Chemical Studies Based on Isotope Effects 1947-67


Equilibrium Molecular Properties

Molecules that differ only in isotopic constitution show differences in chemical behavior that permit inferences to be drawn concerning intramolecular and intermolecular forces. Calculations of molecular properties from first principles require precise knowledge of molecular properties, such as partition functions, which are difficult to calculate in closed form and are computationally costly. The "Partition Function" is a mathematical construct from which many molecular properties can be predicted with great precision: "Know the partition function, know everything about the molecule", well, almost everything.

A theoretical treatment of the effects of isotopic substitution on equilibrium constants showed that it was not necessary to calculate individual partition functions for each isotopic species. Instead, the ratio of such functions, which could be calculated with more accuracy, was the important property. This theory was extended to the separation of isotopes by chemical reactions, which was also investigated experimentally. An extension of this theoretical work provided a basis for the use of isotope effects in the study of mechanisms of chemical and biochemical reactions. This work, and experimental determinations of isotope effects, were an early attempt to determine properties of the elusive "transition state" (see below) that intervenes between reactants and products.

J. Bigeleisen and M. G. Mayer, "Calculation of Equilibrium Constants for Isotopic Exchange Reactions."   J. Chem. Phys. 15 261 (1947).

M. Perlman, J. Bigeleisen and N. Elliott, "Equilibrium in the Exchange of Deuterium between Ammonia and Hydrogen"  J. Chem. Phys. 21 70 (1953).

J. Bigeleisen, "The Relative Reaction Velocities of Isotopic Molecules" J. Chem. Phys. 17 675 (1949).

Properties of the Activated Reaction Complex

In systems at thermodynamic equilibrium differences in chemical properties between isotopically substituted molecules are due to quantum effects. Rates of chemical reaction also are affected by isotopic substitution; the origins of rate effects have been sought within the framework of the transition state theory of chemical reactions, and the predictions have been tested experimentally. It is found that superimposed on the quasi-equilibrium between reactant molecules and activated or transition state molecules, isotopes are differentiated in chemical reaction rates by the velocities with which they cross the potential barrier to chemical reaction or tunnel through it. Since the energy states j of the activated molecules cannot be determined directly, they must either be inferred from experiment or calculated a priori and the use of isotope effects has now been established as a powerful method for obtaining information about the vibrational energy states of the activated molecules. Such determinations have been made for the simple reactions

Cl2 + H2
Br + H2
CF3 + H2,

and the results have been used in the development of a semi-empirical quantum treatment of chemical reactions.

J. Bigeleisen, F. S. Klein, R. E. Weston, and M. Wolfsberg, "Deuterium Isotope Effect in the Reaction of Hydrogen Molecules with Chlorine Atoms and the Potential Energy of the H2Cl Transition Complex," J. Chem. Phys. 30, 1340 (1959).

F. S. Klein, A. Persky, and R. E. Weston, "The Deuterium Isotope Effect in the Chlorine Exchange between Hydrogen Chloride and Chlorine Atoms. A Study of Models for the Tunnel Effect," J. Chem. Phys. 41, 1799 (1964).
R. E. Weston, "Transition State Models and Hydrogen Isotope Effects" Science 158, 332 (1967).

Reaction Mechanisms

Since isotope labeling is a unique probe for the determination of whether the chemical bonding of a particular atom changes during a reaction, isotope effects are very useful in the study of reaction mechanisms. Of particular significance is the question of whether, when a complex molecule breaks with two or more bond ruptures, the bonds rupture simultaneously or in a consecutive fashion with the first break rate controlling. Only isotope effect studies can resolve this question. It has been found that symmetrical azo compounds, with large radicals undergo concerted C-N bond rupture but that unsymmetrical compounds, such as a-phenylethylazomethane, undergo consecutive bond rupture. Through the use of secondary deuterium isotope effects it has been established that the Diels-Alder condensation (the reverse of a bond rupture) with 2-methylfuran and maleic anhydride proceeds by a concerted mechanism. Experiments based on isotope effects carried out elsewhere have shown that in other systems the bond rupture is in some cases simultaneous and in others consecutive. It may be that there is no common mechanism to all Diels-Alder reactions.

S. Seltzer, "The Mechanism of the Diels-Alder Reaction of 2- Methylfuran with Maleic Anhydride," J. Am. Chem. Soc. 87, 1534 (1965).

The Structure of the Hydrated Proton

Isotope effects can be used to determine forces and structure in stable, but labile, species as well as ones of transitory existence. An important example of the former has been the establishment of the nature of the hydrated proton in aqueous solution. For the past half century it has been inferred from thermochemical data that the proton in aqueous solution is properly written H30+(aq). Proof of this structure, difficult to obtain because of the rapid exchange of the proton from one water molecule to the next, has recently been established by two series of isotopic fractionation studies of deuterium between bulk water and the hydronium ion. In one experiment the atom fraction of deuterium in hydronium ion in equilibrium with water of known isotopic composition was established by NMR. In the second experiment the amount of deuterium transported from water to establish equilibrium with hydronium ion of known concentration was established by mass spectrometric analysis. Combination of the two results led uniquely to the conclusion that three protons are strongly bound in equivalent positions in the hydronium ion.

K. Heinzinger and R. E. Weston, "Isotopic Fractionation of Hydrogen between Water and the Aqueous Hydrogen Ion," J. Phys. Chem. 68, 744 (1964).

Intermolecular Forces and Structure in Liquids

Through development of the statistical mechanical theory it has been possible to use isotope effects to obtain new and unique information about intermolecular forces and the motions of molecules in liquids and solids. For a monatomic substance such as neon, the second moment of the frequency spectrum for the solid, derived from isotopic vapor pressures, when compared to that derived from neutron scattering or from heat capacities showed the magnitude of the anharmonic effects. Comparison of the liquid with the solid gave a clear correlation with the structural change on melting as determined by neutron diffraction.

The study of isotope effects on vapor pressures of polyatomic molecules has revealed new information about the influence of intermolecular forces on molecular motion. The rotations of N2O and CH4 have been shown to be hindered in the liquid. In the case of methane this was later verified by inelastic neutron scattering measurements. A 23% difference between the vapor pressures of HT and D2 observed in the temperature range 20-30K, has been shown to be a consequence of the coupling of rotation with translation when the center of gravity of a molecule is not coincident with the center of intermolecular force; this discovery of translation-rotation coupling has not been verified by spectroscopic experiments done elsewhere. Through the study of the vapor pressures of a homologous series of deutero-ethylenes, including the cis-, trans- and gem-dideutero isomers, the symmetry-controlled coupling of rotation with vibration has been established experimentally. The magnitude of the effect is in good agreement with results of model calculations.

J.  Bigeleisen and E. Roth, "Vapor Pressures of the Neon Isotopes," J. Chem. Phys. 35, 68 (1961).

J. Bigeleisen and S. V. Ribnikar, "Structural Effects in the Vapor Pressures of Isotopic Molecules. 180 and 15N Substitution in N2O," J. Chem. Phys. 35, 1297 (1961).

J. Bigeleisen, S. V. Ribnikar and W. A. Van Hook, "Molecular Geometry and the Vapor Pressure of Isotopic Molecules. The Equivalent Isomers cis-, gem-, and trans-dideuteroethylenes,"  J. Am. Chem. Soc. 83, 2956 (1961).

Theoretical Chemistry and Isotope Effects

The development of the statistical mechanical theory of isotope effects in terms of ordered quantum corrections has established the physical basis of isotope effects and given new insights. The first quantum correction leads to a correlation between isotope effects and chemical bonding and establishes the power of the isotope effect method as a probe for the chemical bonding of each atom in a molecule of any complexity. An alternative approach to this problem has involved the reduction of isotope effect problems to forms suitable for numerical calculation by high speed computers. Programs developed here, and now used widely by workers in the field, have been applied to the study of model systems, with results similar to those obtained from the quantum correction method. A direct consequence of the development of the quantum corrections has been the quantitative formulation of the rules of the mean and of the description of isotopic isomers.

M. J. Stern, W. A. Van Hook, and M. Wolfsberg, "Isotope Effects on Internal Frequencies in the Condensed Phase Resulting from Interactions with the Hindered Translations and Rotations -- The Vapor Pressures of the Isotopic Ethylenes" J. Chem. Phys. 39, 3179 (1963).

M. Wolfsberg and M. J. Stern, "Secondary Isotope Effects as Probes for Force Constant Changes," Pure and Applied Chem. 8, 325 (1964).

M. J. Stern and M. Wolfsberg, "A Simplified Procedure for the Theoretical Calculation of Isotope Effects Involving Large Molecules," J. Chem. Phys. 45, 4105 (1966).

Technological Application

The fundamental research program on isotope effects provides the basis for new and improved processes for the separation of isotopes useful for the generation of nuclear power and in nuclear technology. One such process developed here has been the liquid ammonia-gaseous hydrogen countercurrent system for the production of heavy water. This method, apparently the cheapest way to produce heavy water at present, is being used as the primary enrichment process in the new French plant.

M. L. Perlman, J. Bigeleisen, and N. Elliott, "Equilibrium in the Exchange of Deuterium Between Ammonia and Hydrogen," J. Chem. Phys. 21, 70 (1953).

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Last Modified: June 28, 2012