Relativistic Terms Research Articles

Quasirelativistic study of 125Te nuclear magnetic shielding constants and chemical shifts

AbstractCalculations for 125Te magnetic shielding constants and chemical shifts were carried out using a quasirelativistic Hamiltonian including the spin‐free relativistic, one‐ and two‐electron spin–orbit, and relativistic magnetic interaction terms. For the tellurium‐containing series Te(CH3)2, TeH2, TeF6, Te(CH3)4, and Te(CH3)2Cl2, the relativistic effects amounted to as much as 1300 ppm and were very important for qualitatively reproducing the absolute value of the 125Te shielding constants obtained experimentally. On the other hand, for the 125Te chemical shifts the relativistic effects were less important, because they cancelled each other between the sample and reference compounds. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1502–1508, 2001

Nonintegrability and chaos in the anisotropic Manev problem

The anisotropic Manev problem, which lies at the intersection of classical, quantum, and relativity physics, describes the motion of two point masses in an anisotropic space under the influence of a Newtonian force-law with a relativistic correction term. Using an extension of the Poincaré–Melnikov method, we first prove that for weak anisotropy, chaos shows up on the zero-energy manifold. Then we put into the evidence a class of isolated periodic orbits and show that the system is nonintegrable. Finally, using the geodesic deviation approach, we prove the existence of a large nonchaotic set of uniformly bounded and collisionless solutions.

Relativistic Corrections to Astrometric Shifts Due to Gravitational Microlensing

Gravitational microlensing has proved to be a versatile astrophysical tool. Recently, the question of whether higher order relativistic corrections can influence the observable properties of microlensing has been addressed. This paper extends earlier studies, investigating higher order relativistic terms in astrometric shifts during microlensing events, revealing that they produce no effects. The magnitude of the relativistic corrections is examined in an astrophysical context and is found to be negligible.

Relativistic fluctuations and anomalous Darwin terms in superconductors

The anomalous Darwin term, one of the recently derived relativistic corrections to the conventional theory of superconductivity, is analyzed in detail. This analysis leads to the prediction of unusual types of fluctuations, of relativistic origin, in superconductors. An alternative derivation of the anomalous Darwin term, much simpler than that given originally, is presented and used to clarify some puzzling features of the original derivation. The question of observability of the anomalous Darwin term and the relativistic fluctuations is discussed and the relation to the conventional Darwin term and to earlier proposed superconducting Darwin terms is clarified.

Relativistic effects and the halogen dependencies in the13C chemical shifts of CH4?nIn, CH4?nBrn, CCl4?nIn, and CBr4?nIn (n=0-4)

Linear and nonlinear halogen dependencies of the 13C magnetic shielding constants of CH4−nIn, CH4−nBrn, CCl4−nIn, and CBr4−nIn were fairly reproduced by the ab initio generalized unrestricted Hartree–Fock (GUHF)/finite perturbation (FP) method including spin-orbit (SO) interaction and spin-free relativistic (SFR) terms. As seen from the experimental trends, the calculated 13C chemical shifts in CCl4−nIn and CBr4−nIn depend linearly on n=0–4, while those in CH4−nIn and CH4−nBrn depend nonlinearly. We found that both the linear and nonlinear dependencies are due to the relativistic effects, and especially due to the Fermi–Contact (FC) term originating from the SO interaction. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 528–536, 2001

Quasi-Relativistic Study of 199Hg Nuclear Magnetic Shielding Constants of Dimethylmercury, Disilylmercury and Digermylmercury

Quasi-relativistic ab initio calculations were performed for 199Hg nuclear magnetic shielding constants and chemical shifts in a series of Hg(XH3)2 (X = C, Si, and Ge) compounds. The relativistic terms included were the spin-free relativistic (SFR) term, the one- and two-electron spin−orbit (SO) terms, and the relativistic magnetic interaction (RMI) term. The second-order Douglas−Kroll (D-K) form was adopted for the one-electron SO, SFR, and RMI terms, and the Breit−Pauli form for the two-electron SO term. The calculated results show that the SFR, SO, and RMI terms are all important for calculating the 199Hg shielding constants and chemical shifts of the compounds in question. The SFR and SO terms strongly couple with each other, and the RMI term also strongly affects the paramagnetic and Fermi-contact (FC) terms. The calculated 199Hg chemical shifts are in reasonable agreement with experimental data only if the SFR, SO, and RMI terms are included and tight s basis functions of mercury are used. We found that the total trend of the chemical shifts in Hg(XH3)2 (X = C, Si, and Ge) originates from the sum of the FC and paramagnetic terms, which are the effects of the relativity and the electronegativity of the ligand, respectively.

Les pseudopotentiels à norme conservée relativistes étendus

The extended norm-conserving pseudopotentials developed by Shirley et al., in the nonrelativistic case, has been extended to the relativistic case. We have discussed the importance of the relativistic terms added in the case of the hard pseudopotentials. This correction allows us to revise the precision linked to the nonlinearity of the electronic structure methods on a solid in the particular case of heavy atoms.

Detection and processing of electromagnetic and near-field acoustic signals in elasmobranch fishes.

The acoustic near field of quietly moving underwater objects and the bio-electric field of aquatic animals exhibit great similarity, as both are predominantly governed by Laplace's equation. The acoustic and electrical sensory modalities thus may, in directing fishes to their prey, employ analogous processing algorithms, suggesting a common evolutionary design, founded on the salient physical features shared by the respective stimulus fields. Sharks and rays are capable of orientating to the earth's magnetic field and, hence, have a magnetic sense. The electromagnetic theory of orientation offers strong arguments for the animals using the electric fields induced by ocean currents and by their own motions in the earth's magnetic field. In the animal's frame of reference, in which the sense organs are at rest, the classical concept of motional electricity must be interpreted in relativistic terms. In the ampullae of Lorenzini, weak electric fields cause the ciliated apical receptor-cell membranes to produce graded, negative receptor currents opposite in direction to the fields applied. The observed currents form part of a positive-feedback mechanism, supporting the generation of receptor potentials much larger than the input signal. Acting across the basal cell membranes, the receptor potentials control the process of synaptic transmission.

Stability in the anisotropic Manev problem

The anisotropic Manev problem describes the motion of two point masses in an anisotropic space under the influence of a Newtonian force-law with a relativistic correction term. In this paper we prove the existence of a large, open and connected manifold of solutions of the planar anisotropic Manev problem that are uniformly bounded and collisionless.

The barrier to linearity of hydrogen sulphide

High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory, as well as full configuration interaction (FCI) benchmarks, with basis sets ranging from [S/H] [4s3p1d/2s1p] to [9s8p7d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best technically possible value for the barrier to linearity of hydrogen sulphide. Following careful extrapolations of MP2, CCSD and CCSD(T) energies to the complete basis set (CBS) limit and inclusion of small corrections due to scalar relativistic terms, core polarization and core correlation effects, and the diagonal Born–Oppenheimer correction (DBOC), the final electronic (vibrationless) extrapolated barrier height of this study is 24 423±75 cm −1.

Anharmonic force field, vibrational energies, and barrier to inversion of SiH3−

The full quartic force field of the ground electronic state of the silyl anion (SiH3−) has been determined at the CCSD(T)-R12 level employing a [Si/H]=[16s11p6d5f/7s5p4d] basis set. The vibrational energy levels, using the quartic force field as a representation of the potential energy hypersurface around equilibrium, have been determined by vibrational perturbation theory carried out to second, fourth, and sixth order. The undetected vibrational fundamental for the umbrella mode, ν2, is predicted to be 844 cm−1. High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory with basis sets ranging from [Si/H] [5s4p2d/3s2p] to [8s7p6d5f4g3h/7s6p5d4f3g] have been employed to obtain the best possible value for the inversion barrier of the silyl anion. The rarely quantified effects of one- and two-particle relativistic terms, core correlation, and the diagonal Born–Oppenheimer correction (DBOC) have been included in the determination of the barrier for this model system. The final electronic (vibrationless) extrapolated barrier height of this study is 8351±100 cm−1.

Electron Collision Excitation of Fine‐Structure Levels in Siv

Electron collision excitation strengths of inelastic transitions among the 52 fine-structure levels of the ground 3s23p and excited 3s3p2, 3s23d, 3s24s, 3p3, 3s24p, 3s3p3d, 3s24d, 3s24f, and 3s3p4s configurations in S IV are calculated using full Breit-Pauli R-matrix method. The target levels are represented by configuration-interaction wave functions, and the mass, Darwin, and spin-orbit relativistic terms are included in the scattering equations. The collision strengths in the threshold energy regions are dominated by the complicated resonance structures. Our collision strengths are compared with earlier available calculations and significant differences are noted. The collision strengths are integrated over a Maxwellian distribution of electron energies to obtain effective collision strengths over a wide temperature range.

Collision Strengths from Ground Levels of Ti XIII Using Relativistic–Breit–Pauli Approximation

The R-matrix method is used to calculate collision strengths from the ground state to the first twenty-six fine structure levels of neon-like titanium by including the relativistic term coupling co-efficients in the Semi–Breit–Pauli approximation. Configuration interaction wave functions are used to represent the fifteen lowest LS-coupled target states in the R-matrix expansion. Results obtained are compared with other calculations. This is the first detailed calculation. on this ion in which relativistic, exchange, channel couplings and short-range correlation effects are taken into account.

Numerical resolution of some nonlinear Schr�dinger-like equations in plasmas

Schrödinger-like equations play an essential role in the modeling of plasmas created by laser beams, and taking into account of relativistic terms yields a new kind of nonlinearity in them, as compared to the classical case. A numerical scheme involving a new handling of absorbing conditions suitable for Schrödinger-like equations is given, and several general models are studied: the classical cubic case linked to the Kerr effect for an anharmonic plasma, where numerical experiments prove the efficiency of our code applied to the computation of solitons and explosive solutions. Furthermore, new kinds of explosive solutions are computed, and we numerically show the essential role of the ground state to get approximations of the cubic explosive solution by global ones. A multiphotonic ionization model is also studied including higher-order terms in the nonlinearity. In this case, we obtain stable structures physically explained by competing saturation processes. These structures have been experimentally detected. Finally, a relativistic model involving the Lorentz kinematic factor in the evolution equations is investigated numerically; filamentary structures are found in agreement with predicted relativistic phenomena. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 672–696, 1999

Relativistic theory of nuclear shielding in one-electron atoms 1. Theoretical foundations and first-order terms

The nuclear shielding in NMR spectroscopy is given in relativistic theory (Pyper, N. C., 1983, Chem. Phys. Lett., 96, 204) as the sum of the exact relativistic analogues of the non-relativistic diamagnetic and paramagnetic terms augmented by a further purely relativistic term. In this paper this theory, based on the Gordon decomposition of the Dirac current, is extended to encompass the point charge—point dipole model of the nucleus, the previous formulation (Pyper, 1983) being restricted to spatially extended descriptions of the nuclear charge and magnetization. For the point nucleus case, analytical expressions for both the purely relativistic shielding contribution and diamagnetic term are derived for all orbitals. The result for the diamagnetic shielding is derived by invoking the relativistic virial theorem, and thus depends only on the orbital energy and magnetic quantum number m. Therefore it shows, for given m, the same ‘accidental’ degeneracy between orbitals differing in the sign of the quantum number κ as the energy. The purely relativistic contribution to the shielding is shown to differ from the electronic contribution to the hyperfine energy by a factor of only m multiplied by fundamental constants. The present purely relativistic term is shown to equal the previous result (Pyper, 1983) even though appearing in a different form. For the interaction with a uniform magnetic field the relativistically exact Hamiltonian obtained from the Gordon decomposition is used with the virial theorem to derive a new expression for the g factor for all orbitals. The resulting simple expression depends only on the orbital energy in addition to the quantum numbers κ and m.

The barrier to linearity of water

High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory, explicitly correlated (linear R12) techniques, and full configuration interaction (FCI) benchmarks, with basis sets ranging from [O/H] [3s2p1d/2s1p] to [8s7p6d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best possible value for the barrier to linearity of water. Attention is given to the degree of accord among extrapolations of conventional MP2, CCSD, and CCSD(T) energies to the complete basis set (CBS) limit and corresponding linear R12 schemes for these correlation methods. Small corrections due to one- and two-particle relativistic terms, core correlation effects, and the diagonal Born–Oppenheimer correction (DBOC) have been incorporated. The final electronic (vibrationless) extrapolated barrier height of this study is 11 127±35 cm−1. Anharmonic force fields have been determined at the aug-cc-pCVTZ CCSD(T) level at equilibrium and at a linear reference geometry. These and previous sextic force fields are in general accord with the expansion terms of recent global potential energy hypersurfaces but also highlight some of their weaknesses.

Neutron polarizabilities from Compton scattering on the deuteron?

A calculation of deuteron Compton scattering using non-relativistic perturbation theory is presented,with the primary motivation of investigating the feasibility of determining the neutron polarizabilities from this type of experiment. This calculation is expected to be valid for energies below 100 MeV. Pion-exchange, relativistic, and recoil corrections are also included. The low-energy theorem for gauge invariance is shown to be satisfied. The relative effects of the different terms and their effects on the determinations of the polarizabilities are discussed at energies of 49, 69, and 95 MeV. The cross-section is dominated by the seagull, polarizability, and electromagnetic multipole interactions. Relativistic and pion-exchange terms are also important, while recoil corrections and multipoles of $L$=2 and greater are negligible. The calculation provides a reasonable description of the experimental data points at 49 and 69 MeV. The polarizabilities are difficult to determine at these energies. A more accurate determination of the polarizabilities may be possible at 95 MeV.

Propagation of a monochromatic electromagnetic plane wave in a medium with nonsimple motion

An exact analytical solution is obtained for the trajectory of the wave vector of a monochromatic electromagnetic plane wave in a medium with nonsimple motion. It is shown that the spatial dragging of the electromagnetic wave by the moving medium can be described correctly in the general case only if relativistic terms of order β2 are taken into account.

Perturbed energy eigenvalues of the Salpeter equation in the oscillator-representation method

On the basis of the oscillator-representation method, we obtain the energy eigenvalue formulae upto the second order in the perturbation Hamiltonian for the 1S-6S, 1P, 2P, 1D and 2D states of the heavy quarkonia. The application of the formulae to the 1S-6S states in the linear confining potential suggests that we cannot neglect the effect of the relativistic kinetic terms on the energy eigenvalues in the excited states of the charmonia.

Ab initio calculations on cis-[ PtCl2(PMe3)2] : Search for a model chemistry for platinum(II) complexes

The capacity of Hartree-Fock (HF), Moller-Plesset second order perturbation (MP2), and density functional (DF) calculations to predict the experimental dipole moment and the metal-ligand bond lengths of a planar platinum(II) complex, cis-[ PtCl2 (PMe3 )2 ] , was investigated. Highly erroneous results were obtained from uncorrelated HF calculations and from MP2 and DF calculations which included the 5s and 5p electrons of platinum in a frozen core or in an effective core potential. DF calculations including these (n-1)s and (n-1)p electrons in the valence space are shown to have the ability to correctly reproduce the platinum-ligand bond lengths and the dipole moment, provided that sufficiently large basis sets including polarization functions are used. MP2 calculations yielded dipole moments comparable to those obtained from DF calculations with the same basis set and reproduced better the difference between the Pt-Cl and Pt-P bond lengths, but required 2-6 times more computer time. The best agreement between calculated and experimental dipole moment and bond length values was obtained with DF calculations using the program ADF, provided that the scalar relativistic terms were included in the hamiltonian. Our results indicate that the mutual influence of the platinum-ligand bonds in trans-position (the so-called trans -influence) involves both electron correlation and relativistic effects.