Brian M. Hoffman

Diffusion theory of multidimensional activated rate processes: The role of anisotropy

We consider an anisotropic multidimensional barrier crossing problem, in the Smoluchowski (diffusion) limit. The anisotropy arises from either or both the shape of the potential energy surface and anisotropic diffusion. In such situations, the separatrix, which separates reactant and product regions of attraction, does not coincide with the ridge of the potential surface, which separates reactant and product wells, thus giving rise to a complicated time evolution. In the asymptotically long time limit, the time evolution is governed by crossing the separatrix and is exponential with a rate which may be obtained as a generalization of Kramers’ theory to the anisotropic situation. In contrast, in long, though not asymptotically long times, the time evolution is dominated by repeated crossings of the ridge, and is nonexponential. Such nonexponential time evolution has been observed in many biochemical reactions, where many degrees of freedom and anisotropic diffusion processes lead to complicated dynamical b...

Charge and spin transfer and optical properties in conducting porphyrin compounds

Anisotropic materials made from stacked macrocycles have potential applications as organic conductors and nonlinear optical materials. Using self‐consistent‐field local density theory, we have been exploring the ground and excited state electronic structures of metal substituted tetraazaporphyrins, phthalocyanines, and tetrabenzoporphyrins. The calculated and measured polarized optical absorption peaks are in satisfactory agreement. The theoretical dipole oscillator strengths provide absolute intensities for verification of transition assignments, which are helpful for identifying low‐lying states and excitation mechanisms.

A simple method for hyperfine-selective heteronuclear pulsed ENDOR via proton suppression

A major reason for the importance of ENDOR spectroscopy ( 1) in the study of metal complexes is that the technique is inherently broad-banded: all coupled nuclei having spin I > 0 can be detected with comparable sensitivity (2). Unfortunately, at X-band magnetic fields ( -0.3 T at g = 2) the proton ENDOR spectrum often overlaps with and obscures the spectra of important heteronuclei such as 14N, 13C 57Fe or 33S. One solution is to work at higher microwave frequency (2, 3). In adiitioi, three elegant, two-dimensional pulsed-ENDOR techniques (4) have been developed to address this problem by hyperfine selection at X band (57). We now describe a simple one-dimensional pulsed-ENDOR method for hyperfine selection of heteronuclear ENDOR signals through the suppression of the proton pattern. As the technique also leads to enhancement of the intensities of heteronuclear signals, we call it POSHEENDOR (proton suppression, heteronuclear enhancement). Two of the currently available pulsed-ENDOR techniques for hyperiine selection are formally equivalent and can be loosely grouped as ELDOR-ENDOR experiments. Buhlmann et al. (5) used field jumps within a Davies ENDOR sequence (4, 8) to achieve selection, whereas Thomann and Bernard0 (6) used microwave frequency jumps. However, these methods require two-dimensional experiments to obtain a complete hyperfme-selected spectrum and thus need large blocks of time for data acquisition. In addition, they require equipment beyond that necessary for ordinary Davies ENDOR. The third technique, developed by de Beer et al. ( 7)) utilizes a Mims ENDOR sequence (4, 9). In this method, hyperfine selection is achieved by systematic variation of time between the first and second microwave pulses in a stimulated-echo sequence. This procedure is restricted by the time required for a 2D experiment as well as by limitation of the Mims sequence to smaller hypetine couplings. The hyperfine selection technique we describe employs the fact that in a Davies ENDOR sequence,

Polycrystalline ENDOR patterns from centers with axial EPR spectra. General formulas and simple analytic expressions for deriving geometric information from dipolar couplings

Abstract We present a formulation for rapid simulations of polycrystalline ENDOR patterns for systems whose EPR spectra exhibit axial-resolved magnetic interactions (g tensor and “central”-nucleus hyperfine couplings). The ENDOR response of interest is from a nucleus with nonaxial hyperfine couplings and unresolved splittings. The equations simplify when the hyperfine tensor of the nucleus being observed in ENDOR has axial symmetry in its principal axis frame, as would occur for an I = 1 2 nucleus (1H or 19F) interacting by a through-space, electron-nuclear dipolar interaction. In such cases the field dependence of the ENDOR frequencies can be described by simple analytic functions, well suited to least-squares determination of metrical parameters that define the nuclear position. Sample calculations are given for a proton interacting with a nitroxide radical.

Reply to Comment on: Diffusion theory of multidimensional activated rate processes: The role. of anisotropy

The problem of two dimensional overdamped anisotropic diffusion is governed by two small parameters, (i) the thermal energy e=kBT/AV, where AV is a reference activation energy (e.g., the height of the saddle point above the bottom of the reactant well), and (ii) the anisotropy parameter S = qx /q,, where qx and vY are the two damping coefficients (assuming the friction tensor is diagonal). Therefore the two limits, (a) first e-0, then S-+0, and (b) first S -0, then e+O, must be considered separately, because it is not a priori clear that they are interchangeable. Indeed, there are cases when they are not, as correctly pointed out in Ref. 2. It should be pointed out however that the analysis presented in Ref. 1 is concerned with the limit (a). The limit (b) is considered there only for the case A > 0, for which the limits (a) and (b) are indeed interchangeable (here A = V, at the saddle point). The results for the case A&O in Ref. 1 are valid only in the limit (a), so that the comment “the cases A<0 can be handled in a similar manner” is misleading, as correctly pointed out in Ref. 2. Unfortunately, some of the statements, as well as the result

Single-crystal EPR and ENDOR study of nitrogenase from clostridium pasteurianum

Abstract The molybdenum-iron (MoFe) protein of nitrogenase from Clostridium pasteurianum forms monoclinic crystals in space group P21. The unit cell comprises two molecules, each of which possesses a molecular twofold symmetry axis and binds two chemically identical molybdenum-iron cofactors (M centers). Thus, there are four magnetically distinct M centers within the unit cell related by two different symmetry operations: a molecular twofold axis of symmetry in the bc ∗ plane relates the two EPR centers within a molecule; a crystallographic twofold screw axis of symmetry along the b axis of the unit cell relates the two different molecules in a unit cell. Single-crystal EPR studies at X-band (9.5 GHz) and Q-band (35 GHz) microwave frequencies have been employed to determine g tensors in the crystallographic frame for the four magnetically distinct M centers. Determination of these tensors has been achieved by a novel procedure that relies heavily on the symmetry relations between sites; it rests primarily on measurements that only involve rotation of the magnetic field parallel to a single plane of the crystal and uses g values from frozen-solution samples instead of additional rotations. Single-crystal 1H ENDOR spectra of the M centers are presented.