Electrostatic interpretation of zeros

1988 ◽  
pp. 241-250 ◽  
Author(s):  
E. Hendriksen ◽  
H. van Rossum
Keyword(s):  
Electrostatic Interpretation

The electrostatic calculation of molecular energies - IV. Optimum paired-electron orbitals and the electrostatic method

1956 ◽  
Vol 235 (1201) ◽  
pp. 224-234 ◽  
Keyword(s):  
Simple Procedure ◽  
Wave Functions ◽  
Optimum Form ◽  
Method Of Calculation ◽  
Hartree Fock ◽  
Electron Orbital ◽  
Electrostatic Method ◽  
Valence States ◽  
Paired Electron ◽  
Electrostatic Interpretation

Equations which determine the optimum form of paired-electron orbitals are derived. It is shown that for large nuclear separations these equations become the Hartree-Fock equa­tions for appropriate valence states of the separated atoms. An electrostatic interpretation of chemical bonding is developed using optimum paired-electron orbital functions. For these wave functions this simple procedure yields results identical with those obtained by the conventional method of calculation based on the Hamiltonian integral. Numerical computations by the electrostatic method are also discussed.

scholarly journals Electrostatic interpretation of zeros of orthogonal polynomials

2018 ◽  
Vol 146 (12) ◽  
pp. 5323-5331 ◽  
Author(s):  
Stefan Steinerberger
Keyword(s):  
Orthogonal Polynomials ◽  
Zeros Of Orthogonal Polynomials ◽  
Electrostatic Interpretation

scholarly journals ON LAGUERRE–SOBOLEV TYPE ORTHOGONAL POLYNOMIALS: ZEROS AND ELECTROSTATIC INTERPRETATION

2013 ◽  
Vol 55 (1) ◽  
pp. 39-54
Author(s):  
LUIS ALEJANDRO MOLANO MOLANO
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Inner Product ◽  
Sobolev Type ◽  
Electrostatic Model ◽  
Order Linear Differential Equation ◽  
Standard Methods ◽  
Linear Differential ◽  
Electrostatic Interpretation ◽  
Image Position

AbstractWe study the sequence of monic polynomials orthogonal with respect to inner product $$\begin{eqnarray*}\langle p, q\rangle = \int \nolimits \nolimits_{0}^{\infty } p(x)q(x){e}^{- x} {x}^{\alpha } \hspace{0.167em} dx+ Mp(\zeta )q(\zeta )+ N{p}^{\prime } (\zeta ){q}^{\prime } (\zeta ),\end{eqnarray*}$$ where $\alpha \gt - 1$, $M\geq 0$, $N\geq 0$, $\zeta \lt 0$, and $p$ and $q$ are polynomials with real coefficients. We deduce some interlacing properties of their zeros and, by using standard methods, we find a second-order linear differential equation satisfied by the polynomials and discuss an electrostatic model of their zeros.

scholarly journals Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Rafael G. Campos ◽  
Marisol L. Calderón
Keyword(s):  
Closed Form ◽  
Complex Plane ◽  
Complex Number ◽  
Bessel Polynomials ◽  
The Real ◽  
Bessel Polynomial ◽  
Limit Points ◽  
Electrostatic Interpretation ◽  
Approximate Expressions

We find approximate expressionsx̃(k,n,a)andỹ(k,n,a)for the real and imaginary parts of thekth zerozk=xk+iykof the Bessel polynomialyn(x;a). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions ofk,nandais obtained. It is shown that the resulting complex numberx̃(k,n,a)+iỹ(k,n,a)isO(1/n2)-convergent tozkfor fixedk.

Why Are Carborane Acids so Acidic? An Electrostatic Interpretation of Brønsted Acid Strengths

2005 ◽  
Vol 44 (26) ◽  
pp. 9613-9615 ◽  
Author(s):  
P. Balanarayan ◽  
Shridhar R. Gadre
Keyword(s):  
Bronsted Acid ◽  
Brønsted Acid ◽  
Brönsted Acid ◽  
Electrostatic Interpretation

scholarly journals An electrostatic interpretation of the zeros of sieved ultraspherical polynomials

2020 ◽  
Vol 61 (5) ◽  
pp. 053501
Author(s):  
K. Castillo ◽  
M. N. de Jesus ◽  
J. Petronilho
Keyword(s):  
Ultraspherical Polynomials ◽  
Electrostatic Interpretation

scholarly journals Electrostatic interpretation for the zeros of certain polynomials and the Darboux process

2001 ◽  
Vol 133 (1-2) ◽  
pp. 397-412 ◽  
Author(s):  
F.Alberto Grünbaum
Keyword(s):  
Electrostatic Interpretation
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