ABSTRACT
I. Introduction ........................................................................................................................ 89
II. Born-Oppenheimer Approximation and Molecular Vibrations/Potential
Energy Surfaces ................................................................................................................. 90
A. Born-Oppenheimer Approximation.......................................................................... 90
B. The Adiabatic Correction to the Born-Oppenheimer Approximation..................... 91
C. Molecular Vibrations/Potential Energy Surfaces ...................................................... 96
1. General................................................................................................................. 96
2. The Determination of Harmonic Force Constants in Valence
Coordinates .......................................................................................................... 97
3. The Determination of Harmonic Force Constants in Cartesian
Displacement Coordinates................................................................................... 98
D. Two Important Equalities for Harmonic Frequencies of Isotopomers ..................... 99
III. The Statistical Mechanics of Equilibrium Isotope Effects in the Gas Phase ................. 100
A. Equilibrium Constants.............................................................................................. 100
B. Rate Constants.......................................................................................................... 102
C. The Symmetry Number in Isotope Chemistry ........................................................ 104
IV. Numerical Calculations of Isotope Effects ...................................................................... 109
A. “Early” Calculations ................................................................................................ 109
B. Isotope Effect Calculations Coupled with A Priori Calculation of
Electronic Structures ................................................................................................ 110
1. Some General Considerations of Electronic Structure Calculations................ 110
2. The Program THERMISTP............................................................................... 112
References..................................................................................................................................... 115
This chapter traces the principles underlying the understanding of the theory of isotope effects
from quantum mechanics to the calculation of isotope effects on equilibrium constants and on
rate constants (within the transition state theory often associated with Henry Eyring
and commonly
referred to as TST). In order to keep this chapter from becoming too lengthy, it became necessary to
restrict this discussion to some specific topics in isotope effect theory; the title of this chapter arises
from this requirement. There are many topics which are missing. The missing topics include isotope
effects on molecular dipole moments and polarizabilities and isotope effects on rates within theories
beyond TST, including the successful applications of variational transition state theory, especially
by D.G. Truhlar (e.g., Ref. 2). Explicit consideration here is limited to molecular systems in the
ideal gas phase. W.A. Van Hook discusses the theory of condensed phase isotope effects in this
volume (W.A. Van Hook, Chapter 4 in this volume). In writing this chapter, the author has been
aware of some overlap of purpose with the chapter in this volume by his colleague Jacob Bigeleisen
(J. Bigeleisen, Chapter 1 in this volume) and he has tried to avoid overlap of content.
