145 research outputs found
Kohn-Sham formalizmustól eltérő (hatványsoros) sűrűség funkcionál algoritmus kidolgozása kémiai potenciálfelületek vizsgálatára. = Non Kohn-Sham formalism density functional algorithm (using power series) for calculating chemical potential energy surfaces.
A sűrűsĂ©g funkcionálok (DFT) rĂ©szletes analĂzisĂ©t vĂ©geztem. Ebben a több-elektron sűrűsĂ©g tulajdonságait Ă©s viselkedĂ©sĂ©t analizáltam a kĂ©t Hohenberg-Kohn (HK) tĂ©tel tekintetĂ©ben. Az analĂzis kiterjedt a sűrűsĂ©g funkcionál Ă©s a sűrűsĂ©g differenciál-, illetve integrál operátorainak formáira a dimenziĂłk kĂĽlönbözĹ‘ szintjein a variáciĂłs elv (4N dim.) Ă©s a HK tĂ©telek (3 dim.) között. Kimondtam az 1. Ă©s 2. HK tĂ©telek általánosĂtását 3 Ă©s 4N közötti dimenziĂłkra (N= elektronok száma) [doi: 10.1016/j.theochem.2008.03.007]. Az elektronikus Schrödinger egyenletet 3 dimenziĂłra redukáltam, melyben a Thomas-Fermi kinetikus Ă©s Parr elektron-elektron taszĂtás energia funkcionál közelĂtĂ©sek alapján egy algoritmust [DOI: 10.1002/jcc.21161] dolgoztam ki a molekulák egy-elektron sűrűsĂ©gĂ©nek kompakt kifejezĂ©sĂ©re, valamit az alapállapot energia számolására. A feladat Ăgy a funkcionálok nehĂ©zkes minimalizálásárĂłl egy egyváltozĂłs fĂĽggvĂ©ny minimum keresĂ©sĂ©re redukálĂłdik. Ez, mint generátor fĂĽggvĂ©ny szolgálhat kĂ©sĹ‘bbi, pontosabb egy-elektron sűrűsĂ©g modellekben. RĂ©szbeni alkalmazáskĂ©nt, olyan rendszerekre, mely fĂ©matomokat is tartalmaz, egy általam jĂłl ismert rendszert választottam, a metil-piruvát fĹ‘ orientáciĂłinak vizsgálatát cinkona alkaloidok (cinkonin Ă©s izo-cinkonin) erĹ‘terĂ©ben. Ezen az Ăşton a kĂĽlönbözĹ‘ mechanisztikus modellek eredete az aktĂvált ketonok hidrogĂ©nezĂ©sĂ©re cinkona alkaloiddal mĂłdosĂtott platina felĂĽleten közös rendszerbe volt foglalhatĂł [DOI: 10.1021/jp9064467]. | A detailed analysis of density functionals (DFT) is performed. The properties and behavior of multi-electron density are analysed between the two Hohenberg-Kohn (HK) theorems. The analysis has covered the forms of density functionals and density differential- and integral operators in different dimensions between the variational principle (4N dim.) and HK theorems (3 dim.). The generalization of 1st and 2nd HK theorems is stated between 3 and 4N dim. (N= # of electrons) [doi: 10.1016/j.theochem.2008.03.007]. The electronic Schrödinger equation is reduced to 3 dimension, based on the Thomas-Fermi kinetic- and Parr electron-electron repulsion energy approximate functionals. An algorithm [DOI: 10.1002/jcc.21161] is described for the compact expression of one-electron density of molecules, as well as for the ground state electronic energy. In this way, the task is reduced from the difficult minimization of functionals to locate the minima of a one-variable function. This can serve as generator function in more accurate one-electron density models. Partial application of the method above for systems containing metal atoms, the investigation of main orientations of methyl-piruvat was chosen in the force field of cinkona alkaloids (cinkonin and izo-cinkonin). As a consequence, the origin of different mechanistic models for the hydrogenation of activated ketons on cinkona alkaloid modified platinum surface was revealed [DOI: 10.1021/jp9064467]
Reformulation of the Gaussian error propagation for a mixture of dependent and independent variables
A LEAST-SQUARE COMPUTATION METHOD FOR SMOOTHING AND DIFFERENTIATION OF TWO-DIMENSIONAL DATA
A computation method to smooth and differentiate data of the z=/(x, y) kind is introduced. Requiring only that the datapoints be equi-distant in x and equi-distant in y, smoothing parameters can be calculated for general use. The greatest advantage of the method is that even higher-level mixed partial derivatives can be calculated directly from the datapoints
STATISTICAL MECHANICAL CALCULATION OF THE EXCESS FREE ENTHALPY OF METAL SURFACES
The excess free enthalpy of metal surfaces is calculated using Ising's model for both
one- and two-dimensional surfaces. The result is in good agreement with experimentally
obtained data
Reformulation of the Gaussian error propagation for a mixture of dependent and independent variables
The Gaussian error propagation is a state of the art expression in error analysis for estimating standard deviation for an expression f(x1,…,xn,z) via its variables. One of its basic assumptions is the independence of the measurable variables in its argument. However, in practice, measurable quantities are correlated somehow, and sometimes, z depends on some of the xi’s. We provide the generalized version of the Gaussian error propagation formula in this case. We will prove this with the formula for total derivative of a general multivariable function for which some of its variables are not independent from the others; a counterpart to the probability approach of this subject
Semi-analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian expansion of Distance Operators W= RC1-nRD1-m, RC1-nr12-m, r12-nr13-m
Abstract. The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb
integrals (r1)…(rk) W(r1,…,rk) dr1…drk, where the one-electron density(r1), is a linear combination (LC) of
Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or
any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron
and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical
expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical
expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer,
positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|
-u
, of which only the
u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the
different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation
calculations. Solving the related linear equation system (LES), the expansion
|r|-u k=0L i=1M Cik r
2k exp(-Aik r
2
)
is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic
expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|
-u
) are useful
for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian
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