Derivatives of spin dynamics simulations

We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate and more reliable than the finite difference approximations typically employed. The resulting derivatives may be used in fitting, optimization, performance evaluation and stability analysis of spin dynamics simulations and experiments. Keywords: NMR, EPR, simulation, analytical derivatives, optimal control, spin chemistry, radical pair.Comment: Accepted by The Journal of Chemical Physic

Toroidal circular dichroism

We demonstrate that the induced toroidal dipole, represented by currents flowing on the surface of a torus, makes a distinct and indispensable contribution to circular dichroism. We show that toroidal circular dichroism supplements the well-known mechanism involving electric dipole and magnetic dipole transitions. We illustrate this with rigorous analysis of the experimentally measured, polarization-sensitive transmission spectra of an artificial metamaterial, constructed from elements of toroidal symmetry. We argue that toroidal circular dichroism shall be found in large biomolecules with elements of toroidal symmetry and should be taken into account in the interpretation of circular dichroism spectra of organics

Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered

Efficient algorithms for the discovery of optimal control designs for coherent control of quantum processes are of fundamental importance. One important class of algorithms are sequential update algorithms generally attributed to Krotov. Although widely and often successfully used, the associated theory is often involved and leaves many crucial questions unanswered, from the monotonicity and convergence of the algorithm to discretization effects, leading to the introduction of ad-hoc penalty terms and suboptimal update schemes detrimental to the performance of the algorithm. We present a general framework for sequential update algorithms including specific prescriptions for efficient update rules with inexpensive dynamic search length control, taking into account discretization effects and eliminating the need for ad-hoc penalty terms. The latter, while necessary to regularize the problem in the limit of infinite time resolution, i.e., the continuum limit, are shown to be undesirable and unnecessary in the practically relevant case of finite time resolution. Numerical examples show that the ideas underlying many of these results extend even beyond what can be rigorously proved.Comment: 19 pages, many figure

Uniform illumination of optically dense NMR samples

We demonstrate a simple, inexpensive method for in situ laser illumination of NMR samples using a stepwise tapered optical fibre to deliver light uniformly along the axis of a 5 mm NMR tube. The optical path length of the incident light inside the sample is about 3 mm, allowing efficient illumination of optically dense samples. The degradation in spectral resolution and the reduction in filling factor are both minimal. Probe modifications are not required

Chemically amplified ¹⁹F-¹H nuclear Overhauser effects

Chemically induced dynamic nuclear polarisation (CIDNP) is explored as a source of nuclear hyperpolarisation in heteronuclear Overhauser effect experiments. A photochemical reaction proceeding through a radical pair intermediate is used to enhance 19F nuclear magnetisation in 3-fluorotyrosine by more than an order of magnitude with a corresponding increase in the amplitudes of 19F–1H cross-relaxation and cross-correlation effects. The reactions employed are cyclic and leave the sample chemically unchanged. The potential for enhancing the sensitivity of heteronuclear NOEs in 19F-labelled proteins is discussed

Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction

We report progress with an old problem in magnetic resonance—that of the exponential scaling of simulation complexity with the number of spins. It is demonstrated below that a polynomially scaling algorithm can be obtained (and accurate simulations performed for over 200 coupled spins) if the dimension of the Liouville state space is reduced by excluding unimportant and unpopulated spin states. We found the class of such states to be surprisingly wide. It actually appears that a majority of states in large spin systems are not essential in magnetic resonance simulations and can safely be dropped from the state space. In restricted state spaces the spin dynamics simulations scale polynomially. In cases of favourable interaction topologies (sparse graphs, e.g. in protein NMR) the asymptotic scaling is linear, opening the way to direct fitting of molecular structures to experimental spectra

Increasing the sensitivity of time-resolved photo-CIDNP experiments by multiple laser flashes and temporary storage in the rotating frame.

Pulse sequences have been developed that add up time-resolved photo-CIDNP signals from n successive laser flashes not in the acquisition computer of the NMR spectrometer but in the experiment itself, resulting in a greatly improved signal-to-noise ratio. For this accumulation, CIDNP is first stored in the transverse plane and then on the z axis, and finally superimposed on CIDNP produced by the next flash. These storage cycles also result in a very efficient background suppression. Because only one free induction decay is acquired for n flashes, the noise is digitized only once. The signal gain is demonstrated experimentally and analyzed theoretically. Losses are mostly due to nuclear spin relaxation, and to a small extent to instrument imperfections. With 10 laser flashes, a signal increase by a factor of about 7.5 was realized. As their main advantage compared to signal averaging in the usual way, these sequences yield the same signal-to-noise ratio with fewer laser flashes; the theoretical improvement is by a factor of n

Theoretical analysis of scalar relaxation in 13C-DNP in liquids

Dynamic nuclear polarization in the liquid state via Overhauser effect is enabled by the fluctuations of the electron-nuclear hyperfine interaction. Fermi contact (or scalar) hyperfine coupling can be modulated by molecular collisions on timescales of a few picoseconds and shorter, enabling an effective polarization transfer even at high magnetic fields. However, only a few studies have presented a theoretical analysis of the scalar mechanism. Here we report the current understanding of the scalar relaxation in liquid-state DNP and present different modeling strategies based on analytical relaxation theory and numerical calculations from molecular dynamics simulations. These approaches give consistent results in identifying the timescale of the fluctuations of the scalar interaction that drives C-DNP in the model system of CHCl doped with nitroxide radical. Subpicosecond fluctuations arise not only from random molecular collisions but are also present when target molecule and polarizing agent form a transient complex that persists for tens of picoseconds. We expect that these kind of interactions, possibly based on hydrogen bond-like complexations, might be present in a large variety of compounds

Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software

We describe a general method for the automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations for liquid-phase spin dynamics in the algebraically challenging case of rotationally modulated interactions. The processing typically takes no more than a few seconds (on a contemporary single-processor workstation) and yields relaxation rate expressions that are completely general with respect to the spectral density functions, relative orientations, and magnitudes of the interaction tensors, with all cross-correlations accounted for. The algorithm easily deals with fully rhombic interaction tensors, and is able, with little if any modification, to treat a large variety of the relaxation mechanisms encountered in NMR, EPR, and spin dynamics in general