Long-range Coulomb forces and localized bonds

1999 ◽  
Vol 55 (5) ◽  
pp. 698-711 ◽  
Author(s):  
Christoph Preiser ◽  
Jens Lösel ◽  
I. David Brown ◽  
Martin Kunz ◽  
Aniceta Skowron
Keyword(s):  
Long Range ◽  
Coordination Sphere ◽  
Inorganic Compounds ◽  
Coulomb Field ◽  
Bond Valence ◽  
Coulomb Interactions ◽  
Ionic Model ◽  
Distant Field ◽  
Electric Flux ◽  
Definition Of

The ionic model is shown to be applicable to all compounds in which the atoms carry a net charge and their electron density is spherically symmetric regardless of the covalent character of the bonding. By examining the electric field generated by an array of point charges placed at the positions of the ions in over 40 inorganic compounds, we show that the Coulomb field naturally partitions itself into localized regions (bonds) which are characterized by the electric flux that links neighbouring ions of opposite charge. This flux is identified with the bond valence, and Gauss' law with the valence-sum rule, providing a secure theoretical foundation for the bond-valence model. The localization of the Coulomb field provides an unambiguous definition of coordination number and our calculations show that, in addition to the expected primary coordination sphere, there are a number of weak bonds between cations and the anions in the second coordination sphere. Long-range Coulomb interactions are transmitted through the crystal by the application of Gauss' law at each of the intermediate atoms. Bond fluxes have also been calculated for compounds containing ions with non-spherical electron densities (e.g. cations with stereoactive lone electron pairs). In these cases the point-charge model continues to describe the distant field, but multipoles must be added to the point charges to give the correct local field.

New lanthanide–nitrogen bond-valence parameters

2005 ◽  
Vol 61 (4) ◽  
pp. 429-434 ◽  
Author(s):  
Agata Trzesowska ◽  
Rafal Kruszynski ◽  
Tadeusz J. Bartczak
Keyword(s):  
Atomic Number ◽  
Coordination Sphere ◽  
Coordination Compounds ◽  
Inorganic Compounds ◽  
Bond Valence ◽  
Bond Lengths ◽  
Nitrogen Bonds ◽  
Oxygen Bond ◽  
Bond Valence Parameter ◽  
Nitrogen Bond

The bond-valence parameters (R ij ), which connect bond valences and bond lengths, have been computed for lanthanide–nitrogen bonds. It has been found that values of bond-valence parameters decrease with increasing lanthanide atomic number in coordination compounds, and that they are smaller than the R ij parameters of inorganic compounds. As expected, the lanthanide–nitrogen bond-valence parameters are larger than lanthanide–oxygen bond-valence parameters. There are no obvious dependencies between the number of N atoms in the coordination sphere and the bond-valence parameter value.

Roaming Reactions and Dynamics in the van der Waals Region

2020 ◽  
Vol 71 (1) ◽  
pp. 77-100 ◽  
Author(s):  
Arthur G. Suits
Keyword(s):  
Long Range ◽  
Internal State ◽  
Chemical Reactivity ◽  
Van Der Waals ◽  
Quantum Effects ◽  
Experimental Results ◽  
Unexpected Formation ◽  
Chemical Systems ◽  
Definition Of

Roaming reactions were first clearly identified in photodissociation of formaldehyde 15 years ago, and roaming dynamics are now recognized as a universal aspect of chemical reactivity. These reactions typically involve frustrated near-dissociation of a quasibound system to radical fragments, followed by reorientation at long range and intramolecular abstraction. The consequences can be unexpected formation of molecular products, depletion of the radical pool in chemical systems, and formation of products with unusual internal state distributions. In this review, I examine some current aspects of roaming reactions with an emphasis on experimental results, focusing on possible quantum effects in roaming and roaming dynamics in bimolecular systems. These considerations lead to a more inclusive definition of roaming reactions as those for which key dynamics take place at long range.

scholarly journals Piezoelectric Energy Harvesting Prediction and Efficient Management for Industrial Wireless Sensor

2020 ◽  
Vol 10 (23) ◽  
pp. 8486
Author(s):  
Alex Mouapi ◽  
Nadir Hakem ◽  
Nahi Kandil
Keyword(s):  
Long Range ◽  
Design Method ◽  
Wireless Sensor ◽  
Energy Harvest ◽  
Area Network ◽  
Wide Area Network ◽  
Operating Modes ◽  
Efficient Management ◽  
Piezoelectric Energy ◽  
Definition Of

The vibrations, due to their abundance in most industrial processes, constitute an attractive solution for the power supply of Industrial Wireless Sensor (IWS). However, the amount of energy that can be harvested presents numerous fluctuations due to the engines’ different operating modes (overload, full load, or even operation without charge). Most designs do not incorporate this fluctuation in the definition of the specifications of the autonomous IWS. This paper then presents a design method to ensure the node’s energy autonomy while maximizing its Quality of Service (QoS). To precisely define the specifications of the IWS, vibration measurements were carried out at its location for one month. The recorded data was used to propose a new Predictor of the Harvestable Energy from Vibrations (PHEV). A comparative evaluation of the proposed PHEV performances with a state-of-the-art predictor is carried out. The results obtained show that the PHEV makes it possible to minimize the Root Mean Square Error (RMSE) from 28.63 mW to 19.52 mW. A model of energy dissipation in IWS, considering the Internet of Things’ requirements, was established. The model is based on Long-Range (LoRa)/Long-Range Communication Wide Area Network (LoRaWan). The amount of data transmitted is then maximized according to the expected energy harvest rate by setting up a Maximization Data Size Protocol (MDSP). The proposed method makes it possible to ensure an acceptable QoS without resorting to reconfigurable circuits, which are sometimes bulky for miniature devices such as the IWS.

The nature of discrete second-order self-similarity

2003 ◽  
Vol 35 (02) ◽  
pp. 395-416 ◽  
Author(s):  
A. Gefferth ◽  
D. Veitch ◽  
I. Maricza ◽  
S. Molnár ◽  
I. Ruzsa
Keyword(s):  
Fixed Points ◽  
Long Range ◽  
Power Laws ◽  
Complete Classification ◽  
Second Order ◽  
General Definition ◽  
Long Range Dependence ◽  
Self Similarity ◽  
New Treatment ◽  
Definition Of

A new treatment of second-order self-similarity and asymptotic self-similarity for stationary discrete time series is given, based on the fixed points of a renormalisation operator with normalisation factors which are not assumed to be power laws. A complete classification of fixed points is provided, consisting of the fractional noise and one other class. A convenient variance time function approach to process characterisation is used to exhibit large explicit families of processes asymptotic to particular fixed points. A natural, general definition of discrete long-range dependence is provided and contrasted with common alternatives. The closely related discrete form of regular variation is defined, its main properties given, and its connection to discrete self-similarity explained. Folkloric results on long-range dependence are proved or disproved rigorously.

New Bond-Valence Sum Model

1997 ◽  
Vol 53 (6) ◽  
pp. 885-894 ◽  
Author(s):  
J. P. Naskar ◽  
S. Hati ◽  
D. Datta
Keyword(s):  
Oxidation State ◽  
Coordination Sphere ◽  
Metal Ion ◽  
Nickel Complexes ◽  
Bond Valence ◽  
Oxidation States ◽  
Linear Variation ◽  
Axial Bond ◽  
Inorganic Complexes ◽  
Bond Valence Sum

A new expression is devised empirically to accommodate zero and some negative oxidation states in the bond-valence sum approach. The method is worked out in detail for a number of homoleptic copper and nickel complexes of various coordinating atoms in several oxidation states of the metals. An implication of the expression is a linear variation between 1/r eq and 1/r ax in octahedral MX 6 moieties, where r eq and r ax are, respectively, the average equatorial and axial bond lengths. This is verified in Cu2+ X 6 chromophores for X = F, O, N and S. The usefulness of the new expression in assessing the compatibility of a coordination sphere with an oxidation state of a metal ion is demonstrated by exemplary applications to some inorganic complexes, azurin and urease.

Sign in / Sign up

Export Citation Format

Share Document