Energetic Contributions to the Two-Electron Bond: A Simplified Group Function (SGF) Analysis

1987 ◽  
Vol 40 (4) ◽  
pp. 635 ◽  
Author(s):  
PE Schipper
Keyword(s):  
Electron Transfer ◽  
Power Series ◽  
Short Range ◽  
Covalent Bonding ◽  
Zeroth Order ◽  
Group Function ◽  
Effective Power ◽  
First Order ◽  
Excitonic States ◽  
Covalent Interactions

The group function (GF) formalism coupled with the limit in which intergroup electron interchange symmetry is rigorously neglected (the simplified group function (SGF) approach) is shown to lead to a resolution of intergroup bonding as an effective power series in overlap density. The successive orders are shown to correspond to a concomitant resolution into traditional bonding contributions: zeroth order leads to the conventional excitonic description (no electron transfer or interchange); first-order terms may be interpreted as dative bonding, in which electron transfer configurations mix with the excitonic states; and finally, second-order terms correspond directly to the incorporation of electron interchange symmetry and hence to pure covalent bonding. A conceptual parallelism of the division of long range (static, inductive and dispersive) interactions with short range (ionic, dative and covalent) interactions is drawn to emphasize the unity of these apparently disparate limits in the SGF/GF analysis. Explicit application to the archetypical two-electron bond highlights the conceptual simplicity of the approach, and is compared to a commensurate MO and VB analysis expressed in terms of the same integrals. The results show clearly why such a simple resolution is difficult to extract from MO and VB approaches, which are philosophically biased towards the strong bonding limit.

scholarly journals Perturbation Solution for One-Dimensional Flow to a Constant-Pressure Boundary in a Stress-Sensitive Reservoir

2021 ◽  
Author(s):  
Amarjot Singh Bhullar ◽  
Gospel Ezekiel Stewart ◽  
Robert W. Zimmerman
Keyword(s):  
Approximate Solution ◽  
Pore Pressure ◽  
Constant Pressure ◽  
Initial Permeability ◽  
Order Perturbation ◽  
Zeroth Order ◽  
One Dimensional ◽  
First Order ◽  
Outflow Boundary ◽  
Perturbation Solutions

Abstract Most analyses of fluid flow in porous media are conducted under the assumption that the permeability is constant. In some “stress-sensitive” rock formations, however, the variation of permeability with pore fluid pressure is sufficiently large that it needs to be accounted for in the analysis. Accounting for the variation of permeability with pore pressure renders the pressure diffusion equation nonlinear and not amenable to exact analytical solutions. In this paper, the regular perturbation approach is used to develop an approximate solution to the problem of flow to a linear constant-pressure boundary, in a formation whose permeability varies exponentially with pore pressure. The perturbation parameter αD is defined to be the natural logarithm of the ratio of the initial permeability to the permeability at the outflow boundary. The zeroth-order and first-order perturbation solutions are computed, from which the flux at the outflow boundary is found. An effective permeability is then determined such that, when inserted into the analytical solution for the mathematically linear problem, it yields a flux that is exact to at least first order in αD. When compared to numerical solutions of the problem, the result has 5% accuracy out to values of αD of about 2—a much larger range of accuracy than is usually achieved in similar problems. Finally, an explanation is given of why the change of variables proposed by Kikani and Pedrosa, which leads to highly accurate zeroth-order perturbation solutions in radial flow problems, does not yield an accurate result for one-dimensional flow. Article Highlights Approximate solution for flow to a constant-pressure boundary in a porous medium whose permeability varies exponentially with pressure. The predicted flowrate is accurate to within 5% for a wide range of permeability variations. If permeability at boundary is 30% less than initial permeability, flowrate will be 10% less than predicted by constant-permeability model.

Interpretation of Electron Transfer Spectra of Iridium (IV) and Osmium(IV) Mixed Chloro-Bromo Complexes

1967 ◽  
Vol 22 (6) ◽  
pp. 945-954 ◽  
Author(s):  
Chr. Klixbüll Jørgensen ◽  
W. Preetz
Keyword(s):  
Electron Transfer ◽  
Faraday Effect ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
University Of Virginia ◽  
First Order ◽  
Order Of Magnitude ◽  
Moderate Difference ◽  
The University ◽  
As If

The previous M.O. treatment of unsubstituted hexahalides has been modified, taking the results on Faraday effect obtained at the University of Virginia into account. The absorption spectra previously measured of the complexes (M=Os, Ir) trans-MCl4Br2— and trans-MCl2 Br4— are interpreted by a M.O. treatment for the symmetry D4h as electron transfer transitions, including a first-order relativistic (spin-orbit coupling) correction. The concept of holohedrized symmetry is sufficiently valid to allow a description of MCl5Br— and MClBr5— as if they were tetragonal with centre of inversion and ƒac-(or cis-)MCl3Br3— as if they were cubic. It is shown that the ligand-ligand antibonding effects have the same order of magnitude as the moderate difference in optical electronegativity between Cl- and Br-.

scholarly journals Particles, conformal invariance and criticality in pure and disordered systems

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
Gesualdo Delfino
Keyword(s):  
Conformal Invariance ◽  
Disordered Systems ◽  
Short Range ◽  
Recent Progress ◽  
Quenched Disorder ◽  
Exact Methods ◽  
Special Position ◽  
Infinite Dimensional ◽  
First Order ◽  
The Continuum

AbstractThe two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra. However, some sectors of the theory, and most notably criticality in systems with quenched disorder and short-range interactions, have appeared out of reach of exact methods and lacked the insight coming from analytical solutions. In this article, we review recent progress achieved implementing conformal invariance within the particle description of field theory. The formalism yields exact unitarity equations whose solutions classify critical points with a given symmetry. It provides new insight in the case of pure systems, as well as the first exact access to criticality in presence of short range quenched disorder. Analytical mechanisms emerge that in the random case allow the superuniversality of some critical exponents and make explicit the softening of first-order transitions by disorder.Graphic abstract

scholarly journals ANISOTROPIC NULL STRING COSMOLOGIES

1998 ◽  
Vol 13 (39) ◽  
pp. 3169-3177 ◽  
Author(s):  
IOANNIS GIANNAKIS ◽  
K. KLEIDIS ◽  
A. KUIROUKIDIS ◽  
D. PAPADOPOULOS
Keyword(s):  
Equations Of Motion ◽  
String Tension ◽  
Perturbative Expansion ◽  
Speed Of Light ◽  
Zeroth Order ◽  
First Order ◽  
Cosmological Background ◽  
String Propagation ◽  
Analytical Expressions ◽  
Null String

We study string propagation in an anisotropic, cosmological background. We solve the equations of motion and the constraints by performing a perturbative expansion of the string coordinates in powers if c2 — the worldsheet speed of light. To zeroth order the string is approximated by a tensionless string (since c is proportional to the string tension T). We obtain exact, analytical expressions for the zeroth- and first-order solutions and we discuss some cosmological implications.

A Slender-Ship Theory of Wave Resistance

1983 ◽  
Vol 27 (01) ◽  
pp. 13-33
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Successive Approximations ◽  
Zeroth Order ◽  
Remarkable Effect ◽  
Ship Wave ◽  
First Order ◽  
Wigley Hull ◽  
Low Froude Number ◽  
The Waves

A new slender-ship theory of wave resistance is presented. Specifically, a sequence of explicit slender-ship wave-resistance approximations is obtained. These approximations are associated with successive approximations in a slender-ship iterative procedure for solving a new (nonlinear integro-differential) equation for the velocity potential of the flow caused by the ship. The zeroth, first, and second-order slender-ship approximations are given explicitly and examined in some detail. The zeroth-order slender-ship wave-resistance approximation, r(0) is obtained by simply taking the (disturbance) potential, ϕ, as the trivial zeroth-order slender-ship approximation ϕ(0) = 0 in the expression for the Kochin free-wave amplitude function; the classical wave-resistance formulas of Michell [1]2 and Hogner [2] correspond to particular cases of this simple approximation. The low-speed wave-resistance formulas proposed by Guevel [3], Baba [4], Maruo [5], and Kayo [6] are essentially equivalent (for most practical purposes) to the first-order slender-ship low-Froude-number approximation, rlF(1), which is a particular case of the first-order slender-ship approximation r(1): specifically, the first-order slender-ship wave-resistance approximation r(1) is obtained by approximating the potential ϕ in the expression for the Kochin function by the first-order slender-ship potential ϕ1 whereas the low-Froude-number approximation rlF(1) is associated with the zero-Froude-number limit ϕ0(1) of the potentialϕ(1). A major difference between the first-order slender-ship potential ϕ(1) and its zero-Froude-number limit ϕ0(1) resides in the waves that are included in the potential ϕ(1) but are ignored in the zero-Froude-number potential ϕ0(1). Results of calculations by C. Y. Chen for the Wigley hull show that the waves in the potential ϕ(1) have a remarkable effect upon the wave resistance, in particular causing a large phase shift of the wave-resistance curve toward higher values of the Froude number. As a result, the first-order slender-ship wave-resistance approximation in significantly better agreement with experimental data than the low-Froude-number approximation rlF(1) and the approximations r(0) and rM.

First-order changes in ionic/covalent bonding

1992 ◽  
Vol 130 (1) ◽  
pp. 77-86 ◽  
Author(s):  
John B. Goodenough
Keyword(s):  
Covalent Bonding ◽  
First Order

Synthesis, Properties and Application in Optical Memory of a Photochromic Diarylethene Bearing Pyrimidine and Pyridine Ring

2012 ◽  
Vol 490-495 ◽  
pp. 3733-3737
Author(s):  
Shu Hong Jing ◽  
Shou Zhi Pu ◽  
Shi Qiang Cui
Keyword(s):  
Uv Light ◽  
Optical Memory ◽  
Order Reaction ◽  
Pmma Film ◽  
Zeroth Order ◽  
First Order ◽  
Synthesis Properties ◽  
Fluorescence Switching ◽  
Photochromic Reaction ◽  
Hexane Solution

A new photochromic diarylethene compound, 1-(2,4-dimethoxy-5-pyrimidine)-2-[2-methyl-5-(3-pyridine)-3-thienyl]perfluorocyclopentene(1a), was synthesized, and its photochromic reactivity, fluorescent and electrochemical property were also investigated. Diarylethene 1a changed the color from colorless to pink upon irradiation with UV light, in which absorption maxima were observed at 520 and 519 nm in hexane and PMMA film, respectively. The the photochromic reaction kinetics indicated that the cyclization processes of 1 belong to the zeroth order reaction and the cycloreversion process belong to the first order reaction. This new photochromic system also exhibited remarkable fluorescence switching in hexane solution and this new photochromic system also exhibited remarkable optical storage character.

Aromatic oxidation by cobaltic acetate in acetic acid

1969 ◽  
Vol 47 (3) ◽  
pp. 387-392 ◽  
Author(s):  
Koichiro Sakota ◽  
Yoshio Kamiya ◽  
Nobuto Ohta
Keyword(s):  
Activation Energy ◽  
Electron Transfer ◽  
Acetic Acid ◽  
Bond Energy ◽  
Hydrogen Abstraction ◽  
Steric Factor ◽  
Benzyl Acetate ◽  
Kcal Mole ◽  
First Order ◽  
Reversible Electron Transfer

A detailed kinetic study of oxidation of toluene and its derivatives by cobaltic acetate in 95 vol% acetic acid is reported. The reaction was found to be profoundly affected by a steric factor and rather insensitive to the C—H bond energy. The order of reactivities of various alkylbenzenes is quite reversal to that of hydrogen abstraction reactions. The reaction was of first-order with respect to toluene, of second-order with respect to cobaltic ion and of inverse first-order with respect to cobaltous ion. The oxidation by cobaltic ion seems to proceed via an initial reversible electron transfer from toluene to cobaltic ion, yielding [Formula: see text] which is oxidized into benzyl acetate by another cobaltic ion. The apparent activation energy for toluene was found to be 25.3 kcal mole−1, and the same activation energy was found for ethylbenzene, cumene, diphenylmethane, and triphenylmethane.

Sign in / Sign up

Export Citation Format

Share Document