Ilya Kuprov

Chemical compass model of avian magnetoreception

Approximately 50 species, including birds, mammals, reptiles, amphibians, fish, crustaceans and insects, are known to use the Earth’s magnetic field for orientation and navigation. Birds in particular have been intensively studied, but the biophysical mechanisms that underlie the avian magnetic compass are still poorly understood. One proposal, based on magnetically sensitive free radical reactions, is gaining support despite the fact that no chemical reaction in vitro has been shown to respond to magnetic fields as weak as the Earth’s (∼50 μT) or to be sensitive to the direction of such a field. Here we use spectroscopic observation of a carotenoid–porphyrin–fullerene model system to demonstrate that the lifetime of a photochemically formed radical pair is changed by application ofu2009≤50 μT magnetic fields, and to measure the anisotropic chemical response that is essential for its operation as a chemical compass sensor. These experiments establish the feasibility of chemical magnetoreception and give insight into the structural and dynamic design features required for optimal detection of the direction of the Earth’s magnetic field.

Spinach – A software library for simulation of spin dynamics in large spin systems

We introduce a software library incorporating our recent research into efficient simulation algorithms for large spin systems. Liouville space simulations (including symmetry, relaxation and chemical kinetics) of most liquid-state NMR experiments on 40+ spin systems can now be performed without effort on a desktop workstation. Much progress has also been made with improving the efficiency of ESR, solid state NMR and Spin Chemistry simulations. Spinach is available for download at http://spindynamics.org.

Second order gradient ascent pulse engineering

We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of spin ensembles and other quantum systems. These include more accurate gradients, convergence acceleration using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.

Training Schrödinger’s cat: quantum optimal control

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments.

Design Principles and Theory of Paramagnetic Fluorine-Labelled Lanthanide Complexes as Probes for 19F Magnetic Resonance: A Proof-of-Concept Study

The synthesis and spectroscopic properties of a series of CF(3)-labelled lanthanide(III) complexes (Ln=Gd, Tb, Dy, Ho, Er, Tm) with amide-substituted ligands based on 1,4,7,10-tetraazacyclododecane are described. The theoretical contributions of the (19)F magnetic relaxation processes in these systems are critically assessed and selected volumetric plots are presented. These plots allow an accurate estimation of the increase in the rates of longitudinal and transverse relaxation as a function of the distance between the Ln(III) ion and the fluorine nucleus, the applied magnetic field, and the re-rotational correlation time of the complex, for a given Ln(III) ion. Selected complexes exhibit pH-dependent chemical shift behaviour, and a pK(a) of 7.0 was determined in one example based on the holmium complex of an ortho-cyano DO3A-monoamide ligand, which allowed the pH to be assessed by measuring the difference in chemical shift (varying by over 14 ppm) between two (19)F resonances. Relaxation analyses of variable-temperature and variable-field (19)F, (17)O and (1)H NMR spectroscopy experiments are reported, aided by identification of salient low-energy conformers by using density functional theory. The study of fluorine relaxation rates, over a field range of 4.7 to 16.5 T allowed precise computation of the distance between the Ln(III) ion and the CF(3) reporter group by using global fitting methods. The sensitivity benefits of using such paramagnetic fluorinated probes in (19)F NMR spectroscopic studies are quantified in preliminary spectroscopic and imaging experiments with respect to a diamagnetic yttrium(III) analogue.

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.

Polynomially scaling spin dynamics II: further state-space compression using Krylov subspace techniques and zero track elimination

We extend the recently proposed state-space restriction (SSR) technique for quantum spin dynamics simulations [Kuprov et al., J. Magn. Reson. 189 (2007) 241-250] to include on-the-fly detection and elimination of unpopulated dimensions from the system density matrix. Further improvements in spin dynamics simulation speed, frequently by several orders of magnitude, are demonstrated. The proposed zero track elimination (ZTE) procedure is computationally inexpensive, reversible, numerically stable and easy to add to any existing simulation code. We demonstrate that it belongs to the same family of Krylov subspace techniques as the well-known Lanczos basis pruning procedure. The combined SSR+ZTE algorithm is recommended for simulations of NMR, EPR and Spin Chemistry experiments on systems containing between 10 and 10(4) coupled spins.

Long-lived nuclear singlet order in near-equivalent 13c spin pairs

Molecules that support (13)C singlet states with lifetimes of over 10 min in solution have been designed and synthesized. The (13)C(2) spin pairs in the asymmetric alkyne derivatives are close to magnetic equivalence, so the (13)C long-lived singlet states are stable in high magnetic field and do not require maintenance by a radiofrequency spin-locking field. We suggest a model of singlet relaxation by fluctuating chemical shift anisotropy tensors combined with leakage associated with slightly broken magnetic equivalence. Theoretical estimates of singlet relaxation rates are compared with experimental values. Relaxation due to antisymmetric shielding tensor components is significant.

Variable angle NMR spectroscopy and its application to the measurement of residual chemical shift anisotropy

The successful measurement of anisotropic NMR parameters like residual dipolar couplings (RDCs), residual quadrupolar couplings (RQCs), or residual chemical shift anisotropy (RCSA) involves the partial alignment of solute molecules in an alignment medium. To avoid any influence of the change of environment from the isotropic to the anisotropic sample, the measurement of both datasets with a single sample is highly desirable. Here, we introduce the scaling of alignment for mechanically stretched polymer gels by varying the angle of the director of alignment relative to the static magnetic field, which we call variable angle NMR spectroscopy (VA-NMR). The technique is closely related to variable angle sample spinning NMR spectroscopy (VASS-NMR) of liquid crystalline samples, but due to the mechanical fixation of the director of alignment no sample spinning is necessary. Also, in contrast to VASS-NMR, VA-NMR works for the full range of sample inclinations between 0° and 90°. Isotropic spectra are obtained at the magic angle. As a demonstration of the approach we measure ¹³C-RCSA values for strychnine in a stretched PDMS/CDCl₃ gel and show their usefulness for assignment purposes. In this context special care has been taken with respect to the exact calibration of chemical shift data, for which three approaches have been derived and tested.

Probing the structure, conformation, and stereochemical exchange in a family of lanthanide complexes derived from tetrapyridyl-appended cyclen

A series of lanthanide complexes have been synthesized from 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraazacyclododecane. Crystallographic studies indicate that, in the solid phase, all of the lanthanide ions are 9-coordinate and are bound to eight N atoms from the donor ligand, with the ninth site being filled by a counterion or solvent molecule. In solution, time-resolved luminescence studies indicate that the luminescence exhibits contributions from two species corresponding to the nonhydrated and hydrated forms. The NMR spectra in protic media show the presence of two dominant isomers on the NMR time scale; furthermore, the spectra are very different from those obtained for 1,4,7,10-tetraazacyclododecane-N,N,N,N-tetraacetic acid (DOTA) and its derivatives. The different forms of the complex undergo slow conformational and enantiomeric exchange in solution, which has been measured by NMR. The exchange path has been mapped out by density functional theory calculations and shows multiple metastable conformations (with respect to the dihedral angles of the cyclen ring). This contrasts with the established NMR behavior of DOTA complexes, which has been described by a two-state solution equilibrium.