1. Goals

• Learn the rudiments of computational chemistry, an area of chemistry undergoing explosive growth.
• Obtain a hands-on introduction to a modern computational chemistry program -- PC Spartan Plus.
• Compare the bond angles predicted by VSEPR to those obtained from calculations and experiments.
• Explore the utility of electron density models.

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2. Background

2.1 What is Computational Chemistry?

Computational chemistry (a.k.a. molecular modeling) is the application of computer-based models to the simulation of chemical processes and the computation of chemical properties. It accounts for roughly a third of the supercomputer usage worldwide. According to a recent text book, "Today, the situation has been reached where, in many cases, the computational chemist can substitute the computing machine for the test tube."

2.2 Why Computational Chemistry?

Computational chemistry is a valuable tool for experimental chemists to bypass tedious, time consuming, costly, and sometimes dangerous experiments. In the drug industry, computer design of molecules with specified properties is now becoming more common.

EXAMPLE: A new method for synthesizing useful antibacterial agents was recently devised using computer calculations.

Furthermore, computational chemistry allows one to investigate molecules that are too unstable to be studied experimentally, analyze quantities (such as atomic charges) that are not experimentally observable, and rectify incorrect experimental assignments.

EXAMPLE: Based on spectroscopic experimental results, Gerhard Herzberg, a Nobel prize winning scientist, concluded that the methylene radical (:CH₂) with two unpaired electrons had a linear geometry. Sophisticated calculations by Bender and Schaefer, however, demonstrated that methylene was bent with a bond angle of 135.1° . Further experiments of methylene confirmed the latter assignment. The measured bond angle was 137.7°.

Also, computational chemistry allows one to both calculate certain quantities (such as heats of formation) with more accuracy than can be determined experimentally (special cases only) and improve one’s general understanding of chemical phenomena.

EXAMPLE: Understanding how an expensive catalyst such as Pt works can lead to finding cheaper alternatives. The rational design of catalysts is a long sought after goal of chemists.

2.3 What can be Calculated with Computational Chemistry?

Properties of stable molecules, properties of transition states, and reaction rates can be calculated using computational chemistry methods. Each of the above three type of calculation is described further below.

I. Molecular Properties

Selected examples of molecular properties that can be calculated:

• Molecular Geometry: The arrangement of nuclei for which the potential energy is a minimum.
• Probability Density: Orbital (wavefunction) squared represents the probability distribution function for an electron in a particular molecular orbital (Chemistry 111).
• Total Electron Density: Experimentally found by analyzing X-ray diffraction data of crystals.
• UV-Visible spectroscopy: Calculate the energy difference between ground and first excited electronic state (the basic principles are similar to the H-atom emission spectrum).
• Vibrational analysis and IR spectroscopy: Vibrational transitions of molecules occur in the infrared region of the electromagnetic spectrum.
• Atomic charges: The total charge on an atom is the net excess of nuclear charge over electronic charge. Atomic charges are difficult to compute.
• Dipole moments: An electric dipole consists of two equal and opposite charges separated by a distance. Molecules that have a permanent dipole are classified as polar.
• Ionization energies: The minimum energy needed to remove the most loosely bound electron from a molecule in the gas phase.
• Electron affinity: The energy released when an electron attaches to a gas phase molecule.
• Dissociation energies: To calculate the dissociation energy theoretically, one subtracts the calculated electronic energy at the equilibrium geometry from the calculated energies of the separated atoms that form the molecule.

II. Transition State Energy and Geometry Calculations:

The transition state (a.k.a. the activated complex) is a molecule (lasting only a few molecular vibrations) that is formed by the reactant molecules before they form the product. While the geometry of even complex stable molecules can be obtained routinely via x-ray crystallography, detailed structural characterization of transition states by experimentation is virtually impossible.

III. Reaction Rates:

The computation of reaction rates (kinetics) is perhaps the most demanding type of computational chemistry calculation. Reaction rates have been calculated only for a limited number of reactions. Examples:

H + H2 --> H2 + H (calculations agree well with experimental data)

F + H2 --> FH + H (need for further calculations)

2.4 Brief Introduction to the Five Major Methods of Computational Chemistry:

1. Ab initio:

• Means based on first principles.
• Uses an electronic structure method based on quantum mechanics and uses no experimental parameters in calculations.
• The major disadvantage of ab initio quantum chemistry is the heavy demands on computer power.

2. Density Functional Theory (DFT):

• Uses electronic structure method based on quantum mechanics.
• DFT is a less expensive alternative to ab initio calculations.
• Method not available in PC Spartan Plus

3. Semiempirical:

• This is also an electronic structure method based on quantum mechanics.
• Calculations use experimental parameters to simplify the computation.
• Examples of semiempirical methods available in PC Spartan Plus: AM1, PM3.

• Newtonian mechanics (classical physics) is used to predict the structures and properties of molecules. Since the theory is not based on quantum mechanics, electrons are not treated explicitly in molecular mechanics.
• Treats molecules as spheres (nuclei) connected by springs (bonds). Actually, molecules are treated as though they are a collection of charged balls connected by springs.
• MM can be used for very large systems containing many thousands of atoms because the above approximation markedly simplifies calculations.
• Molecular mechanics methods cannot be used to address bond making or breaking because electrons are not treated explicitly in these methods.
• SYBIL is the only Molecular Mechanics method available in PC Spartan Plus.

5. Molecular Dynamics (MD):

• MD also uses Newtonian mechanics (classical physics).
• MD makes it possible to study the dynamic behavior of a collection of molecules as large as 1000 molecules.
• MD is not available in PC Spartan Plus.

3. Equipment and Materials

PC Spartan Plus is loaded on the PC computers in rooms 230 and 215. If the program does not work on a particular PC, check with your lab instructor to ensure that the appropriate hardware lock is installed.

PC Spartan Plus comprises six independent program modules: a graphical user interface, three modules for geometry optimization calculations, a module for the calculation of molecular properties, and a module for computing graphical surfaces. Without leaving the graphical interface, the user can construct a complex molecular structure, refine its geometry, specify a task and level of calculation, designate any graphical surfaces for later display, and then submit for calculation.

4. PCSpartan Plus Tutorial

4.1.1. General Operating Features of PC Spartan Plus

To launch PC Spartan Plus, double click on the PC Spartan Plus icon in the desktop. If the icon is not present, click on Start on the taskbar of Windows 95 located on the lower left of the screen. Highlight Programs, then click on PC Spartan Plus. PC Spartan Plus’s window will appear with its menu bar at the top of the screen. Maximize the window. Program functions may be accessed using pull-down menus under the headings in the menu bar. Entries under the individual menu items control all of the program’s functions. Two or more molecules can be simultaneously displayed in the window. However, only one molecule may be selected at a time. The selected molecule has access to all capabilities while non-selected molecules may only be displayed as static images.

4.1.2. Learning How to Use PC Spartan Plus

We will use acetonitrile to illustrate the basics of PC Spartan Plus.

Before beginning the exercise, create a new folder on the c: drive and give it your last name. To do so, open Windows Explorer, click on file, new, and finally folder. Next, type in your last name. At the end of the exercise, you will delete this folder.

1. Based on your understanding of Lewis structures, draw the structure of acetonitrile (CH₃CN).

   A three dimensional image of this molecule can be found in a Molecular Gallery (http://www.wellesley.edu/Chemistry/Flick/molecules/newlist.html).

In steps 2,3, and 4 we will build (draw) the acetonitrile molecule.

2. Back in PC Spartan Plus, select New from the File menu to enter the build mode. The entry model kit appears at the right of the screen. (see below)

   

   Among the simple building blocks incorporated into PC Spartan Plus’s entry model kit are "atomic fragments." These fragments specify the atom type (e.g., carbon) and environment (e.g., tetrahedral – a carbon atom attached to four other atoms). Relatively few fragments allow construction of a wide variety of simple molecules. In addition to atomic fragments (e.g., ), the entry model kit also contains libraries of functional groups (e.g. amide) and rings (e.g. phenyl), and additional tools for molecule building. Click (left mouse button) on tetrahedral carbon () from the library of fragments. Bring the cursor anywhere on the blue part of the screen and click. Tetrahedral carbon with its four free valences indicated by "yellow vectors" appears.

   The entry model kit connects atomic fragments (as well as groups and rings) through free valences. Valence electrons are outer electrons of an atom which are involved in chemical bonding. Any free valences remaining will automatically be converted to hydrogen atoms upon exiting build mode and will revert to free valences upon reentering build mode.

    

3. Click on the linear carbon from the model kit, then click on the tip of one of the free valences of the tetrahedral carbon atom on screen. The linear carbon is automatically connected to the tetrahedral carbon by a single bond. To obtain a better view rotate the structure by moving the mouse while pressing the left button. . If you make a mistake, use the Delete Atom button to remove atoms or valences.

   PC Spartan Plus’s entry model kit connects atoms only through the same type of free valence, e.g., single to single, double to double, etc.

    

4. Click on the triple bond containing nitrogen from the model kit, then click on the triple free valence of the linear carbon on the screen. This connects carbon and nitrogen by a triple bond
   
   
5. In this step, a preliminary structure refinement of the initial molecular geometry will be performed. First, rotate the structure to obtain a better view. Next, click on Minimize in the model kit to perform a crude minimization of potential energy to obtain a better geometry. At the equilibrium geometry of the molecule, the slope (gradient) of the potential energy should be zero. The iterations (number of cycles of calculations), the molecular mechanics (one of the computational chemistry methods discussed previously) strain energy (-0.183 kcal/mol), the gradient, as well as information about the symmetry of the molecule appear below the menu bar. Click on Done to remove them.
   
   
6. In this step you will perform several operations (e.g., rotations) on the acetonitrile molecule. Select View from the Build menu. This removes the model kit from the screen and replaces the ball-and-wire model of acetonitrile with a tube model. This model can be manipulated using the mouse in conjunction with the keyboard. Functions associated with the two-button mouse are summarized in the following table:

   .

   keyboard	left mouse button	right mouse button
   no action	picking, X/Y rotate	X/Y translate
   Shift	Z rotate	scaling
   Control	global X/Y rotate	global X/Y translate
   Control + Shift	global Z rotate	global scaling
   Alt	bond rotation	bond stretching

    

   The left mouse button is used for both picking (of graphical objects and/or of menu items), and for rotation of objects, and the right mouse button is used for translation or scaling of objects. Rotation and translation functions may be modified by holding down specific keys (Shift, Control, Alt) in addition to the appropriate mouse buttons. With no keys depressed, the left mouse button gives rise to rotation about the X and Y (screen) axes; the right mouse button gives rise to translation in the X and Y (screen) directions. Together with the Shift key, the left mouse button gives rise to rotation about the Z direction and the right mouse button gives rise to scaling. The Control key (Ctrl) in conjunction with the left or right mouse buttons and (optionally) the Shift key signifies that rotations or translations are to be carried out globally, i.e., on all molecules presently displayed, rather than only on the "selected" molecule. In build mode only, use of the Alt key in addition to the left mouse button allows for rotation about a "selected" bond.

7. To picture the acetonitrile structure in various renditions, try several options in the Model menu.
   
   
8. Labeling the atoms can be useful to look at the molecule’s structure. To do this, select Ball and Wire from the Model menu. This model, along with the wire model, are the only models for which the atom numbers may be displayed. Select Labels from the Model menu. Numbers appear next to the individual atoms together with atomic symbols, and a check mark appears to the left of Labels in the Model menu. The numbering is somewhat arbitrary and helps distinguish between atoms of the same type. Remove the atom labels by again selecting Labels from the Model menu; the check mark disappears.
   
   
9. Next, the molecule’s geometry will be examined through bond distances, bond angles, and dihedral angles . Select Distance from the Geometry menu. The model displayed is replaced by a ball-and-wire model and a message appears below the menu bar (Distance: Select 2 atoms, a bond, or a distance constraint). Clicking on two atoms results in each being marked in a gold sphere and the distance between the two being displayed below the menu bar. When the two atoms are bonded, an alternative is to click on the bond. Another distance maybe obtained by selecting another pair of atoms (or another bond), and so forth. When you are finished, click on Done.
   
   
10. To obtain a more accurate structure, a geometry optimization calculation will be performed on acetonitrile using an ab initio method (one of the five computational chemistry methods discussed previously). Select Calculation from the Setup menu. Perform the following operations:
    1. Select Geometry Optimization from the Task pop-up menu. This specifies optimization of equilibrium geometry.
    2. Select 3-21G(*) from the Level pop-up menu. This specifies a type of ab initio calculation for performing the computation.
       
    3. Verify that Charge is 0 (the molecule is neutral) and Multiplicity is 1 (these are the defaults). You can modify the contents of these boxes, if necessary, for other molecules.
    4. OPTIONAL: Give the molecule a name in the box to the right of Title.
    5. Click on OK to exit the dialog.
    
    
11. To performs the actual calculation, select Submit from the Setup menu. In the dialog which appears, you need to specify your last name (the newly created folder) next to Save in:, supply a name for your job in the text box File Name, and then click on Save. (You must save or else the calculation cannot be performed.) A new dialog appears telling you that your calculation has started. Click on OK to remove the dialog box . When the calculation is done after a few minutes, you will be notified with a pop-up menu. Click on OK to remove the dialog box.
    
    
12. Next, we will examine the results of your calculations. Select Output from the Display menu. The output for the calculation will appear at the left of the screen. Information inside the viewing area may be scrolled in the usual manner. At the "top" of the output is the title you have provided, the task at hand (‘geometry optimization"), the level of calculation ("3-21G(*)), as well as other relevant information, such as the initial set of atomic coordinates. The next series of lines that appear tell the history of the optimization process. Each line provides results for a particular geometry; "Energy =" gives the energy (in hartrees; 1 hartree = 627.5 kcal/mol) for this geometry and "rmsG ="gives the root-mean-square gradient. Ideally, the energy will approach a minimum value for an optimized geometry and rmsG will approach zero. If the geometry was not optimized satisfactorily, an error message, such as "Optimization has exceeded N steps - Stop," will be displayed following the last optimization cycle. Next, the new atomic coordinates for the geometry optimized molecule is displayed.

At the end of the output is a listing of atomic charges and the calculated dipole moment (the measure of the extent to which a separation exists between the centers of positive and negative charge within a molecule). Because charge distributions provide information about a molecule's reactivity, chemists are very interested in obtaining charge distributions via electronic structure calculations. Unfortunately, there are several methods of calculating atomic charges (and dipole moments) and different methods yield different results! PC Spartan Plus uses two methods for calculating atomic charges (and dipole moments):

1. Mulliken Population Analysis
2. Fits to Electrostatic Potentials
   

The output may be removed from view by reselecting Output from the Display menu.

13. The dipole moment is also available from the Display menu under Properties. Select Dipole from the sub-menu which appears. The dipole moment appears below the menu bar. In addition, the dipole moment vector is displayed on the screen attached to a ball and wire model. Click on Done to remove both. Remember that the dipole moment vector is defined to point from the positive charge to the negative charge (physics uses the opposite convention). 
    
    
14. Next, we will calculate the isoelectron density surface of the molecule which serves to locate chemical bonds, indicate overall molecular shape and size, and illustrate the electrostatic potential (the energy of interaction of a point positive charge with the nuclei and electrons of a molecule). Select Surfaces from the Setup menu. Select density from the Surface pop-up menu, and elpot from the Property pop-up menu. This specifies calculation of an isoelectron density surface onto which the value of electrostatic potential has been mapped. This will be referred to as an "electrostatic potential map." Click on Add; the line "surface=density property=elpot pending" appears in the box at the top of the dialog. Click on OK to close the dialog.
    
    
15. Select Submit from the Setup menu in order to submit the job. Handle the various message boxes as you did during the geometry optimization. When the calculation has completed, select Surfaces from the Display menu. Click on the text string "surface=density…" at the top of the dialog to highlight it. Click on the button to the left of Display Surface and then select any of the various display styles. Click on OK to exit the dialog. Repeat the last few instructions to change the display surface.

    Two or more molecules, or two or more copies of one molecule, may be simultaneously displayed although only one molecule may be selected. The selected molecule has access to all program capabilities while non-selected molecules may only be displayed as static images. Selection of one of the molecules currently on screen occurs by clicking on the molecule.

    
    A revealing comparison follows by displaying a transparent density surface along with a space-filling model on the same structure. Reenter the Surfaces dialog under the Display menu, highlight the line "surface=density…" and then select Transparent (or Mesh) from among the style options. Click on OK. Replace whatever model you are using by a space-filling model. You can now see clearly that the two images are nearly identical.
    
    

16. In this step we will examine the electrostatic potential map you calculated in steps 14 and 15. Return to the tube model and then reenter the Surfaces dialog in the Display menu. Highlight the line, then select Solid from the style choices, and finally click on the button to the left of Map Property. This requests display of the electrostatic potential map. Exit the dialog by clicking OK. Examine the graphic which appears on the screen. The shape of the surface is the same as before, and the color indicates values of the electrostatic potential evaluated on this surface. The potential is coded according to the visible spectrum (red<orange< yellow<green <blue), with red corresponding to the most negative potentials and blue corresponding to the most positive potentials. Nitrogen will appear negative (electron rich) and the hydrogens will appear positive (electron poor). This is reasonable as nitrogen is the most electronegative atom in the molecule and the hydrogens are the most electropositive. Electronegativity is the measure of the electron-attracting power of a bonded atom. The electrostatic potential map suggests that the dipole moment which you calculated earlier has the hydrogens at the positive end and the nitrogen at the negative end. Go back and examine the dipole moment vector again to see if this is indeed the case.
    
    
17. Remove acetonitrile from the screen (choose Close from the File menu).
    
    
18. Close PC Spartan Plus by clicking on the most upper right hand box with an "x" in it in the window.
    
    
19. Delete the new folder with all the files you created to leave room for others who will be performing the tutorial. Select Programs under the Start icon on the task bar at the bottom of the screen. Select Windows Explorer. A large window separated into two parts will appear. Select the folder you created and delete it.

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