Electron density description of atoms and molecules

Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates

“…In the framework of the modern density functional theory, [1][2][3][4][5] the physical and chemical properties of a many fermion system may be completely described by means of the single-particle probability density, which is to be denoted by ͑r͒ in position space and ␥͑p͒ in momentum space. The spread or extent of these quantum-mechanical probability densities is measured by the Boltzmann-Shannon information entropy, which for one-dimensional systems is defined as S ϭϪ ͵ Ϫϱ ϱ ͑x͒ln ͑x ͒dx, ͑1͒…”

Discrete Entropies of Orthogonal Polynomials

“…This proves (18)- (19). On the other hand, if GCD(j, 2n) = 2d < 2n, then by Proposition 6, j/d is even and n/d is odd, and by (iii) of Proposition 5,…”

“…This interest originated in the framework of the modern density functional theory [14,15,19], that states that the physical and chemical properties of fermionic systems (atoms, molecules, nuclei, solids) may be completely described by means of the single-particle probability density. For instance, if the solution of the time-independent Schrödinger equation in a D-dimensional position space for an single particle system, HΨ( r) = EΨ( r) , r = (x 1 , .…”

Derivation of von Weizsäcker Equation Based οn Green-Gauss Theorem

“…. , N is set of occupied one-electron Kohn-Sham eigenfunctions [2,1,11,10,3]. If each eigenfunction Ψ i (r) is occupied by one electron, then the electron charge distribution is defined as…”

“…The key point is that ThomasFermi model is exact only for the free electron gas. The Thomas-Fermi model applied to molecular systems gives quite poor results [10,11]. More reliable model was introduced by von Weizsäcker, which is derived using the density matrix formalism.…”