Before bringing this discussion of Tst to a close, I need to stress that this theory is not exact. It assumes that the reacting molecules are nearly in thermal equilibrium, so it is less likely to work for reactions in which the reactant species are prepared in highly non- equilibrium conditions. Moreover, it ignores tunneling by requiring all reactions to proceed through the ts geometry. For reactions in which a light atoms (i.e, an H or d atom)is transferred, tunneling can be significant, so this conventional form of TST can provide substantial errors in such cases. Nevertheless, TST remains the most widely used and successful theory of chemical reaction rates and can be extended to include tunneling and other corrections as we now illustrate B. Variational Transition State Theory Within the tST expression for the rate constant of a bi-molecular reaction, krate=K kT/h(qab/V(qv(aB for of a uni-molecular reaction, krate =K kT/h i(qav)/(qa vi, the height(E*)of the barrier on the potential energy surface ppears in the TS species'partition function gaB, or ga, respectively. In particular, the ts partition function contains a factor of the form exp(E*/kT)in which the Born- Oppenheimer electronic energy of the ts relative to that of the reactant species appears. This energy E* is the value of the potential energy e(S)at the Ts geometry, which we denote So It turns out that the conventional TS approximation to krate over-estimates reaction rates because it assumes all trajectories that cross the ts proceed onward to products unless the transmission coefficient is included to correct for this In the variational transition state theory (VTST), one does not evaluate the ratio of partition functions 88 Before bringing this discussion of TST to a close, I need to stress that this theory is not exact. It assumes that the reacting molecules are nearly in thermal equilibrium, so it is less likely to work for reactions in which the reactant species are prepared in highly non￾equilibrium conditions. Moreover, it ignores tunneling by requiring all reactions to proceed through the TS geometry. For reactions in which a light atoms (i.e., an H or D atom) is transferred, tunneling can be significant, so this conventional form of TST can provide substantial errors in such cases. Nevertheless, TST remains the most widely used and successful theory of chemical reaction rates and can be extended to include tunneling and other corrections as we now illustrate. B. Variational Transition State Theory Within the TST expression for the rate constant of a bi-molecular reaction, krate = k kT/h (qAB*/V)/{(qA/V)(qB /V)}or of a uni-molecular reaction, krate = k kT/h {(qA*/V)/(qA/V)}, the height (E*) of the barrier on the potential energy surface appears in the TS species’ partition function qAB* or qA*, respectively. In particular, the TS partition function contains a factor of the form exp(-E*/kT) in which the Born￾Oppenheimer electronic energy of the TS relative to that of the reactant species appears. This energy E* is the value of the potential energy E(S) at the TS geometry, which we denote S0 . It turns out that the conventional TS approximation to krate over-estimates reaction rates because it assumes all trajectories that cross the TS proceed onward to products unless the transmission coefficient is included to correct for this. In the variational transition state theory (VTST), one does not evaluate the ratio of partition functions