c15 JWBS043-Rogers September 13, 2010 11:28 Printer Name: Yet to Come
MOLECULAR QUANTUM CHEMISTRY 239quantum mechanical affirmation of the two-electron bond postulated by G. N. Lewis
and is familiar from general chemistry. We have the first instance of a calculated
orbital overlapleading to stability for a molecular system. The term orbital has been
substituted for the classical mechanical term orbit in recognition of the substitution
of a probability function for a definite point location in space.
In the negative linear combinationc 1 ψ 1 −c 2 ψ 2 , we have the first example of
anantibond. The probability function for the antibond shows that electrons are
repelled from the region between the nuclei, leading to the opposite of a Lewis bond.
Antibonding orbitals lie higher in energy than bonding orbitals. In some instances,
infusion of energy into a molecule by incident radiation can cause electrons to be
promoted from a bonding to an antibonding orbital. Only some wavelengths are
absorbed. If the absorbed radiation is in the visible range (sunlight), we see the
wavelengths left over after selective absorption as color.
Neither Schrodinger’s nor Heisenberg’s work was directed toward chemical bond- ̈
ing, so one cannot make the argument, “Well, they knew the answer before they set
up the problem.” The H H bond in molecular hydrogenis a consequence of the
quantum nature of matter. This point of view was developed into thevalence bond
theory by Linus Pauling (1935). Much of theoretical chemistry was to be dominated
by valence bond theory (for better or for worse) for the next four decades.
Hartree (1928) is usually credited with the critical suggestion that atomic problems
involving many electrons can be treated as a collection of simpler problems in which
a single electron moves in an average electrostatic field created by the nucleus and all
the other electrons.^1 The electrostatic attraction between a nucleus and an electron is
far greater than the energy of a chemical bond. Therefore it is reasonable to suppose, as
Hartree did, that one-electron wave functions would resemble Schrodinger’s solutions ̈
for the hydrogen atom, being identical in the angular part and differing only in
the radial probability distribution function—that is, the probable distance from the
nucleus. This is thecentral field approximation.
Fock (1930) and Slater (1930), utilizing the prior concept of electron spin (Uhlen-
beck and Goudsmit, 1925), recognized that the spin of an electron can be oriented
in two ways, with or against its orbital motion. Therefore, electron spin must have
a double-valued quantum numberms=±1. A double-valued quantum number de-
mands that there be two wave functions per orbital, identical in all respects except
for their different spins. The two wave functions must beantisymmetricjust as your
right and left hands are roughly identical in shape except that they are mirror images
of one another (antisymmetric). Two trial functionsφ(1) andφ(2), having opposed
spinsα, andβ, can combine in four ways, only one of which is antisymmetric:ψ=φα(1)φβ(1)
ψ=φα(2)φβ(2)
ψ=φα(1)φβ(2)+φα(2)φβ(1)
ψ=φα(1)φβ(2)−φα(2)φβ(1) ←(^1) Hartree himself gave credit to Bohr.