ratio of partition functions. The denominator of this ratio contains the conventional partition functions of the reactant molecules and can be evaluated as discussed in Chapter 7. However, the numerator contains the partition function of the TS species but with one vibrational component missing (i.e, vib=Ik-13N-7exp(-hv /2KT)(1-exp(-hv /kT))) Other than the one missing vib, the Ts's partition function is also evaluated as in Chapter 7. The motion along the reaction path coordinate contributes to the rate expression in terms of the frequency (i.e, how often) with which reacting flux crosses the ts region given that the system is in near-thermal equilibrium at temperature t. pute the frequency with which traje ross the Ts and proceed onward to form products, one imagines the TS as consisting of a narrow region along the reaction coordinate S; the width of this region we denote ds. We next ask what the classical weighting factor is for a collision to have momentum ps along the reaction coordinate. Remembering our discussion of such matters in Chapter 7, we know that the momentum factor entering into the classical partition function for translation along the reaction coordinate is(1/h)exp(- P /2ukT)dps. Here, u is the mass factor associated with the reaction coordinate s. We can express the rate or frequency at which such trajectories pass through the narrow region of width Ss as(p/uds), with p /u being the speed of passage(cm s" )and 1/8s being the inverse of the distance that defines the ts region. So (p /uos has units of s". In summary, we expect the rate of trajectories moving through the Ts region to be (/h)exp(-ps 12ukt)dps(p/uos)5 ratio of partition functions. The denominator of this ratio contains the conventional partition functions of the reactant molecules and can be evaluated as discussed in Chapter 7. However, the numerator contains the partition function of the TS species but with one vibrational component missing (i.e., qvib = Pk=1,3N-7 {exp(-hnj /2kT)/(1- exp(-hnj /kT))}). Other than the one missing qvib, the TS's partition function is also evaluated as in Chapter 7. The motion along the reaction path coordinate contributes to the rate expression in terms of the frequency (i.e., how often) with which reacting flux crosses the TS region given that the system is in near-thermal equilibrium at temperature T. To compute the frequency with which trajectories cross the TS and proceed onward to form products, one imagines the TS as consisting of a narrow region along the reaction coordinate s; the width of this region we denote ds. We next ask what the classical weighting factor is for a collision to have momentum ps along the reaction coordinate. Remembering our discussion of such matters in Chapter 7, we know that the momentum factor entering into the classical partition function for translation along the reaction coordinate is (1/h) exp(-ps 2 /2mkT) dps . Here, m is the mass factor associated with the reaction coordinate s. We can express the rate or frequency at which such trajectories pass through the narrow region of width ds as (ps /mds), with ps /m being the speed of passage (cm s-1) and 1/ds being the inverse of the distance that defines the TS region. So, (ps /mds) has units of s-1. In summary, we expect the rate of trajectories moving through the TS region to be (1/h) exp(-ps 2 /2mkT) dps (ps /mds )