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The variational theorem guarantees that the lowest value of that gives rise to a nontrivial (that is, not all zero) solution vector (,, …,) represents the best LCAO approximation of the energy of the most stable π orbital; higher values of with nontrivial solution vectors represent reasonable estimates of the energies of the remaining π ...
The off-diagonal Hamiltonian matrix elements are given by an approximation due to Wolfsberg and Helmholz that relates them to the diagonal elements and the overlap matrix element. [2] = + K is the Wolfsberg–Helmholz constant, and is usually given a value of 1.75. In the extended Hückel method, only valence electrons are considered; the core ...
This is still used occasionally as an approximation, though the more precise PPP Pariser–Parr–Pople method succeeded it in 1953. "Extended Hückel MO theory" ( EHT ) applies to both sigma and pi electrons, and has its origins in work by William Lipscomb and Roald Hoffmann for nonplanar molecules in 1962.
For table salt in 0.01 M solution at 25 °C, a typical value of () is 0.0005636, while a typical value of is 7.017, highlighting the fact that, in low concentrations, () is a target for a zero order of magnitude approximation such as perturbation analysis. Unfortunately, because of the boundary condition at infinity, regular perturbation does ...
In 1923, Peter Debye and Erich Hückel reported the first successful theory for the distribution of charges in ionic solutions. [7] The framework of linearized Debye–Hückel theory subsequently was applied to colloidal dispersions by S. Levine and G. P. Dube [8] [9] who found that charged colloidal particles should experience a strong medium-range repulsion and a weaker long-range attraction.
Hückel or Huckel may refer to: Erich Hückel (1896-1980), German physicist and chemist Debye–Hückel equation (named after Peter Debye and Erich Hückel), in chemistry, a method of calculating activity coefficients; Hückel method (named after Erich Hückel), a method for the determination of energies of molecular orbitals
There is no general analytical solution for mixed electrolytes, curved surfaces or even spherical particles. There is an asymptotic solution for spherical particles with low charged DLs. In the case when electric potential over DL is less than 25 mV, the so-called Debye-Huckel approximation holds.
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak ...