRotate molecule in canvas’ plane Apple+dragDrag one molecule across canvas Option+dragDrag all molecules across canvas Control+dragZoom in Option+Apple+dragUpon starting the program an unlabelled window appears - the “shortcut” menu:

III. Molecular Geometry

A. 3-D Shapes from Lewis StructuresConsider the shapes of three molecules, H2O, NH3, and CH4 based on VSEPR. 1a) Sketch Lewis structures for H2O, NH3, and CH4. Also specify the electron pair geometry and molecular geometry for each one.

2

1b) Specify the values of bond angles you’d expect according to the VSEPR model.

B. 3-D Shapes from SPARTANNow use SPARTAN to answer these questions. We’ll build the molecules and calculate their minimum-energy structure.

1. Building moleculesTo build molecules, select ‘New’ from the File menu. In the “Model Kit” popup window, use the ‘Entry’ mode.

WaterIn the ‘Entry’ palette, click on the , then click on the green canvas. Click and drag on the canvas to rotate the molecule for a better view. Then, select the “-H” from the model kit, and click on an “empty bond” to add the H’s. Then choose ‘View’ from the Build menu (or click on in the shortcut menu). Select ‘Save’ from the File menu, and save your file in a new folder on your H: drive - there is a ‘New Folder’ button in the save dialog box.There are several “models” for viewing the molecule in the Model menu - experiment with them, and pick the representation you like the best. Be sure to look at the molecule as a ‘Space Filling’. You can switch to a different model at any time; the model does not influence the calculations.

MethaneDrag the water molecule out of the center of the canvas, choose File/’New’ (or click

from the shortcut menu) and build CH4, (use from the ‘Entry’ pallet); note that if you don’t put H atoms on the C, the program will do it for you automatically when you select . Save the molecule. You can switch from molecule to molecule by clicking on any part of the molecule that you want; the title of the main window tells you which is selected. The atom that you click turns brown; if you next click on the canvas, you can deselect that atom but not the molecule.

AmmoniaAgain, move the methane away from canvas center, start a new molecule and build NH3 (use from the ‘Entry’ pallet). Save the molecule as before.

2. Calculating molecule structure and energyNext, we will have SPARTAN calculate the optimum (i.e. minimum energy) structure for these molecules. Select a molecule by clicking on it and then set up the calculations by:

Select ‘Calculations…’ from the Setup menu. In the dialog box, choose the following: ‘Calculate:’ Equilibrium Geometry, ‘with:’ Hartree-Fock / 6-31+G*.

3

Then click “OK”. We will use these settings for the most of the exercise.1 To start the calculation, select ‘Submit’ from the Setup menu. The calculation should finish in less than a minute. When the first molecule is done, move on to the others.

Now, we’ll examine the calculated bond angles, and see how the structures of H2O, NH3, and CH4 compare with what you expect based on VSEPR theory.

To measure the bond angle in water, select “Measure Angle” from the Geometry menu (or click on in the shortcut menu) and click on “H”, then “O”, then the other H. The atoms will be shaded in brown as they are selected, and the value will appear in the lower right corner of the SPARTAN window when you have three atoms selected. It is critical that the central atom (“O” in this case) is selected second – otherwise the value you get will not be for the H-O-H bond angle. SPARTAN tells you the order that you selected the atoms at the bottom of the window to the right of the word ‘Angle’. Record the H-O-H bond angle. Select View( ) to get the other molecules back to the screen. Measure the bond angles in CH4 and NH3 and record the results.

Note the trend in bond angles, and try to explain its origin. Here are some considerations to guide you: For which molecule does the bond angle deviate the most from the ideal VSEPR value? Which deviates least? Is the bond angle larger or smaller than in the ideal VSEPR value? Can you explain the trends in bond angle deviation?

1c) Are any of the calculated angles different from the ideal VSEPR values? If so, can you explain why? If not, see the next section.

C. Effect of Lone Pairs on VSEPR Bond Angles: Electron Density Surfaces “Electron density surfaces” are maps of where the electrons are located in the molecule - SPARTAN produces a shape that literally corresponds to the electron density that you specify. There are two electron density surfaces we will look at: “bonds” of a molecule, which represents the region where there is enough electron density to

constitute a bond, or a lone pair of electrons. “size” of a molecule, or the “outermost edge” of the molecule’s electron cloud

To calculate these surfaces, select a molecule and choose ‘Surfaces’ from the Setup menu. In the popup window click on the ‘Add’ button while holding down the Option key. Accept density in the Surface pull-down menu, click the Static Isovalue checkbox, select bond (in the mini scroll down menu), and choose High for Resolution. Then click “OK”.

1 The first line was tell the program to adjust the bond lengths and angles until the potential energy of the molecule reaches a minimum value. The “Hartree-Fock/6-31+G*” describes the method the program is using to model the electron distribution – which ultimately dictates the structure. The only tidbit you need to take from this is the following fact: The program calculates the molecular structure with the lowest energy. NOTE: This is the underlying basis of the VSEPR model. Since the electron pairs (either bonded or lone) are negatively charged, molecules adopt geometries that render them as far apart as possible, minimizing the repulsion of the negative charges, which in turn gives the lowest potential energy.

4

To calculate the “size” surface, Option-click on ‘Add’ again, accept density in the Surface pull-down menu, click the Static Isovalue checkbox, accept size and choose High for Resolution. Then click “OK”.

Note that the bond surface and size surface are the same operation to SPARTAN - only the electron density value changes: 0.08 for the bond surface, 0.002 for the size surface.

‘Submit’ these from the Setup menu. To view the surfaces, click the checkbox next to the left of the surface you wish to view (Isovalue=0.002 is “size”; Isovalue=0.08 is “bond”) in the ‘Surfaces’ dialog box. You will not be able to see the “bond” surface and the “size” surface at the same time since the bond surface is inside the size surface.

Make the surfaces transparent so that you can see the skeleton of atoms inside:Select ‘Properties’ from the Display menu. The dialog box should be labeled ‘Surface Properties’ - set the Style to Transparent. Note: this function is a bit “buggy” - if you have problems, leave the window open and click on the molecule that you want to see. In the ‘Surfaces’ window toggle the surface off and on by clicking on the checkbox.

Calculate and examine the bond surfaces for each molecule and answer the following:

Comparing the “bond” surfaces of water and ammonia to that for methane,2a) Why is there such a large electron density on the central atom away from the H’s.

2b) Why do you suppose that the electron density described in 2a is more diffuse than that between the central atom and H atoms?

2c) Generalize: Are the spatial requirements for a “lone pair” and a “bonded pair” the same? Which requires more space - a bonded pair, or a lone pair? Why?

While viewing the “size” surfaces for each molecule, consider the following. Recall that this view is meant to represent the molecule at its nearest contact distance.3a) How does the molecule’s electron density compare to the “Ball and Wire” or “Ball and Spoke” molecular models? Are these models accurate descriptions of the molecule? Explain.

5

3b) Which molecular model best describes the molecule’s “size” surface?

3c) What are the advantages and disadvantages of a “Ball and Spoke” model vs. a “Space Filling” model in describing a molecule?

3d) Which simple shape best describes the molecules: tetrahedron, cube, or sphere ?

Save and close all three molecule files before continuing.D. Molecules with “Expanded Octets”-OPTIONALMolecules with 5 electron pairs about the central atom assume a trigonal bipyramidal electron pair geometry, and those with 6 electron pairs assume an octahedral electron pair geometry.2 When no lone pairs are present, the molecular geometry and electron pair geometry are the same, as is the case with PF5 and SF6, viz.

F

P

F

F

FF S

F

F

FF

F F90°

90°

90°120°

Trigonal Bipyramidal (PF5) and Octahedral (SF6) Geometries.

When lone pairs are present, however, it is difficult to determine the best orientation of lone and bonded pairs of electrons. Consider the trigonal bipyramidal case (as depicted by PF5 above): the key issue is that the five locations around the central atom are not equivalent. Those directly above and below the P are called axial sites, and the other three are called equatorial. That is, there are three positions around the central atom in the same plane (the equitorial plane) and two positions above and below that plane (the axial positions). To better visualize this, do the following:

Create a new project, and select the ‘Expert’ tab in the “Model Kit” window. Click and hold on the “C” icon next to “Element” and a periodic table appears. Drag over to Cl. To make a Cl atom with five electron groups around it, choose from the list below the element icon. Click on the canvas and then rotate the molecule around until you understand its shape.

2 It may seem unusual that the central atom has more than four electron pairs - atoms in most molecules have eight electrons – a.k.a. the “octet” rule. But, atoms from the third row (e.g. S, P, Cl) and below are larger, and can accommodate 10 or even 12 electrons in some instances.

6

When lone pairs are present, a natural question is: “Do they go into the axial sites or the equatorial sites, or is there really any difference?” We’ll answer this question by examining the ClF3 molecule.

Question: What is the “best” structure for the ClF3 molecule?4a) Using the appendices, sketch the Lewis structure of ClF3.

4b) With three bonded pairs and two lone pairs about the central atom, there are three possible structures. Sketch them.

Now, build the three possible structures in SPARTAN that you sketched, saving each one:Select a single-bonded F atom ( ) from the ‘Expert” palette and add a F atom in three locations on the central Cl. Then delete the last two bonds by selecting “Delete” from the Build menu (or from the shortcut menu) and clicking on the gold parts of the empty bonds. You must delete the bonds or they will become H’s in the calculation.

Make sure that each structure is unique (and that you didn’t somehow make two of the same) in the molecule view. Then calculate the structure for each molecule in turn using the same calculation settings you used for water, ammonia, and methane. When you are done, you should have two structures that are the same, despite your care in building three unique structures. What happened?

For SPARTAN, recall that the ‘best’ structure is the one with the lowest energy.3 Recall the three possible outcomes for a calculation (described in section II above). The program will return:

a molecule with the same general shape reasonable initial guess a molecule with a different shape poor initial guess an “exploded” molecule extremely poor initial guess

To determine which structure is best, compare the energy for each structure:Select each molecule in turn (click on an atom for the structure that you want, then click on the canvas). The energy will be displayed at the bottom of the View window.

Two points: You’ll notice that the energy is 1) negative, and 2) expressed in units called “Hartrees”. The value is negative by convention (the “zero of energy is taken to be a set of bare nuclei with no electrons present, and adding the negatively-charged electrons to the arrangement of positively charged nuclei lowers the energy.) A Hartree is large amount of energy by chemical standards (1 Hartree = 2625.5 kJ/mol). So a structure that is a 0.1 Hartree lower in energy more stable by about 262 kJ/mol.

7

3 A stable structure is not necessarily the best, minimum energy structure. Rather it could be a “meta-stable” or “quasi-stable” structure. This situation is illustrated in the picture below, a graph of energy vs. bond angle for a hypothetical molecule XY2, which has a bent minimum energy structure and a linear structure that is quasi-stable.

The 180° (linear) structure corresponds to a stable shape, but it is not as low (stable) as the 110° (bent) structure. When SPARTAN calculates the best structure for XY2, the “starting guess” for the Y-X-Y angle will affect the result: if we guess an angle between ~90 and 150, the calculated shape will be bent; if we guess an angle between ~160 and 200, the calculated shape will be linear; if we guess 155 (right at the top of the peak), either shape could result. The program adjusts the geometry to lower the energy (that is, it will try to march “downhill” in energy), even if there’s a more stable structure the other way.

8

E

Y-X-Y Bond Angle 110° 180°

X Y—X—YY Y *

155°

So, examine the energy values for the stable structure you obtained, and determine which is the minimum energy structure.4c) Based on SPARTAN, specify the electron-pair geometry and molecular geometry for the most stable (i.e. lowest energy) structure of ClF3.

4d) Based on SPARTAN’s results, which structure for ClF3 is the least stable. Explain.

4e) What are the values of the bond angles of ClF3 based strictly on VSEPR theory?

4f) Sketch SPARTAN’s lowest energy geometry, label it with the calculated the bond angles, and briefly explain why they differ from the ideal VSEPR values?

4g) Generalize: Which sites in a trigonal bipyramidal geometry have more space for lone pairs – axial or equatorial?

When you are done, close all three ClF3 molecules and reopen water, methane, and ammonia.

IV. Polarity: Dipole Moments

In this part, we will combine our understanding of 3D shape with some new insight into bond polarity, and determine whether a given molecule is “polar” or “non-polar”. In order for a molecule to be considered polar, it must:

i) have polar bondsii) have an asymmetrical orientation, such that the bond polarity is unbalanced.

Bonds are considered polar when the electronegativity values for the atoms involved differ by more than ~0.5. In the absence of a table of electronegativity values, the following rough guidelines may help you identify bonds that are considered polar:

F bonded to any non-metal = polar, with excess negative charge on F. N,O,Cl bonded to anything (except F) is polar, with negative charge on N, O, or Cl. Bonds between other non-metals (H,S,C,P…) are most often non-polar

9

Clarification: It should be noted that any bond between two different atoms has some degree of charge separation (or “polarity”). In spite of this, chemists refer to bonds with minimal charge separation as “non-polar”.

To visualize how polar bonds add up to render a given molecule polar or non-polar, chemists use “bond dipoles”, arrows that point along the polar bonds, the components for which reinforce each other (that is, are added) or cancel out (are subtracted) to give the overall polarity of the molecule. The molecule’s polarity is represented by a quantity called the dipole moment, which is real and measurable. “Bond dipoles”, however, are strictly hypothetical. Note below how the horizontal contribution of the bond dipoles cancels out in water, while the vertical part reinforces.

O

HH

O

HH

O-H bond Dipoles The Dipole Moment in H2O

Before we begin the calculations, answer these questions:

5a) Are C-H bonds polar? ______

Are N-H bonds polar? ______

Are O-H bonds polar? ______

Rank them in order of increasing polarity and rationalize the trend.

Look at the shapes of water, methane, and ammonia and try to decide if the bond dipoles cancel out or not in each case.5b) Is CH4 polar?

Is NH3 polar?

Is H2O polar?

In each case, sketch how the dipole moment is oriented for the molecule. If a molecule is

not polar, briefly explain why. (There may be more than one reason – if so, state both).

SPARTAN can display the dipole moments for each molecule:Select a molecule and choose ‘Properties’ from the Display menu. In the “Molecule Properties” popup window the calculated dipole moment appears in the lower left. Clicking on the checkbox will display the dipole moment vector on the molecule. This will also show its actual orientation. The arrow points toward the negative charge.

10

5c) Record SPARTAN’s results (polar or nonpolar, and direction of dipole moment) for each molecule.Do your answers in 5b agree with the SPARTAN results?

Try three more molecules: BF3, PF3, and CH2F2. Provide answers based either on what you know and have learned, or use SPARTAN.

5c) Are BF3, PF3, and CH2F2 polar molecules (Lewis structure for CH2F2 is below)? Make a 3-D sketch with an arrow that shows the orientation of the dipole moment, or write “no net dipole” as appropriate. If the molecule is not polar, explain why.

V. Polarity: Visualizing Charge DistributionIn this last part, we will use SPARTAN to illustrate molecular polarity. Returning to H2O, NH3 and CH4, we will calculate ‘surfaces’ on which the net electric charge in the molecule is mapped onto an electron density surface using variations in color.

The “Potential” or electric charge is mapped by coloring the positively charged part of the surface blue, and the negatively charged part red. Neutral regions are greenish or yellowish in color. Recall that charge within the molecule arises because electrons spend, on average, more time around electronegative elements; these elements don’t have the nuclear charge to offset the excess electron density they attract, so they appear negatively charge. The reverse is true for electropositive elements.

11

C

H

F

H

F

To map surface potential onto the “size” electron density for water, open the ‘Surfaces’ window from the Setup menu, Option-click on ‘Add’, choose density for Surface, potential for Property, click the Static Isovalue checkbox and accept size, and High for Resolution. Then ‘Submit’ the jobs from the Setup menu. Note that you can map charge onto “bond” surfaces in a similar manner.

Repeat this mapping for NH3, and CH4. As before, make the surface transparent so you can see the molecule model inside.

The program employs the widest range of possible colors for each molecule so that all bonds may appear to be polar until we set a common scale for all.

This scale can be set in the “Surface Properties” window (accessed via ‘Properties’ in the Display menu). Note the From/To values for all three molecules (e.g. for H2O, the default values are (about): From: -48.6…, To: 58.3); find a From/To range that will work for all three molecules and set this range for all three (preferably with round numbers like -50 to +50).

You should see a clear trend in the charge distribution for this trio of molecules. Recall again that for the molecule as a whole to be polar, two things must hold true. First, it must have polar bonds. Second, the symmetry of the molecule must be such that polarity of the individual bonds (the bond dipoles) does not cancel out. Do these trends agree with your predictions in 5b?6a) Based on these surface views, which molecule is most polar? Which is least polar?

6b) Looking at the areas of a potential-mapped density surface is positive or negative, is the charge is distributed the same for each molecule? If not, what kinds of molecular features concentrate positive charge? Negative charge?

Molecules used in the Boiling Points LabIn the lab (which you did not do) where you measured the boiling point for hydrocarbons, ketones, and alcohols, you noted clear trends in the data with increasing molecular weight (or number of carbons in the chain). There were also clear jumps when changing from hydrocarbon to ketones to alcohols. We will build representative molecules for each and examine their charge distribution surfaces.

Below are the Lewis structures for the three molecules (electron lone pairs not included): pentane, 1-pentanol, and 2-pentanone.

12

H

C

H

H

C

H

H

C

H

H

C

H

H

C

H

H H O

H

C

H

H

C

H

H

C

H

H

C

H

H

C

H

H H

H

C

H

H

C

H

H

C

H

H

C

H

C

H

H H

O

Note that these molecules have multiple “centers”, whereas all the prior examples had just one. 7a) Which molecule would you predict to be most polar? Which is least? (Hint: look at each carbon as a center, examine how the dipole for that center would be oriented - if it has a dipole at all - and then ask if dipoles from different centers can cancel or not.)We will use SPARTAN to answer these same questions, but the molecules are large enough that we will have to change our calculation method or wait a very long time.Pentane

Choose from the ‘Entry’ tab in the Model Kit and click on the canvas; click a second time on a bond and a second C atom appears. Keep adding C atoms until you get a 5-atom chain (notice already how Lewis structure is a poor description for this molecule), then select .

Next ‘Setup’ the calculation:‘Calculate:’ Equilibrium Geometry‘with:’ Semi-Empirical / AM1

‘Submit’ this job. When done, ‘Add’ a map of the charge for the “size” surface and ‘Submit’ again.

1-PentanolRepeat the process outlined for pentane, except you need to end the carbon chain with a .

2-PentanoneUse for the second carbon and for the others in the carbon chain. If you rotate the chain to an appropriate angle, the ‘Ball and Spoke” model will show two bonds extending from the second carbon; choose a O atom and connect it to the second carbon - you should still be able to see the C=O double bond when you are done. ‘Setup’ and ‘Submit’ the molecule, and calculate the charged electron density surface for the “size” surface.

Set the same color scale for all three molecules to allow comparison.

7b) Which molecule’s surface indicates that it is most polar? Which molecule is least polar? (If you’re not sure, check the dipole moments).

7c) Is each molecule “uniformly” polar? If not, what kinds of molecular structure produce polar regions and which non-polar? Can you explain these results using a table of electronegativities?

CleanupWhen you are finished, you can drag the folder with your files in it to the TRASH.

13

Appendices

Guidelines for Drawing Lewis Structures

1) Count total number of valence electrons (including charge).

2) Calculate number of electrons needed to complete octets for all atoms (2 electrons for H).

3) #bonds = [(octet e) - (valence e)]/2

4) Arrange atoms and connect with single bonds. Clues:

a) Formulas reflect order of atoms: HCN b) ABn molecules: a “central atom” (A), surrounded by a bunch of others (B).

(e.g. CO2, NH3, SF4, …) c) Element that forms the most bonds is the central atom; this atom is often the least

electronegative atom as well.d) H &F only bond to 1 atom, are always “terminal” and never “central”. Other halogens

(Cl, Br, & I) are usually “terminal” atoms - rarely central atoms.

5) Add electrons to complete octets of “outer” atoms.

6) Put remaining electrons on central atom.

7) If central atom lacks octet, use multiple bonds.

8) Use formal charge to decide if central atom expands it octet (assuming that it can).

14

Electron Pair Geometries

15

Molecular Geometries

16

Electronegativities

17