Rovibrational contributions

Fig. 3. Orientationally averaged total stopping cross section St for protons impinging on H2O as a function of proton velocity along with the experimental results of Reynolds et ah (filled circles) [28]. 5 e, and represent the electronic, nuclear, and rovibrational contributions to the stopping, respectively.

For this molecule, FSHG measurements are available for a much larger number of frequencies. Thus, there is little doubt about the accuracy of the experimental values and a dispersion curve could be fitted to the measured data (corrected for rovibrational contributions) without referring to calculated dispersion coefficients [2, 3, 6]. 

Going beyond the narrow framework of electronic structure theory other major challenges become apparent. The rovibrational contributions to NLO properties are known to be significant. This includes both the vibrational averaging as well as pure (ro)vibrational contributions. The development of general, accurate and efficient methods for Are calculation of vibrational contributions is an important area for future research. It requires input from electronic structure calculations and the Aieoretlcal interface between electronic and vibrational structure theory is an Important issue in this research. For a more detailed discussion we refer to a later Chapter of this book. 

Fig. 9. Stopping cross section per atom for proton projectiles colliding with atomic and molecular hydrogen targets as a function of the acceptance angle 0 for projectiles energies of 0.5, 1.5, 5.0, 10.0, and 25.0 keV. Note the nuclear plus rovibrational contributions when large scattering angles are taken into account.

Calculated Rovibrational Contributions, Temperature Corrections, and Nuclear Magnetic Shielding Constants at 300 K [<7(300 K)] in Comparison with Corresponding Shielding Constants Derived from Experimental Spin-Rotation Constants" ... 

Both time-independent and time-dependent approaches are viable to perform such computations. Within the time-independent approach, the most widely used method for computing the rovibrational contributions to NMR properties is by means of second-order perturbation theory. To first order, the vibrationally averaged value of a property Q is expressed as... 

Fig. 12. Partitionings of hydrogen fragment translational energy distribution into three components. The solid line denotes the contribution from H2S — 8H(,4 "S+ ) + H which yields a resolved structure with a rovibrational state assignment on the top. The dotted line denotes the contribution of hydrogen from the SH(442 +) —> S(3P) + H reaction, which is a reflection of the solid curve but the structure is smeared out. The corresponding rotational quantum numbers of the parent molecule SI I (A 2>l 1 ) l =0 is marked on the bottom. The remaining part of the P(E) spectrum is represented by the square-like dashed curve.

Although apparently simple, there is a lot of subtlety in this model. The most important parameter in determining the translational energy dependence of the activation energy is AE. If we reduce AE, then the slope of E (Elmm) increases, which is found in the results of the full quantum dynamics calculations the slope is greater for the J 0 -> 4 transition than for J 0 - 6. AE is the shift in the threshold due to the thermal motion, it is the amount of energy surface motion contributes to aid the dissociation or rovibrational excitation. Why this should vary from one particular transition to... 

Qei and Qvtbrot denote electronic and rovibrational partition fimctions, respectively. In general, the contributions of the internal degrees of freedom of A and B cancel in g and gviiroXA)gv iro((B ), such that only contributions Irom the external rotations of A and B and the relative motion, summarized as "transitional modes", need to be considered. Under low temperature quantum conditions, these can be obtained by statistical adiabatic channel (SACM) calculations [9],[10] while classical trajectory (CT) calculations [11]-[14] are the method of choice for higher temperatures. CT calculations are run in the capture mode, i.e. trajectories are followed Irom large separations of A and B to such small distances that subsequent collisions of AB can stabilize the adduct. 

Laser photodissociation of ketene at 230 nm has been investigated in molecular beams. The experimental rovibrational population distribution has been compared to predictions from phase-space theory for the channels leading to CO + CH2(a Ai) and CO + CH2(b Bi). The calculations are not compatible with the latter channel, suggesting that it does not contribute significantly to the dissociation process. The photodissociation of singlet ketene by two-step IR + UV excitation has been studied using state-selective detection of CH2 by laser-induced fluorescence, and the results compared with... 

Although rate constant of process 17b has not been measured, it will be the same order as that of process 17a with a somewhat smaller stabilization efficiency. The contribution of process 16 is expected to be much smaller than that of processes 17a and 17b, because the ki value is too small to probe the product HeNe (B 1/2) ion under our experimental conditions. The vibrational and rotational distributions were determined by a spectral simulation. No significant changes in rovibrational distributions were found under the conditions, where process 17a or 17b was dominant. The NqiNi ratio of HeNe" (B 1/2) was 100 10 and the rotational temperatures of the v = 0 and 1 levels were 70-110 and 40-70 K, respectively. 

Eq. (2.112) represents an anharmonic expansion in the quantum number V. We insist, of course, on the essential difference between the one- and three-dimensional case, as in the latter case, we also obtain the rotational contribution to the energy spectrum. As a matter of fact, the final outcome of the dynamical symmetry 0(4) is the (well-approximated) rovibrational spectrum of a three-dimensional Morse oscillator. Its physical parameters can easily be related to the algebraic quantities A, N, Eg, and B by means of the following relations ... 

The most important difference with the local eigenvalues obtained for the bent case [Eq. (4.33)] is found in the double dependence on the vibrational angular momentum quantum number Ig, which appears in the expectation values of both C- 2 and C 2 operators. In the bent-to-linear correlation pattern for rovibrational energy levels (Fig. 33) we achieve the exact linear limit for /I 0 (we recall that the bent limit is obtained with A[2 = 2Aj2). This means that in the eigenvalues (4.54), the dominant term in Ig is derived from the Cjj operator. However, it is possible to account for minor adjustments of energy terms explicitly dependent on Ig, by adding (small) contributions related to the operator Cjj- In the linear case, it is convenient to use, in place of the absolute value, the square of this operator, in such a way that the vibrational spectrum recalls the usual Dunham series (written in normal quantum numbers)... 

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