Showing papers by "Jack H. Freed published in 1981"

Calculation of ESR spectra and related Fokker–Planck forms by the use of the Lanczos algorithm

Abstract: The applicability of the Lanczos algorithm in the general ESR (and NMR) line shape problem is investigated in detail. This algorithm is generalized to permit tridiagonalization of complex symmetric matrices characteristic of this problem. It is found to yield very accurate numerical solutions with at least order of magnitude reductions in computation time compared to previous methods. It is shown that this great efficiency is a function of the sparsity of the matrix structure in these problems as well as the efficiency of selecting an approximation to the optimal basis set for representing the line shape problem as distinct from actually solving for the eigenvalues. Furthermore, it is found to aid in the analysis of truncation to minimize the basis set (MTS), which becomes nontrivial in complex problems, although the efficiency of the method is not very strongly dependent upon the MTS. It is also found that typical Fokker–Planck equations arising from stochastic modeling of molecular dynamics have the property of being representable by complex–symmetric matrices that are very sparse, so calculation of associated correlation functions can be very effectively implemented by the Lanczos algorithm. It is pointed out that large problems leading to matrices of very large dimension can be efficiently handled by the Lanczos algorithm.

Rotational jumps of the tyrosine side chain in crystalline enkephalin. Hydrogen-2 NMR line shapes for aromatic ring motions in solids

Abstract: Deuterium NMR spectra of polycrystalline (tyrosine-3,5-*H2) (Leus)enkephalin show that the aromatic tyrosyl ring of this pentapeptide is executing 180' flips about the Cfl-C' axis in the solid state. Specifically, the axially symmetric powder pattern observed at low temperature collapses to an axially asymmetric pattern with TJ 0.6 at high temperature. Computer simulations of the NMR line shapes, which account for spectral distortions induced by the quadrupole echo technique, indicate that at room temperature the flipping rate is approximately 5 X IO4 s-* and that it increases to about lo6 s-I at 101 "C. In the past few years it has become apparent that solid-state NMR spectra can be employed to investigate the rate and mechanism of molecular reorientation processes in solids, and there are now several examples in the literature which demonstrate this point."" To date these studies have focussed on small crystalline molecules, but the techniques are equally applicable to large molecules such as peptides and proteins, where they can be used to obtain information on phenomena such as the motion of amino acid side chains. As part of a study of side-chain reorientation in peptides and proteins by solid-state NMR, we report here an investigation of the motion of the aromatic tyrosine ring in polycrystalline (Le~~jenkephalin. Specifically, the 2H NMR powder line shapes of ( tyrosine-3 ,S2H2) ( LeuS) enkephalin show that the tyrosyl group is not rigid, but instead is executing jumps of 180' about the Co-Cc axis of the aromatic ring. At room temperature the jump rate is approximately lo4 s-l and inceases to about IO6 s-' at 101 OC. (Le~~lenkephalin is a natural pentapeptide with the sequence Tyr-Gly-Gly-Phe-Leu which has been chemically labeled with (3,5-ZH2)tyrosine for this study as is depicted in Figure 1. The peptide is of considerable interest because of its structural similarity to opiate agonists. Theoretical and experimental evidence from solution measurementsl2 reveal that enkephalin may exist in a relatively rigid conformation in which the phenyl and tyrosyl rings are separated by a distance similar to that of opiates, so that these groups may participate in binding to the receptor. (Leus)enke- phalin has been crystallized, and its structure determined;l3-l5 the X-ray studies have suggested that the orientation of the tyrosyl side chain is not unique, the ring experiencing disorder of either a static or dynamic nature. Because of the possible existence of dynamic disorder, and because NMR can detect this type of disorder and reveal the details of its nature, a solid-state NMR investigation of (Leus)enkephalin appeared promising. Experimental Section ~~-(3,5-2H,)Tyrosine was purchased from Merck, Sharpe, and Dohme (St. Louis, Mo.). The DL form was resolved by treatment of the N-trifluoroacetyl derivative with carboxypeptidase A to yield the L isomer of the free amino acid. The latter was used to synthesize (Leus)enke- phalin by the procedure reported previously.12 The 2H labeled peptide was recrystallized from ethanol. Samples for the NMR experiments typically consisted of approxi- mately 50 mg of the 2H-labeled peptide and were placed in vacuum- sealed glass tubes. The ZH NMR spectra were obtained on a home-built spectrometer operating at 45.1 MHz for 2H, using a quadrupole echo pulse seq~encc.'~~'~ The r/2 pulse width was 2-2.5 ps and the T value in the echo experiment was 30 ps. In order to ensure that the line shapes we obtain are accurate, we have found it necessary to employ quadrature, rather than single sided, phase detection. With the latter method gross

ESR studies of 0−2 adsorbed on Ti supported surfaces: Analysis of motional dynamics

Abstract: Temperature‐dependent ESR spectra of O−2 adsorbed on Ti ions supported on porous Vycor glass were observed over the range 4.2 to 400 °K. These spectra were obtained under normal high vacuum conditions as well as under UHV conditions (P⩽10−9 Torr) and are very well resolved. It was observed that the line position of the g tensor component that is perpendicular to the internuclear axis of O−2 remained constant with temperature, whereas the other two components of the g tensor shift in position with temperature, and are accompanied by drastic line shape changes. This observation indicates that the molecular motion of O−2 on the surface is highly anisotropic, consisting essentially of planar rotation about the axis perpendicular to the internuclear axis of O−2 and parallel to the normal to the surface. Furthermore, the observation of nonequivalent 17O hfs of O−2 suggests that the internuclear axis of O−2 might be tilted slightly from the surface and/or one oxygen is closer to the Ti4+. The ESR line shapes w...

Classical time‐correlation functions and the Lanczos algorithm

Abstract: It is shown how the Lanczos algorithm (LA) can be applied to classical systems, leading naturally to a continued fraction representation equivalent to that obtained by Mori for the correlation functions. The relation of the LA to the method of moments suggests its utility for study of the theoretical structure, while the computational efficiency of the LA suggests its use for computer calculation of correlation functions. (AIP)

A UHV-ESR study of the reaction of NO2 adsorbed on copper

Abstract: We describe in detail an experimental design which permits the high sensitivity study of ESR from paramagnetic species that may form on clean metal (and oxide) surfaces. The heart of the design is the ultra-high vacuum ESR cavity. The new phenomenon CREMSEE (cyclotron resonance from microwave-induced secondary electron emission), which is observed under high vacuum conditions, is characterized in some detail. In particular, it is found to be a sensitive indicator of surface bonding. The results of a detailed study of the reaction of NO2 with Cu performed in the UHV-ESR system are presented. It is shown that the initial oxidation process may be monitored by CREMSEE, while an ESR signal is only seen when H2 O is present. The primary role of the H2 O is to form a hydrated surface copper complex which is magnetically concentrated but microcrystalline. These results are then compared with a study on supported Cu performed under conventional vacuum conditions.

A cryostat for investigating spin polarized hydrogen

Abstract: A low temperature spin polarized hydrogen apparatus is discussed Fluxes into the hydrogen cell of 10 14 atoms/sec have been achieved Hydrogen atom concentrations of 1 × 10 16 atoms/cm 3 have been observed in fields of 9 Tesla and at 06 K, as determined by strain gauge measurements and calorimetric methods