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 sűrűség funkcionálok (DFT) részletes analízisét végeztem. Ebben a több-elektron sűrűség tulajdonságait és viselkedését analizáltam a két Hohenberg-Kohn (HK) tétel tekintetében. Az analízis kiterjedt a sűrűség funkcionál és a sűrűség differenciál-, illetve integrál operátorainak formáira a dimenziók különböző szintjein a variációs elv (4N dim.) és a HK tételek (3 dim.) között. Kimondtam az 1. és 2. HK tételek általánosítását 3 és 4N közötti dimenziókra (N= elektronok száma) [doi: 10.1016/j.theochem.2008.03.007]. Az elektronikus Schrödinger egyenletet 3 dimenzióra redukáltam, melyben a Thomas-Fermi kinetikus és Parr elektron-elektron taszítás energia funkcionál közelítések alapján egy algoritmust [DOI: 10.1002/jcc.21161] dolgoztam ki a molekulák egy-elektron sűrűségének kompakt kifejezésére, valamit az alapállapot energia számolására. A feladat így a funkcionálok nehézkes minimalizálásáról egy egyváltozós függvény minimum keresésére redukálódik. Ez, mint generátor függvény szolgálhat későbbi, pontosabb egy-elektron sűrűség modellekben. Részbeni alkalmazásként, olyan rendszerekre, mely fématomokat is tartalmaz, egy általam jól ismert rendszert választottam, a metil-piruvát fő orientációinak vizsgálatát cinkona alkaloidok (cinkonin és izo-cinkonin) erőterében. Ezen az úton a különböző mechanisztikus modellek eredete az aktívált ketonok hidrogénezésére cinkona alkaloiddal módosított platina felületen közös rendszerbe volt foglalható [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

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

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

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

Solving the non-relativistic electronic Schrödinger equation with switching the electron-electron Coulomb integrals off and on

The non-relativistic electronic Hamiltonian, H(a)= HHne+aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution of real (physical) a=1 case is generated thereafter from it to calculate the total electronic energy (Etotal electr,K) mainly for ground state (K=0). This strategy is worked out with utilizing generalized Moller-Plesset (MP), square of Hamiltonian (H2 ) and Configuration interactions (CI) devices. Applying standard eigensolver for Hamiltonian matrices (one or two times) buys off the needs of self-consistent field (SCF) convergence in this algorithm, along with providing the correction for basis set error and correlation effect. (SCF convergence is typically performed in the standard HF-SCF/basis/a=1 routine in today practice.