Out-of-plane motion

The widths of the narrow Lorentzians representing slow motions in the plane and perpendicular to the plane of the bilayer are compared in Ligures 11a and 11b, respectively. Lor the in-plane motion, the MD values for Q = 0.5 A agree well with the experimental results, but the increase with Q is significantly overestimated in the simulation compared to the experimental values. This suggests that the slower component of the in-plane motion in the simulation is too fast at short distances. On the other hand, the MD line widths for the slower component of the out-of-plane motion agree well with the experimental results at 30% hydration. As in the case of the LISL, the simulation predicts a slight anisotropy not seen in the experimental data. 

Analysis of neutron data in terms of models that include lipid center-of-mass diffusion in a cylinder has led to estimates of the amplitudes of the lateral and out-of-plane motion and their corresponding diffusion constants. It is important to keep in mind that these diffusion constants are not derived from a Brownian dynamics model and are therefore not comparable to diffusion constants computed from simulations via the Einstein relation. Our comparison in the previous section of the Lorentzian line widths from simulation and neutron data has provided a direct, model-independent assessment of the integrity of the time scales of the dynamic processes predicted by the simulation. We estimate the amplimdes within the cylindrical diffusion model, i.e., the length (twice the out-of-plane amplitude) L and the radius (in-plane amplitude) R of the cylinder, respectively, as follows ... 

The similarity in the behaviour of coupling constants as a function of e in both radicals allows to discuss vibrational averaging effects simply in terms of the potential governing the out-of-plane motion. 

Fig. 5.19 Low-frequency Fe modes of Fe(TPP)(NO) predicted on the basis of B3LYP calculations. The modes mainly involve porphyrin core translation, Fe-NO torsion, Fe-N-O bending, and Fe out-of-plane motion coupled to doming of the porphyrin core. Arrows representing mass-weighted atomic displacements are 100(my/mFe) longer than the zero-point vibrational amplitude of atom j. Color scheme as in Fig. 5.15 (taken from [101])...

FIG. 2 Molecular orientation angles at liquid interfaces for rodlike molecules. The out-of-plane motion is a rotation away from the OZ axis, whereas the in-plane motion is performed with the OX, OY) plane. 

The ab initio molecular dynamics study by Hudock et al. discussed above for uracil included thymine as well [126], Similarly to uracil, it was found that the first ultrafast component of the photoelectron spectra corresponds to relaxation on the S2 minimum. Subsequently a barrier exists on the S2 surface leading to the conical intersection between S2 and Si. The barrier involves out-of-plane motion of the methyl group attached to C5 in thymine or out-of-plane motion of H5 in uracil. Because of the difference of masses between these two molecules, kinematic factors will lead to a slower rate (longer lifetime) in thymine compared to uracil. Experimentally there are three components for the lifetimes of these systems, a subpicosecond, a picosecond and a nanosecond component. The picosecond component, which is suggested to correspond to the nonadiabatic S2/S1 transition, is 2.4 ps in uracil and 6.4 ps in thymine. This difference in the lifetimes could be explained by the barrier described above. 

Problems arise in two situations firstly, if the molecule is linear, no complete set of 3N — 6 internal coordinates is possible. For this case, a method for constructing PES in terms of Cartesian coordinates could be used.56 Secondly, if the molecule is planar, atom-atom distances (or their reciprocals) cannot provide a complete set of internal coordinates, since they cannot describe out-of-plane motion. However, we have found the coordinates Zn so useful that we retain these coordinates and avoid planar geometries (except for three atoms, when only linear geometries are taboo). That is,... 

Fig. 28. Schematic of potential energy surfaces of the vinoxy radical system. All energies are in eV, include zero-point energy, and are relative to CH2CHO (X2A//). Calculated energies are compared with experimentally-determined values in parentheses. Transition states 1—5 are labelled, along with the rate constant definitions from RRKM calculations. The solid potential curves to the left of vinoxy retain Cs symmetry. The avoided crossing (dotted lines) which forms TS5 arises when Cs symmetry is broken by out-of-plane motion. (From Osborn et al.67)...

As shown in Figure 2.2, the isotropic g tensor shift (Agiso) is almost linearly dependent on the NO bond length, whereas it does not display any regular trend with respect to out-of-plane motion. 

This intermolecular potential for ADN ionic crystal has further been developed to describe the lowest phase of ammonium nitrate (phase V) [150]. The intermolecular potential contains similar potential terms as for the ADN crystal. This potential was extended to include intramolecular potential terms for bond stretches, bond bending and torsional motions. The corresponding set of force constants used in the intramolecular part of the potential was parameterized based on the ab initio calculated vibrational frequencies of the isolated ammonium and nitrate ions. The temperature dependence of the structural parameters indicate that experimental unit cell dimensions can be well reproduced, with little translational and rotational disorder of the ions in the crystal over the temperature range 4.2-250 K. Moreover, the anisotropic expansion of the lattice dimensions, predominantly along a and b axes were also found in agreement with experimental data. These were interpreted as being due to the out-of-plane motions of the nitrate ions which are positions perpendicular on both these axes. 

Langer and Doltsinis [41, 42] find that the nonadiabatic transition parameter (10-10) is correlated to variations in the C(5)C(6) bond length as well as to out-of-plane motions. The importance of this degree of freedom for radiationless decay has been pointed out previously by Zgierski et al. [103],... 

The secondary, slower process with an exponential coefficient of 293 fs is concerned more with nonadiabatic transitions out of the CT state, where out-of-plane structural fluctuations play a more significant role. Indeed, this time-scale seems appropriate, as the time for a phase cycle of these out-of-plane motions (0 and ) is of the order of 100 to 200 fs, and P10 is observed to have the largest magnitude when both time-derivatives (d0/dt and d

[Pg.295]

Changes in the energy gap, AE, and the nonadiabatic transition probability, P10, in the aqueous solution simulations are dominated in the initial stages by the coupled proton-electron transfer event and the subsequent relaxation of the system into the excited CT state. Similar to the gas phase, variations in AE and P10 at longer time-scales were found to depend strongly on the out-of-plane motions of the system (for instance the dihedral angles 0 and ). However, the presence of... 

In aqueous solution, nonradiative decay of 9H-keto G is slowed down considerably due to the fact that the crucial out-of-plane motions are damped and the... 

Not all IR absorptions are due to bond stretches. Many of the absorptions in the fingerprint region of an IR spectrum are due to bending and out-of-plane motions. 

Dynamic fluorescence anisotropy is based on rotational reorientation of the excited dipole of a probe molecule, and its correlation time(s) should depend on local environments around the molecule. For a dye molecule in an isotropic medium, three-dimensional rotational reorientation of the excited dipole takes place freely [10]. At a water/oil interface, on the other hand, the out-of-plane motion of a probe molecule should be frozen when the dye is adsorbed on a sharp water/oil interface (i.e., two-dimensional in respect to the molecular size of a probe), while such a motion will be allowed for a relatively thick water/oil interface (i.e., three-dimensional) [11,12]. Thus, by observing rotational freedom of a dye molecule (i.e., excited dipole), one can discuss the thickness of a water/oil interface the correlation time(s) provides information about the chemi-cal/physical characteristics of the interface, including the dynamical behavioiu of the interfacial structure. Dynamic fluorescence anisotropy measurements are thus expected... 

The low frequency motions of vinyl radical correspond to out-of-plane vibrations (wagging and torsion) and in-plane inversion at the radical center. The out-of-plane motions have the same effect as the methyl inversion, albeit with a significantly smaller... 

The conclusion is supported by vibrational FT-IR and FT-Raman spectra of 33a-g in the neutral and doped state [104,105], A comparison of the intensities of the FT-IR bands from 1,3,5-trisubstituted benzene end group signals near 704 cmwith the intensities of the C-H out of plane motion of l,2-tro s-disubstituted ethylenes near 964 cm shows a linear decrease of the intensity ratios with increasing chainlength approaching very small values for 8-10 units. 

The GA and GT combinations are somewhat less strongly bound. It was noted by the authors that these structures are not true minima. The single negative eigenvalue probably refers to an out-of-plane motion of a side group (the authors enforced full planarity), and so is probably not a serious concern to this discussion. These two dimers have in common the presence of a pair of H-bonds nitrogen serves as the proton donor in all of these. 

Changing the subunit from HX to H2Y adds a number of new vibrational modes to the dimer. Nonetheless, the D-bonded form of the water dimer is more stable than the H-bonded complex . The energy difference of 60 cm" is attributed chiefly to the out-of-plane motion that shears the bond which is of higher frequency for a proton than a deuteron, consistent with the observations for the HF dimer. 

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