Intramolecular modes

A covalent bond (or particular nomial mode) in the van der Waals molecule (e.g. the I2 bond in l2-He) can be selectively excited, and what is usually observed experimentally is that the unimolecular dissociation rate constant is orders of magnitude smaller than the RRKM prediction. This is thought to result from weak coupling between the excited high-frequency intramolecular mode and the low-frequency van der Waals intemiolecular modes [83]. This coupling may be highly mode specific. Exciting the two different HE stretch modes in the (HF)2 dimer with one quantum results in lifetimes which differ by a factor of 24 [84]. Other van der Waals molecules studied include (NO)2 [85], NO-HF [ ], and (C2i J )2 [87]. 

As discussed in section A3.12.2. intrinsic non-RRKM behaviour occurs when there is at least one bottleneck for transitions between the reactant molecule s vibrational states, so drat IVR is slow and a microcanonical ensemble over the reactant s phase space is not maintained during the unimolecular reaction. The above discussion of mode-specific decomposition illustrates that there are unimolecular reactions which are intrinsically non-RRKM. Many van der Waals molecules behave in this maimer [4,82]. For example, in an initial microcanonical ensemble for the ( 211 )2 van der Waals molecule both the C2H4—C2H4 intennolecular modes and C2H4 intramolecular modes are excited with equal probabilities. However, this microcanonical ensemble is not maintained as the dimer dissociates. States with energy in the intermolecular modes react more rapidly than do those with the C2H4 intramolecular modes excited [85]. 

Furthemiore, IVR is not rapid between the C2H4 intramolecular modes and different excitation patterns of these modes result in different dissociation rates. As a result of these different timescales for dissociation, the relative populations of the vibrational modes of the C2H4 dimer change with time. 

While being very similar in the general description, the RLT and electron-transfer processes differ in the vibration types they involve. In the first case, those are the high-frequency intramolecular modes, while in the second case the major role is played by the continuous spectrum of polarization phonons in condensed 3D media [Dogonadze and Kuznetsov 1975]. The localization effects mentioned in the previous section, connected with the low-frequency part of the phonon spectrum, still do not show up in electron-transfer reactions because of the asymmetry of the potential. 

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

The Raman spectrum in Fig. 10 for solid Ceo shows 10 strong Raman lines, the number of Raman-allowed modes expected for the intramolecular modes of the free molecule [6, 94, 92, 93, 95, 96, 97]. As first calculated by Stanton and Newton [98], the normal modes in molecular Ceo above about 1000 cm involve carbon atom displacements that are predominantly tangential... 

The thirty-two silent modes of Coo have been studied by various techniques [7], the most fruitful being higher-order Raman and infra-red spectroscopy. Because of the molecular nature of solid Cqq, the higher-order spectra are relatively sharp. Thus overtone and combination modes can be resolved, and with the help of a force constant model for the vibrational modes, various observed molecular frequencies can be identified with specific vibrational modes. Using this strategy, the 32 silent intramolecular modes of Ceo have been determined [101, 102]. 

The Raman and infrared spectra for C70 are much more complicated than for Cfio because of the lower symmetry and the large number of Raman-active modes (53) and infrared active modes (31) out of a total of 122 possible vibrational mode frequencies. Nevertheless, well-resolved infrared spectra [88, 103] and Raman spectra have been observed [95, 103, 104]. Using polarization studies and a force constant model calculation [103, 105], an attempt has been made to assign mode symmetries to all the intramolecular modes. Making use of a force constant model based on Ceo and a small perturbation to account for the weakening of the force constants for the belt atoms around the equator, reasonable consistency between the model calculation and the experimentally determined lattice modes [103, 105] has been achieved. 

Although in the frequency region of the conventionally measured infrared and Raman spectra (400-4000 cm ) only intramolecular modes appear, some particular bands can be sensitive to intermolecular interactions typical of the different modes of packing of chains with identical conformations. 

The resonance splitting of intramolecular modes in the crystalline state is often called Davydov splitting or factor group splitting . In contrast to the static field effects of the crystal, this splitting is due to the dynamical interaction of the constituents in the primitive cell... 

Experimental studies of liquid crystals have been used for many years to probe the dynamics of these complex molecules [12]. These experiments are usually divided into high and low-frequency spectral regions [80]. This distinction is very important in the study of liquid crystalline phases because, in principle, it can discriminate between inter- and intramolecular dynamics. For many organic materials vibrations above about 150 cm are traditionally assigned to internal vibrations and those below this value to so-called lattice modes . However, the distinction is not absolute and coupling between inter- and intramolecular modes is possible. 

Another important question deals with the intramolecular and unimolecular dynamics of the X-—RY and XR -Y- complexes. The interaction between the ion and molecule in these complexes is weak, similar to the intermolecular interactions for van der Waals molecules with hydrogen-bonding interactions like the hydrogen fluoride and water dimers.16 There are only small changes in the structure and vibrational frequencies of the RY and RX molecules when they form the ion-dipole complexes. In the complex, the vibrational frequencies of the intramolecular modes of the molecule are much higher than are the vibrational frequencies of the intermolecular modes, which are formed when the ion and molecule associate. This is illustrated in Table 1, where the vibrational frequencies for CH3C1 and the Cr-CHjCl complex are compared. Because of the disparity between the frequencies for the intermolecular and intramolecular modes, intramolecular vibrational energy redistribution (IVR) between these two types of modes may be slow in the ion-dipole complex.16... 

The analysis is performed for the calculations with rrot=0 K for the CH3C1 reactant, so that the angular momentum distribution for the complex P(j) is the distribution of orbital angular momentum for complex formation P(i). This latter distribution is given in ref. 37. Jm , the quantum number for j, varies from 282 for Enl = 0.5 kcal/mol to 357 for rel = 3.0 kcal/mol. The term k iEJ) in equation 24 is written as k (.EJ)=k Ejyf E), where k EJ) is the classical RRKM rate constant with the CH3C1 intramolecular modes inactive and / ( ) is treated as a fitting factor. 

Additional experimental, theoretical, and computational work is needed to acquire a complete understanding of the microscopic dynamics of gas-phase SN2 nucleophilic substitution reactions. Experimental measurements of the SN2 reaction rate versus excitation of specific vibrational modes of RY (equation 1) are needed, as are experimental studies of the dissociation and isomerization rates of the X--RY complex versus specific excitations of the complex s intermolecular and intramolecular modes. Experimental studies that probe the molecular dynamics of the [X-. r - Y]- central barrier region would also be extremely useful. 

Another possibility here is to use entropic acceleration. In this way, it is possible to use a substrate that first reacts in an intramolecular mode to give an intermediate, which then undergoes an intermolecular reaction with a second molecule. An impressive older example is a radical cyclization/trapping in the synthesis of prostaglandin F2a, as described by the Stork group [20]. A key step here is the radical transformation of the iodo compound 0-32 using uliu3Sril I formed in situ from... 

Further investigations in this field revealed that the described domino sequence can also be performed in an intramolecular mode to afford to 2-acyl-3-halocyclohex-anols 2-78 from 2-77 (Scheme 2.17) [24e],... 

So far, only those domino Knoevenagel/hetero-Diels-Alder reactions have been discussed where the cycloaddition takes place at an intramolecular mode however, the reaction can also be performed as a three-component transformation by applying an intermolecular Diels-Alder reaction. In this process again as the first step a Knoevenagel reaction of an aldehyde or a ketone with a 1,3-dicarbonyl compound occurs. However, the second step is now an intermolecular hetero-Diels-Alder reaction of the formed 1 -oxa-1,3 -butadiene with a dienophile in the reaction mixture. The scope of this type of reaction, and especially the possibility of obtaining highly diversified molecules, is even higher than in the case of the two-component transformation. The stereoselectivity of the cycloaddition step is found to be less pronounced, however. 

Examples for [4+2]/[3+2] domino processes, in which both cycloadditions proceed in an intramolecular mode, are the SnCl4-catalyzed transformation of 4-128 and 4-131, respectively to give 4-130 and 4-133 via the corresponding nitronates 4-129 and 4-132 (Scheme 4.27) [44],... 

Et3SiH/Ni(cod)2 brings about the reaction of an aldehyde and an alkyne to provide the silylated allyl alcohol (Eq. 190).350 The reaction also occurs in an intramolecular mode. 

After elimination of ethoxytrimethylsilane, 7,7-dimethyl-1-norbomene (6) rearranges to 3,3-dimethyl-2-norbomylidene (7), which undergoes a 1,3-CH insertion reaction into the endo-6-H to give tricyclane 8. Nortricyclane formation has been shown to be the fastest intramolecular mode of stabilization of 2-norbomylidene.5,6... 

The above relations can easily be generalized to the case when each molecule has several vibrational modes, e.g., displays not only stretching but bending vibrations as well.123 To classify these intramolecular modes, introduce the... 

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