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If the structure of a compound is known, the empirical bond valence - bond length correlation of Eq. 2 can be used to estimate the bond valences from their observed bond lengths. Eq. 1 can then be used to check that the structure is chemically valid; any deviation between the atomic valence and the bond valence sum needs to be accounted for.
The intense blue color of Prussian blue is a consequence of an intervalence charge transfer band. In chemistry, intervalence charge transfer, often abbreviated IVCT or even IT, is a type of charge-transfer band that is associated with mixed valence compounds. It is most common for systems with two metal sites differing only in oxidation state.
The bond angle for water is 104.5°. Valence shell electron pair repulsion (VSEPR) theory (/ ˈ v ɛ s p ər, v ə ˈ s ɛ p ər / VESP-ər, [1]: 410 və-SEP-ər [2]) is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. [3]
One of Pauling's examples is olivine, M 2 SiO 4, where M is a mixture of Mg 2+ at some sites and Fe 2+ at others. The structure contains distinct SiO 4 tetrahedra which do not share any oxygens (at corners, edges or faces) with each other. The lower-valence Mg 2+ and Fe 2+ cations are surrounded by polyhedra which do share oxygens.
The main insight of the AKLT paper was that this construction could be generalized to obtain exactly solvable models for spin sizes other than 1/2. Just as one end of a valence bond is a spin 1/2, the ends of two valence bonds can be combined into a spin 1, three into a spin 3/2, etc.
Many such mixed-valence compounds absorb certain wavelengths of visible light resulting from intervalence charge transfer. In this case, orange-red light around 680 nanometers in wavelength is absorbed, and the reflected light appears blue as a result. Like most high-chroma pigments, Prussian blue cannot be accurately displayed on a computer ...
The total wave function is optimized using the variational method by varying the coefficients of the basis functions in the valence bond orbitals and the coefficients of the different spin functions. In other cases only a sub-set of all possible spin functions is used. Many valence bond methods use several sets of the valence bond orbitals.
So the expansion can be written as: = where K = m 1 b 1 + m 2 b 2 + m 3 b 3 for any set of integers (m 1, m 2, m 3). From this theory, an attempt can be made to predict the band structure of a particular material, however most ab initio methods for electronic structure calculations fail to predict the observed band gap.