Spinning simulation

Levitt et al.69 have used the double quantum solid state NMR in the studies of bond lengths for a series of five 13C labelled samples of rhodopsin. On the basis of DQ-filtered signal trajectories and numerical spin simulations of the signal points, the through-space dipole-dipole coupling between neighbouring 13C nuclei has been estimated. Estimated dipole-dipole couplings have been converted into the intemuclear distances (Table 2) [32],... 

Despite the benefits of high resolution, measurements of wideline spectra of quadrupolar nuclei under static or MAS conditions are still commonly used in a variety of applications. For both integer and half-integer spins, simulations of quadrupolar lineshapes can yield full sets of NMR parameters associated with quadrupolar and chemical shift tensors and can be used for studying molecular dynamics. 

The proton, expanded proton and COSY (two-dimensional proton-proton correlation) spectra are shown in Figures 7, 8 and 9. The proton assignments are listed in Table 4. Due to the closely similar shifts of the protons on positions 9 (geminal), 11 and 12, it was difficult to determine the assignments. However, computer modeling of the assigned shifts, using second order spin simulation, produced a spectrum that closely matched the experimentally observed one. 

Spin, simulates stagnation-flow configurations, including heterogeneous chemistry at the stagnation surface. 

In conclusion, in order to simulate the paramagnetic relaxation it is necessary to perform both a MD simulations of the molecular motion around the jon, and a electron spin simulation. 

N. Kawashima and J. Gubernatis (1995) Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations. J. Stat. Phys. 80, p. 169... 

NMR ANALYSIS The 470 MHz HNMR spectra of benzaldehyde before and after the formation of a-cyclodextrin displayed a first-order pattern. The results are summarized in Table I. Spectra of a-cyclodextrin tefore and after inclusion of benzaldehyde cleaily showed a second-order pattern (Figure 7). A rigorous computer spin-simulation allowed us to determine their chemical shifts and coupling constants CTables I and II). The calculated values appear in reasonable agreement with those reported by Wood et al, (2 except for the H-6 protons. The discrepancy which appears is presumably due to the limited resolution of the previously measured 220 MHz HNMR spectrum. A 500 MHz spectrum of a-cyclodextrin recently reported by Yamamoto and hioue (27) is almost identical to our spectnim. However, no attempt was reported to calculate the accurate chemical shifts and coupling constants. 

NMR ANALYSIS Inoue et al recently reported the relative chemical shift and coupling constant assignments of p-cyclodextrin at pD 3 and pD 10 with the aid of two-dimension 500 MHz H COSY experiments (38). These data provide initial values for computer spin calculation (Figure 11) although only approximate data based on the first-order analysis were shown. All spectral data were measured in 0.2N NaOD solution because of the limited solubility in neutral solution. Upon complexation with -cyclodextrin marked spectral changes were observed. The precise chemical shifts and coupling constants calculate from computer spin simulation are summarized in Tables IV and V. 

Walls et al investigated the dynamics for dipole-coupled nuclear spin systems under conditions of high spin polarization both theoretically and numerically. Quantum spin simulations were performed which demonstrate that the transverse magnetization decays more rapidly as 9 > ti/2, where theta is the initial tip angle applied to the spins. Simple analytical models are used to demonstrate the increased decay of the transverse magnetization as 9 > ti/2. 

The confonnational mobility of a-cyclodextrin derivative 24 and some related compounds in solvents such as benzene, dichloromethane, and chloroform has been thoroughly investigated by dynamic n.m.r. spectroscopy, and the H-n.m.r. chemical shifts and coupling constants for a- and P-cyclodextiin and their permethyl ethers in neutral aqueous media have been assigned to obtain accurate data, the experimental spectra were analysed with the Raccoon spin simulation program. The structure of the copolymer obtained by treatment of l,4-anhydro-2,3-0-benzylidene-a-D-ribopyranose and l,4-anhydro-2,3-di-0-benzyl-a-D-ribopyranose with SbCls (see Chapter 5) has been determined from its C-n.m.r. spectrum and its optical rotation. ... 

Figure Bl.13.7. Simulated NOESY peak intensities in a homoniielear two-spin system as a fiinetion of the mixing time for two different motional regimes. (Reprodiieed by pennission of Wiley from Neiihaiis D 1996 Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chiehester Wiley) pp 3290-301.)...

From SCRP spectra one can always identify the sign of the exchange or dipolar interaction by direct exammation of the phase of the polarization. Often it is possible to quantify the absolute magnitude of D or J by computer simulation. The shape of SCRP spectra are very sensitive to dynamics, so temperature and viscosity dependencies are infonnative when knowledge of relaxation rates of competition between RPM and SCRP mechanisms is desired. Much use of SCRP theory has been made in the field of photosynthesis, where stnicture/fiinction relationships in reaction centres have been connected to their spin physics in considerable detail [, Mj. 

Closs G L and Forbes M D E 1991 EPR spectroscopy of electron spin polarized biradicals in liquid solutions. Technique, spectral simulation, scope and limitations J. Phys. Chem. 95 1924-33... 

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

Fig. 4. Simulated nmr spectmm for a molecule having three interacting spin systems and where = lOHz, = —3Hz, and = 12Hz at...

Imperforate Bowl Tests The amount of supernant hquid from spin tubes is usually too small to warrant accurate gravimetric analysis. A fixed amount of shiny is introduced at a controlled rate into a rotating imperforate bowl to simulate a continuous sedimentation centrifuge. The liquid is collected as it overflows the ring weir. The test is stopped when the solids in the bowl build up to a thickness which affects centrate quality. The solid concentration of the centrate is determined similarly to that of the spin tube. 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

D. P. Landau, M. Krech. Spin dynamics simulations of ferro- and antiferromagnetic model systems comparison with theory and experiment. J Phys Condens Matter 77 R175-R213, 1999. 

The calculations that have been carried out [56] indicate that the approximations discussed above lead to very good thermodynamic functions overall and a remarkably accurate critical point and coexistence curve. The critical density and temperature predicted by the theory agree with the simulation results to about 0.6%. Of course, dealing with the Yukawa potential allows certain analytical simplifications in implementing this approach. However, a similar approach can be applied to other similar potentials that consist of a hard core with an attractive tail. It should also be pointed out that the idea of using the requirement of self-consistency to yield a closed theory is pertinent not only to the realm of simple fluids, but also has proved to be a powerful tool in the study of a system of spins with continuous symmetry [57,58] and of a site-diluted or random-field Ising model [59,60]. 

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