Humboldt State University ® Department of Chemistry

Richard A. Paselk

	Atomic Structure and Bonding - A Quantum View
	© R. Paselk 2004
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Structure and Bonding* Supplement

 

Atomic Structure: a short review

Atomic structure is characterized/determined by the Atomic number, Z, which tells us how many electrons and protons the free atom has.

• Z tells us what the element is, where it resides on Periodic table, and thus what its chemistry is like.
  • Remember, chemistry is due largely to the outer electrons of an atom, which corresponds to the old Group numbers for the representative elements!
• Atomic weight, AW, gives the mass of the individual particle, and has a subtle influence on chemistry. It has a greater influence on small mass atoms (a difference in neutron number has a greater % effect on mass), since chemical differences are due essentially to differences in vibrational modes of an atom in a covalent bond and how fast the atoms move.
• Much of chemistry can be crudely understood by looking at the size of atom and its nuclear charge "visible" to the outside world (that not "cancelled" by the inner electons).

Electrons around atoms are arranged in shells : regions of electron occupancy having the same average radial distance from the nucleus. As additional electrons are added additional shells are added making the atom larger. (Note that each additional shell shows up as a new period in the Periodic table.)

• For a better picture we need to look at orbitals. For simplicity we will confine our discussion to elements in Periods 1 & 2 so we can focus on just s and p atomic orbitals.
  • s orbitals are spherical, thus shield nuclei essentially completely when they are filled. (Remember from physics, for a spherically distributed field, like gravity or charge, we can consider all to reside at a point in the middle of the field. Thus a spherically distributed set of, say, 4+ charges and 2- charges will look like 2+ charges to the outside world!) You can see the spherical nature of the 2s orbital in the figure. If you click on this image you can also look at a movie of these orbital rotating in space.
    • (A note on these images. These images and movies are provided for your entertainment and greater insight, and because I think they're really cool. You might think of these images as the result of a strobe effect - they are what the orbitals and atoms would look like if we could take "strobe" photos of the electrons moving in their undeterminant paths! The orbital and atomic images I have included are rigorously calculated using the Schrödinger equation (they are all based on hydrogen, so only two particles are involved, the proton and one electron - we assume other atoms are similar). Each dot represents the result of solving this equation [there are 10,000 dots in the s orbital image]. Because of the statistical nature of Quantum mechanics, on average two calculations were required for each dot, one kept, and one discarded. )
  • p orbitals are bi-lobe shaped, with three in a shell along mutually perpendicular axis. The first image/movie represents the 2 p_xorbital. The second movie shows the three 2p orbitals and how they add up to a completely spherical distribution! (Caution, if you're off campus note the size of this movie - it will take a while to download!)

Electronic Configurations of Atoms: Under normal earth conditions atoms are in their ground state configurations, that is the electrons all occupy the lowest energy orbitals available. Of course only two electrons of paired spin may occupy an orbital. And electrons "spread out" to occupy as many orbitals in each subshell (orbital type) as possible.

Bonding

Review terms: valence shell, electropositive and electronegative, ionic and covalent bonds, molecule, Lewis structure, non-bonding & lone-pair electrons.

• Ionic bonds: are formed when one or more electrons are transferred from one atom to another, with the resulting ions held together by electrostatic forces. Note that these are strong bonds (high melting point), but they are non-specific and can easily "transfer" from one ion to another, so they tend to be brittle. An example of an ionic bond is seen in the figure and movie. Note that the inner, "core" electrons for both atoms are shown as yellow dots, while the valence electrons for both atoms are shown as green.
  • Notice how spread-out the outer electron (green dot-cloud) of sodium is - it is not very tightly held to the atom.
  • On the other hand the outer (green dot-cloud) seven electrons of chlorine are much more tightly held to the atom - much of the electron density overlaps with the core electrons.
  • The movie accessed through the Na + Cl figure shows the formation of a NaCl ion pair in vacuo.
    • Notice how the outer electrons of the sodium atom "jump" to the chlorine atom when they are still well separated.
    • The resulting ions are then attracted to each other until the electron clouds "touch" - interpenetrating slightly and repelling.

• Covalent bonds: In these cases what we see is a sharing of electrons.
  • You will note in the Cl(2) figure showing the inner, core, electrons of a chlorine molecule (Cl₂) show no overlap. Thus they are not involved in bonding at all, just as you might expect from the Lewis model and Lewis structures.
  • The two Cl(2) molecule figures and movies show the overlap of the outer electrons - covalent bonding is a phenomena of the outer, valence electrons.
    • In the middle figure the upper diagram is a plot of the electron density in the x-y plane. There doesn't appear to be much overlap at all of the outer electrons. But keep in mind that only 2 of the 14 outer electrons of the Cl₂ molecule are involved in the bond (and that all of the p electrons are equal and indistinguishable in the filled orbital sets).
    • The lower diagram in this figure shows the corresponding dot-image, while the figure at the right shows the dot-image again in larger size with higher resolution.

• A bond formation movie for chlorine is shown below along with its Morse curve. The green region of the curve corresponds to the movie. If you are off campus note the large download size of the movie!
  • Notice the gradual overlap which occurs as the atoms approach.
• The Morse curve plots the energy of the system vs. the separation of the nuclei. The stable bond occurs at the low point of the curve. The black portion of the curve shows the very rapidly increasing repulsion as the non-bonding electron clouds begin to overlap.

 

 

Bond Formation and Bonding - the Quantum Picture

As we saw above, covalent bonds are formed when two atoms share one or more electron pairs - there is an overlap of the orbitals of the two atoms. In the simplest case, that of hydrogen, the resulting bond and molecule are cylindrically symmetrical, as seen in the figure and QuickTime movie of hydrogen. You might also note that hydrogen is nearly spherical as a molecule because the nuclei can approach each other so closely since there is no inner electron shell. Cylindrically symmetrical bonds like hydrogen's are known as sigma bonds. They may be formed by overlap of two s orbitals as in hydrogen, an s orbital and a p orbital lobe, two p orbital lobes (as seen in Cl₂ above) etc.

 

 

As seen in the Morse curve below the two hydrogen atoms come together until the energy is minimized. The H2 bonding QuickTime movie visualizes this process, the movement of the atoms corresponding to the colored region of the Morse curve.

Finally, the image below gives a cross-section of the electron density for the hydrogen bonding process. In this image, the density is shown as a false color map, with violet indicating low density, and going to red for high densty.

*The animations and visualizations on these pages are copyrighted. They were created by Mervin P. Hanson, Richard L. Harper, Richard A. Paselk and John B. Russell from calculations performed by Mervin P. Hanson. This work was supported by the National Science Foundation, Apple Computer, and Humboldt State University.

© R A Paselk

Last modified 23 November 2004