Re: How do shared electrons move around the atoms in a covelant bond?

Greetings, Tom:

In one respect, this is an extremely complex subject.  Mathematically,
Quantum Mechanics is our best description of how electrons behave, but
there are limits.  The limits are somewhat akin to the "3-body problem"
in Gravitational Physics.  We know all about how to compute the results
of any two objects gravitationally interacting with each other, but if
just one more object is added, we have NO generic tool adequate for the
task.  Instead we make a successive series of approximations, taking two
of the 3 objects at a time.  It works, but is very tedious.  Thus you
may understand that just one hydrogen atom (proton interacting with
electron) is a 2-body problem, with respect to Quantum Physics.  We can
indeed describe this pair extremely well, but if we add only one more
particle, a mathematical nightmare begins.  The simplest possible
covalent bond, which exists between two whole hydrogen atoms, is
actually a 4-body problem....

In other respects we know in a general way quite a bit about what goes
on, and I will attempt to describe it here.  There are, of course,
various items of background information that must be presented, before a
coherent picture can be imagined.

The first important thing is the "image" of a lone electron.  This is an
object smaller than 0.0000000000000001 (or 10E-17) meters.  Our best
instruments can't measure anything so small as an electron; for all we
know, it has the dimensions of a perfect mathematical point -- but we
don't know that for sure, either.  (The smallest meaningful length in
modern Physics is a computed dimension known as the Planck length, which
is about 10E-35 meters, while a mathematical point would have a size of
exactly zero.) Next, and just as important, the exact location of an
average electron is very often quite unknown.  We CAN momentarily locate
an electron, but in the very next moment, thanks to something known as
the Uncertainty Principle, it WILL be located somewhere else, quite
probably at some random distance and direction from the previous
location.  For this reason the electron is often described as a sort of
"large and foggy" object:  Its most likely location is somewhere in the
center of the "fog", but every iota of the "substance" of this "fog" is
actually nothing more than another POSSIBLE LOCATION -- a momentary
location -- for the tiny tiny electron.

It happens that every subatomic particle described by Quantum Mechanics
and the Uncertainty Principle can be said to have some of the electron's
"foggy" nature.  The total amount of a given particle's "fog" is simply
and inversely proportional to the mass of the particle:  The more mass a
particle possesses, the less far it jumps about, and so the smaller is the 
totality of its possible jump-locations, or "patch of fog".  The
proton, for example, has more than 1800 times the mass of an electron;
its "fog patch" is therefore more than 1800 times smaller than the
electron's.  This is small enough for the "fog" itself to resemble a
particle, but in fact the proton, being roughly 10E-15 meters in
diameter, is quite a bit  smaller than the "fog" of its random-jump
locations.

Next, when proton and electron get together to form a hydrogen atom, a
peculiar thing happens to the description of the electron's "fogginess".
A phenomenon known as the "wave/particle duality" must now be examined
closely.  This rule states that every solid particle has some wave-like
properties, while every wave-like object has some solid-particle
properties.  The details are quite mathematical, of course, but the
consequences are known to be true.  Thus THE major reason why the point-
like electron jumps all over the place IS the wave-particle duality.
Even when supposedly stationary, the wave-like properties of an electron
REQUIRE it to be "jumping in place"; it is never really still.  And the
"fogginess" of an electron's location is the obvious result.

However, note that a wave is generally described as a reasonably smooth
undulation.  Even an electron can do this much, when it is experiencing
an overall motion from Point A to a distant Point B.  Only when it is
supposedly stationary is an electron's wavy nature utterly erratic.  So
let us now take a proton, and insert it into the middle of an electron's
"fog patch":  The electron begins to orbit about the proton.  Since this
is an actual motion of the electron, ordinary wave-like undulations will
be a part of that motion.  When the electron is in the smallest possible
orbit, its motion around the proton may be described like this:  One
complete orbit is precisely one perfect undulation.  (To better
visualize this, take a piece of paper and draw one standard sinusoidal
waveform.  Then roll the paper up, undulation outside, so that the
beginning and ending points of the waveform connect.  The proton would
be located in the center of the paper ring.)  Each possible larger orbit
for an electron gives it room to undulate exactly twice, or three times,
or four, etc.

Quantum Mechanics permits two electrons to occupy one orbit.  It also
defines "shells" about an atomic nucleus, each of which may contain a
number of orbits.  The innermost shell contains just one orbit for two
electrons; the next shell contains a "subshell" with one room for only
one orbit, and a second subshell with room for three orbits, for a total 
of eight electrons in that overall shell.  And so on.  Standard high-
school chemistry classes will offer students the concepts of "shells",
"subshells", "orbitals", and the like, so I need not repeat it all here.

The next important thing concerns the location of an electron when it is
undulating in orbit about a proton.  Each moment, it DOES exist at one
precise location along that orbit.  Our macroscopic view still sees
"fogginess", however.  We might say, "At this moment, the electron is
most probably located about here, but there is a small chance we can
find it over here, completely on the other side of the atom."  Now think
about the electric charge on the proton:  The reason the electron is in
orbit is because of electrical attraction.  From a macroscopic distance,
we might see an atom as an electrically neutral object, but if we look
closely ...

Now at some PARTICULAR moment the proton will be located at Point A, and
the electron will be located at Point B, as depicted below:

 (C)                                   (A)proton        (B)electron

I wish to bring your attention to Point C, and ask, "Do we detect zero
electric charge at that point?  The answer is, "No, we can detect some
of the positive charge of the proton."  And if we next ask, "What if
there is an electron, part of another atom, located at Point C?" -- then
the answer is, "There will be some electrical attraction between that
other atom's electron at Point C and the proton at Point A."

This attraction between two hydrogen atoms is a good enough reason why
they would tend to join together, to make a hydrogen molecule.  The form
or arrangement that the four particles take should be relevant to your
Question.  To approach it, let me begin with just one proton and both
electrons:
                               electron

                                proton

                               electron

This would be a "negatively charged hydrogen ion".  Since the electrons
repel each other electrically, they always move such that the proton
stays between them.  They may most easily be imagined moving, say,
clockwise about the proton in the above depiction.  HOWEVER, it is more
important that you imagine that circle turned on its edge!  Visualize
the "upper" electron moving downwards, first towards you and then away
from you, while the "lower" electron is moving upwards, first away from
you and then towards you.  Twiddle your thumbs, to keep that in mind as
I add the second proton:
                               electron

                         proton        proton

                               electron

With the electrons still circling in the same kind of orbit as just
described above, the only change is the location of that circle relative
to the original proton.  In this diagram, we can see that each proton
gets an equal share of both electrons.  Also, the smallest possible
orbit for electrons around each proton becomes exactly the SAME orbit,
with respect to the two protons.  And because there is now only one
orbit to talk about, capable of holding exactly two electrons, it is
completely filled by one electron from each hydrogen.  (Please note that
these diagrams are not to scale; an electron's orbit is about 100,000
times larger than a proton.)

Now lets move on to a more complex case: a fluorine molecule.  A single
atom of fluorine has 9 electrons in two "shells", grouped like so:  two
occupy the innermost electron "shell", two occupy the inner "subshell"
of the outer "shell", and five occupy three "orbitals" of the outer
"subshell" of the outer "shell".  Since each "orbital" can contain only
two electrons, there are two full "orbitals" and one half-full "orbital"
in that outer "subshell".  That half-full "orbital" is the ONLY thing
which concerns us here!  It is exactly equivalent to the half-full orbit
of a lone hydrogen atom:
                              electron

                    (fluorine)        (fluorine)

                              electron

I am using (fluorine) to indicate the nucleus and 8 electrons; the 9th
electron of each is in the same type of shared orbit as previously
described for the hydrogen molecule.

Next, how about a water molecule?  I shall use some abbreviations, to
reduce clutter in the following diagram:

                (H)   2e   (O)
                                   e

                         e
                               (H)

The oxygen nucleus and 6 electrons is (O), a hydrogen nucleus is (H),
and an electron is simply  e.  Depicted are two electrons ON the "plane"
of the diagram (at an angle), and a second pair denoted by 2e represents
one-in-front and one-behind the "plane" of the diagram.  As time passes
and the electrons move in their orbits, we might be able to draw this:

                       e

                 (H)       (O)

                       e     2e
                          
                               (H)

Now the pair of electrons formerly located at an angle is located 
one-in-front and one-behind the "plane" of the diagram.  Remember that
electrons repel each other, so they stay as far apart as they can.

While the water molecule contains two single covalent bonds, the oxygen
molecule contains a double bond, of which I shall sketch two views:

                    e                              e

              (O)   2e   (O)                  e   2(O)   e

                    e                              e

This may look like four electrons in the same orbit, but more correctly
we should treat it as two "orbitals" that just happen to mostly overlap.
The double bond between two carbon atoms (or between a carbon and an
oxygen) is basically the same.

Depicting the triple bond of the nitrogen molecule is similar:

                                  e      e

                               e    2(N)     e

                                  e      e

Of course the 2(N) represents two nitrogen nuclei, each having 4 
electrons.  One is located in front, and one is located behind the plane
of the diagram.  The remaining six electrons occupy three overlapping/
shared "orbitals".  Notice how closely the electrons are forced to be
located near each other.  This implies something of a weakness in a
triple bond (it is weaker for carbon than for nitrogen, because carbon
atoms are smaller, so the electrons are even closer together).  It also
provides a good reason why carbon is not known to ever form a quadruple
bond.

Well, I hope the preceding has been appropriatly informative, and hasn't
been too far off the mark.