Calcul des déplacements chimiques par la méthode des perturbations finies au niveau INDO avec GIAO et approximation de London. I. 13C et 1H

1982 ◽  
Vol 60 (8) ◽  
pp. 957-969 ◽  
Author(s):  
E. Vauthier ◽  
S. Odiot ◽  
F. Tonnard
Keyword(s):  
Perturbation Method ◽  
Chemical Shifts ◽  
Average Precision ◽  
Electron Densities ◽  
Screening Constant ◽  
First Order ◽  
Finite Perturbation

A formalism for the calculation of σ in the finite perturbation method is developed by keeping hermitian the first order perturbed matrix in B. The σ formalism is separated into mono, di, and triatomic terms, and the importance of the electron densities of neighboring and remote bonds is shown. 13C chemical shifts depend only slightly on the remote bonds in contrast to those for 1H. A calculation of the screening constant for a series of 16 sp and sp2 carbons gives an average precision of 5 ppm for the 13C nuclei. [Journal Translation]

Calculation of proton N.M.R. chemical shifts by means of a finite perturbation method

1977 ◽  
Vol 33 (2) ◽  
pp. 463-482 ◽  
Author(s):  
Masahiro Kondo ◽  
Isao Ando ◽  
Riichirö Chüjö ◽  
Atsuo Nishioka
Keyword(s):  
Perturbation Method ◽  
Chemical Shifts ◽  
Finite Perturbation

On Integrating Factors and a Perturbation Method

1995 ◽  
Author(s):  
W. T. van Horssen
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Integrating Factors ◽  
Complete Solutions

Abstract In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.

Application of Homotopy Perturbation Method for Harmonically Forced Duffing Systems

2011 ◽  
Vol 110-116 ◽  
pp. 2277-2283 ◽  
Author(s):  
Xiang Meng Zhang ◽  
Ben Li Wang ◽  
Xian Ren Kong ◽  
A Yang Xiao
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Primary Resonance ◽  
Effective Technique ◽  
Duffing System ◽  
First Order ◽  
Homotopy Perturbation ◽  
Analytical Approximations ◽  
Case Based

In this paper, He’s homotopy perturbation method (HPM) is applied to solve harmonically forced Duffing systems. Non-resonance of an undamped Duffing system and the primary resonance of a damped Duffing system are studied. In the former case, the first-order analytical approximations to the system’s natural frequency and periodic solution are derived by HPM, which agree well with the numerical solutions. In the latter case, based on HPM, the first-order approximate solution and the frequency-amplitude curves of the system are acquired. The results reveal that HPM is an effective technique to the forced Duffing systems.

Correlation of the chemical shifts with ?-electron densities in mono-derivatives of benzene, pyridine, and pyrazine

1968 ◽  
Vol 17 (5) ◽  
pp. 951-958
Author(s):  
G. G. Dvoryantseva ◽  
V. P. Lezina ◽  
V. F. Bystrov ◽  
T. N. Ul'yanova ◽  
G. P. Syrova ◽  
...  
Keyword(s):  
Chemical Shifts ◽  
Electron Densities ◽  
Derivatives Of

Elektronendichte und chemische Verschiebung der Styryldiazin- und Diazaphenanthrenprotonen / Electrondensity and Proton Chemical Shift of Styryldiazines and Diazaphenanthrenes

1972 ◽  
Vol 27 (2) ◽  
pp. 310-319
Author(s):  
H.-H. Perkampus ◽  
Th. Bluhm ◽  
J. Knop
Keyword(s):  
Ring Current ◽  
Chemical Shifts ◽  
Lone Pair ◽  
Current Effect ◽  
Electron Densities ◽  
Paramagnetic Effect ◽  
Nitrogen Lone Pair ◽  
Chemische Verschiebung ◽  
Lone Pair Electrons ◽  
Proton Chemical Shifts

AbstractProton chemical shifts in styryldiazines and diazaphenanthrenes linearly correlate with SCF-π-electron densities of the attached carbon atom and with the electron densities of the hydrogen atom (calculated by the CNDO/2 method). The observed deviations from linearity are discussed in terms of ring current effect, steric effects and the paramagnetic effect of the nitrogen lone pair electrons. An appreciable weakening of ring current is found for diazaphenanthrenes with two adjacent N-atoms. Under the same condition the paramagnetic effect on ortho-hydrogens is increased.

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