Propensity Rules

Chalasinski G, Kendall R A, Taylor H and Simons J 1988 Propensity rules for vibration-rotation induced electron detachment of diatomic anions application to NH -> NH + e J. Phys. Chem. 92 3086-91... 

Simons J 1981 Propensity rules for vibration-induced electron detachment of anions J. Am. Chem. See. 103 3971-6 Acharya P K, Kendall R A and Simons J 1984 Vibration-induced electron detachment in molecular anions J. Am. Chem. See. 106 3402-7... 

Perhaps the best way to sum up the general conclusions regarding our studies of coordinatively unsaturated metal carbonyls is in a series of propensity rules with the understanding that these rules may be modified by future studies. The rules are ... 

In this case we can see that the promoting mode can accept at least one vibrational quantum (due to the term 0)/, + ( t). This is usually called the propensity rule. 

Troisi A, Ratner MA (2006) Molecular transport junctions propensity rules for inelastic electron tunneling spectra. Nano Lett 6(8) 1784-1788... 

Gagliardi A, Solomon GC, Pecchia A, Frauenheim T, Di Carlo A, Hush NS, Reimers JR (2007) A priori method for propensity rules for inelastic electron tunneling spectroscopy of single-molecule conduction. Phys Rev B 75(17) 174306-174308... 

Paulsson M, Frederiksen T, Ueba H, Lorente N, Brandbyge M (2008) Unified description of inelastic propensity rules for electron transport through nanoscale junctions. Phys Rev Lett 100(22) 226604... 

Fig. 4. Comparison of lower-resolution spectral profiles for the composite D — E PE band, (a) Experimental recording of Ref. [6]. (b) Result of the present calculation utilizing the parameter values of Table 3 and including the modes v2 and vi6 — f18 with all couplings. The Elu and B2u vibronic symmetries are drawn separately as dashed lines, their 1.4 1 weighted sum is given by the full line (FWHM = 88 meY). (c) Same as (b), but employing the propensity rule Af6 = Af7 = Af8 = 0. For more details see text.

Fig. 6. Time-dependent electronic population of the E2B2u state of Bz+ for a vertical transition. The wave-packet is located initially at the E state surface and seen to undergo an efficient radiationless transition at a time scale of 10-20 fs. The results of the full calculation (solid line) and of the propensity rule (dashed line) are compared.

For comparison, the figure also contains the result of a calculation using the propensity rule of Ref. [12]. In this calculation the weaker coupling (either JT or PJT) for each of the modes vi6 — has been suppressed, that is, Af6 = Af7 = Afjf = 0 been assumed. The result, represented by the dashed line in the figure, reproduces the overall behaviour of the full calculation rather well. Finer details differ considerably in the two curves. This holds more for the PE spectral envelope which has been included as panel (c) in Fig. 4. It underlines the need to include all coupling terms in order to arrive at an accurate description of the simultaneous JT and PJT interactions in this system. 

The last question that we will address concerns the final vibrational and rotational state distributions of the diatomic fragments. Although the excited resonance states can live up to nanoseconds or even microseconds, the final distributions do not follow simple statistical laws which were briefly spoken about in Section 10.3.2. On the contrary, they manifest either prominent propensity rules or dynamical features similar to those discussed in the context of direct dissociation. 

Under the assumptions of a harmonic oscillator and an interaction potential, which is linear in (r — re), only the next lowest vibrational channel n = n — 1 can be populated. The propensity rule n — n — 1 is a strict selection rule. 

Andresen, P., Beushausen, V., Hausler, D., Liilf, H.W., and Rothe, E. (1985). Strong propensity rules in the photodissociation of a single rotational quantum state of vibra-tionally excited H2O, J. Chem. Phys. 83, 1429-1430. 

At the transition state for the F-(H20) + CH3C1 reaction, the hydrogen bond from water is entirely to the F—that is, there is no evidence for water transfer at the methyl transfer transition state (see Figure 1-1), which is consistent with the propensity rule mentioned above, in that the water does not migrate. However, it is also consistent with the possibility that water migrates after the transition state is passed. 

Mattheus, A., Fischer, A., Ziegler, G., Gottwald, E. and Bergmann, K. (1986). Experimental proof of a Am -C j propensity rule in rotationally inelastic differential scattering, Phys. Rev. Lett., 56, 712-715. 

Figure 8. Time-resolved photoelectron spectra revealing vibrational and electronic dynamics during internal conversion in DT. (a) Level scheme in DT for one-photon probe ionization. The pump laser prepares the optically bright state S2. Due to ultrafast internal conversion, this state converts to the lower lying state Si with 0.7 eV of vibrational energy. The expected ionization propensity rules are shown S2 —> Do + e (ei) and Si —> D + (b) Femtosecond time-...

We derived a dynamical propensity rule for transitions as follows From Eq. (6), one can derive an approximate analytical form for i(p,q) [44,45] ... 

The dynamical propensity rule for (forward) transitions is derived as... 

Up to moderately high energy ( 179%) of the activation barrier for reactant product in the Are isomerization reaction, the fates of most trajectories can be predicted more accurately by Eq. (11) as the order of perturbation calculation increases, except just in the vicinity of the (approximate) stable invariant manifolds (e.g., see Eig. 5), and that the transmission coefficient K observed in the configurational space can also be reproduced by the dynamical propensity rule without any elaborate trajectory calculation (see Eig. 6). Our findings indicate that almost all observed deviations from unity of the conventional transmission coefficient k may be due to the choice of the reaction coordinate whenever the k arises from the recrossings, and most transitions in chemical... 

The enthalpy of formation of the azide radical is 467 SkJmoR. The spin-allowed dissociation to N( D) and N2(X 1 +) is endoergic by 225kJmol, the dissociation enthalpy to N( S) - -N2(X i +) is 0.5 IkJmol. The azide radical is only stable because this spin-forbidden decomposition pathway has an appreciable energy barrier. In aqueous solution, it primarily exists as a monomer, in contrast to other halide or pseudohaUde radicals that exist as the less reactive dimers (e. g. Brs (SCN)2 ). Reaction ofthe azide radical with halogen atoms or other small molecules hke O2, NO, CO, and CO2 produces molecules in electronically excited states because of propensity rules, which can be used for chemically pumped lasers. The azide ion is also formed during high-pressure photolysis of sodium azide. 

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