Small Terms
In the 1920s much spectroscopic evidence made it clear that the Coulomb Hamiltonian is missing certain terms. Especially for molecules containing heavier atoms, these terms, although much smaller than kinetic and Coulomb energies, are nonnegligible. These spectroscopic observations led to the introduction of a new degree of freedom for electrons and nuclei, namely spin. This empirical concept was given a theoretical basis by Paul Dirac when he introduced a relativistically correct (Lorentz covariant) form of the one-particle Schrödinger equation. The Dirac equation predicts that spin and spatial motion of a particle interact via spin-orbit coupling. In analogy spin-other-orbit coupling was introduced. The fact that particle spin has some of the characteristics of a magnetic dipole led to spin-spin coupling. Further terms without a classical counterpart are the Fermi-contact term (interaction of electronic density on a finite size nucleus with the nucleus), and nuclear quadrupole coupling (interaction of a nuclear quadrupole with the gradient of an electric field due to the electrons). Finally a parity violating term predicted by the Standard Model must be mentioned. Although it is an extremely small interaction, it has attracted a fair amount of attention in the scientific literature because it gives different energies for the enantiomers in chiral molecules.
The remaining part of this article will ignore spin terms and consider the solution of the eigenvalue (time-independent Schrödinger) equation of the Coulomb Hamiltonian.
Read more about this topic: Molecular Hamiltonian
Famous quotes containing the words small and/or terms:
“Whatever it was I lost, whatever I wept for
Was a wild, gentle thing, the small dark eyes
Loving me in secret.
It is here. At a touch of my hand,
The air fills with delicate creatures
From the other world.”
—James Wright (1927–1980)
“A radical is one of whom people say “He goes too far.” A conservative, on the other hand, is one who “doesn’t go far enough.” Then there is the reactionary, “one who doesn’t go at all.” All these terms are more or less objectionable, wherefore we have coined the term “progressive.” I should say that a progressive is one who insists upon recognizing new facts as they present themselves—one who adjusts legislation to these new facts.”
—Woodrow Wilson (1856–1924)