4,756 research outputs found
Ornstein-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
Asymptotic form at large r of a third-order linear homogeneous differential equation for the ground-state electron density of the He atom
No full textIn earlier work a linear differential equation satified by the Schwartz ground-state electron density rho(R) for (non-relativistic) He-like atomic ions with large atomic number Z has been derived. Here, we utilize the asymptotic expansion at large r given by Amovilli and March for the neutral He atom. We thereby show that a linear differential equation of the same general shape as that satisfied by the Schwartz rho(r) again emerges for the neutral He atom itself, in the asymptotic limit of large r. We argue that essential input into the final differential equation for the He ground-state electron density will be the ionization potential plus the atomic polarizability
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
Analytic inhomogeneous electron liquid and its density for model spin-compensated two-electron atomic ions with Coulomb confinement: an exact nonrelativistic Hamiltonian
No full textAn 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
Oral History Interview with Norman Ulmer
No full textThe National Museum of the Pacific War presents an oral interview with Norman Ulmer. Ulmer joined the Navy in March 1941 and received basic training in Newport, Rhode Island. He received quartermaster signaling training in San Diego. Upon completion, he was assigned to the flag allowance aboard USS Chicago (CA-29) under Rear Admiral Newton. Ulmer witnessed the devastation at Pearl Harbor one week after the attack. In February 1942 he left Pearl Harbor for the South Pacific on USS Yorktown (CV-5) under Rear Admiral Fletcher. He recalls interactions with the natives of Tongatapu. But soon after, his ship was bombed and he lost 38 crewmen. He watched USS Lexington (CV-2) burn. And he witnessed a commander’s accidental death. When the Yorktown was finally sunk, Ulmer was rescued by USS Russell (DD-414). He was reassigned to USS Essex (CV-9) and survived a kamikaze attack during the Battle of Leyte Gulf. Ulmer returned home and was discharged in 1946 as a signalman, first class. He retired in 1982 as a veteran’s employment representative for the Pennsylvania Department of Labor and Industry
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
Two-dimensional electrostatic analog of the March model of C60 with a semiquantitative application to planar ring clusters
No full textThe 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
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