212,666 research outputs found
The March model applied to boron cages
No full textAbstract: The so-called March model of fullerene, in which a self-consistent spherical distribution of pi electrons is combined with the proper nuclear-nuclear potential energy for the correct structure, is here extended to boron cages. The Thomas-Fermi approximation of the initial studies is here replaced by Hartree-Fock calculations. Explicit results for B-2k and B-2k+1(+), with k ranging from 15 to 27, are discussed and compared with calculations on similar clusters found in the literature. (C) 2001 Elsevier Science B.V. All rights reserved
Approaching the s-wave model ground state energy of He-like atomic ions: results from a model Hamiltonian
No full textAmovilli, Howard and March model Hamiltonian is here extended to an arbitrary interparticle interaction strength. The model remains analytically solvable and the ground state wavefunction with a given, variationally determined, choice of parameters provides an approximate two-electron correlated s-wave function. Results are given for the series of nuclear charges between Z= 1 and 10. More than 60 % of s-wave correlation energy is recovered
An exact coupled cluster theory for Moshinsky and Hookean two-electron model atoms with spin-compensated ground states
No full textAbstract: The Moshinsky (M) and Hookean (H) models of two-electron atoms replace the electron-nuclear interaction by harmonic forces. The difference between them resides in the interparticle interaction, the H model retaining e(2)/r(12) as in helium, whereas the M atom is entirely harmonic. Using a 'coupled cluster' representation that = exp((X) over cap)Phi, (X) over cap is shown to be the sum of a one-body operator (X) over cap (1) and a two-body contribution (X) over cap (2). For Phi taken as a product of Gaussian functions, the one-body operator (X) over cap (1), is of length scaling form. In the M model, (X) over cap (2) is proportional to r(12)(2), whereas in the H model it is given explicitly as an infinite series in powers of r(12). Finally, some comments are added about the He-like ions in the limit of large atomic number. (C) 2003 Elsevier B.V. All rights reserved
The key role of electron-nuclear potential energy in determining the ground-state energy of inhomogeneous electron liquids in both real and model atoms
No full textRecent density functional theory (DFT) work of Gál and March (GM) on the ground-state energy E of a two-electron model atom (like He but with inverse square law interparticle repulsion) related E to the electron–nuclear potential energy by . Also the model of GM satisfies , but now with harmonic confinement. While modern non-relativistic DFT requires numerical treatment of real atoms, in the exact limit of DFT at large Z, the Thomas–Fermi (TF) theory is regained, where much analytical work can be done. This yields, as , the non-relativistic energy of such neutral atoms as . The correlated electron density is finally considered briefly in the two models cited above
The exchange-correlation potential of DFT obtained from a semiempirically fine-tuned Hartree-Fock density for inhomogeneous electron liquids
No full textAbstract: The present authors have given an exact theory of the exchange-correlation potential V-xc(r) in terms of (i) the exact ground-state electron density n(r) and (ii) the idempotent Dirac density matrix gamma(r,r') generated by the DFT one-body potential V(r), having n(r) as its diagonal element. Here, we display two approximate consequences: (a) a form of V-xc(r) generated by the semiempirically fine-tuned HF density of Cordero et al. (N.A. Cordero, N.H. March, and J.A. Alonso, Phys. Rev. A 75, 052502 (2007)) and (b) the exchange-only potential V-x(r) determined solely by the HF ground state density for the Be atom
A form of the single-particle kinetic energy density of an inhomogeneous electron liquid from a combination of one-body potential and ground-state electron density
No full textAbstract: Gal and March have recently proposed a form of the single-particle kinetic energy density in density functional theory in terms of the one-body potential V(r) and the ground-state electron density n(r) generated thereby. Here, with a minor modification of the GM form, examples are given for (a) harmonic trapping and (b) a bare Coulomb potential. The case of the He atom is also considered, via the Chandrasekhar variational wave function. Finally, the use of the semiempirical fine-tuned Hartree-Fock n(r) for spherical atoms due to Cordero et al. is briefly referred to
Two-dimensional electrostatic analog of the March model of C60 with a semiquantitative application to planar ring clusters
No full textOrnstein-Zernike function and Coulombic correlation in the homogeneous electron liquid
No full textAbstract: Adopting the original Ornstein-Zernike (OZ) definition of the direct correlation function c(r), the present study deals with the deviation Delta(r) of c(r) induced by Coulomb correlation in the homogeneous electron liquid beyond the OZ function c(FH)(r) for purely Fermi hole (FH) statistical correlations. It is first stressed that Delta(r) at large r is proportional to the Coulomb potential energy e(2)/r, suitably scaled with the plasma frequency. Both r space and k space formulations are presented. In k space, direct numerical use is made of inequalities due to Kugler [Phys. Rev. A 1, 1688 (1970)] by employing analytic representations of the pair correlations due to Gori-Giorgi [Phys. Rev. B 61, 7353 (2000)] as a function of the uniform electron density. Then, in r space, consideration is given to differential equations proposed by Dawson and March [Phys. Chem. Liq. 14, 131 (1984)] and also in the recent study of Nagy and Amovilli [J. Chem. Phys. 121, 6640 (2004)]. In both approaches, one-body potentials enter, into which Coulombic interelectronic repulsions are subsumed. Finally, Gaskell's [Proc. Phys. Soc. London 77, 1182 (1961)] variational ground-state wave function is shown to be related to the OZ direct correlation function in k space
Personal Papers (MS 80-0002)
No full textLetter from Isaac H. Kempner to A. H. Ormsby inviting him and his wife to his house on March 24, 1949
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