Dependence Of Coupling Constants Research Articles

Bound States of Energy Dependent Singular Potentials

We consider attractive power-law potentials depending on energy through their coupling constant. These potentials are proportional to 1/|x| m with m ≥ 1 in the D = 1 dimensional space, to 1/r m with m ≥ 2 in the D = 3 dimensional space. We study the ground state of such potentials. First, we show that all singular attractive potentials with an energy dependent coupling constant are bounded from below, contrarily to the usual case. In D = 1, a bound state of finite energy is found with a kind of universality for the eigenvalue and the eigenfunction, which become independent on m for m > 1. We prove the solution to be unique. A similar situation arises for D = 3 for m > 2, except that, in this case, the solution is not directly comparable to a bound state: the wave function, though square integrable, diverges at the origin.

Role of zero-point vibrational corrections to carbon hyperfine coupling constants in organic π radicals

By analyzing a set of organic π radicals, we demonstrate that zero-point vibrational corrections give significant contributions to carbon hyperfine coupling constants, in one case even inducing a sign reversal for the coupling constant. We discuss the implications of these findings for the computational analysis of electron paramagnetic spectra based on hyperfine coupling constants evaluated at the equilibrium geometry of radicals. In particular, we note that a dynamical description that involves the nuclear motion is in many cases necessary in order to achieve a semi-quantitatively predictive theory for carbon hyperfine coupling constants. In addition, we discuss the implications of the strong dependence of the carbon hyperfine coupling constants on the zero-point vibrational corrections for the selection of exchange-correlation functionals in density functional theory studies of these constants.

Orbital-dependent Rashba coupling in bulk BiTeCl and BiTeI

By all-electron ab initio calculations, the layered polar semiconductor BiTeCl is shown to host giant bulk Rashba spin splitting, similar to the recently reported compound BiTeI. In both materials, the standard Rashba–Bychkov model is no longer applicable, because of huge band extrema shifts even in the absence of spin–orbit coupling and a strong momentum dependence of the Rashba coupling constant (αR). By assuming αR to be orbital dependent, a phenomenological extension of the Rashba–Bychkov model is proposed which explains the splitting behavior of states with small in-plane momentum.

Communication: On the isotope anomaly of nuclear quadrupole coupling in molecules

The dependence of the nuclear quadrupole coupling constants (NQCC) on the interaction between electrons and a nucleus of finite size is theoretically analyzed. A deviation of the ratio of the NQCCs obtained from two different isotopomers of a molecule from the ratio of the corresponding bare nuclear electric quadrupole moments, known as quadrupole anomaly, is interpreted in terms of the logarithmic derivatives of the electric field gradient at the nuclear site with respect to the nuclear charge radius. Quantum chemical calculations based on a Dirac-exact relativistic methodology suggest that the effect of the changing size of the Au nucleus in different isotopomers can be observed for Au-containing molecules, for which the predicted quadrupole anomaly reaches values of the order of 0.1%. This is experimentally detectable and provides an insight into the charge distribution of non-spherical nuclei.

Analysis of the interactions between difluoroacetylene and one or two hydrogen fluoride molecules based on calculated spin–spin coupling constants

A theoretical study of FCCF:(HF)n complexes, with n=1 and 2, has been carried out by means of ab initio computational methods. Two types of complexes are formed: those with FH⋯π interactions and those with FH⋯FC hydrogen bonds. The indirect spin–spin coupling constants have been calculated at the CCSD/aug-cc-pVTZ-J computational level. Special attention has been paid to the dependence of the different intramolecular coupling constants in FCCF on the distance between the coupled nuclei and the presence or absence of the hydrogen fluoride molecule. The sensitivity shown by these coupling constants to the presence of hydrogen fluoride is quite notorious.

Broken symmetry DFT calculations of exchange coupling constants for manganese–porphyrin quasi-one-dimensional molecular magnets

We report the results of broken symmetry density functional theory (BS-DFT) calculations providing the exchange coupling constants for two quasi-one-dimensional manganese–porphyrin compounds, [MnOEP][HCBD] and [MnTtBuPP][HCBD] (OEP = octaethylporphyrinato, TtBuPP = meso-tetrakis-(4′-tert-butylphenyl)porphinato, HCBD = hexa-cyanobutadiene). The different magnetic behaviour of these materials is due mainly to the distinct binding modes of the cyanocarbon unit. We compare and contrast the results of BS-DFT calculations for magnetic dinuclears, which properly model the actual molecular magnets, to determine the geometry dependence of the exchange interaction. The exchange coupling constants resulting from BS-DFT calculations vary strongly with the functional used, hybrid functionals such as B3LYP leading to results that better correlate with the constants determined experimentally. Structure-properties correlations reveal the determinant role of the Mn–(N≡C)TCNE bond angle on the ferrimagnetic coupling between the S 1 = 2 spin located on the MnIII–porphyrin donor and the S 2 = 1/2 spin positioned on the cyanocarbon acceptor. Based on a phenomenological model providing the geometry dependence of the exchange coupling constants, we fitted the results of the DFT calculations and obtained parameters describing the ferromagnetic and the antiferromagnetic parts of the superexchange interaction. The large differences between the magnetic properties of the two Mn–HCBD systems are explained based on the correlation between the exchange coupling constant and the overlap between the Mn(III) d and the HCBD π* orbitals and on the torsion angle of the butadiene backbone, which affects dramatically the nature of the π* orbital in the case of the nonplanar HCBD.

Theoretical studies of the dependence of nuclear quadrupole coupling constants on intermolecular forces

We study the performance of density functional methods in the calculation of nuclear quadrupole coupling constants (NQCCs), focusing on the effects of weak intermolecular forces. We begin with an analysis of isolated molecule values, comparing the density functional theory (DFT) results for uracil and thymine obtained by applying 11 different functionals with the Møller–Plesset second-order perturbation theory (MP2) values and with accurate experimental data. Next, using a subset of these DFT functionals we examine the interaction-induced changes of NQCCs for weak solute–solvent interactions, with the solvent effect described as a function of the dielectric constant; for adenine–thymine and guanine–cytosine complexes, in which we observe significant effects due to proton transfer in the hydrogen bonds, and for a hexamine complex in the solid state. Three applied DFT functionals provide a similar, satisfying description of the influence of intermolecular forces on the quadrupole coupling constants, in particular when hydrogen bonding leads to large changes of these constants.

Coupled cluster and DFT calculations of 14N nuclear quadrupole coupling constants

AbstractThe dependence of 14N quadrupole coupling constants calculated using coupled cluster theory on the level of approximation is examined for a series of small molecules. For HCN, HNC, CH3CN, and CH3NC, we use the coupled cluster singles‐and‐doubles with a noniterative perturbative triples correction—CCSD(T)—approach, and we analyze the basis set dependence of the results. For aziridine, diazirine, and cyclopropyl cyanide, we use the CCSD(T) approach, but smaller basis sets, and for the largest studied molecules—quinuclidine and hexamine—we present CCSD results. The differences between computed and experimental values for the best basis sets used are ≈ 5% at the CCSD level and decrease noticeably at the CCSD(T) level. The ‐ N≡C bonds are an exception—in this case the quadrupole coupling constants are very small, hence the differences between theory and experiment become larger (up to 9%). We also consider the performance of density functional theory, comparing the results for different density functionals with the coupled cluster values of the same constants. Most of the functionals provide results systematically improved with respect to the Hartree–Fock values, with 14N coupling constants in ‐ N≡C bonds being again an exception. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

First-principles study of phonon linewidths in noble metals

Phonon lifetimes in Cu, Ag, and Au at low and high temperatures were calculated along high symmetry directions using density functional theory combined with second-order perturbation theory. Both harmonic and third-order anharmonic force constants were computed using a supercell small displacement method, and the two-phonon densities of states were calculated for all three-phonon processes consistent with the kinematics of energy and momentum conservation. A nonrigorous Gr\"uneisen model with no $q$-dependence of the anharmonic coupling constants offers a simple separation of the potential and the kinematics, and proved semiquantitative for Cu, Ag, and Au. A rule is reported for finding the most anharmonic phonon mode in fcc metals.

Room-Temperature Ionic Liquids Discerned Via Nitroxyl Spin Probe Dynamics

The temperature dependence of the rotational correlation times, τ(c), of the nitroxide spin probes TEMPO, TEMPOL, TEMPAMINE, and Fremy's salt in the ionic liquids 1-ethyl-3-methylimidazolium ethylsulfate, 1-butyl-3-methylimidazolium hexafluorophosphate, 1-ethyl-3-methylimidazolium tetrafluoroborate, and 1-butyl-3-methylimidazolium tetrafluoroborate is scrutinized. The rotation correlation times vary between 54 and 1470 ps at 300 K. Within a temperature range of 280-380 K, the rotational tumbling is well described by the extended Debye-Stokes-Einstein law. The hydrodynamic radii are smaller than the geometrical radii though. This discrepancy can partly be accounted for by microviscosity effects and deviations from the spherical shape. This study is distinguished from similar studies by the fact that proton superhyperfine coupling constants could be resolved for all nitroxides in the ionic liquids by carefully optimizing the experimental protocol. As a consequence, many rotational correlation times reported here are smaller than those found previously. Furthermore, the temperature dependence of the nitrogen ESR coupling constants is reported and discussed in detail. A surprising effect of adventitious water is reported for TEMPAMINE.

Geometrical Embedding Governs a Dramatic Variation of Electron Paramagnetic Resonance Hyperfine Coupling Constants of Disulfide Radical Anions

Among the large variety of experimental techniques amenable to probe disulfide radical anions, electron paramagnetic resonance (EPR) spectroscopy provides the most definitive assignment of these versatile transient intermediates in biochemistry [Stubbe et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 8979-84; J. Am. Chem. Soc. 2009, 131, 200-211]. EPR parameters along both a series of 12 aliphatic 1,2-dithia-cycloalkane radical anions and a representative set of 18 short-loop peptides are investigated by means of density functional theory. While the g-tensor remains quasi-isotropic (with diagonal terms very close to 2.0, as expected for a σ* singly occupied orbital), we evidence a dramatic conformational dependence of isotropic sulfur hyperfine coupling constants (hcc). Potential energy surface exploration of the prototypical dimethyldisulfide rationalizes their 3-4-fold amplitude, with values ranging between 10 and 29 G for aliphatic moieties. Sulfur hcc's are readily decomposed into three geometrical components: intersulfur distance, dihedral, and valence angles, with the latter being predominant. Increasing (respectively decreasing) contribution of sulfur atomic s orbital to the σ* molecular orbital, with a concomitant higher (respectively weaker) density around the sulfur nuclei, can be monitored on Walsh diagrams along each degree of motion. In peptidic disulfide radical anionic systems, sulfur hcc's are dissymmetrized and span an even larger range of values, from 14 to 40 G. Again, dependence is governed by the mechanical embedding of the -CH(2)-S∴S-CH(2)- motif, this time with a noticeable contribution from the hemibond lenghtening and some punctual short-range additive electrostatic contributions. This analysis comes within the scope of a unified picture of both spectroscopy and reactivity of the mechanochemistry of disulfide hemibonds.

Isotope Effects and the Temperature Dependences of the Hyperfine Coupling Constants of Muoniated sec-Butyl Radicals in Condensed Phases

Reported here is the first μSR study of the muon (A(μ)) and proton (A(p)) β-hyperfine coupling constants (Hfcc) of muoniated sec-butyl radicals, formed by muonium (Mu) addition to 1-butene and to cis- and trans-2-butene. The data are compared with in vacuo spin-unrestricted MP2 and hybrid DFT/B3YLP calculations reported in the previous paper (I), which played an important part in the interpretation of the data. The T-dependences of both the (reduced) muon, A(μ)′(T), and proton, A(p)(T), Hfcc are surprisingly well explained by a simple model, in which the calculated Hfcc from paper I at energy minima of 0 and near ±120° are thermally averaged, assuming an energy dependence given by a basic 2-fold torsional potential. Fitted torsional barriers to A(μ)′(T) from this model are similar (~3 kJ/mol) for all muoniated butyl radicals, suggesting that these are dominated by ZPE effects arising from the C−Mu bond, but for A(p)(T) exhibit wide variations depending on environment. For the cis- and trans-2-butyl radicals formed from 2-butene, A(μ)′(T) exhibits clear discontinuities at bulk butene melting points, evidence for molecular interactions enhancing these muon Hfcc in the environment of the solid state, similar to that found in earlier reports for muoniated tert-butyl. In contrast, for Mu−sec-butyl formed from 1-butene, there is no such discontinuity. The muon hfcc for the trans-2-butyl radical are seemingly very well predicted by B3LYP calculations in the solid phase, but for sec-butyl from 1-butene, showing the absence of further interactions, much better agreement is found with the MP2 calculations across the whole temperature range. Examples of large proton Hfcc near 0 K are also reported, due to eclipsed C−H bonds, in like manner to C−Mu, which then also exhibit clear discontinuities in A(p)(T) at bulk melting points. The data suggest that the good agreement found between theory and experiment from the B3LYP calculations for eclipsed bonds in the solid phase may be fortuitous. For the staggered protons of the sec-butyl radicals formed, no discontinuities are seen at all in A(p)(T), also demonstrating no further effects of molecular interactions on these particular proton Hfcc.

NMR analysis of conformationally dependent nJC, H and nJC, C in the trisaccharide α‐L‐Rhap‐(1 → 2)[α‐L‐Rhap‐(1 → 3)]‐α‐L‐Rhap‐OMe and a site‐specifically labeled isotopologue thereof

An array of NMR spectroscopy experiments have been carried out to obtain conformationally dependent (1)H,(13)C- and (13)C,(13)C-spin-spin coupling constants in the trisaccharide α-L-Rhap-(1 → 2)[α-L-Rhap-(1 → 3)]-α-L-Rhap-OMe. The trisaccharide was synthesized with (13)C site-specific labeling at C2' and C2″, i.e. in the rhamnosyl groups in order to alleviate (1)H spectral overlap. This facilitated the measurement of a key trans-glycosidic proton-proton cross-relaxation rate using 1D (1)H,(1)H-T-ROESY experiments as well as a (3)J(C, H) coupling employing 1D (1)H,(13)C-long-range experiments, devoid of potential interference from additional J coupling. By means of both the natural abundance compound and the (13)C-labeled sample 2D (1)H,(13)C-J-HMBC and (1)H,(13)C-HSQC-HECADE NMR experiments, total line-shape analysis of (1)H NMR spectra and 1D (13)C NMR experiments were employed to extract (3)J(C, H) , (2)J(C, H), (3)J(C, C), and (1)J(C, C) coupling constants. The (13)C site-specific labeling facilitates straightforward determination of (n)J(C, C) as the splitting of the (13)C natural abundance resonances. This study resulted in eight conformationally dependent coupling constants for the trisaccharide and illustrates the use of (13)C site-specific labeling as a valuable approach that extends the 1D and 2D NMR methods in current use to attain both hetero- and homonuclear spin-spin coupling constants that subsequently can be utilized for conformational analysis.

T-dependent Nuclear Hyperfine Coupling at the In Site in CeIrIn5

Temperature dependence of Knight shift K at 115 In sites in heavy fermion superconductor CeIrIn 5 has been determined for applied magnetic field parallel to a - and c -axes. The Knight shift versus the static susceptibility χ: ( K -χ) plot is non-linear at low temperatures in this compound, indicating that the hyperfine coupling constant depends on temperature. The T -dependence of hyperfine coupling constant is related with the modification of electronic state due to a heavy fermion formation. The non-linear relation between K and χ is discussed.

Chiral density waves in quarkyonic matter

We study the phase diagram of strongly interacting matter including the inhomogeneous phase of Chiral Density Waves (CDW) within the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model. We discuss the phase structure taking into account density and flavour dependence of the Polyakov loop potential parameter and temperature dependence of the four-point coupling constant of the NJL model. It is shown that the CDW phase exists and that can be interpreted as a special realisation of quarkyonic matter. This fact is of particular interest because the existence of homogeneous quarkyonic matter is strongly constrained. This also indicates that the study of inhomogeneous phases at finite temperatures and baryon densities are of special importance.

SENSITIVITY OF THE H3O+INVERSION-ROTATIONAL SPECTRUM TO CHANGES IN THE ELECTRON-TO-PROTON MASS RATIO

Quantum mechanical tunneling inversion transition in ammonia NH3 is actively used as a sensitive tool to study possible variations of the electron-to-proton mass ratio, mu = m_e/m_p. The molecule H3O+ has the inversion barrier significantly lower than that of NH3. Consequently, its tunneling transition occurs in the far-infrared (FIR) region and mixes with rotational transitions. Several such FIR and submillimiter transitions are observed from the interstellar medium in the Milky Way and in nearby galaxies. We show that the rest-frame frequencies of these transitions are very sensitive to the variation of mu, and that their sensitivity coefficients have different signs. Thus, H3O+ can be used as an independent target to test hypothetical changes in mu measured at different ambient conditions of high (terrestrial) and low (interstellar medium) matter densities. The environmental dependence of mu and coupling constants is suggested in a class of chameleon-type scalar field models - candidates to dark energy carrier.

Self-Assembled 3D Heterometallic CuII/FeII Coordination Polymers with Octahedral Net Skeletons: Structural Features, Molecular Magnetism, Thermal and Oxidation Catalytic Properties

The new three-dimensional (3D) heterometallic Cu(II)/Fe(II) coordination polymers [Cu(6)(H(2)tea)(6)Fe(CN)(6)](n)(NO(3))(2n)·6nH(2)O (1) and [Cu(6)(Hmdea)(6)Fe(CN)(6)](n)(NO(3))(2n)·7nH(2)O (2) have been easily generated by aqueous-medium self-assembly reactions of copper(II) nitrate with triethanolamine or N-methyldiethanolamine (H(3)tea or H(2)mdea, respectively), in the presence of potassium ferricyanide and sodium hydroxide. They have been isolated as air-stable crystalline solids and fully characterized including by single-crystal X-ray diffraction analyses. The latter reveal the formation of 3D metal-organic frameworks that are constructed from the [Cu(2)(μ-H(2)tea)(2)](2+) or [Cu(2)(μ-Hmdea)(2)](2+) nodes and the octahedral [Fe(CN)(6)](4-) linkers, featuring regular (1) or distorted (2) octahedral net skeletons. Upon dehydration, both compounds show reversible escape and binding processes toward water or methanol molecules. Magnetic susceptibility measurements of 1 and 2 reveal strong antiferromagnetic [J = -199(1) cm(-1)] or strong ferromagnetic [J = +153(1) cm(-1)] couplings between the copper(II) ions through the μ-O-alkoxo atoms in 1 or 2, respectively. The differences in magnetic behavior are explained in terms of the dependence of the magnetic coupling constant on the Cu-O-Cu bridging angle. Compounds 1 and 2 also act as efficient catalyst precursors for the mild oxidation of cyclohexane by aqueous hydrogen peroxide to cyclohexanol and cyclohexanone (homogeneous catalytic system), leading to maximum total yields (based on cyclohexane) and turnover numbers (TONs) up to about 22% and 470, respectively.

Conformational dependence of 13C shielding and coupling constants for methionine methyl groups

Methionine residues fulfill a broad range of roles in protein function related to conformational plasticity, ligand binding, and sensing/mediating the effects of oxidative stress. A high degree of internal mobility, intrinsic detection sensitivity of the methyl group, and low copy number have made methionine labeling a popular approach for NMR investigation of selectively labeled protein macromolecules. However, selective labeling approaches are subject to more limited information content. In order to optimize the information available from such studies, we have performed DFT calculations on model systems to evaluate the conformational dependence of (3)J (CSCC), (3)J (CSCH), and the isotropic shielding, sigma(iso). Results have been compared with experimental data reported in the literature, as well as data obtained on [methyl-(13)C]methionine and on model compounds. These studies indicate that relative to oxygen, the presence of the sulfur atom in the coupling pathway results in a significantly smaller coupling constant, (3)J (CSCC)/(3)J (COCC) approximately 0.7. It is further demonstrated that the (3)J (CSCH) coupling constant depends primarily on the subtended CSCH dihedral angle, and secondarily on the CSCC dihedral angle. Comparison of theoretical shielding calculations with the experimental shift range of the methyl group for methionine residues in proteins supports the conclusion that the intra-residue conformationally-dependent shift perturbation is the dominant determinant of delta(13)Cepsilon. Analysis of calmodulin data based on these calculations indicates that several residues adopt non-standard rotamers characterized by very large approximately 100 degrees chi(3) values. The utility of the delta(13)Cepsilon as a basis for estimating the gauche/trans ratio for chi(3) is evaluated, and physical and technical factors that limit the accuracy of both the NMR and crystallographic analyses are discussed.

Corrections for the polarization-dependent efficiency and new neutron-proton analyzing power data at 7.6 MeV

We present new corrections for the polarization-dependent efficiency (PDE), which introduces a false asymmetry into measurements of $n\text{\ensuremath{-}}p$ analyzing power ${A}_{y}(\ensuremath{\theta})$ caused by double scattering in the neutron side detectors. To accomplish this, we created a new database of $^{12}\mathrm{C}$$(\mathrm{nP\vec},n)$ ${A}_{y}(\ensuremath{\theta})$ by using a combination of fits to data, phase-shift analysis, and $R$-matrix analysis. Our recorrection for PDE of previously reported $n\text{\ensuremath{-}}p$ ${A}_{y}(\ensuremath{\theta})$ data at 7.6 and 12.0 MeV and new data at 7.6 MeV indicate that we have achieved a superior representation of $^{12}\mathrm{C}$$(\mathrm{nP\vec},n)$. Our results continue to suggest a possible charge dependence of the pion-nucleon coupling constant.

Topological anti-topological fusion in four-dimensional superconformal field theories

We present some new exact results for general four-dimensional superconformal field theories. We derive differential equations governing the coupling constant dependence of chiral primary correlators. For $$ \mathcal{N} = 2 $$ theories we show that the Zamolodchikov metric on the moduli space and the operator mixing of chiral primaries are quasi-topological quantities and constrained by holomorphy. The equations that we find are the four-dimensional analogue of the tt* equations in two-dimensions, discovered by the method of “topological anti-topological fusion” by Cecotti and Vafa. Our analysis relies on conformal perturbation theory and the superconformal Ward identities and does not use a topological twist.