Graphic Visualization of Atomic and Molecular Orbitals

I. Introduction.

This is a computer graphics exercise for Physical Chemistry which will enable students to gain a better intuitive grasp of the atomic and molecular orbital sizes and shapes. This is made possible by the midas molecular graphics package, which is ordinarily used for displaying macromolecules, but has been adapted in this exercise to draw electron dot density maps of atomic and molecular orbitals in three dimensions. The student will be able to manipulate the orbital models using the mouse and view them from various angles to more readily comprehend their shapes. What you will be seeing on the screen for each atomic or molecular orbital is a large pattern of dots representing the spatial distribution of electron positions obeying the actual probability density y2. One can think of these dot density maps as the superposition of several thousand independent measurements of the electron position. Here y, the wave functions, are readily accessible and are the hydrogen-like atomic orbitals taken from tables found in any standard P. Chem. text. For atoms with more than one electron, the appropriate effective atomic number Zeff has been used in place of Z, to account for shielding effects. These can also be found in tables. Turn in your observations and answers to the questions indicated in bold on a sheet of notebook paper.

II. General Operating Procedure for the Silicon Graphics Workstations.

The two SGI workstations we will be using for this graphics exercise are located in Foster Hall Room 324.

A. Login procedure.

When you sit down at the workstation, make sure the monitor is turned on, give the mouse a jiggle and you will see the user login screen. There should be a series of icons, one of which is the CHEM351 icon. Double click on it using the first mouse button. No password is required. Shortly you should see a background field of stars and a Unix window labeled winterm.

Wait for a few seconds while the login procedure takes place.

Move the cursor until the arrow is inside this window. You may only interact with a window while the red cursor arrow (or an x) is inside a window. You should see a prompt character that says c351#. If so, the window is ready for your input. If you have problems, be sure to come see the instructor.

B. Launching the midas program.

You may launch the midas program (Molecular Interactive Display and Simulation) by typing the command:

midas

Shortly after this command, an empty window will appear on your screen which can be positioned in the center of the screen by moving the mouse, and then clicking any mouse button.

Then you should expand the midas window to fill the whole screen. This may be accomplished by clicking once with the first mouse button in the ‘expand’ box in the upper right hand corner of the window. Now you are ready to interact inside the midas environment.

C. Basic commands to interact with atomic and molecular orbitals within midas.

1. Bringing up AO and MO. First you will need to bring up a specific set of atomic or molecular orbitals for study. This can be accomplished by executing the command:

source keyword

The particular keyword you use depends on which exercise you are doing as described below.

Let’s bring up the first set here by typing:

source H1s2s3s

This should bring up three atomic orbitals onto the screen, the 1s, 2s and 3s orbitals of Hydrogen. This will be our first exercise. The screen should have three atomic orbitals corresponding to the 1s, 2s and 3s going from left to right. Above the atomic orbitals is a little distance ruler which are two points connected by a dashed line. In the upper right hand corner is a number 10.00 which indicates that the ruler is currently set at 10 Ångstroms of distance.

2. Selecting a model. Next you need to know how to select an orbital to be manipulated. Look in the lower right hand region of the window. There should be a lighted panel that looks like the following:

The set of numbers in the bottom indicate a set of models on the screen. The 0 box is lit up here, indicating that model #0 is selected.

In the H1s2s3s exercise,

model 0 = H1s

model 1 = H2s

model 2 = H3s

model 9 = the point on the left side of the ruler

model 10 = the point on the right side of the ruler

When model 0 is selected and no other, that means that mouse motions will control the motion of the H1s orbital only. By clicking on the numbers 0, 1, 2, 9, and 10, one may toggle on and off mouse control of the other items on the screen. That is what is meant by selecting a model.

3. Mouse motions.

a. x-y rotations: With only model 0 selected, take the mouse, move the cursor near the center of the window, and hold the first mouse button down. Move the mouse around with the first button down. Notice that the H1s orbital goes into rotational motion.

b. z rotations: Release the mouse button and move the cursor to a region of the window outside the circular dashed line you saw when you moved the mouse before. Hold down the first mouse button and move the mouse around outside the circle. You will see rotation around the Z axis, which is the axis coming out of the screen at you.

c. translations: Finally, hold down the middle mouse button and move the mouse around. You will notice that the H1s orbital can be moved around on the screen translationally.

 

4. Working with the ruler. By deselecting all models and turning on models 9 and 10, you should be able to translate the ruler with the middle mouse button. You can stretch and shrink the ruler by turning on only 9 or only 10 and translating either end point of the ruler. Notice how the distance number in the upper right corner changes as you do that.

5. Zooming in and out on the whole picture.

Click on the word Sliders in the lower right hand panel. The panel should change appearance and look like the following:

Now by repeatedly clicking on the right hand end of the scale button, you will zoom in on the picture. Clicking on the left hand end of the scale button will zoom out.

 

6. Changing the thickness of the viewing region.

You are really looking at a slice of space which encompasses most of the orbitals. However, by decreasing the thickness you can actually start to get a cross section of an atomic or molecular orbital. This will be useful for identifying radial nodes, etc. Click on the left hand side of the thickness button to decrease the thickness of the viewing section, etc.

7. Other commands:

a. roll: Does a slow automatic rotation of the selected models. Never have more than one model selected at a time when performing a roll, because with more of them selected, it will rotate them out of the same x-y plane.

b. rock: Rocks the selected model back and forth to create a 3D effect.

c. freeze: Stops a rocking or rolling motion.

d. stop: Shuts down the midas window in order to quit or go to the next exercise.

III. Exercises.

A. Exercise I - Comparing s atomic orbitals with various n values.

Launch this exercise with:

source H1s2s3s

The Hydrogen 1s, 2s and 3s should appear on the screen from left to right, respectively.

model 0 = H1s

model 1 = H2s

model 2 = H3s

model 9 and 10 are the ruler ends

1. First note the relative sizes of these s orbitals as n goes from 1 to 3. Using the distance ruler, approximate the radius of each of these orbitals. Note that they are somewhat fuzzy and it is ambiguous to say exactly how far out the electron goes.

2. Select each one individually and do rotations with the mouse and with the roll command. What can you say about the basic shape of these orbitals?

3. Now decrease the thickness of the viewing slice and see if you can detect radial nodes in any of the orbitals. Based on the ruler, how far from the nucleus are they, and how many? Just estimate.

Now if you are finished working with the s orbitals, execute the command:

stop

B. Exercise II - The p atomic orbitals.

Launch the exercise with:

source H2p3p

This should bring up the hydrogen 2px and 3px atomic orbitals from left to right, respectively.

model 0 = H2px

model 1 = H3px

1. Selecting each model independently, use the mouse motions or roll to study the basic shape of the orbitals. Describe the shape of these orbitals.

2. Find the nodal plane in each, i.e., the angular node.

3. Find any radial nodes that might be present by decreasing the thickness of the viewing slice. The 3p has both an angular and a radial node. Can you find them? If so, make a crude sketch indicating the radial and angular node.

stop

C. Exercise III - Two of the 3d orbitals of Hydrogen.

Launch this exercise by typing:

source H3d

This will bring up H3dz2 and H3dxy.

model 0 = H3dz2

model 1 = H3dxy

Again look at the basic shapes of the orbitals by rotating them individually. Are there any angular nodes? Are there any radial nodes? Make a crude sketch.

D. Exercise IV - s orbitals of many electron species and effective atomic numbers.

Launch this exercise by typing:

source H_He_Na

This will bring up five atomic orbitals. Across the top of the screen from left to right will be the H1s, Helium 1s and Sodium 1s atomic orbitals. At the bottom of the screen you will see the Sodium 2s and Sodium 3s atomic orbitals.

model 0 = H1s

model 1 = He1s (Zeff=1.69)

model 2 = Na1s (Zeff=10.6)

model 3 = Na2s (Zeff=6.85)

model 4 = Na3s (Zeff=2.2)

First examine the relative sizes of the atomic orbitals. Across the top of the screen you see how the 1s orbital decreases in size as the nuclear charge increases. The Na 1s orbital is tiny compared to the 1s orbital of H because the 1s electrons in Na are poorly shielded from the nucleus by the other electrons and feel virtually the whole brunt of the nuclear positive charge. If you had to estimate the diameter of each of these orbitals in Ångstroms, write down what your estimates would be.

Note how much larger the Na 3s electron cloud is compared to all the others. A large electron cloud indicates the degree of looseness with which the electron is held by the atomic species. It is no wonder that the ionization energy of Na is so low compared to most other elements. That 3s electron is relatively easy to remove.

E. Exercise V - Sigma 1s bonding molecular orbital of H2.

Launch this exercise by typing:

source sigma1s

This will bring up the 1ss MO in the lower portion of the screen, and two isolated H1s atomic orbitals at the top of the screen. The atomic orbitals are connected by a dotted line and their distance is indicated at the top right hand corner of the window.

model 0 = 1ss MO model 1= H1s(A) model 2 = H1s(B)

Try selecting only model 2, and translate this H atom until you achieve an overlap with the other H atom at bond distance 1.400 Å. Do you note any difference between the appearance of the true MO and the one you just formed by overlapping the two 1s y2 functions? If so, describe.

The true MO down below is:

y2 = c2{ y1s(A) + y1s(B)}2 = c2{ y1s(A)2 +2 y1s(A) y1s(B)+ y1s(B)2}

The two 1s orbitals manually overlapped above represent:

y2 = c2{ y1s(A)2 + y1s(B)2}

Select model 0 by itself. Rotate it manually with the mouse until you are looking down the axis of the bond. Note the cylindrical symmetry of a sigma bond.

F. Exercise VII - Pi 2p bonding molecular orbital of B2.

Launch this exercise by typing:

source pi2p

This will bring up the 2pp MO of diatomic Boron in the lower portion of the screen, and two isolated Boron 2px atomic orbitals at the top of the screen which were used to form the MO. The atomic orbitals are connected by a dotted line and their distance is indicated at the top right hand corner of the window. Make a sketch of the p bond.

model 0 = 2pp MO

model 1= B2px(A)

model 2 = B2px(B)

Try selecting only model 2, and translate this B atom until you achieve an overlap with the other B atom at bond distance 1.400 Å. Incidentally the 2p electron in Boron experiences a Zeff = 2.42. Do you note any difference in the appearance of the true MO and the one you just formed by overlapping the two 2px y2functions? There should be a slight difference.

Notice the difference between pi bonds and sigma bonds. Select model 0 by itself. Rotate it manually with the mouse until you are looking down the axis of the bond. Note the lack of cylindrical symmetry of a pi bond.

G. Exercise VIII - A Polar Covalent bond - sigma sp bonding molecular orbital of HF.

Launch this exercise by typing:

source sigma1s2p

This will bring up the ssp MO of diatomic HF in the lower portion of the screen, with the Hydrogen atom on the left side, and two isolated atomic orbitals at the top of the screen which were used to form the MO, namely the H1s and a Fluorine 2px having a Zeff = 5.0. The atomic orbitals are connected by a dotted line and their distance is indicated at the top right hand corner of the window.

model 0 = ssp MO

model 1= H1s

model 2 = F2px

Make a sketch of the sigma polar bond indicated by model 0. Try selecting only model 2, and translate this F atom 2p orbital until you achieve an overlap with the H atom at bond distance 0.92 Å. Do you note any difference between the appearance of the true MO and the one you just formed by overlapping the two atomic orbitals? There should be a substantial difference, because the polar covalent bond formed between these atoms does not have equal weighting from the 1s and the 2p orbital. In fact the MO is a linear combination of atomic orbitals (LCAO) with the following weighting determined by variation principal:

yssp = 0.33 y1s(H) + 0.99 y2px(F)

Because of this unequal weighting, the electron density is shifted towards the Fluorine atom, creating a polar covalent bond. This is a consequence of the electronegativity of Fluorine (4.0) relative to Hydrogen (2.0).

Select model 0 by itself. Rotate it manually with the mouse until you are looking down the axis of the bond. Again note the cylindrical symmetry of a sigma bond.

 

IV. Shutdown Procedure.

Now that you are finished with all the exercises, close down your midas window by typing stop, and log out by positioning the cursor over an unoccupied region of the screen and holding down the 3rd (right) mouse button and pulling down to Log out. Answer yes to the "Are you sure?" question.

Turn in your observations and answers to questions on a sheet of notebook paper.