Rate constant for

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

We now make two coimections with topics discussed earlier. First, at the begiiming of this section we defined 1/Jj as the rate constant for population decay and 1/J2 as the rate constant for coherence decay. Equation (A1.6.63) shows that for spontaneous emission MT = y, while 1/J2 = y/2 comparing with equation (A1.6.60) we see that for spontaneous emission, 1/J2 = 0- Second, note that y is the rate constant for population transfer due to spontaneous emission it is identical to the Einstein A coefficient which we defined in equation (Al.6.3). 

With the help of U, an expression for the rate constant for the reaction... 

A specific unimolecular rate constant for the decay of a highly excited molecule at energy E and angular momentum J takes the fomr... 

Table A3.4.3. Rate constants for the reaction of with O, [73], The rate constants are given in temis of the...

Figure A3.5.5. Rate constants for the reaction of Ar with O2 as a fiinction of temperature. CRESU stands for the French translation of reaction kinetics at supersonic conditions, SIFT is selected ion flow tube, FA is flowing afterglow and HTFA is high temperature flowing afterglow.

Midey A J and Viggiano A A 1998 Rate constants for the reaction of Ar" with O2 and CO as a function of temperature from 300 to 1400 K derivation of rotational and vibrational energy effects J. Chem. Phys. at press... 

Viggiano A A, Morris R A and Paulson J F 1994 Effects of f and SFg vibrational energy on the rate constant for charge transfer between and SFg int. J. Mass Spectrom. ion Processes 135 31-7... 

Figure A3.6.3. Solvent polarity dependence of the rate constant for the Menshutkin reaction (data from [14]).

Garrity D K and Skinner J L 1983 Effect of potential shape on isomerization rate constants for the BGK model Chem. Phys. Lett. 95 46-51... 

Grote R F and Hynes J T 1980 The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models J. Chem. Phys. 73 2715-32... 

Straub J E and Berne B J 1986 Energy diffusion in many dimensional Markovian systems the consequences of the competition between inter- and intra-molecular vibrational energy transfer J. Chem. Phys. 85 2999 Straub J E, Borkovec M and Berne B J 1987 Numerical simulation of rate constants for a two degree of freedom system in the weak collision limit J. Chem. Phys. 86 4296... 

Gershinsky G and Berne B J 1999 The rate constant for activated barrier crossing the competition between IVR and energy transfer to the bath J. Chem. Phys. 110 1053... 

Wang H, Sun X and Miller W H 1998 Semiclassical approximations for the calculation of thermal rate constants for chemical reactions in complex molecular systems J. Chem. Phys. 108 9726... 

Figure A3.10.25 Arrhenius plots of CO oxidation by O2 over Rli single crystals and supported Rli/Al203 at PCO = PO2 = 0.01 atm [43]. The dashed line in the figure is the predicted behaviour based on the rate constants for CO and O2 adsorption and desorption on Rli under UHV conditions.

Miller W H, Schwartz S D and Tromp J W 1983 Quantum mechanical rate constants for bimolecular reactions J. Chem. Phys. 79 4889-98... 

Manthe U, Seideman T and Miller WH 1993 Full-dimensional quantum-mechanical calculation of the rate-constant for the H2 + OH H2O + H reaction J. Chem. Phys. 99 10 078-81... 

RRKM theory assumes a microcanonical ensemble of A vibrational/rotational states within the energy interval E E + dE, so that each of these states is populated statistically with an equal probability [4]. This assumption of a microcanonical distribution means that the unimolecular rate constant for A only depends on energy, and not on the maimer in which A is energized. If N(0) is the number of A molecules excited at / =... 

Figure A3.12.3. Hannonic RRKM imimolecular rate constants for C2Hj H+C2H4 dissociation classical state counting (solid curve), quantal state counting (dashed curve). Rate constant is in units of s and energy in kcal moK (Adapted from [17].)...

If K is adiabatic, a molecule containing total vibrational-rotational energy E and, in a particular J, K level, has a vibrational density of states p[E - EjiJ,K). Similarly, the transition state s sum of states for the same E,J, and Kis [ -Eq-Ef(J,K)]. The RRKM rate constant for the Kadiabatic model is... 

The bulk of the infomiation about anhannonicity has come from classical mechanical calculations. As described above, the aidiannonic RRKM rate constant for an analytic potential energy fiinction may be detemiined from either equation (A3.12.4) [13] or equation (A3.12.24) [46] by sampling a microcanonical ensemble. This rate constant and the one calculated from the hamionic frequencies for the analytic potential give the aidiannonic correctiony j ( , J) in equation (A3.12.41). The transition state s aidiannonic classical sum of states is found from the phase space integral... 

Pesiherbe G H and Hase W L 1996 Statistical anharmonic unimolecular rate constants for the... 

Klippenstein S J, East ALL and Allen W D A 1994 First principles theoretical determination of the rate constant for the dissociation of singlet ketene J. Chem. Phys. 101 9198-201... 

Green W H, Moore C B and Polik W F 1992 Transition states and rate constants for unimolecular reactions Ann. Rev. Phys. Chem. 43 591-626... 

Song K and Hase W L 1998 Role of state specificity in the temperature- and pressure-dependent unimolecular rate constants for H02->H+02 dissociation J. Phys. Chem. A 102 1292-6... 

In the case of polarized, but otherwise incoherent statistical radiation, one finds a rate constant for radiative energy transfer between initial molecular quantum states i and final states f... 

In equation (A3.13.24), /c. is the specific rate constant for reaction from level j, and are energy transfer... 

We start from a model in which collision cross sections or rate constants for energy transfer are compared with a reference quantity such as average Leimard-Jones collision cross sections or the usually cited Leimard-Jones collision frequencies [54]... 

The interpretation of emission spectra is somewhat different but similar to that of absorption spectra. The intensity observed m a typical emission spectrum is a complicated fiinction of the excitation conditions which detennine the number of excited states produced, quenching processes which compete with emission, and the efficiency of the detection system. The quantities of theoretical interest which replace the integrated intensity of absorption spectroscopy are the rate constant for spontaneous emission and the related excited-state lifetime. 

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