Theoretical calculation links NMR coupling
constant to molecular geometry
From the outset of his career, Martin
Karplus wanted to develop insights from theoretical chemistry that experimental chemists could put
to use. It did not take him long to get started. In 1959, a few years after he assumed his first
faculty position as an instructor in chemistry at the University of Illinois, Karplus published an
equation that organic chemists would find indispensable in helping establish the conformations of
small molecules and proteins [J. Chem. Phys., 30, 11 (1959)]. The Karplus equation,
as it is now known, describes the relationship between the nuclear magnetic resonance (NMR)
coupling constant and the dihedral angle between vicinal hydrogens (hydrogens attached to
neighboring carbon atoms).
After this first publication of the equation,
Karplus started to get feedback from organic chemists about the use of the equation, and he
realized that he should publish a follow-up communication in the Journal of the American
Chemical Society. The resulting paper [J. Am. Chem.
Soc., 85, 2870 (1963)] is now the 17th most cited article in JACS history.
In the late 1950s, nuclear magnetic resonance was
a mushrooming field. Physicists worked on the theory of NMR while chemists began to garner
information about molecular structure from NMR shifts and splittings. Karplus realized he could
generate theoretical models that linked a molecule's electronic structure to its NMR
As he looked deeper, he made an interesting
observation: The NMR coupling constant between two atoms not directly bonded to each other is not
zero. In other words, the two protons in an HCC9H9 fragment interact--something not predicted by the perfect pairing
model of valence bond theory. "It's a small effect," Karplus says, "and it is only
because NMR is sensitive to such a small effect that you can actually determine the deviation from
"Once I was aware of the existence of
nonzero coupling constants between atoms that weren't bonded to each other," Karplus says,
"I knew what to do--how to attack the problem by using valence bond theory, which I had
learned during my graduate research with Linus Pauling. The work that was required was to estimate
the molecular integrals from which one could actually calculate the deviation from perfect
Karplus came up with an equation relating the
dihedral angle between H' and H to the
coupling constant: JHH' = A + B cos + C cos 2, where A, B, and C are approximately constant for saturated hydrocarbons. The result
calculated for JHH9 was a smooth hill-and-valley curve.
Interestingly, Harold Conroy, then at Yale
University, independently obtained a similar relation by approaching the problem through molecular
orbital theory [Raphael, Ralph A. et al, editors. "Advances in Organic Chemistry: Methods and
Results," Vol. II. New York: Interscience Publishers, 1960].
||RIGID RING Angles between vicinal protons in a cyclohexane can be
measured with NMR J-values.
Karplus' equation quantified something a few
chemists had noticed qualitatively: A proton could interact with its vicinal neighbor, and that
influence varies depending on the geometry of the two protons. For example, E. J. Corey, an organic
chemist then at the University of Illinois and a friend who regularly dined with Karplus, knew from
experiment that orthogonal protons (those having a dihedral angle of 90º) had no interaction,
whereas protons with dihedral angles between 0º and 90º interacted variably.
"And in 1958, a Canadian chemist, Ray V.
Lemieux, came and gave a couple of lectures at the University of Illinois," Corey relates.
"He had measured coupling constants between vicinal protons in a large series of sugars. His
data were paralleling the rates of vicinal elimination as a function of the geometry of the groups
that were leaving during the elimination process."
Karplus also attended Lemieux's lecture. At the
time, Karplus was finishing up his 1959 paper and saw that Lemieux's data fit nicely with his
theoretical calculations. Even better, Karplus realized that his equation could help assign
conformations to organic molecules with some rigidity to them, like Lemieux's sugars.
Once the NMR community got wind of the Karplus
equation, citation of Karplus' research became a fixture of any conformational analysis using NMR.
Corey may have been the first to use it for the determination of the structure of a biooxidation
product of camphor [J. Am. Chem. Soc., 81,
Today, variations of the Karplus equation are
heavily used in establishing protein structure from NMR spectra. "In proteins," Karplus
says, "the main-chain dihedral angles are the essential element of how the polypeptide chain
is folded. You assume when you determine a protein structure that you know the bond lengths and the
bond angles and all the connectivity. So determining the structure is not determining the chemical
structure, but determining the conformation."
"In many ways, my feeling about the uses and
refinements of the 'Karplus equation' is that of a proud father," Karplus wrote in 1996 in an
historical chapter for the "Encyclopedia of Nuclear Magnetic Resonance." "I am very
pleased to see all the nice things that the equation can do, but it is clear that it has grown up
and now is living its own life."
C&EN is celebrating the 125th volume of the
Journal of the American Chemical Society by featuring selected papers from
among its 125 most cited. This paper was ranked 17th.