Intramolecular relaxation

The fact that the value of the characteristic viscosity at high frequencies is not zero indicates the existence of intramolecular (taking into account the solvent molecules) relaxation processes with relaxation times smaller than the reciprocal of the frequency of the measurement. The true limiting value is naturally zero and experiments sometimes reveal a step at a frequency uj which indicates the occurrence of a relaxation process with a relaxation time r a -1 which is compatible to the times of the deformation of a system. This phenomenon may be described by including the relaxing intramolecular viscosity, as it was done by Volkov and Pokrovskii (1978). 

Other types of network defect also exist physical crosslinks and closed loops (Fig. 3.16). Physical crosslinks may be permanent with a locked-in conformation (Fig. 3.16(a)) of temporary by entanglement. The presence of the latter type leads to visco-elastic behaviour, i.e. to creep and stress relaxation. Intramolecular crosslinks decrease the interconnectivity and reduce the number of loadcarrying chains. 

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Borkovec M, Straub J E and Berne B J The influence of intramolecular vibrational relaxation on the pressure dependence of unimolecular rate constants J. Chem. Phys. 85 146... 

Rynbrandt J D and Rabinovitch B S 1971 Direct demonstration of nonrandomization of internal energy in reacting molecules. Rate of intramolecular energy relaxation J. Chem. Phys. 54 2275-6... 

Meagher J F, Chao K J, Barker J R and Rabinovitch B S 1974 Intramolecular vibrational energy relaxation. Decomposition of a series of chemically activated fluoroalkyl cyclopropanes J. Phys. Chem. 78 2535 3... 

Quack M 1982 The role of intramolecular coupling and relaxation in IR-photochemistry Intramolecular Dynamics, Proc. 15th Jerusalem Symp. on Quantum Chemistry and Biochemistry (Jerusalem, Israel, 29 March-1 April 1982) ed J Jortner and B Pullman (Dordrecht Reidel) pp 371-90... 

Similar considerations have been exploited for the systematic analysis of room-temperature and molecular-beam IR spectra in temis of intramolecular vibrational relaxation rates [33, 34, 92, 94] (see also chapter A3.13 V... 

Figure C3.1.7. Time-resolved optical absorjDtion data for the Soret band of photo lysed haemoglobin-CO showing six first-order (or pseudo-first-order) relaxation phases, I-VI, on a logaritlimic time scale extending from nanoseconds to seconds. Relaxations correspond to geminate and diffusive CO rebinding and to intramolecular relaxations of tertiary and quaternary protein stmcture. (From Goldbeck R A, Paquette S J, Bjorling S C and Kliger D S 1996 Biochemistry 35 8628-39.)...

In Debye solvents, x is tire longitudinal relaxation time. The prediction tliat solvent polarization dynamics would limit intramolecular electron transfer rates was stated tlieoretically [40] and observed experimentally [41]. 

Figure C3.2.12. Experimentally observed electron transfer time in psec (squares) and theoretical electron transfer times (survival times, Tau a and Tau b) predicted by an extended Sumi-Marcus model. For fast solvents tire survival times are a strong Emction of tire characteristic solvent relaxation dynamics. For slower solvents tire electron transfer occurs tlirough tire motion of intramolecular degrees of freedom. From [451.

Z-matriccs arc commonly used as input to quantum mechanical ab initio and serai-empirical) calculations as they properly describe the spatial arrangement of the atoms of a molecule. Note that there is no explicit information on the connectivity present in the Z-matrix, as there is, c.g., in a connection table, but quantum mechanics derives the bonding and non-bonding intramolecular interactions from the molecular electronic wavefunction, starting from atomic wavefiinctions and a crude 3D structure. In contrast to that, most of the molecular mechanics packages require the initial molecular geometry as 3D Cartesian coordinates plus the connection table, as they have to assign appropriate force constants and potentials to each atom and each bond in order to relax and optimi-/e the molecular structure. Furthermore, Cartesian coordinates are preferable to internal coordinates if the spatial situations of ensembles of different molecules have to be compared. Of course, both representations are interconvertible. 

Dielectric measurements were used to evaluate the degrees of inter- and intramolecular hydrogen bonding in novolac resins.39 The frequency dependence of complex permittivity (s ) within a relaxation region can be described with a Havriliak and Negami function (HN function) ... 

It should be noted that there is a considerable difference between rotational structure narrowing caused by pressure and that caused by motional averaging of an adiabatically broadened spectrum [158, 159]. In the limiting case of fast motion, both of them are described by perturbation theory, thus, both widths in Eq. (3.16) and Eq (3.17) are expressed as a product of the frequency dispersion and the correlation time. However, the dispersion of the rotational structure (3.7) defined by intramolecular interaction is independent of the medium density, while the dispersion of the vibrational frequency shift (5 12) in (3.21) is linear in gas density. In principle, correlation times of the frequency modulation are also different. In the first case, it is the free rotation time te that is reduced as the medium density increases, and in the second case, it is the time of collision tc p/ v) that remains unchanged. As the density increases, the rotational contribution to the width decreases due to the reduction of t , while the vibrational contribution increases due to the dispersion growth. In nitrogen, they are of comparable magnitude after the initial (static) spectrum has become ten times narrower. At 77 K the rotational relaxation contribution is no less than 20% of the observed Q-branch width. If the rest of the contribution is entirely determined by... 

This simple theoryis based on the expectation that, to a reasonable degree of approximation, proton-proton, dipolar contributions to the measured spin-lattice relaxation-rate are pairwise additive and decrease as a simple sixth power of the interproton distance. The simplified version of the dipole-dipole mechanism is summarized in the following two equations for spin i coupled intramolecularly with a group of spins j... 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

Here, is the magnetization of spin i at thermal equilibrium, p,j is the direct, dipole-dipole relaxation between spins i and j, a-y is the crossrelaxation between spins i and j, and pf is the direct relaxation of spin i due to other relaxation mechanisms, including intermolecular dipolar interactions and paramagnetic relaxation by dissolved oxygen. Under experimental conditions so chosen that dipolar interactions constitute the dominant relaxation-mechanism, and intermolecular interactions have been minimized by sufficient dilution and degassing of the sample, the quantity pf in Eq. 3b becomes much smaller than the direct, intramolecular, dipolar interactions, that is. 

A deviation from the value of l.S indicates that other relaxation mechanisms contribute to the relaxation of spin i. The extent of intramolecular dipole-dipole interactions for spin i is given by ... 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

The relaxation data for the anomeric protons of the polysaccharides (see Table II) lack utility, inasmuch as the / ,(ns) values are identical within experimental error. Obviously, the distribution of correlation times associated with backbone and side-chain motions, complex patterns of intramolecular interaction, and significant cross-relaxation and cross-correlation effects dramatically lessen the diagnostic potential of these relaxation rates. 

For a rigidly held, three-spin system, or when existing internal motion is very slow compared to the overall molecular tumbling, all relaxation methods appear to be adequate for structure determination, provided that the following assumptions are valid (a) relaxation occurs mainly through intramolecular, dipolar interactions between protons (b) the motion is isotropic and (c) differences in the relaxation rates between lines of a multiplet are negligibly small, that is, spins are weakly coupled. This simple case is demonstrated in Table V, which gives the calculated interproton distances for the bicycloheptanol derivative (52) of which H-1, -2, and -3 represent a typical example of a weakly coupled, isolated three-spin... 

Cross-relaxation The mutual intermolecular or intramolecular relaxation of magnetically equivalent nuclei, e.g., through dipolar relaxation. This forms the basis of nOe experiments. 

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

In summary, all the experiments expressly selected to check the theoretical description provided fairly clear evidence in favour of both the basic electronic model proposed for the BMPC photoisomerization (involving a TICT-like state) and the essential characteristics of the intramolecular S and S, potential surfaces as derived from CS INDO Cl calculations. Now, combining the results of the present investigation with those of previous studies [24,25] we are in a position to fix the following points about the mechanism and dynamics of BMPC excited-state relaxation l)photoexcitation (So-Si)of the stable (trans) form results in the formation of the 3-4 cis planar isomer, as well as recovery of the trans one, through a perpendicular CT-like S] minimum of intramolecular origin, 2) a small intramolecular barrier (1.-1.2 kcal mol ) is interposed between the secondary trans and the absolute perp minima, 3) the thermal back 3-4 cis trans isomerization requires travelling over a substantial intramolecular barrier (=18 kcal moM) at the perp conformation, 4) solvent polarity effects come into play primarily around the perp conformation, due to localization of the... 

Close intramolecular contacts (clashes). A rough measure has been proposed and implemented in the program CONCORD [4,11] - the close contact ratio (CCR). The CCR of a 3D stracture is defined as the ratio of the smallest nonbonded distance to the smallest acceptable value for this distance. Normally, structures with CCR>0.8 are acceptable. Some programs as CORINA [5] or CONCORD [4, 11] have fallback procedures for attempting to relax close contacts in structures with unacceptably low CCR. 

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