Energy avoided crossing

FIGURE 17.2 Illustration of the reaction coordinate for a reaction with a change in the electronic state, (a) Potential energy curves for the two electronic states of the system. (A) Avoided crossing that can be seen in single-detenninant calculations. 

The region of the avoided crossing for Nal is the region where the molecule is in a transition state, a state intermediate between those in which the molecule is fully bound or dissociafed. If is fhis region of fhe pofenfial energy curves which had remained inaccessible before investigation wifh femtosecond lasers became possible. 

However, because of the avoided crossing of the potential energy curves the wave functions of Vq and Fi are mixed, very strongly at r = 6.93 A and less strongly on either side. Consequently, when the wave packet reaches the high r limit of the vibrational level there is a chance that the wave function will take on sufficient of the character of Na + 1 that neutral sodium (or iodine) atoms may be detected. 

Figure 3.1 Avoided crossing of potential energy surfaces for LiF...

In order to calculate q (Q) all possible quantum states are needed. It is usually assumed that the energy of a molecule can be approximated as a sum of terms involving translational, rotational, vibrational and electronical states. Except for a few cases this is a good approximation. For linear, floppy (soft bending potential), molecules the separation of the rotational and vibrational modes may be problematic. If two energy surfaces come close together (avoided crossing), the separability of the electronic and vibrational modes may be a poor approximation (breakdown of the Bom-Oppenheimer approximation. Section 3.1). 

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+). 

F ure 9.26. Energy profile along (a) the reaction coordinate at an avoided crossing for a photochemical reaction and (h) an electron transfer process. 

Fig. 28. Schematic of potential energy surfaces of the vinoxy radical system. All energies are in eV, include zero-point energy, and are relative to CH2CHO (X2A//). Calculated energies are compared with experimentally-determined values in parentheses. Transition states 1—5 are labelled, along with the rate constant definitions from RRKM calculations. The solid potential curves to the left of vinoxy retain Cs symmetry. The avoided crossing (dotted lines) which forms TS5 arises when Cs symmetry is broken by out-of-plane motion. (From Osborn et al.67)...

Figure 2, together with Table 2, explains the fact that neither the shortened Si=Si bond length, with respect to Si-Si, nor the increased vibrational frequency is in contradiction to the above statement 3 because minimum and curvature of the ground state energy curve are hardly influenced by the avoided crossing. 

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