Effective Floquet Hamiltonian for spin I = 1 in magic angle spinning NMR using contact transformation

Contact transformation is an operator transformation method in time-independent perturbation theory which is used successfully in molecular spectroscopy to obtain an effective Hamiltonian. Floquet theory is used to transform the periodic time-dependent Hamiltonian, to a time-independent Floquet Hamiltonian. In this article contact transformation method has been used to get the analytical representation of Floquet Hamiltonian for quadrupolar nuclei with spin I = 1 in the presence of an RF field and first order quadrupolar interaction in magic angle spinning NMR experiments. The eigenvalues of contact transformed Hamiltonian as well as Floquet Hamiltonian have been calculated and a comparison is made between the eigenvalues obtained using the two Hamiltonians.     

Emploi d'une méthode de perturbation-variation pour l'étude de la polarisation de spin dans les radicaux libres aromatiques

A perturbation method has been used to deal with the problem of the interaction of configuration in the free aromatic radicals. We have considered only the mono-excitated configurations which are responsible for the specific effects due to the spin polarization; the corresponding wave functions are built up with the set of molecular orbitals LCAO SCF (occupied and virtual) of the ground-state configuration. We thus obtain a good distribution of spin densities on the rings of the studied radicals: the benzyl and the methylene-naphthyls radicals. The spin density on the extracyclic carbon remains too large as in the case of the SCF representation. This may be explained by the shape of the molecular orbital occupied by the unpaired electron in the SCF configuration, and the structure of the method used which disregards the excitated configurations involving this orbital.     

A unitary group formulation of many-body theory: Diagram systematics and use of the spin shifts

This paper shows that the spin-shift formalism developed in B. T. Pickup and A. Mukhopadhyay [Int. J. Quantum Chem. 26 , 101 (1984)] supports a one-component diagrammatics which has a systematics akin to that in the spin-orbital many-body theory. The diagrams are neither Goldstone nor Yutsis type, and characterize the chain U(2R) ? U(R)?SU(2) on which the spin-shift formalism is based. Accordingly, while the lines in such diagrams are labeled by the orbital indices, the diagram structure adequately reflects the irreducible representation of the group U(R). In this sense the paper presents a unitary group approach to the natural generalization of the usual many-body theory for the spin-adapted cases. A set of very simple rules is derived; their similarity with the corresponding rules in the ordinary many-body theory and practical utility are discussed in connection with (a) matrix elements over many-electron spin states and (b) closed- and open-shell many-body perturbation theory. A possibility of integral-driven many-body perturbation theory for open-shells is indicated. Connections of this formalism with others are also discussed.     

Large configuration interaction calculations of nuclear spin—spin coupling constants. I. HD molecule

A method for perturbation calculations of NMR spin—spin coupling constants is presented. The zeroth order wave-function includes correlation by means of large configuration interaction. The rust order correction to the wavefunction is computed by expansion in all singly and doubly excited triplets. Expansion coefficients are found iteratively. The method is applied to the hydrogen molecule yielding, after vibrational averaging, J_HD = 43.48 Hz. The experimental value is 42.94±0.1 Hz. Comparisons are made with other calculations.     

On the zeroth‐order hamiltonian for CASPT2 calculations of spin crossover compounds

Complete active space self‐consistent field theory (CASSCF) calculations and subsequent second‐order perturbation theory treatment (CASPT2) are discussed in the evaluation of the spin‐states energy difference (ΔH_elec) of a series of seven spin crossover (SCO) compounds. The reference values have been extracted from a combination of experimental measurements and DFT + U calculations, as discussed in a recent article (Vela et al., Phys Chem Chem Phys 2015, 17, 16306). It is definitely proven that the critical IPEA parameter used in CASPT2 calculations of ΔH_elec, a key parameter in the design of SCO compounds, should be modified with respect to its default value of 0.25 a.u. and increased up to 0.50 a.u. The satisfactory agreement observed previously in the literature might result from an error cancellation originated in the default IPEA, which overestimates the stability of the HS state, and the erroneous atomic orbital basis set contraction of carbon atoms, which stabilizes the LS states. © 2015 Wiley Periodicals, Inc.     

Influence of the INDO parameterization on the indirect spin–spin coupling constants as calculated by the FPT INDO method

Alterations have been introduced in the semi-empirical INDO parameters in order to study their influence on the Fermi contact term of the indirect spin–spin coupling constants as calculated by the finite perturbation theory (FPT). For this purpose a set of molecules containing hydrogen, carbon and/or fluorine has been selected. In general, most coupling constants are found to be much more sensitive than other molecular properties to small changes in the INDO parameters. This sensitivity depends strongly on the particular calculated coupling constant. In most cases the uncertainty in the INDO parameters leads to uncertainties in the coupling constants which are much greater than their experimental errors.     

Calculations of hydrogen—fluorine and fluorine—fluorine nuclear magnetic spinspin coupling anisotropies for fluorinated ethenes and benzenes oriented in liqiud crystal solvents

Spinspin coupling tensors are calculated using self-consistent perturbation theory and INDO wavefunctions, in order to estimate whether neglect of their anisotropy influences molecular dimensions deduced from the NMR spectra of partially oriented solutes. It is found that anisotropy of cis and trans and many aromatic HF couplings can be neglected but that trans FF couplings are markedly anisotropic. Comparisons are made with the limited experimental results.     

Semiclassical initial value series solution of the spin boson problem

A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom.     

Electron spin polarization of the excited quartet state of strongly coupled triplet-doublet spin systems

The electron spin polarization associated with electronic relaxation in molecules with trip-quartet and trip-doublet excited states is calculated. Such molecules typically relax to the lowest trip-quartet state via intersystem crossing from the trip doublet, and it is shown that when spin-orbit coupling provides the main mechanism for this relaxation pathway it leads to spin polarization of the trip quartet. Analytical expressions for this polarization are derived using first- and second-order perturbation theory and are used to calculate powder spectra for typical sets of magnetic parameters. It is shown that both net and multiplet contributions to the polarization occur and that these can be separated in the spectrum as a result of the different orientation dependences of the +/-1/2<-->+/-3/2 and +1/2<-->-1/2 transitions. The net polarization is found to be localized primarily in the center of the spectrum, while the multiplet contribution dominates in the outer wings. Despite the fact that the multiplet polarization is much stronger than the net polarization for individual orientations of the spin system, the difference in orientation dependence of the transitions leads to comparable amplitudes for the two contributions in the powder spectrum. The influence of this difference on the line shape is investigated in simulations of partially ordered samples. Because the initial nonpolarized state of the spin system is not conserved for the proposed mechanism, the net polarization can survive in the doublet ground state following electronic relaxation of the triplet part of the system.     

Spin symmetry adaptation of the one-electron propagator

A new method is proposed for spin symmetry adaptation of the open-shell one-electron propagator. Possible applications to both diagrammatic perturbation theory and algebraic superoperator approximations of the propagator equations of motion are envisaged.     

Geometric approximation to nuclear spin–spin coupling constants in the water molecule

The geometric aproximation is used within the framework of triple perturbation theory to evaluate the contributions to nuclear spin–spin coupling constants in the water molecule provided by the Fermi contact, the spin–orbit, and the spin–dipolar interactions. The results, obtained with SCF wave functions expanded over Gaussian basis sets of increasing quality, are compared with corresponding coupled Hartree–Fock estimates. The limits of the geometric approximation to coupling constants are discussed.     

A theoretical study of the dielectric solvent effect on vicinal spin coupling constants

The dielectric solvent effect on HCCH, HCNH and HCNC spin coupling constants in ethane, tetrachloroethane and trans N-methylformamide has been calculated by finite perturbation theory based on the INDO and CNDO/2 approximations incorporating solvaton theory. The available experimental data are interpreted using the calculated variations of spin coupling constants. The effect of dielectric constant on the general form of the Karplus relation is included in the finite perturbation calculations.     

Second order of perturbation theory correction to the radial distribution function of a liquid with the interaction potential of hard spheres plus a square-well

A liquid with the interaction potential of hard spheres plus a square-well is analyzed using the Monte-Carlo technique. Numerical results for the perturbation theory series over a square-well potential are obtained in the form of the Barker and Henderson discrete representation. Approximating expressions for the correction to a liquid radial distribution function in the second order of perturbation theory are presented. The obtained results allow us to define this correction with a root-mean-square deviation of about 0.007. It is shown that the given approach provides a complete calculation in the second order of perturbation theory, and also the determination of the third order correction to the free energy for a liquid interacting with the potential of the Lennard-Jones type.     

Electron hopping and magnetic field dependent spin dynamics of radical ions in solution

The role of hopping on the geminate recombination of radical ions (N,N-dimethylaniline cation and anthracene anion) in acetonitrile is studied via the nanosecond time-resolved magnetic field effect on the triplet yield and the influence of donor concentration thereon. Increasing donor concentration leads to lifetime broadening of the magnetic field dependence of the triplet yield. Responsible for this effect is the perturbation of the coherent spin motion caused by hopping of the electron spin between donor sites of different nuclear spin configuration. Comparison of experimental results with calculations based on the semiclassical theory of spin motion yields an estimate of the hopping rates. Deuteration of both radicals influences the halfwidth of the magnetic field effect: at long probing times and low donor concentrations the halfwidth measured for protonated radical ions exceeds the one for the deuterated species: at short delay times and large donor concentrations, i.e. high hopping rates, this isotopic effect is reversed.     

Calculations of spin asymmetries in electron-alkali scattering

In this work we show that in order to calculate spin asymmetries at projectile energies above the ionization threshold, the target continuum needs to be taken into account. However, we demonstrate that this does not imply that in the experiment intermediate excitation into the continuum plays a major role. Rather, any theory, such as the standard close-coupling method, that does not allow for electron flux to be in all open channels is likely to have difficulty in reproducing the measured spin asymmetries.     

Effect of rapidly relaxed electron spin anisotropically coupled to nearby nuclear partners

In practice, many situations arise when a perturbed nuclear spin relies upon the aid of a rapidly relaxed spin neighbor in order to realize thermal equilibrium. Conventional treatments view the efficiently relaxed spin as part of the 'lattice', invoke the secular approximation, and consider the associated time correlation of the lattice variables, phenomenologically. Recently, an ab initio perturbative approach has been proposed for investigation of these spin systems. In this work, a similar formalism is applied to the scenario, in which nuclear spin relaxation is effected via an anisotropically coupled, efficiently relaxed, spin. Interesting conflicts with standard theory are revealed. Furthermore, although left mostly unexplored, this approach lends insight into numerous related aspects of magnetic relaxation including separation of timescales, distinction between spin and spatial averaging, paramagnetic relaxation, Curie spin relaxation, and the dynamic frequency shift.     

Generation of genealogical spin eigenfunctions

A method is given for generating the Yamanouchi-Kotani genealogical spin eigenfunctions which requires neither storage of eigenfunctions for smaller numbers of electrons, nor summations of large order, nor explicit use of results from the theory of representations of the symmetric group. An explicit formula is given for the coefficients of expansion in terms of spin products.     

Quantum-mechanical theory of atom-molecule and molecular collisions in a magnetic field: spin depolarization

A theory for quantum-mechanical calculations of cross sections for atom-molecule and molecular collisions in a magnetic field is presented. The formalism is based on the representation of the wave function as an expansion in a fully uncoupled space-fixed basis. The systems considered include 1S-atom-2Sigma-molecule, 1S-atom-3Sigma-molecule, 2Sigma-molecule-2Sigma-molecule, and 3Sigma-molecule-3Sigma-molecule. The theory is used to elucidate the mechanisms for collisionally induced spin depolarization.     

Transformation of spin projected slater determinants under orbital permutation

This paper gives a proof that spin projected Slater determinants provide a basis for Young's natural representation of the symmetric groups under permutation of the orbitals. The general reduction of sums of spin projected Slater determinants to give functions of pure spatial symmetry type requires this transformation.