Electron-pair radial sum and difference density functions

2009 ◽  
Vol 130 (18) ◽  
pp. 184110 ◽  
Author(s):  
Toshikatsu Koga ◽  
Masahiro Sekiya
Keyword(s):  
Electron Pair ◽  
Density Functions ◽  
Difference Density

Electron-pair radial density functions

2010 ◽  
Vol 48 (4) ◽  
pp. 988-1000 ◽  
Author(s):  
Toshikatsu Koga ◽  
Masahiro Sekiya
Keyword(s):  
Electron Pair ◽  
Density Functions ◽  
Radial Density

ELECTRON CORRELATION STUDIES BY MEANS OF ELECTRON-PAIR DENSITY FUNCTIONS

2002 ◽  
pp. 577-611 ◽  
Author(s):  
Elmer Valderrama ◽  
Xavier Fradera ◽  
Iñaki Silanes ◽  
Jesus M. Ugalde ◽  
Russell J. Boyd
Keyword(s):  
Electron Correlation ◽  
Electron Pair ◽  
Density Functions ◽  
Correlation Studies ◽  
Pair Density ◽  
Electron Pair Density

W-Peakedness: A Simulation based Study

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Suboohi Safdar ◽  
Dr. Ejaz Ahmed
Keyword(s):  
Probability Distributions ◽  
Extensive Study ◽  
Descriptive Statistics ◽  
Target Point ◽  
Density Functions ◽  
Central Value ◽  
Distribution Shape ◽  
Simulation Based ◽  
Different Shapes ◽  
Kurtosis Coefficient

Kurtosis is a commonly used descriptive statistics. Kurtosis “Coefficient of excess” is critically reviewed in different aspects and is called as, measuring the fatness of the tails of the density functions, concentration towards the central value, scattering away from the target point or degree of peakedness of probability distribution. Kurtosis is referred to the shape of the distribution but many distributions having same kurtosis value may have different shapes while Kurtosis may exist when peak of a distribution is not in existence. Through extensive study of kurtosis on several distributions, Wu (2002) introduced a new measure called “W-Peakedness” that offers a fine capture of distribution shape to provide an intuitive measure of peakedness of the distribution which is inversely proportional to the standard deviation of the distribution. In this paper the work is extended for different others continuous probability distributions. Empirical results through simulation illustrate the proposed method to evaluate kurtosis by W-peakedness

1H and 13C NMR spectra of 2,2’-disubstitutedtrans-azobenzenes suitable for preparation of metallized azo dyes

1991 ◽  
Vol 56 (10) ◽  
pp. 2160-2168 ◽  
Author(s):  
Josef Jirman
Keyword(s):  
Nmr Spectra ◽  
Electron Pair ◽  
Phenyl Group ◽  
Aprotic Solvents ◽  
1H And 13C Nmr ◽  
Predominant Form ◽  
Rapid Equilibrium ◽  
Dipolar Aprotic Solvents ◽  
Free Electron Pair ◽  
C Nmr

The 1H and 13C NMR spectra have been measured of six trans-azobenzenes substituted at 2 and 2’ positions with substituents favourable for complex formation with a metal (OH, NH2, NHCOCH3, COOH). From the standpoint of NMR such substituted trans-azobenzenes are present in solution in a rapid equilibrium following from rotation around the bond between C-1 of phenyl group and N atom of azo linkage. The predominant form has the substituent in the syn-position with respect to the free electron pair of the nearer azo nitrogen atom. The equilibrium is affected by dipolar aprotic solvents (such as hexadeuteriodimethyl sulfoxide) by decreasing the presence of the predominant form by 1 to 11%.

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