Descripción: The set of 1:1 and 2:1 complexes of XOOX′ (X, X′ H, CH 3) with lithium cation has been studied to determine if they are suitable candidates for chiral discrimination in an isotropic medium via nuclear magnetic resonance spectroscopy. Conventional nuclear magnetic resonance is unable to distinguish between enantiomers in the absence of a chiral solvent. The criterion for experimental detection is valuated by the isotropic part of nuclear shielding polarisability tensors, related to a pseudoscalar of opposite sign for two enantiomers. The study includes calculations at coupled Hartree-Fock and density functional theory schemes for 17O nucleus in each compound. Additional calculations for 1H are also included for some compounds. A huge static homogeneous electric field, perpendicular to the magnetic field of the spectromer, as big as ≈1.7 108 V m -1 should be applied to observe a shift of ≈1 ppm for 17O magnetic shielding in the proposed set of complexes. © 2011 American Institute of Physics.

Descripción: A theoretical study of the relation between the relativistic formulation of the nuclear magnetic shielding and spin-rotation tensors is presented. To this end a theoretical expression of the relativistic spin-rotation tensor is formulated, considering a molecular Hamiltonian of relativistic electrons and non-relativistic nuclei. Molecular rotation effects are introduced considering the terms of the Born-Oppenheimer decomposition, which couple the electrons and nuclei dynamics. The loss of the simple relation linking both spectral parameters in the non-relativistic formulation is further analyzed carrying out a perturbative expansion of relativistic effects by means of the linear response within the elimination of the small component approach. It is concluded that relativistic effects on the spin-rotation tensor are less important than those of the nuclear magnetic shielding tensor. © 2012 American Institute of Physics.

Descripción: In the present work a set of formal relations connecting different approaches to calculate relativistic effects on magnetic molecular properties are proven. The linear response (LR) within the elimination of the small component (ESC), Breit Pauli, and minimal-coupling approaches are compared. To this end, the leading order ESC reduction of operators within the minimal-coupling four-component approach is carried out. The equivalence of all three approaches within the ESC approximation is proven. It is numerically verified for the NMR nuclear-magnetic shielding tensor taking HX and C H3 X (X=Br,I) as model compounds. Formal relations proving the gauge origin invariance of the full relativistic effect on the NMR nuclear-magnetic shielding tensor within the LR-ESC approach are presented. © 2006 American Institute of Physics.

Descripción: Nitrogen 14 quadrupole coupling constants for H2CN+ and HCN are predicted via ab initio self-consistent-field and configuration interaction theory. Effects of electron correlation, basis set completeness, and geometrical structure on the predicted electric field gradients are analyzed. The quadrupole coupling constant obtained for H2CN+ is one order of magnitude less than in HCN, providing an explanation for the experimental fact that the fine structure of the microwave spectrum of H 2CN+ has not been resolved. This research also allows a reliable prediction of the nuclear quadrupole moment of 14N, namely Q(14N)=2.00×10-26 cm2. © 1986 American Institute of Physics.

Descripción: Computational procedures, based on (i) the Ramsey common origin approach and (ii) the continuous transformation of the origin of the quantum mechanical current density-diamagnetic zero (CTOCD-DZ), were applied at the Hartree-Fock level to determine electric quadrupole polarizabilities of nuclear magnetic shielding for molecules in the presence of a nonuniform electric field with a uniform gradient. The quadrupole polarizabilities depend on the origin of the coordinate system, but values of the magnetic field induced at a reference nucleus, determined via the CTOCD-DZ approach, are origin independent for any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed. On the other hand, theoretical estimates of the induced magnetic field obtained by single-origin methods are translationally invariant only in the limit of complete basis sets. Calculations of electric quadrupole polarizabilities of nuclear magnetic shielding are reported for H2, HF, H2 O, N H3, and C H4 molecules. © 2008 American Institute of Physics.

Descripción: In the present work, numerical results of the nuclear spin-rotation (SR) tensor in the series of compounds HX (X=H,F,Cl,Br,I) within relativistic 4-component expressions obtained by Aucar [J. Chem. Phys. 136, 204119 (2012)10.1063/1.4721627] are presented. The SR tensors of both the H and X nuclei are discussed. Calculations were carried out within the relativistic Linear Response formalism at the Random Phase Approximation with the DIRAC program. For the halogen nucleus X, correlation effects on the non-relativistic values are shown to be of similar magnitude and opposite sign to relativistic effects. For the light H nucleus, by means of the linear response within the elimination of the small component approach it is shown that the whole relativistic effect is given by the spin-orbit operator combined with the Fermi contact operator. Comparison of "best estimate" calculated values with experimental results yield differences smaller than 2-3 in all cases. The validity of "Flygares relation" linking the SR tensor and the NMR nuclear magnetic shielding tensor in the present series of compounds is analyzed. © 2013 American Institute of Physics.

Descripción: We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides C H4, Si H4, Ge H4, and Sn H4. Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data. © 2005 American Institute of Physics.

Descripción: We show that the Pauli-Villars regularized action for a scalar field in a gravitational background in 1 + 1 dimensions has, for any value of the cutoff M, a symmetry which involves non-local transformations of the regulator field plus (local) Weyl transformations of the metric tensor. These transformations, an extension to the regularized action of the usual Weyl symmetry transformations of the classical action, lead to a new interpretation of the conformal anomaly in terms of the (non-anomalous) Jacobian for this symmetry. Moreover, the Jacobian is automatically regularized, and yields the correct result when the masses of the regulators tend to infinity. In this limit the transformations, which are non-local on a scale of 1/M, become the usual Weyl transformations of the metric. We also present the example of the chiral anomaly in 1 + 1 dimensions, showing that the Pauli-Villars regularized action has a non-local symmetry. This symmetry is similar to the one of (lattice) Ginsparg-Wilson fermions, with the ultraviolet cutoff playing the role of the inverse of the lattice spacing. (C) 2000 Elsevier Science B.V.

Descripción: A procedure, based on a continuous transformation of the origin of the (quantum mechanical) current density that sets the diamagnetic contribution to zero (CTOCD-DZ) all over the molecular domain, is applied to determine shielding polarizabilities to first order in a perturbing electric field. In any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed, all the components of the CTOCD-DZ magnetic shielding polarizability are origin independent, and the constraints for charge and current conservation are exactly satisfied. The effects of a static uniform electric field on the nuclear magnetic resonance (NMR) shielding of H2O2, F2, H2C2, H2CO, NH3, HCN, and HNC molecules have been investigated within the CTOCD-DZ method, and compared with the conventional results evaluated via the same basis sets, and with theoretical results taken from the literature. © 2000 American Institute of Physics.

Descripción: A novel method for simulating the statistical mechanics of molecular systems in which both nuclear and electronic degrees of freedom are treated quantum mechanically is presented. The scheme combines a path integral description of the nuclear variables with a first-principles adiabatic description of the electronic structure. The electronic problem is solved for the ground state within a density functional approach, with the electronic orbitals expanded in a localized (Gaussian) basis set. The discretized path integral is computed by a METROPOLIS Monte Carlo sampling technique on the normal modes of the isomorphic ring polymer. An effective short-time action correct to order τ4 is used. The validity and performance of the method are tested by studying two small lithium clusters, namely Li4 and Li5+. Structural and electronic properties computed within this fully quantum-mechanical scheme are presented and compared to those obtained within the classical nuclei approximation. Quantum delocalization effects turn out to be significant as shown by the fact that quantum simulation results at 50 K approximately correspond to those of classical simulations carried out at 150 K. The scaling factor depends, however, on the specific physical property, thus evidencing the different character of quantum and thermal correlations. Tunneling turns out to be irrelevant in the temperature range investigated (50-200 K). © 1998 American Institute of Physics.

Descripción: An alternative approach for the calculation of the electron-positron (e-p) contribution to magnetic properties based on two-component Breit-Pauli spinors is presented. In it, the elimination of the small component scheme is applied to the inverse propagator matrix of e-p pairs. The effect of the positronic manifold is expressed as an operator acting on Breit-Pauli spinors. The operator form thus obtained sums up the relativistic correction as a geometric series and as a result a totally different behavior in the vicinity of a nucleus is obtained as compared to the one of the linear response approximation. This feature has deep influence in numerical values of the e-p contribution to the nuclear magnetic shielding of heavy atoms. Numerical calculations carried out for Kr, Xe, and I show that with this approach, the e-p contributions to this property are in good agreement with those of four-component methods. © 2009 American Institute of Physics.

Descripción: We investigate the importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL2 (L = Cl, Br, I, CH 3) compounds using three different relativistic methods: the fully relativistic four-component approach and the two-component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH3)2 within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ∼2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr 2 and HgI2 when ZORA results are compared with four-component calculations with non-collinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ∼500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. A Gaussian nucleus model for the Coulomb potential reduces the Hg shielding constants by ∼100-500 ppm and the Hg chemical shifts by 1-143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible. © 2011 American Institute of Physics.