Criteria mixed valence

With mixed-valence compounds, charge transfer does not require creation of a polar state, and a criterion for localized versus itinerant electrons depends not on the intraatomic energy defined by U , but on the ability of the structure to trap a mobile charge carrier with a local lattice deformation. The two limiting descriptions for mobile charge carriers in mixed-valence compounds are therefore small-polaron theory and itinerant-electron theory. We shall find below that we must also distinguish mobile charge carriers of intennediate character. 

A general classification scheme for the discussion of the properties of mixed valence compounds has been introduced by Robin and Day 17). Although by no means all the deeply colored transition metal cyanides M [BM(CN) ]2H2O are mixed valence compounds in the strict sense, we will use this classification scheme for the whole group. The classification of the polynuclear cyanides is made on a purely phenomenological basis using the electronic spectra as a criterion. 

Criterion Eight Fractional charge transfer (0 < Z < 1). or mixed-valence. 

As an example of how this stability criterion can be used we consider Eu, which is a divalent metal. In section 3, A n,in(Eu) was ascribed a value of 21kcal/mol. Therefore, in order to find trivalent Eu in a certain type of compound, the heat of formation of this compound formed from pure hypothetically trivalent Eu metal and the other component must numerically be at least 21 kcal/mol Eu larger (more negative Aif than the heat of formation for the divalent compound formed from divalent Eu metal. Similarly we find that mixed valence can occur when the heat of formation difference is close to 21 kcal/mol Eu. 

A simple rule for the occurrence of trans-h A distorted structures 2 at homopolar double bonds was derived from an elementary molecular orbital model treating a-jt mixing and a valence bond treatment . The relation between the singlet-triplet separation (A st) of the constituent ER2 and a +jt bond energy Ea+ was used as a criterion for determining the expected structure of R2E=ER2. The trans-b ai geometry 2 occurs when l/AEa+ < A sT < l/2Ea+n- The first part of the inequality determines the irawi-bending distortion of the double bond, while the second part determines the existence of a direct E=E link. 

The diagonalization of the one-particle density matrix P on the Cl level yields the natural orbitals (NOs) and the occupation numbers of the molecule. In an RHF-SCF calculation, all occupation numbers are either 0 or 2, which means that an MO is either doubly occupied by 2 electrons or not occupied. If we invoke a Cl calculation, the mixing of configurations results in fractional occupation numbers of the NOs. Still in a normal molecule, such as ethane, water, ammonia, etc., the occupation numbers for the ground state will be close to 0 or 2. The occupation numbers of at least two NOs of excited states usually deviate from the values 0 and 2. In a biradicaloid structure occupation numbers will change and typically two of them will be close to 1. However, this method cannot characterize zwitterions since occupation numbers should be close to 0 and 2, respectively, in this case. The approach by Jug and Poredda yields both zwitterionic and diradical character of species, based on the valence criterion of Gopinathan and Jug. The valence is defined according to equation (5), which can be reformulated as equation (6). 

Thus, Eq. 7 shows that Asc/A3 is a suitable criterion for the relevance of chemical expansion of mixed conductors even if this involves complex dependence on defect chemistry. It also emphasises that the chemical expansion coefficient Asc/A3 includes contributions of oxygen ion vacancies as well as changes in ionic radii of cations undergoing gradual reduction to a lower valence state, at least for this class of mixed ionic and p-type conductors. 

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