Current Methods in Inorganic Chemistry [2 followers] Follow Subscription journal (Not entitled to full-text) ISSN (Print) 1873-0418 Published by Elsevier [3039 journals] |
- Current Methods in Inorganic Chemistry
- Abstract: Publication date: 2001
Source:Current Methods in Inorganic Chemistry, Volume 2
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- List of contributors
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 1 General introduction
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 2 Activation of substrates with non-polar single bonds
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 3 Activation of substrates with polar single bonds
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 4 Transition metal-carbene complexes in olefin metathesis and
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 5 Transmetalation
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 6 1,2-Insertion and β-elimination
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 7 1,1-Insertion into metal-carbon bond
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 8 Addition to unsaturated ligands
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 9 Reductive elimination
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Source:Current Methods in Inorganic Chemistry, Volume 3
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- Chapter 1 Introduction
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Source:Current Methods in Inorganic Chemistry, Volume 2
This chapter is intended to recall the principles of magnetism, the definition of magnetic induction and of magnetic induction in a vacuum whichis referred to as magnetic field. Readers may not recollect that the molarmagnetic susceptibility is expressed in cubic meters per mol! Some properties of electron and nuclear spins are reviewed and finally some basicconcepts of the magnetic resonance experiments are refreshed. In summary, this chapter should introduce the readers into the language used by the authors.
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- Chapter 2 The hyperfine shift
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Source:Current Methods in Inorganic Chemistry, Volume 2
This chapter recalls the principles of the hyperfine coupling between electrons and nuclei in terms of energy and deals with its consequences on chemical shift. The equations for contact and pseudocontact shifts are derived and illustrated in a pictorial way. Their physical/chemical backgrounds are discussed as well as their limits of validity. The mechanisms of spin delocalization are illustrated. The perspectives when high field magnets are used are highlighted.
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- Chapter 3 Relaxation
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Source:Current Methods in Inorganic Chemistry, Volume 2
The sole presence of an electron spin causes nuclear relaxation. The correlation time for the electron nucleus interaction is presented as well as equations valid for dipolar and contact interaction. To do so, electron relaxation mechanisms need to be quickly reviewed. All the subtleties of nuclear relaxation enhancements are presented pictorially and quantitatively.
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- Chapter 4 Chemical exchange, chemical equilibria and dynamics
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Source:Current Methods in Inorganic Chemistry, Volume 2
Chemical exchange is capable of affecting the NMR parameters both in terms of shifts and relaxation. The matter is complex and the various detailed treatments may be laborious. Here the exchange of a nucleus between two sites is presented both qualitatively and quantitatively. The exchange time can be measured through saturation transfer experiments. Some thermodynamic parameters are obtained from the NMR parameters by varying the concentration of the species at equilibrium. In this chapter the relaxation due to outer-sphere interactions is introduced as well as the chemical shifts due to bulk paramagnetic effects, which are used to measure the paramagnetism of molecules in solution.
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- Chapter 5 Transition metal ions: Shift and relaxation
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Source:Current Methods in Inorganic Chemistry, Volume 2
The aim of this chapter is that of providing the reader with guidelines for the interpretation of the spectra of compounds with some common metalions. Here, only mononuclear complexes are considered. When dealing with the NMR spectra of a paramagnetic compound in solution, one has first of all to figure out the electron relaxation times (and electron relaxation mechanisms) and the electron-nucleus correlation time, then has to guess nuclear relaxation, in order to set the experiments, and finally has to gain structural and dynamic information from the nuclear relaxation properties and from the hyperfine shifts. The experience of the authors and a fewother pieces of knowledge will be presented in the following sections without any goal of being comprehensive or reviewing the field.
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- Chapter 6 Magnetic coupled systems
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Source:Current Methods in Inorganic Chemistry, Volume 2
Several polymetallic systems experience magnetic coupling, either ferromagnetic or antiferromagnetic. Such magnetic coupling may affect the hyperfine shift and electron relaxation. Beneficial effects are always expected and observed on nuclear relaxation. A series of examples are discussed.
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- Chapter 7 Nuclear overhauser effect
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Source:Current Methods in Inorganic Chemistry, Volume 2
The nuclear Overhauser effect is something very dear to senior NMR researchers. It is the effect which allows us to know which magnetic nuclei are close to other magnetic nuclei, and information on their distances becomes available. Its understanding used to be a must to move towards 2D spectroscopy. Now times are somewhat changed, but…
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- Chapter 8 Two-dimensional spectra and beyond
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Publication year: 2001
Source:Current Methods in Inorganic Chemistry, Volume 2
In this chapter the effects of paramagnetism on several homocorrelated 2D spectroscopies are discussed, and the conditions to minimize the detectability problems arising from these effects are indicated. Emphasis is given to homocorrelated 1H-1H spectroscopies because the adverse effects of paramagnetism are maximal for protons, due to their largest magnetogyric ratio. Once the reader has learned how to optimize these experiments, extension to heterocorrelated 2D or 3D experiments is easy. Finally, those cross correlation effects which are specifically due to the presence of unpaired electrons are discussed.
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- Chapter 9 Hints on experimental techniques
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Source:Current Methods in Inorganic Chemistry, Volume 2
This chapter provides some guidelines on how to acquire simple ID and 2D NMR spectra of paramagnetic molecules. Beginners often loose signals or have problems with the baseline … or may observe artifacts, and then the whole approach may have serious problems.
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- Appendix I NMR properties of nuclei
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix II Dipolar coupling between two spins
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix III Derivation of the equations for contact shift and relaxation
in a simple case- Abstract: 2001
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix IV Derivation of the pseudocontact shift in the case of axial
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix V Relaxation by dipolar interaction between two spins
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix VI Calculation of 〈sz〉: Curie's law
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix VII Derivation of the equations related to NOE
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix VIII Magnetically coupled dimers in the high-temperature limit
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Appendix IX Product operators: Basic tools
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Source:Current Methods in Inorganic Chemistry, Volume 2
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- Chapter 1 Mathematical background
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Publication year: 1999
Source:Current Methods in Inorganic Chemistry, Volume 1
1. The proper description of a microobject (atom, molecule, cluster) is given by quantum mechanics: an operator is attributed to each observable; the operators act on the state vectors (kets); the state vectors bear all the physical information. The Schrödinger equation for stationary states is of key interest. 2. A many-electron wave function can be constructed from the set of occupied one-electron spinorbitals in the form of the Slater determinant. The molecular orbitals in the LCAO form are determined by solving the Roothaan equations. The MO method is improved by the configuration interaction. For evaluation of the matrix elements of operators over the determinantal functions, the Slater rules are helpful. 3. The linear variation method and the perturbation method for stationary states belong to the most important approximate methods of quantum mechanics. The latter exists in several variants. 4. The angular momentum vector can adopt only certain, quantised values and its orientation is limited to only certain, quantised projections. Its eigenfunctions are represented by spherical harmonics. 5. For a proper addition of angular momenta certain vector coupling coefficients are required: the Clebsch-Gordan coefficients, or alternatively the 3j-symbols, the 6j-symbols and 9j-symbols, for the coupling of two, three and four angular momenta, respectively. The 3j-symbols can be calculated through the Racah formula; the 6j-symbols can be expressed in terms of the 3j-symbols; and the 9j-symbols are evaluable with the help of either 3j-symbols or 6j-symbols. For some special cases closed-form formulae also exist. 6. The eigenvectors of the compound angular momentum can be generated by a recursion procedure: two angular momenta are coupled with the help of the Clebsch-Gordan coefficients, forming an intermediate coupling matrix. Then the next angular momentum is added: the next-generation coupling matrix is created from the previous-generation coupling matrix and a new set of the Clebsch-Gordan coefficients. 7. Any second-rank cartesian tensor with nine components is reducible into three parts: a scalar (the trace, one component), the polar vector (three components) and a symmetric traceless tensor (five components). Such a tensor incorporates the isotropic, antisymmetric and anisotropic contributions. An irreducible spherical tensor transforms under the rotations like a spherical harmonic function. The tensor (direct) product of two irreducible tensor operators is, in general, reducible. An irreducible tensor product is formed through a proper linear combination by using the Clebsch-Gordan coefficients. 8. The Wigner-Eckart theorem allows the expression of the matrix element of a tensor operator through the reduced matrix elements (free of projections of angular momenta) and a coupling coefficient (the 3j-symbol). The reduced matrix elements of the compound angular momentum are evaluable according to the decoupling formula in which the reduced matrix elements of the uncoupled angular momenta and a 9j-symbol occur. Such an evaluation does not require an explicit form of the coupled wave functions. The replacement theorem allows one to express the matrix elements of any tensor operator using the matrix elements formed from the angular momentum operators and the ratio of the reduced matrix elements. 9. Group theory is an extremely useful tool for simplifying the relationships in systems possessing symmetry operations. All the information about the symmetry properties is carried by the characters of the irreducible representations within the given point group of symmetry. For theories dealing with the spin, including the magnetic energy levels, the double group concept is applicable.
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- Chapter 2 Macroscopic magnetic properties
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Source:Current Methods in Inorganic Chemistry, Volume 1
Summary o 1. The magnetic susceptibility is introduced as a thermodynamic quantity which requires a partial differentiation of the magnetisation according to the applied field. This differential (isothermal) magnetic susceptibility differs from the frequent definition of mean magnetic susceptibility if the behaviour of the magnetic material is nonlinear. 2. Different experimental techniques, depending on whether they register the magnetic response in static or alternating fields, yield different types of magnetic susceptibility. In certain situations a correction to the demagnetisation effects is necessary. 3. A linkage between quantum theory (Hamiltonian, energy levels) and the macroscopic thermodynamical quantities (magnetisation, magnetic heat capacity, magnetic susceptibility) is given by statistical thermodynamics, in which the partition function adopts a key role.
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- Chapter 3 Microscopic magnetic properties
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Publication year: 1999
Source:Current Methods in Inorganic Chemistry, Volume 1
Summary o 1. The electronic orbital angular momentum, the electron spin and the nuclear spins belong to the magnetoactive components of a molecule. When the energy of the molecule depends upon the magnetic field induction, the electronic magnetic moment and the nuclear magnetic moments, its second derivatives represent a set of magnetic parameters: the (reduced) magnetic susceptibility tensor, the differential electron g-tensor, the electron spin-spin interaction tensor, the magnetic shielding tensors, the nuclear spin-spin interaction tensors and the electron-nuclear hyperfine coupling tensors. 2. The electron spin can be introduced phenomenologically through the Pauli equation which is a natural extension of the Schrödinger equation. The energy shift due to the electron spin interacting with the magnetic field is the Zeeman effect. The spin-orbit interaction term, which will assume a crucial importance in transition metal and lanthanide atoms, can be introduced through some mechanistic speculations. 3. The magnetic parameters can be expressed in terms of the (sum over the states) perturbation theory in which the appropriate perturbation operators, individual for the given type of magnetic interaction, occur. These operators can be derived from the electromagnetic potential acting on the electrons and nuclei. The effect of the nuclear structure is expressed through the nuclear quadrupole moment and the corresponding Hamiltonian term.
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- Chapter 4 Relativistic approach
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Source:Current Methods in Inorganic Chemistry, Volume 1
Summary o 1. The Dirac equation represents a proper relativistic form of the characteristic equation for energy. It is fulfilled for state vectors in a form of a four-component spinor. Since the upper two-component spinor dominates in the positive energy solutions for an electron, a decomposition of the Dirac equation is appropriate. 2. In the presence of the electromagnetic potential a new term appears in the quadratic form of the Dirac equation. This allows an introduction of the intrinsic magnetic moment of an electron, generated by its spin, which interacts with the external magnetic field. 3. The decoupling of the Dirac equation to the two-component form is a rather complicated process. It manipulates the resolvant operator which is transferred from the denominator to the numerator and then exposed to consecutive commutator relations in order to be shifted to the far right. Finally, a number of one-electron terms of the order 1/c 2 is obtained; some of them have no classical analogy and cannot be derived from non-relativistic theories. 4. The Lorenz transformation requires some additional terms in the electron-electron interaction resulting in the Breit operator. The two-electron Breit Hamiltonian consists of the Dirac Hamiltonian for the individual electrons plus the Breit operator. The decoupling of the Breit equation to the upper-upper subspace of interest results in the appearance of several new Hamiltonian terms. 5. Slight modification of the electron g-factor is due to the radiative corrections introduced through quantum electrodynamics. The magnetogyric factor is different for the Zeeman interaction and the spin-orbit term.
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- Chapter 5 Evaluation of magnetic parameters
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Source:Current Methods in Inorganic Chemistry, Volume 1
Summary o 1. Several quantum-chemical methods have been developed for the direct evaluation of magnetic parameters. These are based either on the Rayleigh-Schrödinger, sum-over-the-states, perturbation theory or, alternatively, on the finite perturbation theory. Two main problems arise: the gauge variance in the limited basis set for κ ¯ ¯ , Δ g ¯ ¯ a n d σ ¯ ¯ N , tensors, and the problem of calculation of excitation energies. The first problem is more or less successfully solved by the GIAO, IGLO, LORG, IGIAM, DOGON and CTOCD methods; the second one via the RPA approach. The magnetic parameters are partitioned into the diamagnetic (first-order) and paramagnetic (second-order) contributions. 2. Direct ab initio calculations of magnetic parameters are usually restricted to the magnetic susceptibility and the nuclear shielding tensors. Only recently have calculations of the g-tensor appeared. 3. The evaluation of the magnetic parameters can also be done with the help of the electronic current density. This observable can be visualised by oriented contour lines. 4. The diamagnetic part of the magnetic susceptibility obeys additivity over the atomic or functional groups. Most frequently the set of empirical Pascal constants is exploited in order to give an estimate of the underlying diamagnetism. The temperature-independent paramagnetic term is estimated less accurately. 5. Hand calculations (estimates) of the electronic magnetic parameters κ ¯ ¯ , Δ g ¯ ¯ a n d D ¯ ¯ are enabled through the concept of the molecular Λ-tensor. It needs the evaluation of the matrix elements of the angular momentum and the (empirical) values of the spin-orbit coupling constant ξd and/or splitting parameter λ along with the experimental excitation energies.
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- Chapter 6 Temperature dependence of magnetic susceptibility
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Publication year: 1999
Source:Current Methods in Inorganic Chemistry, Volume 1
Summary o 1. The magnetisation and consequently the magnetic susceptibility can be generated by several methods. Among them the van Vleck formula belongs to the most popular treatment. However, it can be violated at a low temperature and at a high magnetic field. It can then be substituted by more complex numerical treatments. 2. For Curie paramagnets analytic functions were derived: the Brillouin function and its classical analogue, the Langevin function. 3. Fitting the magnetic susceptibility to experimental data needs a proper definition of the error functional which is being minimised. There are several optimisation algorithms based either on the gradient or on non-gradient philosophy. Some of them, like the simulated annealing method, are capable of identifying the global minimum of the error functional.
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- Chapter 7 Types of magnetic materials
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Source:Current Methods in Inorganic Chemistry, Volume 1
There are three principal classes of magnetic materials: diamagnetics, paramagnetics and ordered materials. o 1. The diamagnetics (including superconductors) possess a negative magnetic susceptibility which is temperature independent. In general, diamagnetism is a property of all substances and originates in the presence of spin-paired electrons. 2. The paramagnetics have a positive magnetic susceptibility which, at higher temperatures, follows the Curie law. The paramagnetism is generated by unpaired electrons behaving uncorrelated to each other. There is, however, a small contribution of temperature-independent paramagnetism originating in the presence of low-lying excited states. 3. The magnetically ordered materials include the numerous class of the ferromagnetics (spin magnetic moments of unpaired electrons aligned parallel below T c) and the antiferromagnetics (an antiparallel alignment of spin magnetic moments below T N). An incomplete compensation of the magnetic moments occurs in ferrimagnetics. The temperature behaviour of magnetisation in these materials is, in general, complex. 4. There are several other classes of magnetically ordered materials where the spatial distribution of the microscopic magnetic moments is more complex.
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- Chapter 8 Single magnetic centres
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Publication year: 1999
Source:Current Methods in Inorganic Chemistry, Volume 1
Summary o 1. For Curie paramagnets non-linear behaviour is observed at low temperature and high fields, i.e. when the linear approximation to the Brillouin function is violated. 2. For systems with spin S >- 1 the zero-field splitting of energy levels appears. These substances may exhibit a step increase of the magnetisation (the temperature should be low and the magnetic field high). Consequently the mean and differential magnetic susceptibilities differ substantially. 3. Transition metal centres with magnetic angular momentum, i.e. systems with ground T-terms, exhibit a complicated variance of magnetic susceptibility which is better visualised when the product function (x mol T) and/or the effective magnetic moment μeff is plotted versus the temperature. Its field dependence becomes pronounced with increasing magnetic field at low temperature. 4. A departure from cubic symmetry may generate a denser spacing of relevant, temperature-populated energy levels, and a non-linear magnetic response tends to be more pronounced. 5. Several levels of theory can be distinguished which more or less completely cover the active space of the state kets. When the active space is extended to all (relevant) terms of the given dn electron configuration, then the magnetic parameters, i.e. the Δ g ¯ ¯ , D ¯ ¯ and κ ¯ ¯ p a r a tensors, are blank. If the active space is more restricted, to only a few magnetic levels, the magnetic parameters become filled. Thus, in magnetochemistry no matching of g-factors with electron spin resonance readings is necessary: for a Co(II) system the magnetochemical g-values may be either close to the free-electron value of ge = 2.0023 (when the active space is extended enough) or close to ESR values (g eff = 4 – 13) when only a few magnetic levels are included in the active space.
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- Chapter 9 Spin crossover systems
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Publication year: 1999
Source:Current Methods in Inorganic Chemistry, Volume 1
Summary o 1. Spin crossover (a low-spin to high-spin transition) occurs in many d 4 to d 7 metal complexes and dominates just for iron(II) compounds. It can be monitored by several experimental techniques among which magnetic susceptibility measurements are the most informative. 2. The high-spin mole fraction as a function of temperature can adopt several different profiles: abrupt/gradual, complete/incomplete, one-step/two-step, and with/without hysteresis. 3. Spin crossover is associated with a positive enthalpy change and positive entropy change; thus the change in the Gibbs energy alters the sign at the critical temperature above which the high-spin species becomes thermodynamically more stable. There are several macroscopic (thermodynamic) and microscopic models of spin crossover. Among them the regular solution model and the two-level Ising-like model are formally equivalent. Both deal with the cooperativity parameters which, above a critical value, are responsible for the hysteresis effect. A non-linear dependence of the equilibrium constant of the low-spin to high-spin transition versus inverse temperature (the Arrhenius plot) originates in the non-zero cooperativity parameter. 4. Two-step spin crossover and spin crossover in dinuclear compounds has roots in a proper combination of the inter-sublattice interaction parameter (which is ferromagnetic) and the intra-sublattice one (antiferromagnetic). 5. A large number of different factors influence spin crossover. In addition to temperature-induced spin crossover, light-induced spin transition is also known; this is the basis of the LIESST and reverse-LIESST effects, respectively. Of great interest is the utilisation of thermal hysteresis for data recording and construction of display units.
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