Density functional theory derivatives

Bartolotti, L and E. O. Edney, Density Functional Theory Derived Intermediates from the OH Initiated Atmospheric Oxidation of Toluene, Chem. Phys. Lett., 245, 119-122 (1995). 

Perdew J P, Parr R G, Levy M and Balduz J L Jr 1982 Density-functional theory for fractional particle number derivative discontinuities of the energy Phys. Rev. Lett. 49 1691-4... 

B3LYP Becke-style 3-Parameter Density Functional Theory Through 2nd derivatives (using the Lee-Yang-Parr correlation functional) ... 

Molecular frequencies depend on the second derivative of the energy with respect to the nuclear positions. Analytic second derivatives are available for the Hartree-Fock (HF keyword). Density Functional Theory (primarily the B3LYP keyword in this book), second-order Moller-Plesset (MP2 keyword) and CASSCF (CASSCF keyword) theoretical procedures. Numeric second derivatives—which are much more time consuming—are available for other methods. 

Density functional theory-based methods ultimately derive from quantum mechanics research from the 1920 s, especially the Thomas-Fermi-Dirac model, and from Slater s fundamental work in quantum chemistry in the 1950 s. The DFT approach is based upon a strategy of modeling electron correlation via general functionals of the electron density. 

Besides the already mentioned Fukui function, there are a couple of other commonly used concepts which can be connected with Density Functional Theory (Chapter 6). The electronic chemical potential p is given as the first derivative of the energy with respect to the number of electrons, which in a finite difference version is given as half the sum of the ionization potential and the electron affinity. Except for a difference in sign, this is exactly the Mulliken definition of electronegativity. ... 

Quantum-chemical calculations which utilize the density functional theory (DFT) are now perhaps amongst the most frequently performed because of their relatively low cost and high accuracy. Structural results obtained from DFT based methods are often as good as those derived from MP2 calculations. It is well documented that DFT methods, especially those involving hybrid functionals such as B3LYP, B3P86 and B3PW91, yield reliable... 

In the Hartree-Fock approach, the many-body wave function in form of a Slater determinant plays the key role in the theory. For instance, the Hartree-Fock equations are derived by minimization of the total energy expressed in terms of this determinantal wave function. In density functional theory (3,4), the fundamental role is taken over by an observable quantity, the electron density. An important theorem of density functional theory states that the correct ground state density, n(r), determines rigorously all electronic properties of the system, in particular its total energy. The totd energy of a system can be expressed as a functional of the density n (r) and this functional, E[n (r)], is minimized by the ground state density. 

ROsch N (1999) A Critical Assessment of Density Functional Theory with Regard to Applications in Organometallic Chemistry. 4 109-163 Roucoux A (2005) Stabilized Noble Metal Nanoparticles An Unavoidable Family of Catalysts for Arene Derivative Hydrogenation. 16 261-279... 

Specific aspects examined here include insights and conclusions derived from the most recently performed density functional theory (DFT) calculations, which have been based on a comprehensive model of the electrochemical interface, and the strong disagreements (which seem to defy all recent theoretical efforts) that remain regarding proper interpretation of experimental ORR results and proper identihcation of the ORR mechanism in a PEFC cathode employing Pt catalysts. 

What does this mean We have replaced the non-local and therefore fairly complicated exchange term of Hartree-Fock theory as given in equation (3-3) by a simple approximate expression which depends only on the local values of the electron density. Thus, this expression represents a density functional for the exchange energy. As noted above, this formula was originally explicitly derived as an approximation to the HF scheme, without any reference to density functional theory. To improve the quality of this approximation an adjustable, semiempirical parameter a was introduced into the pre-factor Cx which leads to the Xa or Hartree-Fock-Slater (HFS) method which enjoyed a significant amount of popularity among physicists, but never had much impact in chemistry,... 

Burke, K., Perdew, J. R, Wang, Y., 1998, Derivation of a Generahzed Gradient Approximation The PW91 Density Functional , in Electronic Density Functional Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

Perdew, J. P., Parr, R. G., Levy, M., Balduz, J. L., Jr., 1982, Density Functional Theory for Fractional Particle Number Derivative Discontinuities of the Energy , Phys. Rev. Lett., 49, 1691. 

In a rigorous sense, non-transferability of molecular parts has profound implications on chemical conclusions based on electron densities. Since some of the original results on the utility and reliability of transferred electron densities have been derived within the framework of density functional theory, here we shall follow this approach, and describe a recent result on a general, holographic property of electron density fragments of complete, boundaryless molecular electron densities. 

Applying the variational principle to the energy given by Eq. 1, Kohn and Sham reformulated the density functional theory by deriving a set of one-electron Hartree-like equations leading to the Kohn-Sham orbitals v().(r) involved in the calculation of p(r)15. The Kohn-Sham (KS) equations are written as follows ... 

Wesolowski and Warshel197 introduced a DFT based approach in which all short-range terms in the effective Hamiltonian (Eq. 4.25) were derived entirely from density functional theory and were involved in the construction of the Fock matrix195 196. In this approach, the H croEnv is expressed using explicit functionals of the electron density ... 

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