The potential energy curves of

In the adiabatic picture, the electronic coupling matrix element involves the nuclear kinetic energy operator. The wavefunctions for the two adiabatic 2 + states are mixtures of two dominant configurations, 

There are no C d/dR)C2 cross terms because 4 and (j)2 are mutually orthogonal. The matrix elements of the form 

The We(R) function, resulting from a simple two-state interaction, has a Lorentzian form [Eq. (3.3.14)]. For the Nj B C interaction, We(R) has its maximum in an H-region of numerous constructive and destructive interferences between the vibrational wavefunctions. Thus, slight changes in the vibrational functions resulting from isotopic substitution can drastically alter the vibronic matrix element, 

Another example is in Li2 (Antonova, et al., 2000) where the vibrational, rotational, and isotope dependence of the linewidths is studied. However, the coupling term is taken as constant rather than a Lorentzian form, giving a not so good fit. 

The Golden Rule formula Eq. (7.5.16) for the FWHM and Eq. (7.5.9) for the level shift are expressed in terms of the unperturbed vibrational wavefunc-tions. For strong predissociations, this approximation becomes untenable. Exant methods exist that can determine both the linewidth and the level shift. One method consists of numerically solving the following coupled equations (Lefebvre-Brion and Colin, 1977 Child and Lefebvre, 1978)  

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The fact that the separated-atom and united-atom limits involve several crossings in the OCD can be used to explain barriers in the potential energy curves of such diatomic molecules which occur at short intemuclear distances. It should be noted that the Silicon... 

Sketch an approximate potential energy diagram similar to that shown in Figures 3.4 and 3.7 for rotation about the carbon-carbon bond in 2,2-dimethylpropane. Does the form of the potential energy curve of 2,2-dimethylpropane more closely resemble that of ethane or that of butane ... 

The main features of the radial coupling matrix elements are presented in Fig. 2. In correspondence with the avoided crossings between the potential energy curves of singleelectron capture, sharp peaked functions appear at respectively 6.35, 7.50 and 8.30 a.u.. They are approximately 1.23, 2.53 and 12.21 a.u. high and respectively 0.75, 0.50 and less than 0.10 a.u. wide at half height. 

The potential energy curves of the Z" and 11 states are presented in Fig. 4. They show four avoided crossings in the range 15.0-10.0 a.u.] between the entry channel, the state corresponding to N +(ls2p3s) -t- He )and the three states of single-electron capture N +(ls2s3/) L-i-He+). 

The agreement shown between calculations and experiment gives eonfidence both in the theoretical method used here, and in the analysis of experimental speetra, in particular in the case of metastable state. Furthermore, the interpretation of the transfer-excitation process is straight forward from the knowledge of the potential energy curves of the collisional system. 

The third explanation is based on vertical excitations from the vibration functions outside the potential energy curves of the os-stilbene (Figure 9.5, mode d). 

The potential energy curves of the species AB, AB+, and AB- are used in figure 4.1 to summarize the definitions of the adiabatic ionization energy and electron affinity of AB. Note that the arrows start and end at vibrational ground states (vibrational quantum number v = 0). 

Further, the electron level of adsorbed particles differs from that of isolated adsorbate i>articles in vacuum as shown in Fig. 5-5, this electron level of the adsorbate particle shifts in the course of adsorption by a magnitude equivalent to the adsorption energy of the particles [Gomer-Swanson, 1963]. In the illustration of Fig. 5-5, the electron level of adsorbate particles is reduced in accordance with the potential energy curve of adsorption towards its lowest level at the plane of adsorption where the level width is broadened. In the case in which the allowed electron energy level of adsorbed particles, such as elumo and ehcmio, approaches the Fermi level, ep, of the adsorbent metal, an electron transfer occurs between... 

Figure 9-2 shows the potential energy curves of metallic ions both in transfer equilibrium and in anodic polarization. The anodic and cathodic activation energies Ag and 4 are given as functions of overvoltage t (positive in the anodic and n ative in the cathodic direction), respectively, in Eqn. 9-3 ... 

The potential energy curves of a neutral molecule AB and the potential ionic products from processes 7.18-7.20 are compared below (Fig. 7.11). These graphs reveal that the formation of negative molecular ions, AB, is energetically much more favorable than homolytic bond dissociation of AB and that the AB " ions have internal energies close to the activation energy for dissociation. [65,73,75]... 

CCSD(T) and CR-CCSD(TQ),b results for the potential energy curve of the N2 molecule, as described by the DZ basis set (113), shown in Table 1 and Figure 1. 

Figure 3. The shapes of the potential energy curves of the OH radical from the 2-RDM methods with DQG and DQGT2 conditions as well as the approximate wavefunction methods UMP2 and UCCSD are compared with the shape of the FCl curve. The potential energy curves of the approximate methods are shifted by a constant to make them agree with the FCl curve at equilibrium or 1.00 A. The 2-RDM method with the DQGT2 conditions yields a potential curve that within the graph is indistinguishable in its contour from the FCl curve.

This striking result can be qualitatively understood as related to CB DOS-influenced changes in the 02 anion lifetime [118]. For a diatomic molecule with R as the internuclear coordinate, a transient anion state is described in the fixed nuclei limit [123,124] by an energy and i -dependent complex potential Vo i R,E ) = Fd(2 ) + A( i)—l/2 T( i), where Va R) = a R) + is the potential energy curve of the discrete state, Vg(R) is the... 

H atom elimination is of lower importance from this state, 81 82 IC in the mechanism suggested by Wichramaaratchi et al. is practically identical with 8i 8x used in the terminology of Orlandi s group. The authors of Refs. 55, 83, 121, and 122 all agree that there is a dissociative triplet state, T , which can easily be populated by ISC from 81. We show the potential energy curve of this state (T ) as it has been suggested by Orlandi et al. [83,121]. This state gives only radical decomposition products. In order to explain the results of the biphotonic sensitization experiments (Sec. 2.1) another triplet state —1 eV below 81 (Ti) is also needed. Most probably, this triplet is also dissociative. 

The potential energy curves of excited electronic states need not have potential energy minima, such as those shown in Fig. 3.6. Thus Fig. 3.7 shows two hypothetical cases of repulsive states where no minima are present. Dissociation occurs immediately following light absorption, giving rise to a spectrum with a structureless continuum. Transition a represents the case where dissociation of the molecule AB produces the atoms A and B in their ground states, and transition b the situation where dissociation produces one of the atoms in an electronically excited state, designated A. ... 

The frequency factor, v, should be on the order of the lattice vibrational frequency, or 1013 s-1. The extreme simplicity of the model makes it very convenient for many applications. This theoretical model is now generally referred to as the image-hump model, or the Schottky-hump model, of field desorption. The potential energy curve of this model is not defined at all distances because of the crude nature of the argument it is nevertheless shown schematically in Fig. 2.9(a).48... 

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