Pseudoatom expansions of the H2 electron density

Chandler, G. S.; Spackman, Mark A.; Varghese, J.N.

doi:10.1107/s0567739480001350

Cited by 9 publications

(5 citation statements)

References 22 publications

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“…If a further radial function is added to give a two-term expression, the power of r of the additional function is incremented by one. An earlier study on H2 (Chandler et al, 1980) found that both two-and three-term radial functions give very similar results, and so only single and two-term expansions are examined in the present paper.…”

Section: Pbk(rb) = ~ Pnk Nnk R~ Exp(--¢ N Rt ) (4) N=kmentioning

confidence: 88%

“…The methods used are similar to those described in a previous paper (Chandler, Spackman & Varghese, 1980). For a diatomic molecule the calculated electron density is represented as the sum of two nuclearcentred multipole expansions.…”

Section: Methodsmentioning

confidence: 99%

“…The values of these properties calculated from the SCF wavefunctions are given in Table 1 (Bentley, 1974). The calculation of the properties from the pseudoatom expansion PCmo ~ is straightforward and has been discussed by Chandler et al (1980). Difference-density plots are also valuable in assessing the effectiveness of a pseudoatom expansion.…”

Section: Molecular Wavefunctlons and Physical Propertiesmentioning

confidence: 99%

“…However, this rescaling is not unique and it creates difficulties which are discussed more fully later. The choice of n in (4) and (5) for H and the notatior we use for multipole functions in the following text is given in a previous paper (Chandler et al, 1980). The r exponents, n, used there for the valence quadrupole, octopole and hexadecapole are also employed for the first-row atoms in this paper.…”

Section: Pbk(rb) = ~ Pnk Nnk R~ Exp(--¢ N Rt ) (4) N=kmentioning

confidence: 99%

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Pseudoatom expansions of the first-row diatomic hydride electron densities

Chandler¹,

Spackman²

1982

Acta Cryst Sect A

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Representations of high-quality molecular electron densities are studied. An evaluation of restricted radial functions is made using a least-squares figure of merit, the molecular dipole and quadrupole moments, the electric fields at the nuclei, the electric-field gradients at the nuclei, an approximate energy and differencedensity maps. For the heavy atom, a satisfactory representation has a fixed core function with a variable population and requires optimized dipolar core polarization functions, and an additional monopole term. The heavy-atom valence regions, and the H require expansions to at least the quadrupole level, with one Slater-type radial function per multipole and all exponents optimized. Additional valence radial functions and higher multipoles are required to give completely satisfactory difference-density maps but do not consistently improve the physical properties.

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Section: Pbk(rb) = ~ Pnk Nnk R~ Exp(--¢ N Rt ) (4) N=kmentioning

confidence: 88%

Section: Methodsmentioning

confidence: 99%

Section: Molecular Wavefunctlons and Physical Propertiesmentioning

confidence: 99%

Section: Pbk(rb) = ~ Pnk Nnk R~ Exp(--¢ N Rt ) (4) N=kmentioning

confidence: 99%

See 2 more Smart Citations

Pseudoatom expansions of the first-row diatomic hydride electron densities

Chandler¹,

Spackman²

1982

Acta Cryst Sect A

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“…(2.3) can be condensed in a single term if and only if the rank of matrix C, noted rank(C), is 1, i.e., if and only if the following condition is satisfied: for all i l , j l , i 2 , j 2 such that 1 s i l < i 2 5 1 and 1 5 j l < j 2 5 I' Cil,jlCiz,jz = C i j . j z C i 2 , j l ; (2)(3)(4) so, in this case, the wave function can be written in the form of a generalized HF function: @ = 9 , 4 9 5 .…”

Section: B Wave Functionmentioning

confidence: 99%

Ensemble representable densities for atoms and molecules. I. General theory

Cassam-Chenaı̈

1995

Int J of Quantum Chemistry

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In the previous article we introduced a method to obtain an ensemble density describing a molecule in a crystal from diffraction experiment structure factors. Here the method is applied to the CoC1;-molecular ion in a Cs,CoCI, crystal for which accurate magnetic structure factors are known. First, the approximations involved in the interpretation of polarized neutron experiment are reviewed with special emphasis on the collinearity approximation which has been avoided in this work. Second, the derivation of magnetic structure factors corresponding to theoretical ensemble densities is explained (the spin and the exact orbital contributions have been included). Third, the fitting procedure is presented and results at different levels of approximation are discussed. The main conclusions are: (1) A density built by using several molecular wave functions can give a very good agreement with the experimental data. (2) The ensemble representability constraint is necessary to retrieve physical information from the optimized parameters. (3) Taking into account the proper paramagnetic contribution to the magnetization improves significantly the agreement between theory and experiment. (4) Neglecting the diamagnetic contribution and the fact that the magnetization may be locally noncollinear to the applied external field is fully justified for the system under study.

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Experimental Electron Density Studies of Inorganic Materials

Schmøkel

Overgaard

Iversen

2013

Zeitschrift anorg allge chemie

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The electron density of a molecular scale system is probably the most information-rich observable in natural science, and experimental electron density determination based on X-ray diffraction is a strong field of modern crystallography. Most studies concern small molecule organic or metal-organic crystals, and indeed the experimental method and the subsequent data modeling and analysis have become a very versatile tool for such systems. However, inorganic materials in the form of high-symmetry dense solids, often with extended structures and containing heavy atoms, represent one of the most serious challenges to the X-ray electron density technique. For inorganic materials the scattering from the valence electrons is minute compared with the core electron scattering, and systematic errors such as extinction and absorption can be severe. In some sense studies of inorganic * Prof. Dr. B. Brummerstedt Iversen Fax: +45-8619-6199 E-Mail: bo@chem.au.dk [aHe is in charge of the X-ray crystallography laboratory and he has contributed strongly in the field of X-ray charge densities. Bo Brummerstedt Iversen is Professor at the

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Pseudoatom expansions of the H2 electron density

Cited by 9 publications

References 22 publications

Pseudoatom expansions of the first-row diatomic hydride electron densities

Pseudoatom expansions of the first-row diatomic hydride electron densities

Ensemble representable densities for atoms and molecules. I. General theory

Experimental Electron Density Studies of Inorganic Materials

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