Extending the σ-Hole Concept to Metals: An Electrostatic Interpretation of the Effects of Nanostructure in Gold and Platinum Catalysis

2017 ◽  
Vol 139 (32) ◽  
pp. 11012-11015 ◽  
Author(s):  
Joakim Halldin Stenlid ◽  
Tore Brinck
Keyword(s):  
Platinum Catalysis ◽  
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.

Stereoselective Syntheses of Trisubstituted Olefins via Platinum Catalysis: α-Silylenones with Geometrical Complementarity

2010 ◽  
Vol 132 (34) ◽  
pp. 11926-11928 ◽  
Author(s):  
Douglas A. Rooke ◽  
Eric M. Ferreira
Keyword(s):  
Platinum Catalysis ◽  
Trisubstituted Olefins ◽  
Stereoselective Syntheses

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

Mercury-promotion of platinum catalysis of dehydrogenation and dehydrochlorination

1987 ◽  
Vol 29 (2) ◽  
pp. 193-201 ◽  
Author(s):  
G.C. Georgiades ◽  
S.J. McCarthy ◽  
P.A. Sermon
Keyword(s):  
Platinum Catalysis

scholarly journals Expedient synthesis of E-hydrazone esters and 1H-indazole scaffolds through heterogeneous single-atom platinum catalysis

2019 ◽  
Vol 5 (12) ◽  
pp. eaay1537 ◽  
Author(s):  
Cuibo Liu ◽  
Zhongxin Chen ◽  
Huan Yan ◽  
Shibo Xi ◽  
Kah Meng Yam ◽  
...  
Keyword(s):  
Density Functional ◽  
Stereoselective Synthesis ◽  
Density Functional Theory Calculations ◽  
Building Blocks ◽  
Hydrogenation Reaction ◽  
Biologically Active ◽  
Single Atom ◽  
One Pot ◽  
Platinum Catalysis ◽  
Scalable Synthesis

Unprotected E-hydrazone esters are prized building blocks for the preparation of 1H-indazoles and countless other N-containing biologically active molecules. Despite previous advances, efficient and stereoselective synthesis of these compounds remains nontrivial. Here, we show that Pt single atoms anchored on defect-rich CeO2 nanorods (Pt1/CeO2), in conjunction with the alcoholysis of ammonia borane, promotes exceptionally E-selective hydrogenation of α-diazoesters to afford a wide assortment of N-H hydrazone esters with an overall turnover frequency of up to 566 hours−1 upon reaction completion. The α-diazoester substrates could be generated in situ from readily available carboxylic esters in one-pot hydrogenation reaction. Utility is demonstrated through concise, scalable synthesis of 1H-indazole–derived pharmaceuticals and their 15N-labeled analogs. The present protocol highlights a key mechanistic nuance wherein simultaneous coordination of a Pt site with the diazo N═N and ester carbonyl motifs plays a central role in controlling stereoselectivity, which is supported by density functional theory calculations.

Sign in / Sign up

Export Citation Format

Share Document