Probability distribution time constant potentials

The equilibrium distribution of the dipole will differ negligibly from the distribution over two strictly harmonic potential wells, and the dipole moment correlation function wll be initially of the form derived in the last section. Let us call this As time goes on, the molecule has an increasing probability of escape over the potential barrier. If we regard the probability per unit time of this escape as strictly constant, the condition for which y(0 is the appropriate correlation function has now the diminish ing probability exp (— ft). 

Storm-Mathisen I would like to refer to the Purkinje cells of the cerebellum. The axons of these cells are distributed to the cerebellar nuclei and to the dorsal half of the lateral vestibular (Deiters ) nucleus. Here they produce inhibitory postsynaptic potentials that can be mimicked by iontophoretic application of GABA. Further, GABA, but not other amino acids, is released into the 4th ventricle during activation of the Purkinje cells, so it seems that GABA is the transmitter of these cells. We found 2 to 3 times more GAD in the dorsal half of Deiters nucleus which receives Purkinje terminals than in the ventral half which is devoid of such terminals. We also made lesions of the specific regions in the cerebellar cortex to destroy the Purkinje cells sending their axons to the cerebellar and Deiters nuclei, and measured the GAD activity. This dropped by a factor of 3 in the locations deprived of their Purkinje terminals, but stayed constant elsewhere. The Purkinje terminals and axons constitute only a small fraction of the tissue, probably no more than 10%. The concentration of GAD in these structures must therefore be enormous (Fonnum, Storm-Mathisen and Walberg, 1970). 

The time evolution of the electronic wave function can be obtained in the adiabatic or in the diabatic basis set. At each time step, one evaluates the transition probabilities between electronic states and decides whether to hop to another siu-face. When hopping occurs, nuclear velocities have to be adjusted to keep the total energy constant. After hopping, the forces are calculated from the potential of the newly populated electronic state. To decide whether or not to hop, a Monte Carlo technique is used Once the transition probability is obtained, a random number in the range (0,1) is generated and compared with the transition probability. If the munber is less than the probability, a hop occurs otherwise, the nuclear motion continues on the same surface as before. At the end of the simulation, one can analyze populations, distribution of nuclear geometries, reaction times, and other observables as an average over all the trajectories. 

The enharmonic RRKM unimolecular rate constant for each of the eleven potential energy surfaces was determined at 50.0 kcal/mol from the t = 0 intercept of the trajectory lifetime distribution, equation (15). Time intervals of 1.0 x 10" and 0.5 x 10 s were used in trajectory P(t) histograms, and the resulting rate constants are given in Table 3. Within statistical uncertainties these time intervals give identical rate constants, which means that a At of 1.0 X 10 s is sufficiently small for establishing the intercepts. Bunker found the same result.A comparison between the enharmonic and harmonic RRKM rate constants in Table 3 shows that the enharmonic ones are all approximately a factor of two smaller. A similar enharmonic correction factor was found by Bunker and Pattengill in their triatomic trajectory studies.The enharmonic rate constants are expected to be smaller than the harmonic ones, since anharmonicity increases the HCC density of states and, thus, decreases the dissociation probability. 

---