Monotonicity of the electron momentum density for atomic closed shells in a bare Coulomb field

Smith, Vedene H.; Robertson, Donald D.; Tripathi, A. N.

doi:10.1103/physreva.42.61

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…March 6 showed that the total electron density is a monotonically decreasing function for an arbitrary number of closed shells in the BCF case. In contrast, the same property was also shown for the total momentum density in the closed‐shell case 7. In fact, the one‐particle momentum density Π b ( p ) for ℳ︁ closed shells is given by (see Ref.…”

Section: Introductionsupporting

confidence: 58%

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Bare Coulomb field and atomic reciprocal form factor

Angulo

Romera

2005

Int J of Quantum Chemistry

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ABSTRACT:The reciprocal form factor of N-electron closed shells systems in a bare Coulomb field is shown to be a spherically symmetric, positive, and decreasing function of the radial distance. Nonmonotonicities of the reciprocal form factor appear when studying bare Coulomb field open-shell systems. Analysis of the weight of the interelectronic repulsion term is carried out for some isoelectronic series as well as neutral atoms with N ϭ 1-103.

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Section: Introductionsupporting

confidence: 58%

“…In fact, the one‐particle momentum density Π b ( p ) for ℳ︁ closed shells is given by (see Ref. 7, and references therein): with p j = Z / j [Coulomb potential V ( r ) = − Z / r ]. The normalization will be given by where N is the number of electrons in the system.…”

Section: Introductionmentioning

confidence: 99%

Bare Coulomb field and atomic reciprocal form factor

Angulo

Romera

2005

Int J of Quantum Chemistry

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“…Type II. The 22 cations with Zϭ10,11,[17][18][19]23,24,[27][28][29][35][36][37]41 42,[44][45][46][47][53][54][55] and the 21 anions with Zϭ5 -9, 13-17, 31-35, 39, 49-53 have unimodal ⌸(p) with a local minimum at pϭ0 and a maximum at p max Ͼ0.…”

Section: Modalities Of Momentum Densitiesmentioning

confidence: 99%

Electron-momentum densities of singly charged ions

et al. 1999

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Spherically averaged electron momentum densities ⌸( p) are constructed by the numerical Hartree-Fock method for 54 singly charged atomic cations from He ϩ ͑atomic number Zϭ2) to Cs ϩ (Zϭ55) and 43 anions from H Ϫ (Zϭ1) to I Ϫ (Zϭ53) in their experimental ground state. As in the case of neutral atoms, the Hartree-Fock momentum densities for all these ions can be classified into three types; 28 cations and 10 anions have a unimodal density with a maximum at pϭ0, 22 cations and 21 anions have a unimodal density with a maximum at pϾ0, and 4 cations and 12 anions have a bimodal density with a primary maximum at pϭ0 and a secondary maximum at pϾ0.

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“…Some results have been rigorously proved concerning BCF densities. For instance, March showed that the electron charge density is a monotonically decreasing function for an arbitrary number of closed shells in the BCF case 1, and also the same property holds in the momentum space 3. Additional results for the kinetic and total energies have been also obtained 4–6.…”

Section: Introductionmentioning

confidence: 88%

Effect of the interelectronic repulsion on the information content of position and momentum atomic densities

Angulo¹,

López-Rosa²,

Antolín³

2009

Int J of Quantum Chemistry

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ABSTRACT:The interelectronic repulsion is strongly responsible of the main structural characteristics of the atomic densities and, in particular, of their level of information content. In this work, the effect of such a repulsion on some information-theoretic descriptors is quantified and analyzed by considering different complexities and distances between the Bare Coulomb Field (BCF) and the Hartree-Fock (HF) position and momentum densities of neutral atoms throughout the Periodic Table. In doing so, the Quantum Similarity Index (QSI), the Quadratic Distance (QD), the Jensen-Shannon (JSD) and Fisher (FD) Divergences as well as complexity measures are employed.

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Monotonicity of the electron momentum density for atomic closed shells in a bare Coulomb field

Cited by 9 publications

References 21 publications

Bare Coulomb field and atomic reciprocal form factor

Bare Coulomb field and atomic reciprocal form factor

Electron-momentum densities of singly charged ions

Effect of the interelectronic repulsion on the information content of position and momentum atomic densities

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