Molecular Modeling 2: Computational Chemistry

Authors: J. M. McCormick, E. V. Patterson and M. C. Nagan*

Last Update: August 25, 2009

Introduction

Computational chemists use the principles of quantum mechanics, classical physics and thermodynamics to answer questions about chemical processes. Since its birth in the 1960's, the growth of computational chemistry has generally followed advances in computer technology and it has become an essential tool in chemical research.  It is used both as a guide to new avenues of research and as a way to understand fundamental chemical processes.  Computational chemistry is used in areas as diverse as materials science to pharmaceutical research where most companies have a computational chemistry division that helps guide the development of new drugs.

Of all the areas in computational chemistry, calculations that solve Schrödinger’s equation are the most prevalent. Almost any property associated with where electrons are in the molecule, and how those electrons behave can be calculated. For example, molecular geometries, the polarity of a bond, the molecular orbitals, or the visible spectrum of a molecule can all be calculated using quantum calculations.

In quantum chemistry methods, Schrödinger’s equation (Eqn. 1 where is the Hamiltonian operator, Ψ is the wavefunction and E, the energy, is the eigenvalue of ) is solved to give the electron density and the allowed electronic energies in a molecule (among other things).Solving Schrödinger’s equation is dependent upon two primary considerations: 1) the form of the Hamiltonian and 2) the space electrons are allowed to occupy.

The level of theory describes the type of Hamiltonian and the basis set describes the space electrons are allowed to occupy. In general, the Hamiltonian for a molecule must include terms that take into account the kinetic energy of the electrons, the kinetic energy of the nuclei, electronic-nuclear attraction, electron-electron repulsion and nuclear repulsion, respectively. The full Hamiltonian is impossible to solve for systems with more than one electron. Therefore, certain approximations must be made in order to solve Schrödinger’s equation (Eqn. 1). In this exercise we will use three different levels of theory (essentially different approximations) to solve Eqn. 1: Austin Model 1 (AM1),  Hartree-Föck (HF) and Density Functional Theory (DFT).

The AM1 level of theory is based upon a semi-empirical theory where certain portions of the molecule’s energy are approximated empirically (determined experimentally). In semi-empirical methods, paired core electrons are approximated. Only valence electrons are considered explicitly in a semi-empirical method. In addition, the area the electrons are allowed to occupy is restricted to the bare minimum (H –1 set of s orbitals; C, O, N – 1 set of s, 3 sets of p orbitals).

HF is what is termed an ab initio (Latin: from the beginning) method because the Hamiltonian is based upon fundamental principles. The Hartree Hamiltonian is written where the last term is a single potential that describes an average electron-electron repulsion energy or an interaction potential of electron i with all other electrons j. A general term for electron-electron repulsion and neglect of electron-electron correlation is needed to make the calculation more feasible. Methods that account for electron-electron correlation are available but computationally expensive and are usually restricted to molecules with unpaired electrons.

DFT is similar to HF in that all electrons are considered.  However, in DFT the electron density (|Ψ|²) rather than the explicit Ψ is solved for.  In addition, electron-electron correlation is empirically parameterized based upon the density.  DFT levels of theory are named to give specific information about them, but since these can be long, they are abbreviated (e. g., B3LYP, BPW91, mPWPW91) and often look like a bowl of alphabet soup.

In this exercise you will be using WebMO,¹ which is a web-based, user-friendly interface to the program Gaussian,² to calculate orbital energies and other properties of a series of molecules. 

Experimental

General Instructions

Open a web browser (More Info) and go to the WebMO website http://jade.truman.edu/webmo. If you are reading this on-line, you can simply click on the link to go there.  Once you have reached the Welcome screen, click the "Login Now" button at the bottom of the screen (scroll down if necessary to find it).  The Login screen shown in Fig. 1, will be displayed. 

Enter your username and password (you and your lab partner(s) will share the same username and password, which will be given to you by your instructor).  Click the "Login" button (or just hit enter) and the Job Manager screen (Fig. 2) will be displayed.  You are now ready to set up your first calculation.  IMPORTANT! You and your lab partner must not be logged on to your account at the same time.  If you are, then WebMO will behave erratically.

Figure 1.  WebMO Login Screen.

Figure 2. WebMO's Job Manager screen.

Before performing any calculations you will need to input information about the molecule, what calculations to do and what level of theory that you want the program to use.  The steps are 1) building the molecular framework, 2) selecting the calculation to do (geometry optimization, energy level calculation, etc.), 3) selecting the level of theory, 4) choosing a basis set, and 5) specifying the charge and number of unpaired electrons (multiplicity) on the molecule.  With WebMO you are guided through the configuration process; start it by clicking on "New Job" and selecting "Create New Job".  This will take you to the Build Molecule screen shown in Fig. 3.

Figure 3.  WebMO's Build Molecule screen.

Click "Open Editor" to open the Editor in a pop-up window (Fig. 4).  Click on the "Periodic Table" button, , to display a pop-up periodic table and select the element you want to add (the periodic table will automatically close).  Click on the "Build Button",  ,  and then click in the gray space to add that atom.  Repeat this process until all the atoms you need for your molecule have been added. To draw bonds between atoms, click and drag the mouse from one atom to another. To make a double bond, click and drag the mouse between the atoms twice, three times for a triple bond. Note: It is not usually necessary to specify any bond over a single bond, because the program will determine the number of bonds that are needed.  When you are done drawing the molecule either select File, Close from the Editor's menu bar or click the close button. Click here to learn more about the Editor.

Important:  It is generally unwise to perform a Comprehensive Cleanup on a molecule after you have drawn them.  The module that performs this function gives erroneous results for some molecules.  Unless otherwise directed to do so, do not perform a Comprehensive Cleanup.

Figure 4. WebMO Editor pop-up.

After you have made your molecule and closed the Editor, click on the right hand blue arrow head or "Job Options" under Progress. This will take you to the Configure Job Options Screen shown in Fig. 5.

Figure 5. Configure Job Options Screen from WebMO.

The program will give your job a name based on the molecule that you drew.  Be sure that your job has a unique name (it helps if the name is somewhat descriptive of what the calculation was about, like "H2 geom").  Choose the type of calculation to do from the Calculation Pulldown menu. Choose a theory from the Theory Pulldown menu and then select a basis set from the Basis Set Pulldown menu. If you are performing a calculation on an ion, enter its charge.  For molecules the charge is 0.  Leave the multiplicity as a singlet (this means that there are no unpaired electrons). At this point you are ready to start the calculation.  Before proceeding be sure that you have entered everything correctly and have written down everything that you entered in this screen in your laboratory notebook.  When you are satisfied and have recorded the information, click the right hand blue arrow head or "Submit Job."

You should now return to the Job Manager screen. The Job Manager lists all the jobs you have submitted to be calculated along with pertinent information about them (from left to right this is job number, job name, type of job, the date you submitted it, job status, the length of the job).  In the far right column ("Actions") there will be displayed one of several icons ("View", "Kill", "Restart") that you can use to control how the computer handles your job. If you made a mistake, one of two things usually happens; the program terminates your job and your results file contains nothing (or gibberish) or the program runs forever.  If you find yourself in the latter situation, or for any other reason want to stop a job, click the "Kill" icon ().  You can restart a stopped job by clicking on the "Restart" icon () which is displayed whenever a job is terminated abnormally. When your job is finished, its status will be Complete and the "View" icon () will be displayed to the right of the job. After you have submitted a job it is a good idea to occasionally click on the "Refresh" button on the bottom left-hand of the screen to get the most up to date information about your jobs.

Important: If you have a calculation that crashes for no apparent reason, first check your input to be sure you have entered everything properly (given it a name, specified a basis set, etc.).  If these look correct, then just click the "Restart" icon located under the "Actions" column on the Job Manager screen. 

When you click on the "View" icon, the results of your calculation will be displayed on the View Results screen like the one shown in Fig. 6.  At the top of the screen will be displayed the job number, the name your gave the job and what calculations were performed.  Below this will be the Viewer, which is similar to that on the Build Molecule screen, but with some new buttons and actions that are listed in Table 1.

Figure 6.  A portion of the View Results screen.

Table 1. Buttons on the WebMO Viewer that are active in the View Results Screen.

Below this will be a listing of the calculated quantities, which vary depending on what you told the computer to calculate.  Be sure to scroll all the way to the bottom of this screen.

H₂ Molecular Orbital Calculation

In the Job Manager screen click on "Create New Job" and then open the Structure Editor in the Build Molecule screen.  Add two H atoms to the window.  Click on one H atom and drag the mouse to the second to create a bond between them.  Close the Editor and select "Job Options".  Perform a "Geometry Optimization" calculation using "Hartree-Fock" theory and the "3-21G" basis set.  Set the charge to "0" and the multiplicity to "Singlet." Give your job a name and submit it after you have recorded all the inputted information in your notebook.  What you have told the computer to do is to repeatedly solve Schrödinger's equation each time adjusting bond angles and lengths (in this case, only the bond length) until it find the lowest energy structure. Once the job is complete, click on the "View" button in the Job Manager screen to look at the output.

Once the H₂ geometry is set, we can perform a molecular orbital calculation on H₂. In a molecular orbital calculation, you will specifically ask the program to render the shapes of the molecular orbitals from what is known about the wavefunction. From the View Results screen, click on "New Job Using This Geometry". You should now be in the Build Molecule screen. Click on the blue right hand arrow head or "Job Options". For this new job the Calculation is "Molecular Orbitals," Theory is "Hartree-Fock," the Basis Set is "3-21G," the Charge is "0" and the Multiplicity is "Singlet." Give the job a name and record everything in your notebook.  Click either the right hand blue arrow head or "Submit Job." When the job is complete click on View and scroll down to the section called "Molecular Orbitals". To view a molecular orbital, click the "View" button to the right of the molecular orbital. For H₂, there are two molecular orbitals labeled "1" and "2". These are the s (bonding) and s* (antibonding) molecular orbitals, respectively. A screen may appear asking you what to do. Click "Open" to open the MOViewer file (*.mo). Note: MOViewer is only available on University computers that are running the student image. Sketch a picture of the orbitals in your laboratory notebook or print them out and attach them later. Be sure to label your drawings!  Record the energies of the molecular orbitals in your notebook. 

N₂ Molecular Orbital Calculation

Build N₂ and perform a "Geometry Optimization" on N₂ using Hartree-Fock theory and the 3-21G basis set (remember that N₂ is a singlet and has no charge). On the optimized structure, perform a "Molecular Orbitals" calculation. View the σ_2p and the two π_2p (bonding) orbitals. They are molecular orbitals 7, 5 and 6, respectively. Sketch them in your notebook or print them out. Be sure to label your drawings! Record the energy and occupancy of all the molecular orbitals listed in your notebook. 

Structure of N₂O

Build N₂O (an uncharged singlet) and perform a geometry optimization on it using Hartree-Fock theory and the 6-31G(d) basis set.

When the job is complete, click on the View button and scroll down to the section called "Partial Charges." The partial charge on each atom is listed by atom number and element.  Click on the "View" button to graphically display the partial charges on each atom in the viewer at the top of the page. Draw the three atoms of N₂O in your notebook and show the calculated partial charges.

Bond Orders of N₂O

Once you have recorded everything you need from the View Results screen, scroll back to the top of page and click on "New Job Using This Geometry" to return to the Build Molecule screen. Select "Job Options" and set up a "Bond Order" calculation using Hartree-Fock theory and the 6-31G(d) basis set.  The charge is again 0 and the multiplicity is singlet.  Name the job, record the job's information and submit it. 

When the job is complete, view the results and scroll down to the section called "Bond Order". There you will find a matrix where an entry indicates the bond order between the atom listed in the row heading (on the left) and the column heading (on the top).  Entries where the row and column headings are the same are 0.000 (the bond order of an atom with itself is zero). 

In the Viewer, click on the "Select" button, .  Then click on the central N (atom will be highlighted) and then while depressing the shift key, click on the other N.  The N-N bond length will be displayed in the Viewer's status window; record this number (the units of bond length used here are Ångstroms, symbol Å, 1 Å = 1x10^-10 m).  Un-select the terminal N by holding the shift key and clicking on it.  Now select the O and record the N-O bond length.  You can determine the N-N-O bond angle by highlighting all three atoms.

Draw a picture of N₂O in your notebook which shows the calculated N-N and N-O bond orders for all nearest neighbors and the N-N and N-O bond lengths.

Structure of ClF₃

Draw the Lewis structure for ClF₃ in your notebook.  Predict the structure of ClF₃ with VSEPR theory (assuming that Cl is the central atom and that the F are all bonded only to the Cl) and use this as the starting point to build ClF₃ in WebMO. Perform a "Geometry Optimization" on ClF₃ using the semi-empirical theory AM1.  Under the Basis Set Pulldown, select "Other." Delete whatever basis set is displayed in the pop-up window and hit OK.  The words "Other ()" should now be displayed in the Basis Set Pulldown. Continue on setting up the calculation, remembering that ClF₃ has no charge and it is a singlet.

While this is calculation is running, set up another geometry optimization calculation for ClF₃ using the VSEPR geometry as the starting point.  This time use the theory B3LYP and the basis set 6-31G(d).

Sketch the structures predicted by each calculation.  Determine the Cl-F bond lengths (there are three of them ) and the F-Cl-F angles (there may be several) and include these on your sketches.

Now perform a "Geometry Optimization" on the ClF₃ structure predicted by AM1 theory, but using the theory B3LYP and the 6-31G(d) basis set.  Record the results of this calculation in your notebook.

Bond Polarity

Create separate jobs for the following molecules: CH₄, CH₃BH₂, CH₃NH₂, CH₃OH and CH₃F. Perform a geometry optimization on each using HF theory and the basis set 6-31G(d).  All of these molecules are singlets and have no charge. Note: You will get better results if you do a Comprehensive Cleanup of each of these molecules (done in the Viewer after you draw them) before you submit them.

When the jobs are complete, go to the View Results screen for each molecule. Sketch a picture of each molecule in your notebook based on the structure shown in the Viewer.  Scroll down to the section called "Dipole Moment" and write down the dipole moment value (the unit of dipole moment is the Debye). Click on "View" and scroll back up to the Viewer to see the direction of the dipole (i. e., which direction are the electrons pulled in the bond).  Add the dipole moment of each molecule to its sketch using the crossed arrow formalism ()to indicate the direction of the dipole.

Results and Analysis

H₂ and N₂

Draw a molecular orbital energy diagram for H₂ using eV (electron volts) as the energy unit. Assume the atomic H 1s orbitals are at 0.000 eV. Note: the program use Hartrees as its energy unit (1 Hartree = 30.358 eV).  Include in your MO diagram the pictures of the the s and s* orbitals.

Draw a molecular orbital energy diagram in your notebook for N₂, including all bonding and antibonding MOs (use the occupancies to help place the electrons).  Include your pictures of the the s_2p and the two p_2p orbitals.  Use eV as the energy unit.

In the Lewis dot structure of N₂ we would predict three bonds and two lone pairs arising from the valence electrons.  Is this consistent with the MO picture?  How would MO theory describe the three bonds in N₂?  How would it describe the lone pairs?

The nitrogen atoms have two areas of electron density around them (the triple bond and a lone pair).  What hybridization would Valence Bond theory predict each N atom has?  How does this compare to the MO description? (Hint: think about the following: how are the bonds described? how are the lone pairs described? do the valence bond orbitals look like the molecular orbitals?)

N₂O

Draw resonance structures for N₂O and calculate the formal charges on each atom.  Use VSEPR theory to predict the structure of N₂O.  Are the predictions of the resonance structures and VSEPR consistent with the predictions of MO theory?  How are they the same and how are they different?  Based upon your MO calculation, which resonance structure is dominant? Why is this resonance structure dominant?

The N-N bond length in N₂O has been measured to be 1.128 Å and the N-O bond length has been measured to be 1.184 Å.³  Given the average bond lengths shown in Table 2, are the measured bond lengths and the calculated bond lengths consistent with the bond orders?  How well did the calculation do in obtaining the true values of the bond lengths?

Table 2.  Average bond lengths for different N-N and N-O bonds.⁴

ClF₃

On your VSEPR-predicted structure of  ClF₃ indicate the predicted distortions from the ideal angles caused by the repulsion of the bonding pairs by the lone pairs.   Do your predictions (using different levels of theory) match that predicted by VSEPR? Which theory gives a better match to the VSEPR model? Why?

The structure of ClF₃ has been determined at -120 °C using X-ray crystallography,⁵ and is shown in Fig. 7.  Also shown in Fig. 7 are the measured bond angles and bond lengths. Which of the models considered (VSEPR, AM1 or B3LYP) gives a better qualitative agreement to the actual structure of ClF₃? Which gives a better quantitative agreement to the actual structure?

Figure 7. Structure of ClF₃ as determined by X-ray crystallography at -120 °C showing the relevant bond angles and bond distances.⁵  Here the fluorines are represented by yellow-green balls and the chlorine by a darker green ball.

With ClF₃ you should have found that the AM1 calculation gave the wrong answer and that when you start from a structure that is not close to the "true" structure, you are not guaranteed that you can arrive at the "true" answer.  These illustrate two important considerations in computational chemistry (and anywhere where we use computer models): the appropriateness of the model and the problem of "local" versus "global" minima.  The AM1 result is an example of the first consideration because AM1 theory ignores important aspects of bonding, which are included in the B3LYP model, that lead to an incorrect predicted structure.  The trigonal planar structure predicted by AM1 theory is a local minimum (it is a structure that has a low energy, but not the lowest energy) from which the program cannot escape even using a better model.  Although computers are very good at performing calculations, they have no chemical intuition, which is why the human element is an essential component of computational chemistry.
 

Bond Polarity

The experimentally determined dipole moments for compounds considered here are given in Table 3.⁶  Note that there is no entry for CH₃BH₂.  Qualitatively rationalize the calculated dipole moment's direction and magnitude with what you know about electronegativity. How do the calculated dipole moments quantitatively compare with the actual values?  If we were able to measure the dipole moment of CH₃BH₂, how do you predict it would compare to the calculated value?

Table 3. Experimental dipole moments measured in the gas phase.⁶

Conclusions

Use the outline for a Report of Physical Phenomena as the basis for your discussion of conclusions.  Be sure to answer the questions posed in the Results and Analysis section above.

Summary of Results

No summary tables are required for this exercise.

References

1. Polik, W. F and Schmidt, J. R. WebMO Pro 6.0;  WebMO LLC: Holland, MI, 2005.

 

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3. Pyykko, P. and Zhao, Y. J. Phys. Chem. 1990, 94, 7753-7759, and references therein.

 

4. Huheey, J .E. Inorganic Chemistry, 3^rd Ed.; Harper and Row, NY, 1983, p. A-32ff.

 

5. Burbank, R. D. and Bensey, F. N. J. Chem. Phys. 1953, 21, 602-8.

 

6. Handbook of Chemistry and Physics, 64^th Ed., Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1983.