A partial differential equation for pseudocontact shift

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data

A standard format and a graphical user interface for spin system specification

We introduce a simple and general XML format for spin system description that is the result of extensive consultations within Magnetic Resonance community and unifies under one roof all major existing spin interaction specification conventions. The format is human-readable, easy to edit and easy to parse using standard XML libraries. We also describe a graphical user interface that was designed to facilitate construction and visualization of complicated spin systems. The interface is capable of generating input files for several popular spin dynamics simulation packages.Comment: Submitted for publicatio

Molecular structure refinement by direct fitting of atomic coordinates to experimental ESR spectra

An attempt is made to bypass spectral analysis and fit internal coordinates of radicals directly to experimental liquid- and solid-state electron spin resonance (ESR) spectra. We take advantage of the recently introduced large-scale spin dynamics simulation algorithms and of the fact that the accuracy of quantum mechanical calculations of ESR parameters has improved to the point of quantitative correctness. Partial solutions are offered to the local minimum problem in spectral fitting and to the problem of spin interaction parameters (hyperfine couplings, chemical shifts, etc.) being very sensitive to distortions in molecular geometry.Comment: Submitted for publicatio

Pseudocontact shifts from mobile spin labels

This paper presents a detailed analysis of the pseudocontact shift (PCS) field induced by a mobile spin label that is viewed as a probability density distribution with an associated effective magnetic susceptibility anisotropy. It is demonstrated that non-spherically symmetric density can lead to significant deviations from the commonly used point dipole approximation for the PCS. Analytical and numerical solutions are presented for the general partial differential equation that describes the non-point case. It is also demonstrated that it is possible, with some reasonable approximations, to reconstruct paramagnetic centre probability distributions from the experimental PCS data

Feedback control optimisation of ESR experiments

Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is sample-specific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance -- an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library

Parallel density matrix propagation in spin dynamics simulations

Several methods for density matrix propagation in distributed computing environments, such as clusters and graphics processing units, are proposed and evaluated. It is demonstrated that the large communication overhead associated with each propagation step (two-sided multiplication of the density matrix by an exponential propagator and its conjugate) may be avoided and the simulation recast in a form that requires virtually no inter-thread communication. Good scaling is demonstrated on a 128-core (16 nodes, 8 cores each) cluster.Comment: Submitted for publicatio

Exact NMR simulation of protein-size spin systems using tensor train formalism

We introduce a new method, based on alternating optimization, for compact representation of spin Hamiltonians and solution of linear systems of algebraic equations in the tensor train format. We demonstrate the method's utility by simulating, without approximations, a 15N NMR spectrum of ubiquitin—a protein containing several hundred interacting nuclear spins. Existing simulation algorithms for the spin system and the NMR experiment in question either require significant approximations or scale exponentially with the spin system size. We compare the proposed method to the Spinach package that uses heuristic restricted state space techniques to achieve polynomial complexity scaling. When the spin system topology is close to a linear chain (e.g., for the backbone of a protein), the tensor train representation is more compact and can be computed faster than the sparse representation using restricted state spaces