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It follows from these definitions, that the valence of an atom is equal to the sum of the valences of all the bonds it forms. This is known as the valence sum rule, Eq. 1, which is central to the bond valence model. = (Eq. 1) A bond is formed when the valence shells of two atoms overlap.
In valence bond theory, however, the generated structures are not necessarily orthogonal with each other, and oftentimes have substantial overlap between the two structures. As such, when considering non-orthogonal constituent orbitals (i.e. orbitals with non-zero overlap) the non-diagonal terms in the overlap matrix would be non-zero, and must ...
The Hückel energy of the molecule is , where the sum is over all Hückel orbitals, is the occupancy of orbital i, set to be 2 for doubly-occupied orbitals, 1 for singly-occupied orbitals, and 0 for unoccupied orbitals, and is the energy of orbital i. Thus, the delocalization energy, conventionally a positive number, is defined as
Abegg's rule is sometimes referred to as "Abegg’s law of valence and countervalence". In general, for a given chemical element (as sulfur ) Abegg's rule states that the sum of the absolute value of its negative valence (such as −2 for sulfur in H 2 S and its positive valence of maximum value (as +6 for sulfur in H 2 SO 4 ) is often equal to 8.
The VB wavefunction of CH 4 + would be an equal combination of 4 structures, each having 3 two-electron bonds, and 1 one-electron bond. Based on group theory arguments, these states must give rise to a triply degenerate T 2 state and a single degenerate A 1 state.
A valence bond structure resembles a Lewis structure, but when a molecule cannot be fully represented by a single Lewis structure, multiple valence bond structures are used. Each of these VB structures represents a specific Lewis structure. This combination of valence bond structures is the main point of resonance theory.
The linearized augmented-plane-wave method (LAPW) is an implementation of Kohn-Sham density functional theory (DFT) adapted to periodic materials. [1] [2] [3] It typically goes along with the treatment of both valence and core electrons on the same footing in the context of DFT and the treatment of the full potential and charge density without any shape approximation.
Valence bond (VB) computer programs for modern valence bond calculations:-CRUNCH, by Gordon A. Gallup and his group. [1] GAMESS (UK), includes calculation of VB wave functions by the TURTLE code, due to J.H. van Lenthe. [2] GAMESS (US), has links to interface VB2000, and XMVB.