(1)H relaxation dispersion in solutions of nitroxide radicals: Effects of hyperfine interactions with (14)N and (15)N nuclei

(1)H relaxation dispersion of decalin and glycerol solutions of nitroxide radicals, 4-oxo-TEMPO-d(16)-(15)N and 4-oxo-TEMPO-d(16)-(14)N was measured in the frequency range of 10 kHz-20 MHz (for (1)H) using STELAR Field Cycling spectrometer. The purpose of the studies is to reveal how the spin dynamics of the free electron of the nitroxide radical affects the proton spin relaxation of the solvent molecules, depending on dynamical properties of the solvent. Combining the results for both solvents, the range of translational diffusion coefficients, 10(-9)-10(-11) m(2)∕s, was covered (these values refer to the relative diffusion of the solvent and solute molecules). The data were analyzed in terms of relaxation formulas including the isotropic part of the electron spin - nitrogen spin hyperfine coupling (for the case of (14)N and (15)N) and therefore valid for an arbitrary magnetic field. The influence of the hyperfine coupling on (1)H relaxation of solvent molecules depending on frequency and time-scale of the translational dynamics was discussed in detail. Special attention was given to the effect of isotope substitution ((14)N∕(15)N). In parallel, the influence of rotational dynamics on the inter-molecular (radical - solvent) electron spin - proton spin dipole-dipole coupling (which is the relaxation mechanism of solvent protons) was investigated. The rotational dynamics is of importance as the interacting spins are not placed in the molecular centers. It was demonstrated that the role of the isotropic hyperfine coupling increases for slower dynamics, but it is of importance already in the fast motion range (10(-9)m(2)∕s). The isotope effects is small, however clearly visible; the (1)H relaxation rate for the case of (15)N is larger (in the range of lower frequencies) than for (14)N. It was shown that when the diffusion coefficient decreases below 5 × 10(-11) m(2)∕s electron spin relaxation becomes of importance and its role becomes progressively more significant when the dynamics slows done. As far as the influence of the rotational dynamics is concerned, it was show that this process is of importance not only in the range of higher frequencies (like for diamagnetic solutions) but also at low and intermediate frequencies.     

Entanglement generation between two spin-s magnetic impurities in a solid via electron scattering

We present a scheme for generating entanglement between two magnetic impurities in a solid-state system via electron scattering. The scheme applies to impurities of arbitrary quantum spin number. We show that resonance conditions yield generation of a maximally entangled state of the impurities' spins, regardless of the value of the electron–impurity coupling constant and the impurity spin quantum number. The mechanism behind the scheme is explained in terms of resonance-induced selection rules.     

A new mechanism for electron spin echo envelope modulation

Electron spin echo envelope modulation (ESEEM) has been observed for the first time from a coupled heterospin pair of electron and nucleus in liquid solution. Previously, modulation effects in spin-echo experiments have only been described in liquid solutions for a coupled pair of homonuclear spins in nuclear magnetic resonance or a pair of resonant electron spins in electron paramagnetic resonance. We observe low-frequency ESEEM (26 and 52 kHz) due to a new mechanism present for any electron spin with S > 12 that is hyperfine coupled to a nuclear spin. In our case these are electron spin (S = 32) and nuclear spin (I = 1) in the endohedral fullerene N@C(60). The modulation is shown to arise from second-order effects in the isotropic hyperfine coupling of an electron and (14)N nucleus.     

A partially projected wave function for radicals

A partially projected wave function for odd electron systems with quantum number M=1/2, containing μu spin functions α and μ spin functions α, with fractional spin component αS_z=1/2 and 3/2 are derived from the totally projected wave function. To obtain these wave functions new symmetry relations between Sanibel coefficients for the odd electron case have been found, as well as the relations between primitive spin functions and their spin permutations. The wave function for the doublet state is shown not to contain contamination of the quadruplet state, and the wave function for the quadruplet does not have contamination of the duplet. Both wave functions exhibit equal forms except in the signs of their summation terms. The number of primitive spin functions depends on the number of electrons (n_s), it grows linearly as n_s=(N+3)/2. It can be considered as a generalization of the half projected Hartree–Fock wave function to the odd electron case. The HPHF wave function is defined for even electron systems and consists of only two Slater determinants, it has been shown to introduce some correlation effects and it has been successfully applied to calculate the low-lying excited states of molecules. Therefore, this investigation is the first step to propose a method to calculate the excited states of radicals when other methods are impracticable. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fourier synthesis techniques for NMR spectroscopy in inhomogeneous fields

This paper describes a method for synthesizing spin rotations with arbitrary space dependence on a sample of noninteracting spin 12 by using nonselective radio frequency pulses and pulsed field gradients. This method is used to map out spatial distribution of inhomogeneous B(0) field and to engineer a space dependent evolution of spins that cancels the space dependent phase spins acquire when precessing in an inhomogeneous magnetic field. The technique allows one to record high resolution spectra in inhomogeneous magnetic field by using only time varying linear gradients and rf fields and is expected to find applications in ex situ NMR.     

How deeply are core electrons perturbed when valence electrons are spin polarized? The case study of transition metal compounds

The ferromagnetic and antiferromagnetic wave functions of the KMnF₃ perovskite have been evaluated quantum-mechanically by using an all electron approach and, for comparison, pseudopotentials on the transition metal and the fluorine ions. It is shown that the different number of α and β electrons in the d shell of Mn perturbs the inner shells, with shifts between the α and β eigenvalues that can be as large as 6 eV for the 3s level, and is far from negligible also for the 2s and 2p states. The valence electrons of F are polarized by the majority spin electrons of Mn, and in turn, spin polarize their 1s electrons. When a pseudopotential is used, such a spin polarization of the core functions of Mn and F can obviously not take place. The importance of such a spin polarization can be appreciated by comparing (i) the spin density at the Mn and F nuclear position, and then the Fermi contact constant, a crucial quantity for the hyperfine coupling, and (ii) the ferromagnetic–antiferromagnetic energy difference, when obtained with an all electron or a pseudopotential scheme, and exploring how the latter varies with pressure. This difference is as large as 50% of the all electron datum, and is mainly due to the rigid treatment of the F ion core. The effect of five different functionals on the core spin polarization is documented.     

A new model for Overhauser enhanced nuclear magnetic resonance using nitroxide radicals

Nitroxide free radicals are the most commonly used source for dynamic nuclear polarization (DNP) enhanced nuclear magnetic resonance (NMR) experiments and are also exclusively employed as spin labels for electron spin resonance (ESR) spectroscopy of diamagnetic molecules and materials. Nitroxide free radicals have been shown to have strong dipolar coupling to (1)H in water, and thus result in large DNP enhancement of (1)H NMR signal via the well known Overhauser effect. The fundamental parameter in a DNP experiment is the coupling factor, since it ultimately determines the maximum NMR signal enhancements which can be achieved. Despite their widespread use, measurements of the coupling factor of nitroxide free radicals have been inconsistent, and current models have failed to successfully explain our experimental data. We found that the inconsistency in determining the coupling factor arises from not taking into account the characteristics of the ESR transitions, which are split into three (or two) lines due to the hyperfine coupling of the electron to the (14)N nuclei (or (15)N) of the nitric oxide radical. Both intermolecular Heisenberg spin exchange interactions as well as intramolecular nitrogen nuclear spin relaxation mix the three (or two) ESR transitions. However, neither effect has been taken into account in any experimental studies on utilizing or quantifying the Overhauser driven DNP effects. The expected effect of Heisenberg spin exchange on Overhauser enhancements has already been theoretically predicted and observed by Bates and Drozdoski [J. Chem. Phys. 67, 4038 (1977)]. Here, we present a new model for quantifying Overhauser enhancements through nitroxide free radicals that includes both effects on mixing the ESR hyperfine states. This model predicts the maximum saturation factor to be considerably higher by the effect of nitrogen nuclear spin relaxation. Because intramolecular nitrogen spin relaxation is independent of the nitroxide concentration, this effect is still significant at low radical concentrations where electron spin exchange is negligible. This implies that the only correct way to determine the coupling factor of nitroxide free radicals is to measure the maximum enhancement at different concentrations and extrapolate the results to infinite concentration. We verify our model with a series of DNP experimental studies on (1)H NMR signal enhancement of water by means of (14)N as well as (15)N isotope enriched nitroxide radicals.     

Molecular structure and dynamics of off-center Cu(2+) ions and strongly coupled Cu(2+)-Cu(2+) pairs in BaF(2) crystals: electron paramagnetic resonance and electron spin relaxation studies

X-band and Q-band electron paramagnetic resonance (EPR) spectra of Cu(2+) in BaF(2) crystal were recorded in the temperature range of 4.2-200 K. Spin-Hamiltonian parameters of single Cu(2+) complexes and of Cu(2+)-Cu(2+) pairs were derived and discussed. A special attention was paid to the dimeric species. Their molecular ground state configuration was found as having antiferromagnetic intradimer coupling with the singlet-triplet splitting J=-35 cm(-1). The zero-field splitting being D=0.0365 cm(-1) at 4.2 K increases with temperature as an effect of thermal population of excited dimer configurations. Electron spin echo (ESE) method was used for measurements of electron spin lattice and phase relaxation. The spin-lattice relaxation data show that except for coupling to the host lattice phonons the Cu(2+) ions are involved in local mode motions with energy of 82 cm(-1). Phase relaxation (ESE dephasing) of single Cu(2+) ions is due to spin diffusion at low temperatures. This relaxation is hampered for temperatures higher than 30 K due to the triplet state population of neighboring Cu(2+)-Cu(2+) dimers, which disturb dipolar coupling between Cu(2+) ions. For higher temperatures the relaxation is dominated by Raman T(1) processes. Fourier transform ESE spectrum displays dipolar Cu-F splitting which allowed determination of the off-center shift of Cu(2+) as delta(s)=0.132 nm. The dynamical effects observed in EPR spectra and in electron spin relaxation both for single Cu(2+) ions and Cu(2+)-Cu(2+) pairs are discussed as due to jumps between six off-center positions in the crystal unit cell and jumps between various dimer configurations.     

Entangled electron and nuclear spin states in 15N@C60: density matrix tomography

Procedures of the preparation and detection of entangled electron-nuclear spin states in (15)N@C(60) by combining electron spin resonance and electron nuclear double resonance pulse techniques are presented. A quantitative evaluation of the complete density matrix is obtained by a special density matrix tomography. All four Bell states of a two qubit subsystem were analyzed and experimental decoherence times are presented. In addition, we estimate a quantum critical temperature of T(q)=7.76 K for this system at an electron spin resonance frequency of 95 GHz.     

An investigation of the molecular geometry and electronic structure of nitryl chloride by a combination of rotational spectroscopy and ab initio calculations

The ground-state rotational spectra of the six isotopomers (16)O(2) (14)N(35)Cl, (16)O(2) (14)N(37)Cl, (18)O(16)O(14)N(35)Cl, (18)O(2) (14)N(35)Cl, (16)O(2) (15)N(35)Cl, and (16)O(2) (15)N(37)Cl of nitryl chloride were observed with a pulsed-jet, Fourier-transform microwave spectrometer to give rotational constants, Cl and (14)N nuclear quadrupole coupling, and spin-rotation coupling constants. These spectroscopic constants were interpreted to give r(0), r(s), and r(m) ((2)) versions of the molecular geometry and information about the electronic redistribution at N when nitryl chloride is formed from NO(2) and a Cl atom. The r(m) ((2)) geometry has r(N-Cl)=1.8405(6) A, r(N-O)=1.1929(2) A, and the angle ONO=131.42(4) degrees , while the corresponding quantities for the r(s) geometry are 1.8489 A, 1.1940 A, and 131.73 degrees , respectively. Electronic structure calculations at CCSD(T)cc-pVXZ (X=T, Q, or 5) levels of theory were carried out to give a r(e) geometry, vibration-rotation corrections to equilibrium rotational constants, and values of the (35)Cl and (14)N nuclear hyperfine (quadrupole and spin-rotation) coupling constants in good agreement with experiment. The equilibrium geometry at the CCSD(T)/cc-pV5Z level of theory has r(N-Cl)=1.8441 A, r(N-O)=1.1925 A and the angle ONO=131.80 degrees . The observed rotational constants were corrected for the vibration-rotation effects calculated ab initio to yield semiempirical equilibrium constants which were then fitted to give the following semiempirical equilibrium geometry: r(N-Cl)=1.8467(2) A, r(N-O)=1.1916(1) A, and the angle ONO=131.78(3) degrees .     

The electronic structure of the flavin cofactor in DNA photolyase.

Density functional theory is used to calculate the electronic structure of the neutral flavin radical, FADH(*), formed in the light-induced electron-transfer reaction of DNA repair in cis,syn-cyclobutane pyrimidine dimer photolyases. Using the hybrid B3LYP functional together with the double-zeta basis set EPR-II, (1)H, (13)C, (15)N, and (17)O isotropic and anisotropic hyperfine couplings are calculated and explained by reference to the electron densities of the highest occupied molecular orbital and of the unpaired spin distribution on the radical. Comparison of calculated and experimental hyperfine couplings obtained from EPR and ENDOR/TRIPLE resonance leads to a refined structure for the FAD cofactor in Escherichia coli DNA photolyase. Hydrogen bonding at N3H, O4, and N5H results in significant changes in the unpaired spin density distribution and hyperfine coupling constants. The calculated electronic structure of FADH(*) provides evidence for a superexchange-mediated electron transfer between the cyclobutane pyrimidine dimer lesion and the 7,8-dimethyl isoalloxazine moiety of the flavin cofactor via the adenine moiety.     

On the vibronic coupling approximation: a generally applicable approach for determining fully quadratic quasidiabatic coupled electronic state Hamiltonians

In this report we introduce an iterative procedure for constructing a quasidiabatic Hamiltonian representing N(state)-coupled electronic states in the vicinity of an arbitrary point in N(int)-dimensional nuclear coordinate space. The Hamiltonian, which is designed to compute vibronic spectra employing the multimode vibronic coupling approximation, includes all linear terms which are determined exactly using analytic gradient techniques. In addition, all [N(state)][N(int)] quadratic terms, where [n]=n(n+1)/2, are determined from energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. The use of energy gradient and derivative coupling information enables the large number of second order parameters to be determined employing ab initio data computed at a limited number of points (N(int) being minimal) and assures a maximal degree of quasidiabaticity. Numerical examples are given in which quasidiabatic Hamiltonians centered around three points on the C(3)H(3)N(2) potential energy surface (the minimum energy point on the ground state surface and the minimum energy points on the two- and three-state seams of conical intersection) were computed and compared. A method to modify the conical intersection based Hamiltonians to better describe the region of the ground state minimum is introduced, yielding improved agreement with ab initio results, particularly in the case of the Hamiltonian defined at the two-state minimum energy crossing.     

Generalized electron number distribution functions: real space versus orbital space descriptions

The algebraic expressions previously derived to compute the electron number distribution functions (EDF) for exhaustive partitions of the physical space into sharp-boundary atoms are generalized to allow for the use of fuzzy atoms and orbital-based partitions. In some of the latter, the atomic overlap matrix required to obtain the EDF is analytical. This makes them attractive alternatives to other definitions, as the one based on the atomic basins of the quantum theory of atoms in molecules (QTAIM), which are more physically sound but also much more demanding computationally. We will compute the EDF for a series of test molecules using different fuzzy and orbital-based partitions and compare them to QTAIM EDF. The effects of electron correlation and the use of the core approximation on the EDF will also be explored.     

Unpaired spin densities from NMR shifts and magnetic anisotropies of pseudotetrahedral cobalt(II) and nickel(II) vinamidine bis(chelates)

The distribution of unpaired electron spin over all regions of the organic ligands was extracted from the large positive and negative 1H and 13C NMR paramagnetic shifts of the title complexes. Owing to benevolent line broadening and to very high sensitivities of approximately 254,000 and approximately 201,000 ppm/(unpaired electron spin) for Co(II) and Ni(II), respectively, at 298 K in these pseudotetrahedral bis(N,N'-chelates), spin transmission through the sigma- (and orthogonal pi)-bonding system of the ligands could be traced from the chelate ring over five to nine sigma bonds. Most of those "experimental" spin densities DeltarhoN (situated at the observed nuclei) agree reasonably well with quantum chemical DeltarhoDFT (DFT = density functional theory) values and provide an unsurpassed number of benchmark values for the quality of certain types of modern density functionals. The extraction of DeltarhoN became possible through the unequivocal separation of the nuclear Fermi contact shift components from the metal-centered pseudocontact shifts, which are proportional to the anisotropy Deltachi of the magnetic susceptibility: Experimental Deltachi values were obtained in solution from measured deuterium quadrupole splittings in the 2H NMR spectra of two deuterated model complexes and were found to be nonlinear functions of the reciprocal temperature. This provided the reliable basis for predicting metal-centered pseudocontact shifts for any position of a topologically well-defined ligand at varying temperatures. The related ligand-centered pseudocontact shifts were sought by using the criterion of their expected nonlinear dependence on the reciprocal temperature. However, their contributions could not be differentiated from other small effects close to the metal center; otherwise, they appeared to be smaller than the experimental uncertainties. The free activation energy of N-aryl rotation past a vicinal tert-butyl substituent in the Ni(II) vinamidine bis(N,N'-chelates) is DeltaG++(+74 degrees C) approximately 17.0 kcal/mol and past a vicinal methyl group DeltaG++(-6 degrees C) approximately 13.1 kcal/mol.     

电子自旋、微观可区分性及化学键

本文从分析电子自旋磁矩 (磁极 )的空间性质入手,讨论了电子的可区分性。通过讨论2个电子自旋组态的 8种形式,其中,包括 4种磁极吸引的耦合态、4种磁矩排斥的非耦合态,同理,电子轨旋运动也存在 4种耦合态。自旋耦合、轨旋全耦合需要 8个电子,所以元素周期性为 8音律。磁矩耦合是形成化学键的第一要求,第二才是异核吸引作用 ;化学键的广义表达语言应该是:化学键只能由磁矩耦合的电子组成。对电子的波粒二象性和测不准原理进行了新的理论解释,并讨论了波粒二象性和测不准现象的物理模型。该模型与电子的微观可区分性相一致。     

Properties of mixed micelles of cationic gemini surfactants and nonionic surfactant triton X-100: effects of the surfactant composition and the spacer length

The mixed micelles of cationic gemini surfactants C12C(S)C12Br2 (S=3, 6, and 12) with the nonionic surfactant Triton X-100 (TX100) have been studied by steady-state fluorescence, time-resolved fluorescence quenching, electrophoretic light scattering, and electron spin resonance. Both the surfactant composition and the spacer length are found to influence the properties of mixed micelles markedly. The total aggregation number of alkyl chains per micelle (N(T)) goes through a minimum at X(TX100)=0.8. Meanwhile, the micropolarity of the mixed micelles decreases with increasing X(TX100), while the microviscosity increases. The presence of minimum in N(T) is explained in terms of the competition of the reduction of electrostatic repulsion between headgroups of cationic gemini surfactant with the enhancement of steric repulsion between hydrophilic headgroups of TX100 caused by the addition of TX100. The variations of micropolarity and microviscosity indicate that the incorporation of TX100 to the gemini surfactants leads to a more compact and hydrophobic micellar structure. Moreover, for the C12C3C12Br2/TX100 mixed micelle containing C12C3C12Br2 with a shorter spacer, the more pronounced decrease of N(T) at X(TX100) lower than 0.8 may be attributed to the larger steric repulsion between headgroups of TX100. Meanwhile, the increase of microviscosity and the decrease of micropolarity are more marked for the C12C12C12Br2/TX100 mixed micelle, owing to the looped conformation of the longer spacer of C12C12C12Br2.     

PELDOR on an exchange coupled nitroxide copper(II) spin pair

Transition metal ions play an important role in the design of macromolecular architectures as well as for the structure and function of proteins and oligonucleotides, which makes them interesting targets for spectroscopic investigations. In combination with site directed spin labelling, pulsed electron–electron double resonance (PELDOR or DEER) could be a well-suited method for their characterization and localization. Here, we report on the synthesis and full characterization of a copper(II) porphyrin/nitroxide model system bearing an extended π-conjugation between the spin centres and demonstrate the possibility to disentangle the dipolar through space interaction from the through bond exchange coupling contribution even in the presence of orientational selectivity and conformational flexibility. The simulations used are based on the known experimental and spin Hamiltonian parameters and on a structural model as previously employed for similar systems. The mean exchange coupling of +4(1) MHz (antiferromagnetic) is in agreement with the value of |J| = 3(1) MHz determined from room temperature continuous wave electron paramagnetic resonance (EPR). Thus, as long as the pulse excitation bandwidths are large versus the spin–spin coupling, X-band PELDOR measurements in combination with explicit time trace simulations allow for disentangling the sign and magnitude of through bond electron–electron exchange from the through space dipolar interaction D.     

Testing if the interstitial atom, X, of the nitrogenase molybdenum-iron cofactor is N or C: ENDOR, ESEEM, and DFT studies of the S = 3/2 resting state in multiple environments

A high-resolution (1.16 A) X-ray structure of the nitrogenase molybdenum-iron (MoFe) protein revealed electron density from a single N, O, or C atom (denoted X) inside the central iron prismane ([6Fe]) of the [MoFe7S9:homocitrate] FeMo-cofactor (FeMo-co). We here extend earlier efforts to determine the identity of X through detailed tests of whether X = N or C by interlocking and mutually supportive 9 GHz electron spin echo envelope modulation (ESEEM) and 35 GHz electron-nuclear double resonance (ENDOR) measurements on 14/15N and 12/13C isotopomers of FeMo-co in three environments: (i) incorporated into the native MoFe protein environment; (ii) extracted into N-methyl formamide solution; and (iii) incorporated into the NifX protein, which acts as a chaperone during FeMo-co biosynthesis. These measurements provide powerful evidence that X not equal N/C, unless X in effect is magnetically decoupled from the S = 3/2 electron spin system of resting FeMo-co. They reveal no signals from FeMo-co in any of the three environments that can be assigned to X from either 14/15N or 13C: If X were either element, its maximum observed hyperfine coupling at all fields of measurement is estimated to be A(14/15NX) < 0.07/0.1 MHz, A(13CX) < 0.1 MHz, corresponding to intrinsic couplings of about half these values. In parallel, we have explicitly calculated the hyperfine tensors for X = 14/15N/13C/17O, nuclear quadrupole coupling constant e2qQ for X = 14N, and hyperfine constants for the Fe sites of S = 3/2 FeMo-co using density functional theory (DFT) in conjunction with the broken-symmetry (BS) approach for spin coupling. If X = C/N, then the decoupling required by experiment strongly supports the "BS7" spin coupling of the FeMo-co iron sites, in which a small X hyperfine coupling is the result of a precise balance of spin density contributions from three spin-up and three spin-down (3 upward arrow:3 downward arrow) iron atoms of the [6Fe] prismane "waist" of FeMo-co; this would rule out the "BS6" assignment (4 upward arrow:2 downward arrow for [6Fe]) suggested in earlier calculations. However, even with the BS7 scheme, the hyperfine couplings that would be observed for X near g2 are sufficiently large that they should have been detected: we suggest that the experimental results are compatible with X = N only if aiso(14/15NX) < 0.03-0.07/0.05-0.1 MHz and aiso(13CX) < 0.05-0.1 MHz, compared with calculated values of aiso(14/15NX) = 0.3/0.4 MHz and aiso(13CX) = 1 MHz. However, the DFT uncertainties are large enough that the very small hyperfine couplings required by experiment do not necessarily rule out X = N/C.