Imaginary modes

The Ia and A mechanisms are mutually exclusive, since the 7 -coordinate transition state has an imaginary mode that either describes a concerted entry/leaving of the ligands and the mechanism is Ia (Fig. 6a) or only the motion of the entering (or leaving ligand) and the mechanism is A (Fig. 6b) (104). The Id and D mechanisms are not mutually exclusive and up to now no Id has been computed, most probably due to the omission of the second coordination sphere (104). 

Fig. 6. Structure and imaginary modes of transition states (a) [V(OH)2)5 (OH2)2+] imaginary mode describes concerted entry and leaving of H20 (b) [Mn(OH)2)6 (OH2)2+]j imaginary mode describes only the motion of the entering H20.

The example above used 3 degrees of freedom, but the main features of this example are present for any transition state. Specifically, a transition state in a system with N degrees of freedom is characterized by (N — 1) real vibrational modes and one imaginary mode, while a local minimum has N real vibrational modes. The ideas in the derivation of Eq. (6.8) can be applied to our multidimensional rate expression, Eq. (6.10), to show that within the harmonic approximation,... 

G. R. Fleming The suggestion by Prof. Tannor that you can use imaginary modes to find longer time behavior is interesting. 

The optimized structure with symmetry, shown in Fig. 6(a), has one imaginary mode. The vibrational mode with an imaginary frequency is also depicted in Fig. 6(b). The imaginary mode will move the Dlh structure to C2h one. Hence the D2h symmetry structure is a saddle point between the stable C2 , structures. The energy barrier AE between the C2h minima is 0.2 meV. It should be noted that AE... 

An interesting feature of INM calculations for liquids is that some of the modes are imaginary, corresponding to unstable motion. These imaginary modes seem to contribute little to influence spectra, but they show up universally in densities of states. As is conventional, imaginary modes are plotted in spectra as if they were negative frequencies. 

Triplet states of 16. The A2 state can be pictured as a cycloheptatrienyl radical, whereas the B state resembles a pentadienyl radical, whose terminal atoms interact only weakly with the connecting C-C double bond. In 16 the a electron cannot interchange with the n system at SCF levels of theory (UHF and ROHF) and one finds both states to be minima. Inclusion of dynamic electron correlation increases the energy gap between the two triplet states and the B state is a saddle point at MP2 and BLYP. This situation is reversed at the CASSCF level, where Bi, now a minimum, is only 2-3 kcal mol below the A2 state (transition structure), Following the imaginary mode of A2-16 leads, via intermediate geometries of Cs symmetry, to the Bj state, quite similar to the situation found in the cycloheptatrienyl radical. 

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