Angular probability distributions

Figure 2. Minimum energy path, Vm in cm, as a function of 0 for r=2.28 A together with the n=0,l (coUinear) and n=2 (T-shaped) angular probability distributions for J = 0 vdW levels of HeBr2.

Figure 4. Polar plots of angular probability distributions for the spheroidal hybrids up through n = 4, for ZR = 0 (solid line), 15 (.. . . ), and oo(dashed line). The z-axis is horizontal.

As said above, an important feature of solvation at the water surface is the possibility to get some preferred orientations for the adsorbed molecules. To investigate this issue, the angular probability distributions have been calculated and they are plotted in Fig. 11.7. The distributions for methyl chloride and acetonitrile present small orientational preferences suggesting that both molecules experience high mobility. Orientations in which methyl chloride is parallel to the interface 6 90°) and those with the C-Cl bond pointing towards the air layer (0 < < 90°) seem to be slightly preferred, in agreement with previous studies (see below). In the... 

Fig. 11.7 Angular probability distributions for MeX (X = Cl, CN, OH) molecules at the air-water interfaee...

The angular-dependent adiabatic potential energy curves of these complexes obtained by averaging over the intermolecular distance coordinate at each orientation and the corresponding probability distributions for the bound intermolecular vibrational levels calculated by McCoy and co-workers provide valuable insights into the geometries of the complexes associated with the observed transitions. The He - - IC1(X, v" = 0) and He + 1C1(B, v = 3) adiabatic potentials are shown in Fig. 3 [39]. The abscissa represents the angle, 9,... 

The probability distribution for the n = 2 intermolecular level. Fig. 12c, indicates that this state resembles a bending level of the T-shaped complex with two nodes in the angular coordinate and maximum probability near the linear He I—Cl and He Cl—I ends of the molecule [40]. The measured I C1(B, v = 2f) rotational product state distribution observed following preparation of the He I C1(B, v = 3, m = 2, / = 1) state is plotted in Fig. 12d. The distribution is distinctly bimodal and extends out to the rotational state, / = 21,... 

Fig. 2.2. Isometric projections of probability density pb(0,

In the case of righthanded circular polarized i -type excitation, when orientation of angular momenta takes place and the probability density of the angular momenta distribution is proportional to (1 — cos )2/2 (see (2.13)), only alignment of internuclear axes occurs, described by the probability density, which is proportional to (1/2)[1 + (sin20r)/2j. 

Three components (Q — —1,0,+1) of the multipole moment of rank K = 1 form the cyclic components of the vector. They are proportional to the mean value of the corresponding spherical functions (B.l) for angular momenta distribution in the state of the molecule as described by the probability density p 9,(p). These components of the multipole moments enable us to find the cyclic components of the angular momentum of the molecule ... 

Let us analyze how to find the excited state multipole moments bPq-As explained in the previous paragraph, at excitation by weak light the probability density pb(0, state angular momentum distribution is proportional to the absorption probability G(0,multipole moments, Pq of an excited level b can be found as... 

Applying the latest model, the simplest equation for the probability density of angular momenta distribution in the absorbing state a may be written as follows ... 

Fig. 3.2. Isometric projection of the probability density of angular momenta distribution of ground (lower part) and excited (upper part) states (a) Q excitation (6) (P, R) excitation by light with E z.

The photodissociation process takes place most frequently at excitation of the molecule to a non-bonded state, with subsequent dissociation into products. Since the angular part of the transition probability, according to Chapter 2, is still dependent on the mutual orientation of the E-vector of the initiating light beam and on the transition dipole moment d, one may expect spatial anisotropy of angular momenta distribution both in the dissociation products and in the set of molecules which remains undestroyed. 

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