Additivity of the one‐third power of the electron density in the hydrogen molecule–ion and hydrogen molecule

1990 ◽  
Vol 92 (3) ◽  
pp. 2114-2115 ◽  
Author(s):  
Chengteh Lee ◽  
Slobodan Zdravkovic ◽  
Robert G. Parr
Keyword(s):  
Electron Density ◽  
Hydrogen Molecule ◽  
The One

Developing orbital-free quantum crystallography: the local potentials and associated partial charge densities

2021 ◽  
Vol 77 (4) ◽  
Author(s):  
Vladimir Tsirelson ◽  
Adam Stash
Keyword(s):  
Density Functional Theory ◽  
Electron Density ◽  
Density Functional ◽  
Electronic Energy ◽  
Physical Content ◽  
Functional Theory ◽  
Orbital Free ◽  
The One ◽  
Physical And Chemical ◽  
Quantum Crystallography

This work extends the orbital-free density functional theory to the field of quantum crystallography. The total electronic energy is decomposed into electrostatic, exchange, Weizsacker and Pauli components on the basis of physically grounded arguments. Then, the one-electron Euler equation is re-written through corresponding potentials, which have clear physical and chemical meaning. Partial electron densities related with these potentials by the Poisson equation are also defined. All these functions were analyzed from viewpoint of their physical content and limits of applicability. Then, they were expressed in terms of experimental electron density and its derivatives using the orbital-free density functional theory approximations, and applied to the study of chemical bonding in a heteromolecular crystal of ammonium hydrooxalate oxalic acid dihydrate. It is demonstrated that this approach allows the electron density to be decomposed into physically meaningful components associated with electrostatics, exchange, and spin-independent wave properties of electrons or with their combinations in a crystal. Therefore, the bonding information about a crystal that was previously unavailable for X-ray diffraction analysis can be now obtained.

Application of Cusp-Satisfying Orbitals to Some Two-Electron Systems

1972 ◽  
Vol 50 (17) ◽  
pp. 2887-2890
Author(s):  
J. E. Brown ◽  
D. P. Chong
Keyword(s):  
Electron Density ◽  
Hydrogen Molecule ◽  
Lithium Atom ◽  
Electron Systems ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series

The kind of cusp-satisfying orbitals used earlier for the lithium atom is tested on the helium isoelectronic series and the hydrogen molecule. Excellent values are obtained for the electron density at the nucleus, Qe(0), for the atoms. The results for various wavefunctions for the hydrogen molecule are not as systematic, but are still quite reasonable.

Weak interactions in chain polymers [M(μ-X)2 L 2]∞ (M = Zn, Cd; X = Cl, Br; L = substituted pyridine) – an electron density study

2009 ◽  
Vol 65 (5) ◽  
pp. 600-611 ◽  
Author(s):  
Ruimin Wang ◽  
Christian W. Lehmann ◽  
Ulli Englert
Keyword(s):  
Hydrogen Bonds ◽  
Electron Density ◽  
Critical Points ◽  
Weak Interactions ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Density Distributions ◽  
The One ◽  
Experimental Electron Density ◽  
Density Study

The experimental electron-density distributions in crystals of five chain polymers [M(μ-X)2(py)2] (M = Zn, Cd; X = Cl, Br; py = 3,5-substituted pyridine) have been obtained from high-resolution X-ray diffraction data sets (sin θ/λ > 1.1 Å−1) at 100 K. Topological analyses following Bader's `Atoms in Molecules' approach not only confirmed the existence of (3, −1) critical points for the chemically reasonable and presumably strong covalent and coordinative bonds, but also for four different secondary interactions which are expected to play a role in stabilizing the polymeric structures which are unusual for Zn as the metal center. These weaker contacts comprise intra- and inter-strand C—H...X—M hydrogen bonds on the one hand and C—X...X—C interhalogen contacts on the other hand. According to the experimental electron-density studies, the non-classical hydrogen bonds are associated with higher electron density in the (3, −1) critical points than the halogen bonds and hence are the dominant interactions both with respect to intra- and inter-chain contacts.

Exploring the electron density localization in MoS2 nanoparticles using a localized-electron detector: Unraveling the origin of the one-dimensional metallic sites on MoS2 catalysts

2018 ◽  
Vol 20 (31) ◽  
pp. 20417-20426 ◽  
Author(s):  
Yosslen Aray ◽  
Antonio Díaz Barrios
Keyword(s):  
Electron Density ◽  
The Other ◽  
Local Moment ◽  
Electron Detector ◽  
Moment Representation ◽  
One Dimensional ◽  
Mos2 Nanoparticles ◽  
Mos2 Catalysts ◽  
The One

The nature of the electron density localization in two MoS2 nanoclusters containing eight rows of Mo atoms, one with 100% sulphur coverage at the Mo edges (n8_100S) and the other with 50% coverage (n8_50S) was studied using a localized-electron detector function defined in the local moment representation.

Properties of Aromaticity Indices Based on the One-Electron Density Matrix†

2007 ◽  
Vol 111 (28) ◽  
pp. 6521-6525 ◽  
Author(s):  
Jerzy Cioslowski ◽  
Eduard Matito ◽  
Miquel Solà
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Electron Density Matrix ◽  
The One

Atomic interactions in ethylenebis(1-indenyl)zirconium dichloride as derived by experimental electron density analysis

2005 ◽  
Vol 61 (4) ◽  
pp. 418-428 ◽  
Author(s):  
Adam I. Stash ◽  
Kiyoaki Tanaka ◽  
Kazunari Shiozawa ◽  
Hitoshi Makino ◽  
Vladimir G. Tsirelson
Keyword(s):  
Electron Density ◽  
Topological Analysis ◽  
Electronic Energy ◽  
Ligand Interaction ◽  
Atomic Interactions ◽  
Particle Potential ◽  
Density Analysis ◽  
The One ◽  
Electron Density Analysis ◽  
Experimental Electron Density

A topological analysis of the experimental electron density in racemic ethylenebis(1-indenyl)zirconium dichloride, C20H16Cl2Zr, measured at 100 (1) K, has been performed. The atomic charges calculated by the numerical integration of the electron density over the zero-flux atomic basins demonstrate the charge transfer of 2.25 e from the Zr atom to the two indenyl ligands (0.19 e to each) and two Cl atoms (0.93 e to each). All the atomic interactions were quantitatively characterized in terms of the electron density and the electronic energy-density features at the bond critical points. The Zr—C2 bond paths significantly curved towards the C1—C2 bond were found; no other bond paths connecting the Zr atom and indenyl ligand were located. At the same time, the π-electrons of the C1—C2 bond are significantly involved in the metal–ligand interaction. The electron density features indicate that the indenyl coordination can be approximately described as η1 with slippage towards η2. The `ligand-opposed' charge concentrations around the Zr atom were revealed using the Laplacian of the electron density and the one-particle potential; they were linked to the orbital representations. Bonds in the indenyl ligand were characterized using the Cioslowski–Mixon bond-order indices calculated directly from the experimental electron density.

scholarly journals A re-examination of the adiabatic correction term for the hydrogen molecule

1976 ◽  
Vol 54 (4) ◽  
pp. 651-656 ◽  
Author(s):  
Huw O. Pritchard ◽  
Lutosław Wolniewicz
Keyword(s):  
Energy Level ◽  
Hydrogen Molecule ◽  
Vibrational Energy ◽  
Correction Term ◽  
Internuclear Separation ◽  
Vibrational Energy Level ◽  
The Difference ◽  
The One

The adiabatic coupling correction term [Formula: see text] has been evaluated by two methods, the one used by Kołos and Wolniewicz in 1964 and the one suggested by Kari, Chan, Hunter, and Pritchard in 1973. The difference between the two procedures for H2 amounts to 0.04 cm−1 and is almost independent of internuclear separation in the range R = 1.0–1.8 a.u. Thus, the method of computing the ΔR-term does not affect the vibrational energy level spacings.

scholarly journals A note on the specific heat of the hydrogen molecule

1927 ◽  
Vol 115 (771) ◽  
pp. 483-486 ◽  
Keyword(s):  
Specific Heat ◽  
Hydrogen Molecule ◽  
Wave Functions ◽  
Wave Mechanics ◽  
Nuclear Spins ◽  
Rotational States ◽  
Heat Curve ◽  
Symmetrical Group ◽  
The Moment ◽  
The One

In a recent article F. Hund has treated the problem of the specific heat of the hydrogen molecule on the basis of the wave mechanics. The total number of rotational states are divided due to the homopolar character of the molecule into two groups, to the one of which belong wave functions symmetrical in the two nuclei, and to the other wave functions which are antisymmetrical in the nuclei. Hund has suggested that the presence of both groups in hydrogen may be accounted for by assuming that the nuclei possess a spin, in which case transitions between symmetrical or between antisymmetrical states will have their usual intensity but transitions between symmetrical and antisymmetrical states will be very weak, of the order of the coupling of the nuclear spins. He then writes the following expression for the rotational specific heat, C r /R = σ 2 d 2 / d σ 2 log Q, Q = β [1 + 5 e -6σ + 9 e -20σ + ...] + 3 e -2σ + 7 e -12σ + 11 e -30σ +...., (1) where σ = h 2 /8π 2 I k T and β is the ratio of the weights of the symmetrical group of states to the antisymmetrical group. Hund has found that he obtains a close agreement between (1) and the observed specific heat curve only when β has about the value 2, that is when the symmetrical states have twice the weight of the antisymmetrical. He further obtains for this case I = 1·54 × 10 -41 gm. cm. 2 , the moment of inertia of the H 2 molecule.

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