Isotropic Constants Research Articles

Understanding Thermodynamic and Spectroscopic Properties of Tetragonal Mn12 Single-Molecule Magnets from Combined Density Functional Theory/Spin-Hamiltonian Calculations.

We apply broken-symmetry density functional theory to determine isotropic exchange-coupling constants and local zero-field splitting (ZFS) tensors for the tetragonal Mn12(t)BuAc single-molecule magnet. The obtained parametrization of the many-spin Hamiltonian (MSH), taking into account all 12 spin centers, is assessed by comparing theoretical predictions for thermodynamic and spectroscopic properties with available experimental data. The magnetic susceptibility (calculated by the finite-temperature Lanczos method) is well approximated, and the intermultiplet excitation spectrum from inelastic neutron scattering (INS) experiments is correctly reproduced. In these respects, the present parametrization of the 12-spin model represents a significant improvement over previous theoretical estimates of exchange-coupling constants in Mn12, and additionally offers a refined interpretation of INS spectra. Treating anisotropic interactions at the third order of perturbation theory, the MSH is mapped onto the giant-spin Hamiltonian describing the S = 10 ground multiplet. Although the agreement with high-field EPR experiments is not perfect, the results clearly point in the right direction and for the first time rationalize the angular dependence of the transverse-field spectra from a fully microscopic viewpoint. Importantly, transverse anisotropy of the effective S = 10 manifold is explicitly shown to arise largely from the ZFS-induced mixing of exchange multiplets. This effect is given a thorough analysis in the approximate D2d spin-permutational symmetry group of the exchange Hamiltonian.

Fine structure of a resonantly excitedp-shell exciton in a CdTe quantum dot

We present a polarization-resolved photoluminescence excitation study of the absorption spectrum of a $p$-shell neutral exciton in a single CdTe/ZnTe quantum dot. We find that the fine structure of the $p$-shell exciton is completely analogous to the fine structure of the $s$-shell exciton, including the selection rules and the effects of a magnetic field applied in Faraday and Voigt configurations. The energy spectrum of the $p$-shell exciton is found to be well described by introducing respective isotropic and anisotropic constants of the exchange interaction between a $p$-shell electron and a $p$-shell hole. The typical values of these exchange constants averaged over several randomly selected quantum dots yield ${\ensuremath{\delta}}_{0}^{pp}=(0.92\ifmmode\pm\else\textpm\fi{}0.16)$ meV and ${\ensuremath{\delta}}_{1}^{pp}=(0.58\ifmmode\pm\else\textpm\fi{}0.25)$ meV. Additionally, we demonstrate that the nonresonant relaxation of the $p$-shell exciton conserves the exciton spin to a very high degree for both bright and dark exciton configurations.

Remarks on an inequality of Rogers and Shephard

A classical inequality of Rogers and Shephard states that if K is a centered convex body of volume 1 in Rn then 1 6 g(K, k;F ) := ( volk(PF (K)) voln−k(K ∩ F⊥) )1/k 6 (n k )1/k 6 cn k for every F ∈ Gn,k, where c > 0 is an absolute constant. We show that if K is origin symmetric and isotropic then, for every 1 6 k 6 n − 1, a random F ∈ Gn,k satisfies c1L −1 K √ n/k 6 g(K, k;F ) 6 c2 √ n/k (logn)LK with probability greater than 1 − e−k, where LK is the isotropic constant of K and c1, c2 > 0 are absolute constants.

Communication: spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme.

We report analytical calculations of isotropic hyperfine-coupling constants in radicals using a spin-adapted open-shell coupled-cluster theory, namely, the unitary group based combinatoric open-shell coupled-cluster (COSCC) approach within the singles and doubles approximation. A scheme for the evaluation of the one-particle spin-density matrix required in these calculations is outlined within the spin-free formulation of the COSCC approach. In this scheme, the one-particle spin-density matrix for an open-shell state with spin S and MS = + S is expressed in terms of the one- and two-particle spin-free (charge) density matrices obtained from the Lagrangian formulation that is used for calculating the analytic first derivatives of the energy. Benchmark calculations are presented for NO, NCO, CH2CN, and two conjugated π-radicals, viz., allyl and 1-pyrrolyl in order to demonstrate the performance of the proposed scheme.

Probing the Hydrogen Bonding of the Ferrous-NO Heme Center of nNOS by Pulsed Electron Paramagnetic Resonance.

Oxidation of L-arginine (L-Arg) to nitric oxide (NO) by NO synthase (NOS) takes place at the heme active site. It is of current interest to study structures of the heme species that activates O2 and transforms the substrate. The NOS ferrous-NO complex is a close mimic of the obligatory ferric (hydro)peroxo intermediate in NOS catalysis. In this work, pulsed electron-nuclear double resonance (ENDOR) spectroscopy was used to probe the hydrogen bonding of the NO ligand in the ferrous-NO heme center of neuronal NOS (nNOS) without a substrate and with L-Arg or N-hydroxy-L-arginine (NOHA) substrates. Unexpectedly, no H-bonding interaction connecting the NO ligand to the active site water molecule or the Arg substrate was detected, in contrast to the results obtained by X-ray crystallography for the Arg-bound nNOS heme domain [Li et al. J. Biol. Inorg. Chem. 2006, 11, 753-768]. The nearby exchangeable proton in both the no-substrate and Arg-containing nNOS samples is located outside the H-bonding range and, on the basis of the obtained structural constraints, can belong to the active site water (or OH). On the contrary, in the NOHA-bound sample, the nearby exchangeable hydrogen forms an H-bond with the NO ligand (on the basis of its distance from the NO ligand and a nonzero isotropic hfi constant), but it does not belong to the active site water molecule because the water oxygen atom (detected by (17)O ENDOR) is too far. This hydrogen should therefore come from the NOHA substrate, which is in agreement with the X-ray crystallography work [Li et al. Biochemistry 2009, 48, 10246-10254]. The nearby nonexchangeable hydrogen atom assigned as H(ε) of Phe584 was detected in all three samples. This hydrogen atom may have a stabilizing effect on the NO ligand and probably determines its position.

The benzene radical anion: A computationally demanding prototype for aromatic anions

The benzene radical anion is studied with ab initio coupled-cluster theory in large basis sets. Unlike the usual assumption, we find that, at the level of theory investigated, the minimum energy geometry is non-planar with tetrahedral distortion at two opposite carbon atoms. The anion is well known for its instability to auto-ionization which poses computational challenges to determine its properties. Despite the importance of the benzene radical anion, the considerable attention it has received in the literature so far has failed to address the details of its structure and shape-resonance character at a high level of theory. Here, we examine the dynamic Jahn-Teller effect and its impact on the anion potential energy surface. We find that a minimum energy geometry of C2 symmetry is located below one D2h stationary point on a C2h pseudo-rotation surface. The applicability of standard wave function methods to an unbound anion is assessed with the stabilization method. The isotropic hyperfine splitting constants (Aiso) are computed and compared to data obtained from experimental electron spin resonance experiments. Satisfactory agreement with experiment is obtained with coupled-cluster theory and large basis sets such as cc-pCVQZ.

A SIMPLICIAL POLYTOPE THAT MAXIMIZES THE ISOTROPIC CONSTANT MUST BE A SIMPLEX

The isotropic constant $L_K$ is an affine-invariant measure of the spread of a convex body $K$. For a $d$-dimensional convex body $K$, $L_K$ can be defined by $L_K^{2d} = \det(A(K))/(\mathrm{vol}(K))^2$, where $A(K)$ is the covariance matrix of the uniform distribution on $K$. It is an outstanding open problem to find a tight asymptotic upper bound of the isotropic constant as a function of the dimension. It has been conjectured that there is a universal constant upper bound. The conjecture is known to be true for several families of bodies, in particular, highly symmetric bodies such as bodies having an unconditional basis. It is also known that maximizers cannot be smooth. In this work we study the gap between smooth bodies and highly symmetric bodies by showing progress towards reducing to a highly symmetric case among non-smooth bodies. More precisely, we study the set of maximizers among simplicial polytopes and we show that if a simplicial polytope $K$ is a maximizer of the isotropic constant among $d$-dimensional convex bodies, then when $K$ is put in isotropic position it is symmetric around any hyperplane spanned by a $(d-2)$-dimensional face and the origin. By a result of Campi, Colesanti and Gronchi, this implies that a simplicial polytope that maximizes the isotropic constant must be a simplex.

Dinuclear and polymeric (μ-formato)nickel(II) complexes: Synthesis, structure, spectral and magnetic properties

Two (μ-formato)nickel(II) complexes [Ni2(HCOO)(bz)8(H2O)2](HCOO)3·4H2O (1) and [Ni(tren)(HCOO)]ClO4·H2O (2) were synthesized and characterized by spectroscopic methods. The structure of complexes has been determined by X-ray crystallography. The formato ligand bridges the Ni(II) central atoms forming a dinuclear cation in 1 and a polymeric cationic chain in 2, respectively. The coordination environment of Ni(II) atom is nearly octahedral. Based upon the magnetic data, these two compounds display an exchange interaction of the antiferromagnetic nature along with the zero-field splitting. The results from magnetic analysis of 1 and 2, namely the isotropic exchange constants and the zero-field splitting parameters were further confirmed and studied by DFT method using at B3LYP/def2-TZVP and by CASSCF/NEVPT2, respectively.

Microscopic description of twisted magnet Cu2OSeO3

Twisted structures of chiral cubic ferromagnets MnSi and Cu2OSeO3 can be described both in the frame of the phenomenological Ginzburg–Landau theory and using the microscopical Heisenberg formalism with a chirality arising from the Dzyaloshinskii–Moriya (DM) interaction. Recent progress in quantum first-principal methods allows us to calculate interatomic bond parameters of the Heisenberg model, namely isotropic exchange constants Jij and DM vectors Dij, which can be used for simulations of observed magnetic textures and comparison of their calculated characteristics, such as magnetic helix sense and pitch, with an experimental data. In the present work, it is found that unaveraged microscopical details of the spin structures (local canting) have a strong impact on the global twist and can significantly change the helix propagation number. Coefficients J and D of the phenomenological theory and helix propagation number k=D/2J are derived from interatomic parameters Jij and Dij of individual bonds for MnSi and Cu2OSeO3 crystals and similar cubic magnets with almost collinear spins.

EPR, ESE, and pulsed ENDOR study of the nitrogen donors in 15R SiC grown under carbon‐rich conditions

X‐band field‐sweep electron spin echo and pulsed electron nuclear double resonance (ENDOR) spectroscopy were used to study n‐type 15R SiC wafers grown under carbon (C)‐rich conditions with the aim to verify the recently proposed concept that nitrogen (N) donors substitute both carbon (C) and silicon (Si) sites and may occupy nonequivalent positions at Si sites. It was found that besides the 14N ENDOR spectra of the C substituting quasicubic “k1”, “k2”, and “k3” positions five doublet lines due to 14N nuclei at other lattice positions were observed in the ENDOR spectrum of highly compensated C‐rich n‐type 15R SiC. Three of them with the hyperfine interaction (HFI) constants 34.66, 32.20, and 29.77 MHz were attributed to the N donors substituting “k1”, “k2”, and “k3” positions at Si sites. Two other additional ENDOR spectra were explained by the presence of the C antisite (CSi) defects in C‐rich 15R SiC, which leads to the formation of CSiNC complexes with donor levels close to the conduction‐band minimum and isotropic 14N HFI constants of 21.58 and 25.94 MHz. The energy levels of N donors have been evaluated by comparing the number of ENDOR spectra observed in C‐rich 15R SiC with different degrees of compensation.

An isomorphic version of the Busemann–Petty problem for arbitrary measures

The Busemann–Petty problem for an arbitrary measure $$\mu $$ with non-negative even continuous density in $${\mathbb R}^n$$ asks whether origin-symmetric convex bodies in $${\mathbb R}^n$$ with smaller $$(n-1)$$ -dimensional measure $$\mu $$ of all central hyperplane sections necessarily have smaller measure $$\mu .$$ It was shown in Zvavitch (Math Ann 331:867–887, 2005) that the answer to this problem is affirmative for $$n\le 4$$ and negative for $$n\ge 5$$ . In this paper we prove an isomorphic version of this result. Namely, if $$K,M$$ are origin-symmetric convex bodies in $${\mathbb R}^n$$ such that $$\mu (K\cap \xi ^\bot )\le \mu (M\cap \xi ^\bot )$$ for every $$\xi \in {\mathbb S}^{n-1},$$ then $$\mu (K)\le \sqrt{n} \mu (M).$$ Here $$\xi ^\bot $$ is the central hyperplane perpendicular to $$\xi .$$ We also study the above question with additional assumptions on the body $$K$$ and present the complex version of the problem. In the special case where the measure $$\mu $$ is convex we show that $$\sqrt{n}$$ can be replaced by $$cL_n,$$ where $$L_n$$ is the maximal isotropic constant. Note that, by a recent result of Klartag, $$L_n \le O(n^{1/4})$$ . Finally we prove a slicing inequality $$\begin{aligned} \mu (K)\le C n^{1/4} \max _{\xi \in {\mathbb S}^{n-1}} \mu (K \cap \xi ^\perp ) \mathrm{vol}_{n}(K)^{\frac{1}{n}} \end{aligned}$$ for any convex even measure $$\mu $$ and any symmetric convex body $$K$$ in $${\mathbb R}^n,$$ where $$C$$ is an absolute constant. This inequality was recently proved in Koldobsky (Adv Math 254:33–40, 2014) for arbitrary measures with continuous density, but with $$\sqrt{n}$$ in place of $$n^{1/4}.$$

Neighborhoods on the Grassmannian of marginals with bounded isotropic constant

We show that for any isotropic log-concave probability measure μ on Rn, for every ε>0, every 1⩽k⩽n and any E∈Gn,k there exists F∈Gn,k with d(E,F)<ε and LπFμ<C/ε.

Estimates for the extremal sections of complex "Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML" -balls

Abstract The problem of maximal hyperplane section of B p ( C n ) with p ≥ 1 is considered, which is the complex version of central hyperplane section problem of B p ( R n ) . The relation between the complex slicing problem and the complex isotropic constant of a body is established, an upper bound estimate for the volume of complex central hyperplane sections of normalized complex ℓ p ( C n ) -balls that does not depend on n and p is shown, which extends results of Oleszkiewicz and Pełczyński, Koldobsky and Zymonopoulou, and Meyer and Pajor. MSC:52A21, 46B07.

Optical size effect of organic nanocrystals studied by absorption spectroscopy within an integrating sphere

The size effect of the optical absorption in one of the most typical organic nanocrystals, α-perylene, was studied. The true absorption spectra of nanocrystals suspended in water were measured within an integrating sphere by collecting the whole scattered light. It was experimentally confirmed that the absorption spectra show blueshift as the crystal size is decreased. This was reproduced by the size-dependent absorption spectra calculated for spherical nanocrystals with isotropic and anisotropic dielectric constants to elucidate three mechanisms of the blueshift: size-dependent change in the shape anisotropy of the crystals, longitudinal–transverse mixing, and light propagation effects including scattering on absorption.

The Structure and EPR Behavior of Short Nitroxide Biradicals Containing Sulfur Atom in the Bridge

Two short nitroxide biradicals of similar composition: S(OR6)2 (1) and O=S(OR6)2 (2), where OR6 is 1-oxyl-2,2,6,6-tetramethyl-4-oxypiperidine, have been studied by electron paramagnetic resonance spectroscopy, and X-ray structural analysis. Variations of the intramolecular electron spin exchange in the biradicals, dissolved in toluene and ethanol, as a function of temperature were characterized by changes in the isotropic 14N hyperfine splitting constant a, values of the exchange integral \( \left| J \right|, \) and compared with the X-ray structural data. Thermodynamic parameters of the conformational rearrangements were calculated. Geometry optimization and spin density distribution calculations of biradicals 1 and 2 were carried out on the DFT/UB3LYP/cc-pVdz and DFT/ROPBE/N07D levels of theory. Structural rigidity and probable differences in biradicals behavior are discussed.

On the Mean-Width of Isotropic Convex Bodies and their Associated Lp-Centroid Bodies

For any origin-symmetric convex body $K$ in $\mathbb{R}^n$ in isotropic position, we obtain the bound: \[ M^*(K) \leq C \sqrt{n} \log(n)^2 L_K ~, \] where $M^*(K)$ denotes (half) the mean-width of $K$, $L_K$ is the isotropic constant of $K$, and $C>0$ is a universal constant. This improves the previous best-known estimate $M^*(K) \leq C n^{3/4} L_K$. Up to the power of the $\log(n)$ term and the $L_K$ one, the improved bound is best possible, and implies that the isotropic position is (up to the $L_K$ term) an almost $2$-regular $M$-position. The bound extends to any arbitrary position, depending on a certain weighted average of the eigenvalues of the covariance matrix. Furthermore, the bound applies to the mean-width of $L_p$-centroid bodies, extending a sharp upper bound of Paouris for $1 \leq p \leq \sqrt{n}$ to an almost-sharp bound for an arbitrary $p \geq \sqrt{n}$. The question of whether it is possible to remove the $L_K$ term from the new bound is essentially equivalent to the Slicing Problem, to within logarithmic factors in $n$.

Identification of an isolated arsenic antisite defect in GaAsBi

Optically detected magnetic resonance and photoluminescence spectroscopy are employed to study grown-in defects in GaAs0.985Bi0.015 epilayers grown by molecular beam epitaxy. The dominant paramagnetic defect is identified as an isolated arsenic antisite, AsGa, with an electron g-factor of 2.03 ± 0.01 and an isotropic hyperfine interaction constant A = (900 ± 20) × 10−4 cm−1. The defect is found to be preferably incorporated during the growth at the lowest growth temperature of 270 °C, but its formation can be suppressed upon increasing growth temperature to 315 °C. The AsGa concentration is also reduced after post-growth rapid thermal annealing at 600 °C.

NMR shielding constants in SeH2 and TeH2

Ab initio values of nuclear magnetic resonance shielding constants in SeH2 and TeH2 are calculated. We analyse the role of electron correlation, the magnitude of relativistic effects, the dependence of these results on the basis set and, in addition, the rovibrational effects. The relativistic effects on the isotropic shielding constants calculated with the Dirac–Coulomb Hamiltonian at the Hartree–Fock and Spin-Density Functional Theory levels are very similar, and the electron correlation effects are much smaller. For both molecules, however, the electron correlation contribution to the anisotropy of the heavy atom shielding is much more significant than for the isotropic constant. The total shielding constants derived by adding to the non-relativistic coupled-cluster values the Dirac–Hartree–Fock values of the relativistic effects, σ300 K iso(Se) = 2447 ppm and σ300 K iso(Te) = 4809 ppm, may be applied to define the absolute shielding scales for these heavy nuclei.

Further Unifying Two Approaches to the Hyperplane Conjecture

We compare and combine two approaches that have been recently introduced by Dafnis and Paouris [DP] and by Klartag and Milman [KM] with the aim of providing bounds for the isotropic constants of convex bodies. By defining a new hereditary parameter for all isotropic log-concave measures, we are able to show that the method in [KM], and the apparently stronger conclusions it leads to, can be extended in the full range of the 'weaker' assumptions of [DP]. The new parameter we define is related to the highest dimension k\leq n-1 in which one can always find marginals of an n-dimensional isotropic measure which have bounded isotropic constant.

Detection of Absolute Motion through Measurement of Synchronization Offsets

An absolute reference frame may be defined as the one which is stationary with respect to the center of mass of the Universe and in which speed of propagation of light is an isotropic constant. Any motion with respect to this frame may be referred as absolute motion. In this paper we examine the Sagnac effect of absolute motion in the context of clock synchronization through GPS satellites in common view mode. The e-synchronization of two clocks A and B amounts to introduction of time offsets such that the time taken by a light pulse to propagate between A and B will be measured to be the same in both directions. Synchronization of two clocks through a GPS satellite in common view mode is effectively equivalent to e-synchronization of these clocks and introduces an absolute synchronization mismatch proportional to the absolute velocity and length of the baseline. Measurement of this synchronization offset between the GPS synchronized clocks at the ends of a long baseline will enable the practical detection of absolute motion of earth. Here we propose a simple experiment for detection of absolute motion through measurement of absolute synchronization offsets between two timing laboratories maintaining UTC time.