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Spin Hamiltonian Hamiltonians

While all contributions to the spin Hamiltonian so far involve the electron spin and cause first-order energy shifts or splittings in the FPR spectmm, there are also tenns that involve only nuclear spms. Aside from their importance for the calculation of FNDOR spectra, these tenns may influence the FPR spectnim significantly in situations where the high-field approximation breaks down and second-order effects become important. The first of these interactions is the coupling of the nuclear spin to the external magnetic field, called the... [Pg.1556]

The complete spin Hamiltonian for a description of EPR and ENDOR experiments is given by... [Pg.1557]

CIDNP involves the observation of diamagnetic products fonned from chemical reactions which have radical intemiediates. We first define the geminate radical pair (RP) as the two molecules which are bom in a radical reaction with a well defined phase relation (singlet or triplet) between their spins. Because the spin physics of the radical pair are a fiindamental part of any description of the origins of CIDNP, it is instmctive to begin with a discussion of the radical-pair spin Hamiltonian. The Hamiltonian can be used in conjunction with an appropriate basis set to obtain the energetics and populations of the RP spin states. A suitable Hamiltonian for a radical pair consisting of radicals 1 and 2 is shown in equation (B1.16.1) below [12]. [Pg.1593]

A simple, non-selective pulse starts the experiment. This rotates the equilibrium z magnetization onto the v axis. Note that neither the equilibrium state nor the effect of the pulse depend on the dynamics or the details of the spin Hamiltonian (chemical shifts and coupling constants). The equilibrium density matrix is proportional to F. After the pulse the density matrix is therefore given by and it will evolve as in equation (B2.4.27). If (B2.4.28) is substituted into (B2.4.30), the NMR signal as a fimction of time t, is given by (B2.4.32). In this equation there is a distinction between the sum of the operators weighted by the equilibrium populations, F, from the unweighted sum, 7. The detector sees each spin (but not each coherence ) equally well. [Pg.2100]

MMVB is a hybrid force field, which uses MM to treat the unreactive molecular framework, combined with a valence bond (VB) approach to treat the reactive part. The MM part uses the MM2 force field [58], which is well adapted for organic molecules. The VB part uses a parametrized Heisenberg spin Hamiltonian, which can be illustrated by considering a two orbital, two electron description of a sigma bond described by the VB determinants... [Pg.301]

Experimentalists work with a spin Hamiltonian, which in the latter case would be written... [Pg.308]

The spin Hamiltonian operates only on spin wavefunctions, and all details of the electronic wavefunction are absorbed into the coupling constant a. If we treat the Fermi contact term as a perturbation on the wavefunction theR use of standard perturbation theory gives a first-order energy... [Pg.308]

E. Quantitative Aspects of Tq-S Mixing 1. The spin Hamiltonian and Tq-S mixing A basic problem in quantum mechanics is to relate the probability of an ensemble of particles being in one particular state at a particular time to the probability of their being in another state at some time later. The ensemble in this case is the population distribution of nuclear spin states. The time-dependent Schrodinger equation (14) allows such a calculation to be carried out. In equation (14) i/ (S,i) denotes the total... [Pg.68]

The spin Hamiltonian is thus generated. In particular it can be used to examine the Tq-S mixing of electron spin states and its relationship to the distributions of populations of nuclear spin states. The total spin Hamiltonian is given in equation (15) which contains both electron and nuclear terms. [Pg.69]

As has been shown (Kaptein, 1971b, 1972a) by application of perturbation theory (Itoh et al., 1969), the spin Hamiltonian in equation (17) can be obtained for S and T radical pairs. [Pg.69]

Therefore, the effective isotropic spin Hamiltonian for the radical pair Hrp is given by equation (21). [Pg.70]

The most important contributions to the spin Hamiltonian can be expressed as one-electron operators, and it will be shown that tl matrices Hf and Hf, vanish, as long as the reference state is computed up to one order of perturbation smaller than these matrices. Thus,... [Pg.62]

The simplest iron-sulfur centers, which were first discovered in ru-bredoxins, consist of one iron ion coordinated by a distorted tetrahedron of cysteinyl sulfur atoms. This environment provides a weak ligand field giving a spin equal to and 2 when the ion is Fe(III) and Fe(II), respectively. It also determines the splitting of the ground spin manifold, and consequently the characteristics of the EPR spectrum. This splitting is generally described in the framework of the spin Hamiltonian ... [Pg.423]

The EPR spectra of cell walls saturated with copper has been fitted to the numerical solutions of the spin hamiltonian describing the EPR lineshape of cupric ions. Two simulations have been performed. The first one (Fig. 4.a) considers that all uronic acids of the cell walls are similar the best fit is rather poor. The second one assumes existence of two populations of exchange sites with different parameters. In this case, the optimization is much better and confirms the existence of two different types of uronic acids in the cell wall (Fig. 4.b). [Pg.139]

The ESR measurements were made at RT or 77 K on a Varian E-9 spectrometer (X-band), equipped with an on-line computer for data analysis. Spin-Hamiltonian parameters (g and A values) were obtained from calculated spectra using the program SIM14 A [26]. The absolute concentration of the paramagnetic species was determined from the integrated area of the spectra. Values of g were determined using as reference the sharp peak at g = 2.0008 of the E i center (marked with an asterisk in Fig. 3) the center was formed by UV irradiation of the silica dewar used as sample holder. [Pg.692]

Appendix G Spin-Hamiltonian Operator with Terms... [Pg.1]

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... [Pg.111]

The spin-Hamiltonian concept, as proposed by Van Vleck [79], was introduced to EPR spectroscopy by Pryce [50, 74] and others [75, 80, 81]. H. H. Wickmann was the first to simulate paramagnetic Mossbauer spectra [82, 83], and E. Miinck and P. Debmnner published the first computer routine for magnetically split Mossbauer spectra [84] which then became the basis of other simulation packages [85]. Concise introductions to the related modem EPR techniques can be found in the book by Schweiger and Jeschke [86]. Magnetic susceptibility is covered in textbooks on molecular magnetism [87-89]. An introduction to MCD spectroscopy is provided by [90-92]. Various aspects of the analysis of applied-field Mossbauer spectra of paramagnetic systems have been covered by a number of articles and reviews in the past [93-100]. [Pg.121]

The effective spin Hamiltonian for energetically well isolated and orbitally nongene-rate ground states of transition metal ions with spin S is generally given by [1, 41, 103] ... [Pg.124]


See other pages where Spin Hamiltonian Hamiltonians is mentioned: [Pg.296]    [Pg.1466]    [Pg.1553]    [Pg.1553]    [Pg.1557]    [Pg.1583]    [Pg.1592]    [Pg.1597]    [Pg.7]    [Pg.308]    [Pg.110]    [Pg.128]    [Pg.425]    [Pg.442]    [Pg.173]    [Pg.53]    [Pg.63]    [Pg.63]    [Pg.63]    [Pg.36]    [Pg.425]    [Pg.442]    [Pg.114]    [Pg.78]    [Pg.90]    [Pg.104]    [Pg.121]    [Pg.121]    [Pg.122]    [Pg.124]    [Pg.125]   


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A pseudo-Jahn-Teller system modeled through generalized spin Hamiltonian the C4H4 molecule

Anisotropic spectra spin Hamiltonian

Biological spin Hamiltonians

Biradicals spin Hamiltonian

Breit-Pauli spin-orbit Hamiltonian

Computer-Aided Calculations of Spin-Hamiltonian Parameters

Effective one-electron spin-orbit Hamiltonians

Electronic Hamiltonian, conical intersections spin-orbit interaction

Equivalent Spin-Hamiltonian

External magnetic field spin Hamiltonian

Fine Structure and Spin Hamiltonian

Frozen-core spin-orbit Hamiltonian

General spin Hamiltonians

Ground-state wave function electronic Hamiltonian, spin-orbit

Hamiltonian Phenomenological spin-orbit

Hamiltonian Valence-only spin-orbit

Hamiltonian atomic spin-orbit

Hamiltonian effective second-order spin

Hamiltonian equations, electron spin resonance

Hamiltonian matrix spin-rotation coupling

Hamiltonian operator for spin-orbit coupling

Hamiltonian operator total spin

Hamiltonian pure spin

Hamiltonian spin interaction

Hamiltonian spin-free modified Dirac

Hamiltonian spin-orbit coupling

Hamiltonian, effective spin

Hamiltonian, spin, dimer species

Hamiltonians isotropic spin

Hamiltonians spin-free

Heisenberg spin Hamiltonian

High spins spin Hamiltonian parameters

Hyperfine splitting spin Hamiltonian

Interaction Hamiltonian spin-orbit

Interactions spin Hamiltonian operator

Ising spin Hamiltonian

Liquid crystals spin Hamiltonian

Magnetic Hamiltonian with electron and nuclear spins

Magnetic Hamiltonian with electron spin

Magnetic Hamiltonian with nuclear spin

Manual Calculations of Spin Hamiltonian Parameters

Model Spin Hamiltonians for Isotropic Interactions

NMR Spin Hamiltonian

Nickel complexes spin Hamiltonian parameters

No-pair spin-orbit Hamiltonian

Nuclear magnetic resonance effective” spin Hamiltonians

Nuclear spin Hamiltonian

Only Spin-Orbit Hamiltonians

P,T-odd spin-rotational Hamiltonian

Phenomenological spin Hamiltonians

Phenomenological spin Hamiltonians Hamiltonian

Phenomenological spin Hamiltonians interactions

Quadrupole interactions spin hamiltonian describing

Resonance condition spin Hamiltonian

Rotational Hamiltonian for space-quantised electron spin

Spin Hamiltonian

Spin Hamiltonian

Spin Hamiltonian Parameters from Spectra

Spin Hamiltonian and Relaxation Theory

Spin Hamiltonian application

Spin Hamiltonian case studies

Spin Hamiltonian description

Spin Hamiltonian electronic Zeeman interaction

Spin Hamiltonian electronic structure theory

Spin Hamiltonian first order

Spin Hamiltonian hyperfine coupling

Spin Hamiltonian matrix

Spin Hamiltonian method

Spin Hamiltonian nuclear-orbit interaction

Spin Hamiltonian parameter —molecular structure

Spin Hamiltonian parameters for

Spin Hamiltonian quadrupole coupling

Spin Hamiltonian second order

Spin Hamiltonian simulation

Spin Hamiltonian zero-field splittings

Spin Hamiltonians

Spin Hamiltonians calculation from molecular orbitals

Spin Hamiltonians solving

Spin Part of the Hamiltonian

Spin approximate Hamiltonians

Spin in the Nonrelativistic Hamiltonian

Spin orbit hamiltonian

Spin-Hamiltonian approach

Spin-Hamiltonian concept

Spin-Hamiltonian formalism

Spin-Hamiltonian mapping

Spin-Hamiltonian operator

Spin-Hamiltonian parameters

Spin-Hamiltonian parameters Zeeman term

Spin-Hamiltonian parameters asymmetry

Spin-Hamiltonian parameters measurements

Spin-adapted reduced hamiltonian

Spin-free Hamiltonian

Spin-glass Hamiltonian

Spin-lattice Hamiltonian

Spin-orbit Hamiltonians

Spin-orbit coupling Hamiltonian equation

Spin-orbit coupling effective Hamiltonians

Spin-orbit coupling electronic Hamiltonian

Spin-orbit interaction electronic Hamiltonian

Spin-rotational Hamiltonian

Static spin Hamiltonian

Subject spin Hamiltonian parameters

System-bath coupling spin-boson Hamiltonian

Systems magnetic resonance spin-Hamiltonian parameters

The Nuclear Spin Hamiltonian

The Spin Hamiltonian

The Spin Hamiltonian VB Theory

The Spin Hamiltonian and Ligand-Field Theory

The Spin Hamiltonians

The Spin-Hamiltonian Concept

Total spin Hamiltonian

Triplet state spin Hamiltonian

Two-spin Hamiltonian

Zeeman effect Hamiltonian, spin

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