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The condensed Fukui function or condensed reactivity indicator is the same idea, but applied to an atom within a molecule, rather than a point in three-dimensional space. The Fukui function allows one to predict, using density functional theory , where the most electrophilic and nucleophilic sites of a molecule are.
Yang's main contributions to theoretical chemistry range from fundamental theory to applications of density functional theory. He (with Parr) developed the concepts of the Fukui function, [1] hardness, and softness [2] in density functional theory. He also justified the theoretical ground of potential functional (as in Optimized-Effective ...
This response function is important as the reaction of two components A and B involving a transfer of electrons will depend on the responsiveness of the electron density to electron donation or acceptance, i.e. the derivative of the Fukui function () = (). In fact, from a simplistic viewpoint, the dual descriptor function gives a readout on the ...
The first family of Minnesota functionals, published in 2005, is composed by: M05: [13] Global hybrid functional with 28% HF exchange. M05-2X [14] Global hybrid functional with 56% HF exchange.
To produce simple poles on boson frequencies =, either of the following two types of Matsubara weighting functions can be chosen () = = = (+ ()),() = = (),depending on which half plane the convergence is to be controlled in. () controls the convergence in the left half plane (Re z < 0), while () controls the convergence in the right half plane (Re z > 0).
The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
LibreOffice Calc is the spreadsheet component of the LibreOffice software package. [6] [7]After forking from OpenOffice.org in 2010, LibreOffice Calc underwent a massive re-work of external reference handling to fix many defects in formula calculations involving external references, and to boost data caching performance, especially when referencing large data ranges.