Chemical Bonding and Molecular Modeling

Pre-Lab Requirements:

· Print, read, and bring this laboratory handout and data sheets to the modeling lab, Sims 312.

· Bring your lecture textbook and calculator with you to the modeling lab. You will find them to be helpful resources.

· Print the Lewis structure assignment which will be completed in lab the week before the scheduled molecular modeling lab.

· Turn in the completed pre-lab assignment below, prior to beginning the lab. If you do not have a completed prelab assignment, you will not be allowed to complete the molecular modeling lab.

Introduction

The purpose of this lab project is to investigate the forces that hold atoms together, including the strength of covalent bonds and how electrons are distributed in a molecule using computational methods (Read sections 9.4, 9.5, 9.9, 9.10, and 10.1 from Chemistry and Chemical Reactivity or Sections 2.5-2.8 and 3.1-3.5 from Chemical Principles The Quest for Insight). The calculation of such properties, based on quantum mechanics, was once merely a novelty, but now complements experimental work as a means to uncover and explore new chemistry. One reason for the recent emergence of molecular modeling as an important scientific tool is that the underlying theories have evolved to a point where several important quantities, such as molecular geometry and reaction energetics, can be obtained with sufficient accuracy to actually be of use. Another reason has also been the tremendous advances in computer hardware and increased availability that has occurred during the past two decades. Finally, software development has reached a point where useful results can be obtained with little specialized training. Molecular modeling (the visualization) and computational chemistry (the calculation of chemical properties) are rapidly enhancing how chemical and pharmaceutical research is conducted in industrial, academic, and government labs. For example, drug design is now done by computationally modeling a targeted receptor site (the DNA of a cancer cell, for example) and then modeling various molecular structures that may interact with the receptor site resulting in a therapeutic value (such as disrupting DNA replication and tumor growth). Computational modeling of molecular interactions with these targeted receptors can provide an indication of the most promising new drug candidates from databases that may contain several hundred thousand chemical structures. Once the most promising compounds have been discovered via computational methods, the synthesis and laboratory testing is conducted to determine which of these have the required efficacy (without adverse effects) to sufficiently merit the expense of extensive animal and human testing necessary to obtain FDA approval. By using molecular modeling to rapidly identify the most promising candidate compounds, pharmaceutical companies can decrease both the time and cost associated with developing new medications. This allows companies to test a much wider variety of molecular structures that have potential therapeutic value and greatly enhances the effectiveness of the drug discovery process. (Most of the world’s new medicines are developed by U.S. pharmaceutical companies.) These corporations are now staffed with chemists and physicians who work together in teams to discover and develop new medications that greatly improve the quality and longevity of life for the world’s citizens. To maintain this global competitiveness, U.S. companies need young scientists committed to this worthwhile goal who also well understand the full potential that can be realized with computational tools for rational drug design. Many believe that the full exploitation of molecular modeling capabilities will be made by young scientists who have been trained early in their career to use these tools as an essential part of chemistry.

Molecular Modeling and Quantum Mechanics

Since the 1910’s, it has been known that classical physics utilizes approximations that cannot be applied to small particles, such as atoms and electrons. For example, properties such as the emission of light from gaseous atoms (neon lights), the emission of light from hot objects (tungsten filament light bulbs), and the photoelectric effect (emission of electrons from metal surfaces exposed to light), cannot be explained using classical physical principles. To solve these problems and explain these phenomena, energy was thought to be absorbed or emitted by small particles only in discrete chunks or “quanta”. As such, methods used to calculate molecular properties utilize “quantum mechanics”, rather than “classical or macroscopic mechanics”. For example, with the continued development of smaller and smaller integrated circuits and molecular wires, a quantum mechanical description must now be used to describe how electrons flow through these small electronic devices.

Quantum mechanics is based on a set of assumptions (postulates) that is used to determine the properties for a given system of atoms or molecules. (Better assumptions mean better property values, and therefore is a current strong area of research.) Quantum calculations involve solving the Schrödinger equation in to find the wavefunction and associated energies for a given system. The basic form of the Schrödinger equation is:

HY = E Y

where Y is the wavefunction, H is the energy operator, and E represents the discrete allowed energy values for the system under study. The wavefunction itself has no physical significance, although the square (Y²) can be related to electron density. Integration of the square of the wavefunction over a three dimensional region of space represents the probability of an electron being found in that specific region (this is one of the main postulates of quantum mechanics and is how you arrived at the specific shapes for atomic orbitals as shown in Chapter 3). There are significant obstacles to overcome in solving Schrödinger’s “simple-looking” equation. If a system has more than one electron, then there are only approximate solutions. Electron-electron repulsions in real atoms and molecules introduce a 1/r potential energy term that makes it impossible to exactly solve. These approximate solutions (models) to the Schrödinger equation involve calculating a large number of integrals to determine the wavefunction and associated energies. To complicate matters, single electron wavefunctions are “sums of functions” (called basis functions) that represent the various valence and inner electron orbitals of all the atoms in the molecule. Each basis function is typically a sum of Gaussian type (bell curve – e ^-ar2) mathematical functions. Choosing a Gaussian form speeds the computational evaluation of integrals.

“Severe” approximation solutions to Schrödinger’s equation may lead to models that can be widely applied, but may not yield accurate information. Less severe approximations may lead to models which are more accurate but which may be too costly (in terms of computer time) to be applied routinely. Thus, chemists are typically faced with a choice of models that balance between accuracy and cost. Ab Initio methods are considered some of the most accurate methods available, but are costly and generally best applied to small systems. Semi-empirical methods are less costly and accurate, but can be applied to larger systems, giving results in a reasonable time. Molecular Mechanics methods are even less costly and accurate, but are useful for large bio-molecules, polymers, etc., or to get a “quick” result.

Pre-Lab Assignment (To be turned in prior to lab work!):

If you do not turn in this prelab assignment, you will not be allowed to complete this lab.

On a separate sheet of paper:

1. Draw the Lewis structure(s) for each of the following molecules and molecular ions. Show all lone pairs of electrons and formal charges where appropriate. Look for equivalent resonance structures and draw all equivalent structures where appropriate.

SO₂, BrO₃^-, H₂O, H₂S, PH₃, NH₃

2. Determine the electron pair geometry and the molecular geometry for each of the above molecules and molecular ions.

3. For the molecule N₂O (nitrous oxide), there are five possible Lewis structures. Three have the N-N-O bond skeleton, and two have the N-O-N skeleton.

a. Draw the five Lewis structures, indicating formal charges.

b. By considering the formal charges, can you suggest which structures might be eliminated?

c. Which structures have the smallest formal charges?

d. Because oxygen is more electronegative than nitrogen, it is more likely to have a negative formal charge. Which structure would then be the best description of N₂O?

e. Are the structures that have the N-O-N bond skeleton resonance forms of the structures with the N-N-O skeleton? Explain.

Lab Requirement:

In this first modeling lab exercise, you will use computational chemistry techniques to gain an understanding of the energy changes that occur in a covalent chemical bond as the distance between atoms is varied, and how electrons are distributed in a molecule. You will explore these two properties using a sophisticated and powerful, yet user friendly, molecular modeling program called Spartan.

Print the Attached Data Sheets: Part A, Part B

Lab Goals: Work in pairs of students for data collection. Results and question answers are to be done independently.

· Choose a pair of molecules for you and your partner to work with: (H₂O and H₂S) or (NH₃ and PH₃).

· Draw Lewis structures for your pair of molecules that satisfy the octet rule.

· Use Spartan to build a model of each molecule with an optimal geometry (bond lengths and angles).

· Calculate and graphically display the electron density distribution, with electrical potential for each molecule.

· Calculate and graphically display energy changes that occur as a bond between two atoms is stretched and compressed.

To begin:

Let’s first get familiar with Spartan’s features. Log into your class’ user account on one of the Silicon Graphics modeling computers. If you do not have a password, see your instructor.

1. Start the Spartan software by double left clicking the Spartan desktop icon. For easy viewing, maximize the window by clicking the large square in the upper right hand corner of the Spartan window. The small square icons the program on the desktop. (Note: There are a few differences between the Silicon Graphics graphical user interface and Microsoft’s Windows interface.)

2. In Spartan, note the Menu options (File, Model, Geometry, Build, Setup, Display), the Information Bar just below the Menu options, and the Workspace. Color schemes can be altered, by a left-click and hold, on the “Wavefunction, Inc.” logo menu option, just to the left of the File menu option, but if you’re satisfied with the default colors, just move along. For printing it is recommended to choose a white background.

3. To meet your third goal, let’s build and manipulate a practice molecule, carbon dioxide (CO₂) first. In molecular modeling, you can save time and computer power if you apply some knowledge about the molecule’s shape up front, usually obtained from experimental data, such as spectroscopy data. VSEPR theory and/or Lewis Structures can also be useful starting points. (For instance, in building carbon dioxide, and as a starting point for the three atoms in CO₂, the carbon atom is known to be in between the two oxygens, with an almost linear arrangement, and double bonds between each.)

4. Under File, choose New. The Spartan Builder window opens, along with a Model kit.

5. There are five selectable model kits, Entry, Expert, Library, Peptide, and Nucleotide. Choose the Expert model kit, by left-clicking the Expert button. A periodic table; a set of general bond connectors; a drop down menus of common polyatomic fragments; bond types; and editing features are shown.

6. From the periodic table, choose your central atoms (C). Then choose two linear connectors (-x-) just under the periodic table. Left click on the workspace to place your carbon atom with two connectors. If you make a mistake, left click the Delete button on the model kit, and then left click on the atom to delete.

7. Holding the middle mouse button down and moving the mouse around can rotate the atom or molecule. Holding down the right mouse key and dragging the mouse can translate the molecule. Holding down the Shift key AND right mouse button will zoom and shrink the size. Try each of these movements.

8. Now let’s add the two oxygen atoms to the carbon atom. Left click the oxygen atom and one connector (-x). Don’t worry; we’ll take care of valence bond types below. On the workspace, left click near one carbon connector to connect oxygen. Then connect a second oxygen at the other connector. (Note the connector you’re working on is usually represented with a dashed line. Solid lines represent connectors you’re not working on. Left click on a blank area to de-select everything.)

9. Finally, we need to indicate the double bonding between carbon and oxygen. On the model kit, just below the fragments are the various bond types available. You can choose a partial single bond (…), a full single bond (__), one and a half bonds (…), double bonds (=), triple bonds, etc.

10. Choose the double bond, and double-click each bond between carbon and oxygen. Your model for CO₂ is now complete. You may want to rotate your molecule a bit to check for double bonds. Click on Minimize to perform a molecular mechanic geometry optimization of your molecule. A dialog box appears giving the strain energy, as well as a symmetry classification. Click OK to close the dialog box.

11. Choose File, Save As, and give the model a filename to save the model to disk. Use something short (eight letters or numbers) for a filename, as UNIX operating systems are stricter than Windows about filenames. Avoid punctuation, spaces, etc., and realize UNIX is case sensitive.

12. After saving, choose File, Quit to exit the builder and place your CO₂ molecule on the workspace.

13. Spartan can render the model in various ways, as shown under the Model menu, including Wire, Ball and Wire, Tube, Ball and Spoke, Space Filling, and Polyhedra. From this menu, you can also choose to show or hide hydrogens and/or atomic labels. Atomic labels can only be displayed with the Wire or Ball and Wire renderings. Look at CO₂ using each rendering, but for our purposes, Ball and Wire will work best.

14. Bond distances and angles can be displayed from the Geometry menu. Select Distance from the Geometry menu. A dialog: “Distance: Select 2 atoms, a bond, or a distance constraint” is displayed. Click on two atoms (marked as yellow) or a bond to display the bond distance. Click Done to close the dialog box.

15. With these building and manipulation basics in mind, you are now ready to work with your pair of molecules. Choose File, Close to clear your workspace.

A. Geometry Optimization, Electron Density, and Electrical Potential Plots

In this section, you will build your molecule, further optimize the geometry using an Ab Initio (Hartree-Fock) model, and add an electron density surface onto which the value of the electrostatic potential will be mapped.

1. Build your first molecule, save, and exit the builder to place the molecule on your workspace.

2. Select Ab Initio models from the Setup menu to open the model dialog box.

a. Click inside the Title box, and enter the name of your molecule.

b. Select Geometry Optimization from the Task pull-down menu.

c. Select HF (Hartree-Fock) from the Theory pull-down menu.

d. Select 3-21G* from the Basis pull-down menu.

e. Verify the Total Charge is 0, and Multiplicity is singlet.

f. If the Direct button is checked, remove it.

g. Click Save to exit the dialog box.

3. Select Surfaces from the Setup menu to open the surface calculation dialog box.

a. Select density from the Surface menu.

b. Select elpot from the Property menu.

c. Select med from the Resolution menu.

d. Click on Add, to add the surface to the dialog box, and Save to close the dialog box.

4. Click on Submit from the Setup menu.

5. After the calculation has completed, the results can be displayed from the Display menu.

a. The total energy (in kJ/mol) can be displayed by clicking on the Display menu, Properties, Energy in kJ/mol option. Click Done to remove the dialog.

b. The dipole moment can be displayed by clicking on the Display menu, Properties, Dipole option. The dipole moment (in debyes) is displayed, and the dipole moment vector (+ à -) is attached to the molecular model. Click Done to remove the dialog and vector.

c. To display the Electron Density surface, choose Surfaces from the Display menu.

1. Highlight “surface = density….” at the top of the dialog, then check Display Surface.

2. Check Solid under Style.

3. Click OK to display the surface and exit the dialog. Rotate the molecule to gain a 3-D perspective. Note how the space filling rendering resembles the density surface. In fact, go back to the Surfaces menu under Display, and change the Style to Transparent. Click OK to close the dialog. Now change the rendering to “space filling” to get a better comparison.

4. Return to the rendering to a Ball and Wire Model.

d. To display the electrostatic potential map on the electron density surface, choose Surfaces from the Display menu.

1. This time highlight “surface = density..” as above, check Display Surface, and check Map Property.

2. Select Continuous under Color, and again choose Style to be Solid.

3. Click OK to display the surface.

4. Rotate and examine your molecule.

5. The color scheme indicates colors towards the red as negative regions, while colors towards the blue are positive regions.

6. Note how this surface relates to the Dipole. You can redisplay the dipole vector, as needed.

7. Change the Color mode to Discrete and note the display, then change back to Continuous.

6. Change your background color to white, and Print a copy of your surface to the lab printer (black and white), under the File menu. Label the positive and negative regions, and draw the dipole vector on the printout for your report. Change the background color back to default.

7. Close your first molecule, under File, and repeat this procedure for your second molecule.

B. Coordinate Driving and Potential Energy

In this section, you will systematically change the length of one bond in each of your molecules from 0.5Å to 3.0Å, calculating the energy of the molecule for each bond length. These energies will be graphically displayed, and give you an idea of the strength of the covalent bond between the central atom and hydrogen.

1. Open the file for your first molecule, using File, Open. Select the file from the directory, and click Open.

2. Under Setup, choose Ab Initio method.

a. The Title should still be appropriate.

b. Choose Coordinate Driving for the Task, HF for the Theory, and 3-21G* for the Basis.

c. Total Charge remains 0, Multiplicity remains singlet, and Direct remains unchecked.

d. Click Save to close the dialog.

e. Under Build choose, Coordinate Driving to open the coordinate driving builder.

f. Choose Drive Distance, and left click one of the bonds in your molecule. The two atoms for the selected bond will show yellow, and a Distance dialog box opens.

i. Choose 0.5Å for From, and 3.0Å for the To.

ii. Enter 20 for Steps, meaning you’ll calculate the energy at 0.125Å increments.

iii. Enter 10.00 for Sigma.

iv. Choose OK to close the Distance dialog. This will enter your parameters in the Coordinate Driving Panel.

v. Choose File, Save, and File, Quit to close the dialog.

g. Choose Submit under Setup to begin the calculation. It may take several minutes to complete the calculation.

h. After completion, choose OK to close the dialog, which opens a spreadsheet on the workspace. The molecule’s 20 lengths are added to the spreadsheet.

i. On the spreadsheet, choose Column, Add Energy, in kJ/mol.

j. Under Plot, choose Create, to open the Create Plot dialog.

i. For the x-axis, choose Molecule.

ii. For the y-axis, choose Energy (kJ/mol).

iii. Choose Create to generate a plot on the workspace.

iv. Note the general shape of the plot, as the bond is stretched and compressed. This is often referred to as a “Potential Energy Curve”.

v. Choose Animate at the bottom of the spreadsheet to observe the bond stretching and compressing, and note the energy changes.

k. The bond length is defined as the length with the minimum energy. How does this chart compare with the geometry optimized bond length?

l. Find and record the lowest energy and the energy at 3.0Å by moving the check mark next to the molecule. Calculate the difference in these two energies. The difference between these two energies is the approximate bond energy.

m. Print your curve by again setting the background to white from the Wavefunction, Inc. logo Colors option, followed by File, Print. Include your plot with your report. Reset the background color to the Default.

3. Close your first molecule, under File, and repeat a coordinate driving calculation for your second molecule.

Funding for the molecular modeling equipment and software being used in this project was provided by the National Science Foundation’s ILI program. In April 1996, the National Science Foundation selected Winthrop University to implement a molecular-modeling based undergraduate chemistry curriculum. Within months of the award, Winthrop University provided the necessary matching funds to establish the new molecular modeling lab and to begin implementing a computational chemistry-based curriculum. New labs and exercises in General Chemistry, Organic Chemistry, Physical Chemistry, and Biochemistry are being developed. The department will also be offering a new upper-level course (CHEM541, Computational Chemistry) that fully examines the capabilities of this exciting technology. Chemistry students will also be expected to use molecular modeling to support their year-long research projects and conference presentations. The newly developed curriculum will serve as a model of the full extent to which the technological advances in computational chemistry can be effectively used by undergraduate students. This is the beginning of your computational career.