Benzene normal coordinates

Enumerate the symmetries of the benzene normal coordinates whose displacements render the regular hexagonal configuration unstable in the Ei (mr ) state. 

Information on IR absorptions of chalcogenopyrylium ions is scarce. IR spectra of unsubstituted pyrylium (1) and thiopyrylium (2) have been reported by Yoshida et al. together with a normal coordinate analysis for the in-plane and out-of-plane vibrations (74T2099). Cation 2 yields lower absorption in wave number than 1 because of the mass effect of the heteroatom. The main reason for the difference in the IR spectra between benzene and heterocycles 1 and 2 is ascribed to the contribution of the carbonium ion structures in the latter cations. This contribution is larger in 1 than in 2 because of the electronegativity of the heteroatom (Section II,A). 

Schweitzer and associates investigated the extraction of metal hexanoates and found T1A(HA)3 in benzene and chloroform, T1A(HA)2 in 4-methyl-2-pentanone, and T1A(HA)4 in nitrobenzene (130) TmA3(HA)5 in chloroform and TmA3HA in 4-methyl-2-pentanone (129) and ZnA2HA in all studied solvents (126). This latter composition seems unlikely since the normal coordination number of zinc is 4 or 6. 

The polynuclear cation [(CeHe)3Co3(CO)2] has been reported from the reaction of Hg[Co(CO)4]a or Coa(CO)0 with benzene in the presence of an aluminum trihalide (66, 114). The cation is believed to have the structure (XXXI) analogous to (7r-C5H5)3Ni3(CO)a (289). Neutral polynuclear complexes of the type (arene)Co4(CO)g (arene = benzene, toluene, anisole, />-xylene, mesitylene, tetrahydronaphthalene) have been prepared by the reaction of (RC=CH)Co2(CO)e (R = H or Ph) with norbornadiene in the appropriate aromatic solvent or in some cases by simply warming Co4(CO)i2 with the arene (247, 365). The compounds are believed to have the structure (XXXII) derived from that of Co4(CO)i2 (435) by replacement of three apical CO groups by the arene. A normal coordinate analysis has been carried out on several of... 

To better visualize the situation, we present in Fig. 2 representative cuts through the PES of the benzene cation (Fig. 2a) as well as the monofluoro derivative (Fig. 2b). A linear combination of the normal coordinates of the JT active modes vg — vg is chosen for the benzene cation and one of the totally symmetric modes for the monofluoro benzene cation. Both are defined to minimize the energy of the conical intersection between the A and C states of the monofluoro derivative, and between the X and B states of the parent cation (within the subspace of JT active coordinates). For the parent cation one identifies a low-energy inter-state curve crossing which is mediated by the multimode JT effect in the two degenerate electronic states. The latter is reflected by the symmetric crossing between the two lowest potential energy curves in Fig. 2a which acmally represents a cut... 

Estimates of the mean square displacements in benzene have been made from normal coordinate calculations by Brooks, Cyvin, and Kvande.14 These have been used by Diehl and Niederberger to estimate the last term of Eq. (9) for each dipolar interaction of benzene and then estimate the average structure ra ... 

The first and most important source of additional data to overcome this problem is the changes in vibration frequencies on making an isotopic substitution. The frequencies and normal coordinates change due to the change in mass, but they are functions of the same force constants (provided that the coordinates are geometrically defined). The two B2U species vibrations of benzene may be used to illustrate the use of such data. The observed data are as follows ... 

FIGURE 5 Forms of the normal coordinates for the two solutions for benzene corresponding ) the higher and the lower value of the interaction constant F14> l4 given by the comparison of C4H4 with C4 D4 shown in Figure 4. 

The Hamiltonian will now be summarized for one overtone excited CH oscillator interacting with the N — 1 ring modes. Normal coordinates for the ring Q2,. . . , Q.v and for the overtone excited oscillator Q, are defined by uncoupling the overtone excited oscillator from the ring. The final form for the Hamiltonian then contains terms (both potential and kinetic) which couple the CH stretch mode to the ring modes. The derivation of the vibrational Hamiltonian was presented in Section II.C of Benzene I (103), and we will only summarize the final result here. The vibrational Hamiltonian may be partitioned into the terms... 

Also, our normal coordinate analysis revealed that the Cr-CO-, ring-Cr-C-and the C-Cr-C-bending coordinates are strongly coupled in E symmetry. In AI symmetry, the C-Cr-C umbrella opening mode is coupled with the Cr-C-O parallel bend. For details of the assignments the reader is referred to Table 12, in which we also included mode descriptions based on the criterion of potential energy distribution. The frequency related to the B2U C-C stretching vibration is overestimated, as it is for free benzene and for BzaCr. 

As the values in Table 18 indicate, the coupling between the benzene ring and the rest of the complex cannot simply be neglected, which was often the practice in the course of the normal-coordinate analysis of this compound, based on observed vibrational frequencies. As mentioned before, the normal-coordinate analysis from the reverse vibrational problem cannot provide all of the significant coupling constants of the harmonic force field this is simply due to the paucity of experimental information. Quantum mechanical calculations are necessary to obtain information about the significant coupling constants. 

Here Eg and Ex correspond to eqs 34 and 35. When the total nuclear repulsion energy Ain was kept constant, they found in all three cases that Eg is raised and Ex is lowered upon distortion. The 0 framework was found to be responsible for the C v symmetry of these structures. In a more comprehensive study of this question. Gobbi et al." commented on the role of o and n stabilization in benzene, allyl cation, and allyl anion. Their analysis was based on the first and second derivatives of the SCF canonical orbital energies with respect to normal coordinates Q. Since those energy derivatives show the behavior of the 0 and ji orbitals with respect to the deformation along each normal coordinate, the results indicate whether the orbital is stable or unstable toward... 

Table lO-l. Symmetry Species of the Normal Coordinates of Benzene... 

When only fundamentals are considered, that is, transitions from the ground level to levels with only one quantum of one vibration excited, the selection rules can be expressed very simply. These fundamentals will be active if they have the species of fix, fi, or fx -, otherwise they are inactive. Thus in benzene fi has the species A 2, while /x, fx have the species Eiu- Therefore, the only infrared active fundamentals are those whose normal coordinates are of species A2U or i 2 . 

Fn some cases, r-allylpalladium complex formation by retention syn attack) has been observed. The reaction of the cyclic allyiic chloride 33 with Pd(0) affords the 7r-allylpalladium chlorides 34 and 35 by retention or inversion depending on the solvents and Pd species. For example, retention is observed in benzene, THF, or dichloromethane with Pd2(dba)3. However, the complex formation proceeds by inversion in these solvents with Pd(Ph3P)4, whereas in MeCN and DMSO it is always inversion[33]. The syn attack in this case may be due to coordination of Pd to chlorine in 33, because Pd is halophilic. The definite syn attack in complex formation has been observed using stereoche-mically biased substrates. The reaction of the cxoallylic diphenylphosphino-acetate 36 with phenylzinc proceeds smoothly to give 37. The reaction can be explained by complex formation by a syn mechanism[31]. However, these syn attacks are exceptional, and normally anti attack dominates. 

The coordination of the Rieske cluster in the a subunit of benzene dioxygenase has been studied by site-directed mutagenesis. The replacement of His 98 or His 119 (corresponding to His 83/104 in NDO) by Cys resulted in a protein that was unable to coordinate a normal Rieske-type cluster (53). In the mutant His 98 Cys, a novel EPR spectrum with av = 1-94 was detected that is intermediate between... 

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