ScienceMakers Toolkit Manual - The History Makers

Chemistry
as you will see in some material I have, I indicate that this is what I wanted to do upon completion of undergrad
and Master’s work was to go on and teach at the university level, which happened some time later, not immediately.
Clip 6 - Electron Orbitals: It is the case that I described to you this mean fi eld approximation, I didn’t mention
the name of it, it’s called Hartree Fock, H-A-R-T-R-E-E, after somebody named Hartree and Fock, a Russian,
F-O-C-K. Hartree Fock was the mean fi eld approximation. The issue is: how to describe instantaneous behavior
electrons by doing so-called pulsed Hartree Fock calculations. These typically took the form of what we call
excitations from the determinental wave function for the system. We represented a wave function for an atom or
molecule by a determinant at the smallest, or a linear combination of determinants. So, this is all orbital-based.
That is, the orbitals are one-electron functions, an orbit, this is a generalization of the orbit. These determinental
wave functions are mathematical representations of the behavior of individual electrons in the molecular system.
But it is a fact, and this is done by Hilarus in the early days of quantum mechanics for the helium electron,
a two-electron system, is that if you put in a function which depends on explicit distance between two electrons,
then this can tremendously compact the representation of the wave function of the system. The reason this
wasn’t done routinely in other cases is that the integrals you get that you must evaluate for the expectation value
of the Hamiltonian is an integral, which means you integrate over all space of the electrons of an argument,
which is the complex conjugate of the wave function Hamiltonian operator times the wave function integrated
over all space. So it’s an average of a mathematical quantity. How you represent that wave function is what
we’re talking about, in terms of orbital development, or one which involves explicit correlation. And so it’s the
integral, the complexity of the integrals that you have to evaluate and using exponential functions for descriptions
of orbitals. And in the case of explicit correlation, functions which depend upon inter-electron separation,
which leads to tremendous complexity, that until that time really could not be done for systems beyond two
electrons. If however, instead of using exponential functions, you use Gaussian functions, exponential of minus
alpha RIJ squared, then these integrals become possible to evaluate, and this was a tremendous advance made
by a fellow by the name of S.F. Boise at Cambridge, and which we did, I did, as a part of my thesis, one of the
earliest publications of the explicit correlation. They’ve been done by some others as well, but in the States I
was one of the fi rst. And that paper even today gets referenced: my thesis work. Because it was again one of the
fi rst, and this is why I tell my students, you know, don’t join the pack. You’ve got to try to identify a pathway
which is novel and unique, which may offer then guidance to people in the fi eld. You don’t always win with
this, but it’s a very important dimension in terms of what you do. It’s like anything. If you’re the fi rst, you may
get some recognition.
Clip 7 – Advice: Two young black scientists I met at IBM who came to apply for jobs and said, “All I want is a
job,” and I said, “Man, that’s not the mindset. What will you bring to the table here which will be different from
what we already have? What are the skills and capabilities you have developed, and you must be able to convey
that.” So I used to meet with them at the end of the day and sort of give them some feedback and every now and
then somebody would come in with a sense of that mindset…At least the folks who left had a sense of what I
was trying to convey to them in this regard.
Clip 8 - Molecular Close Coupling: The problem basically was that for [a] diatomic molecule, a molecule
consisting of two atoms bound together by a bond, it rotates besides vibrating. The problem of interest here is
looking at the change of rotational motion as a consequence of the atom hitting the diatomic molecule. This is a
so-called close coupling problem. Why? Because the energy levels for rotation are more closely spaced together
than those of vibration. In other words, you have a ground state vibrational level, a series of rotational levels,
then the next vibrational level, another series of rotational levels which are going right on up. And this means
then that the effect of a change in any given rotational level affects others very strongly, and that’s why it’s
called a close coupling problem. And computationally, or in terms of mathematics, it leads to the need to solve
a system of partial differential equations…It was a problem which Barnstein had indicated was too diffi cult a
problem for a graduate student, with someone with my experience around computers that hopefully I would be
able to make some headway. And I did, in part by talking to people, knowledgeable about close coupling, the
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