Torsional motions

In an ambitious study, the AIMS method was used to calculate the absorption and resonance Raman spectra of ethylene [221]. In this, sets starting with 10 functions were calculated. To cope with the huge resources required for these calculations the code was parallelized. The spectra, obtained from the autocorrelation function, compare well with the experimental ones. It was also found that the non-adiabatic processes described above do not influence the spectra, as their profiles are formed in the time before the packet reaches the intersection, that is, the observed dynamic is dominated by the torsional motion. Calculations using the Condon approximation were also compared to calculations implicitly including the transition dipole, and little difference was seen. 

Rather than calculate the etithaltty conti ibutioti of the torsional states individually, an empirical sum that is an integral multiple of 0.42 kcal mol per torsional degree of freedom is assigned to flexible molecules in MM3, Torsional motion of a methyl gntup is iK)t added k) a calculated because it is included in the... 

The value of the torsional energy increment has been variously estimated, but TORS = 0.42 kcal mol was settled on for the bond contribution method in MM3, In the full statistical method (see below), low-frequency torsional motion should be calculated along with all the others so the empirical TORS inererneut should be zero. In fact, TORS is not zero (Allinger, 1996). It appears that the TORS inererneut is a repository for an energy eiror or errors in the method that are as yet unknown. 

Terms in the energy expression that describe a single aspect of the molecular shape, such as bond stretching, angle bending, ring inversion, or torsional motion, are called valence terms. All force fields have at least one valence term and most have three or more. 

Different motions of a molecule will have different frequencies. As a general rule of thumb, bond stretches are the highest energy vibrations. Bond bends are somewhat lower energy vibrations and torsional motions are even lower. The lowest frequencies are usually torsions between substantial pieces of large molecules and breathing modes in very large molecules. 

It is generally recognized that the flexibility of a bulk polymer is related to the flexibility of the chains. Chain flexibility is primarily due to torsional motion (changing conformers). Two aspects of chain flexibility are typically examined. One is the barrier involved in determining the lowest-energy conformer from other conformers. The second is the range of conformational motion around the lowest-energy conformation that can be accessed with little or no barrier. There is not yet a clear consensus as to which of these aspects of conformational flexibility is most closely related to bulk flexibility. Researchers are advised to first examine some representative compounds for which the bulk flexibility is known. 

When the friction coefficient is set to zero, HyperChem performs regular molecular dynamics, and one should use a time step that is appropriate for a molecular dynamics run. With larger values of the friction coefficient, larger time steps can be used. This is because the solution to the Langevin equation in effect separates the motions of the atoms into two time scales the short-time (fast) motions, like bond stretches, which are approximated, and longtime (slow) motions, such as torsional motions, which are accurately evaluated. As one increases the friction coefficient, the short-time motions become more approximate, and thus it is less important to have a small timestep. 

Bufa-1,3-diene is one of many examples of molecules in which torsional motion may convert a sfable isomer info anofher, less sfable, isomer. The more sfable isomer in fhis case is fhe s-trans form, shown in Figure 6.44(e), and fhe less sfable one is fhe s-cis form, ... 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

Enolate anions (4e) that have been heated by infiared multiple photon absorption for which torsional motion about the H2C-C bond, which destabilizes the 7t orbital containing the extra electron, is the mode contributing most to vibration-to-electronic energy transfer and thus to ejection. 

In this chapter, we first present a brief overview of the experimental techniques that we and others have used to study torsional motion in S, and D0 (Section II). These are resonant two-photon ionization (R2PI) for S,-S0 spectroscopy and pulsed-field ionization (commonly known as ZEKE-PFI) for D0-S, spectroscopy. In Section HI, we summarize what is known about sixfold methyl rotor barriers in S0, S, and D0, including a brief description of how the absolute conformational preference can be inferred from spectral intensities. Section IV describes the threefold example of o-cholorotoluene in some detail and summarizes what is known about threefold barriers more generally. The sequence of molecules o-fluorotoluene, o-chlorotoluene, and 2-fluoro-6-chlorotoluene shows the effects of ort/io-fluoro and ortho-chloro substituents on the rotor potential. These are approximately additive in S0, S, and D0. Finally, in Section V, we present our ideas about the underlying causes of these diverse barrier heights and conformational preferences, based on analysis of the optimized geometries and electronic wavefunctions from ab initio calculations. 

The protein matrix of AvGFP efficiently forbids significant torsional motions of the chromophore, leading to near-maximum and highly homogeneous green fluorescence emission (see Sect. 3.1). Failure to do so results in weakly or non-fluorescent GFPs [113-115], while it was shown recently that the differences in... 

If one rotates about a C-C single bond in a compound of type X-C-C-Y, at each step of this torsional motion there are electron redistributions, and the bond lengths and angles will change. This phenomenon is the basis of the local nature of molecular structure. Several examples are illustrated in Figs. 7.6 and 7.7. 

The dependence of bond lengths and angles on associated torsional angles can be described by conformational geometry functions (CGF) which have the property of being approximately additive (L. Schafer et al. 1986G, in press, G). CGF additivity arises from the fact that the interactions encountered during torsional motion in a complex molecule can be approximately represented as the sum of the interactions encountered by individual structural components. For the case of ALA, for example, it is shown in Fig. 7.19 that... 

Fig. 7.19 Illustration of the additivity of conformational geometry functions for the -ro-tation in (CH3CO)(H)N-C(CH3)(H)(CONHCH3) (ALA). During the torsional motion about the N-C(a) bond of ALA, the interactions within the system are the same as those encountered during the N-C torsion in N-ethyl acetamide (NEA), plus those encountered during the N-C(a) torsion in N-acetyl N -methyl glycine amide offset by 120° as shown (GLY), minus those encountered during the N-C torsion in N-methyl acetamide (NMA).

This fact allows the effective relaxation of steric repulsion. The potential barrier for the motion around the C—C single bonds is smaller than that corresponding to the motion around the central C=C bond. Using the potential functions computed for these motions, and assuming a Boltzmann distribution, average torsional angles of 7.7 and 7.1, at 300 K, are obtained for rotations around Cl—C3 and C1=C2, respectively. This torsional motion seems to be due to the nonplanar structure observed experimentally. 

As a general conclusion, we can say that vicinal hyperconjugative interactions in transition-metal species tend to be much stronger than those in main-group compounds. Torsional degrees of freedom are therefore much more strongly hindered in metallic species, and the notion of pure torsional motion of simple rigid-rotor form lacks physical relevance in this limit. 

Figure 5.65 provides theoretical evidence that resonance-assisted H-bonding can serve as an effective mechanism for switching a methyl rotor from one preferred conformation to another, or for controlling the stiffness of torsional motions in alkylated amides. In particular, the torsional potentials of proteins (more specifically, the Ramachandran b angle at Ca) should be sensitive to N—H- O and related H-bonding interactions involving the amide backbone. In principle, this electronic... 

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