Potential energy surface pseudorotation

Similar to the case without consideration of the GP effect, the nuclear probability densities of Ai and A2 symmetries have threefold symmetry, while each component of E symmetry has twofold symmetry with respect to the line defined by (3 = 0. However, the nuclear probability density for the lowest E state has a higher symmetry, being cylindrical with an empty core. This is easyly understand since there is no potential barrier for pseudorotation in the upper sheet. Thus, the nuclear wave function can move freely all the way around the conical intersection. Note that the nuclear probability density vanishes at the conical intersection in the single-surface calculations as first noted by Mead [76] and generally proved by Varandas and Xu [77]. The nuclear probability density of the lowest state of Aj (A2) locates at regions where the lower sheet of the potential energy surface has A2 (Ai) symmetry in 5s. Note also that the Ai levels are raised up, and the A2 levels lowered down, while the order of the E levels has been altered by consideration of the GP effect. Such behavior is similar to that encountered for the trough states [11]. 

In this section, we extend the above discussion to the isotopomers of X3 systems, where X stands for an alkali metal atom. For the lowest two electronic states, the permutational properties of the electronic wave functions are similar to those of Lij. Their potential energy surfaces show that the baniers for pseudorotation are very low [80], and we must regard the concerned particles as identical. The Na atom has a nuclear spin " K, and K have nuclear... 

A potential energy surface was computed for Berry pseudorotation in IrCl4N02- and Mn(CO)4NO the results confirm the qualitative conformational trends obtained from orbital interaction arguments. 

Figure 2. Franck-Condon windows lVpc(Gi, r, v5) for the Na3(X) - N83(B) and for the Na3(B) Na3+ (X) + e transitions, X = 621 nm. The FC windows are evaluated as rather small areas of the lobes of vibrational wavefunctions that are transferred from one electronic state to the other. The vertical arrows indicate these regions in statu nascendi subsequently, the nascent lobes of the wavepackets move coherently to other domains of the potential-energy surfaces, yielding, e.g., the situation at t = 653 fs, which is illustrated in the figure. The snapshots of three-dimensional (3d) ab initio densities are superimposed on equicontours of the ab initio potential-energy surfaces of Na3(X), Na3(B), and Na3+ (X), adapted from Ref. 5 and projected in the pseudorotational coordinate space Qx r cos

Fig. 8 On the left is the Cr(CO)3 potential energy surface topology traversed after photodissociation of Cr(CO)6 to the conical intersection of the S2 and S0 states at D3h symmetry. The right hand side shows the branching space at the D conical intersection. The pseudorotation coordinate is shown connecting the C4y geometries through a C2y transition structure. The D3(i symmetry is indicted by the gray circle, the transition states by open circles while the three equivalent C4v species are indicated are indicted with solid circles. Adapted from [17]...

To explore the relevance of symmetry allowed conformations to chemically real structures it is necessary to locate steric-energy minima in a potential energy surface that spans all possible conformations. A variety of computational techniques [210] are available, commonly combined with experimental results retrieved from structural databases [211]. Such procedures have revealed the occurrence of countless different rotamers and conformers, arising from pseudorotation and conformational inversion under special environmental conditions. In addition, situations of disorder in the crystalline state are symptomatic in many cases, of the stabilization of variable intermediate forms. 

Microwave [90,91,92] and far-IR [93,94] spectra indicate that the barrier to pseudorotation in tetrahydrofuran is small (0.8 to 2.0kJmol ). Modeling the potential energy surface has... 

The general complementarity of sensitivities in cw and femtosecond spectroscopy has been anticipated by Zewail [66] and it is verified for the Naa molecule excited to its electronic B state (see Sect. 3.2.4). This system has already been studied in great detail by various experimental and theoretical techniques such as cw two-photon ionization spectroscopy [68-70], femtosecond pump probe spectroscopy at high intensities [29, 30, 71], quantum ab initio studies [72-74], two-dimensional simulations of the pseudorot at ional progressions in the cw absorption spectra [75-78], and, finally, three-dimensional simulations by means of empirical potential-energy surfaces (PESs) [79, 80]. 

To verify the nature of the two states, the harmonic vibrational frequencies at the minimum and transition state stationary points are reported in Table VI. For these states, the calculated frequencies in die harmonic approximation may be expected to be similar to those obtained from a full Jahn-Teller description, since the Jahn-Teller distortion in this case is relatively small. The deeper-lying Ui state is demonstrated to be a true minimum in all directions. The slightly less stable (0.006 eV) 82 state retains a single imaginary frequency in one component of the former e asymmetric bend mode and is thus a transition state, in this case to pseudorotation between the equivalent minima. On the full potential energy surface, the three equivalent minima and three equivalent... 

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