π-σ Electronic states in molecules II. The singlet spectrum of ethylene and derivatives

1952 ◽  
Vol 210 (1102) ◽  
pp. 343-354 ◽  
Keyword(s):  
Ground State ◽  
Valence Bond ◽  
Resonance Energy ◽  
Theoretical Explanation ◽  
Conjugated Systems ◽  
Alkyl Substitution ◽  
Transition Rules ◽  
The Right ◽  
Double Nature ◽  
Bond Method

It is suggested that the failure of the Heitler-London-Slater-Pauling method to give the right transition rules for the excited levels in conjugated systems is not due chiefly to shortcomings in the valence bond method (like neglect of ionic structures) but rather to the use of the Hückel approximation (see part I). This is confirmed by a detailed treatment of ethylene as a twelveelectron problem by the valence-bond method. The Hückel approximation is dispensed with, so that six canonical structures are considered. Of these, one corresponds to the perfect pairing scheme, one to π-σ resonance in the double bond and four to π- h resonance ( h being the hydrogen 1 s electron) in the C-H bonds. No purely σ-σ resonance is considered. Most of the necessary exchange integrals are computed in this paper. Two of them, however, are estimated. The treatment can be extended to substituted ethylenes by changing a few exchange integrals. It is necessary here to estimate another integral. A π-σ resonance energy of 0.47 eV is obtained for the ground state of ethylene. The actual positions of the peaks of absorption obtained are not very accurate, as could be expected. They are, however, of the same order as those given by the method of the antisymmetrized molecular orbitals. A first band 1 A 1g - A 1g , forbidden, is obtained. This is identified with the observed faint absorption starting at 2000 Å. The second band, allowed, is double, given by the transitions 1 A 1g - 1 B 1M and 1 A 1g 1 B 2u separated by ca. 0.2 eV (experim ental 0.06 eV). These bands are identified with the strong absorption at 1600 Å. The double nature of this band was hitherto without theoretical explanation. The distance between the first forbidden ban d and the centre of the second is 1.4 eV (experimental ca. 1.1 eV). The second band is shifted towards the red by tetra-alkyl substitution by 0.9 eV (experimental 1 eV). There is no need to have recourse to hyperconjugation to explain this last fact.

Kekulé index for valence bond structures of conjugated systems containing cyclobutadiene

1978 ◽  
Vol 43 (5) ◽  
pp. 1375-1392 ◽  
Author(s):  
Ante Graovac ◽  
Ivan Gutman ◽  
Milan Randić ◽  
Nenad Trinajstić
Keyword(s):  
Valence Bond ◽  
Conjugated Systems

The Old Order Changeth, Yielding Place to the New (Murli Manohar Joshi’s Tenure)

2018 ◽  
Author(s):  
R.V. Vaidyanatha Ayyar
Keyword(s):  
Public Policy ◽  
Case Law ◽  
Theoretical Explanation ◽  
Educational Institutions ◽  
Original Intent ◽  
Policy Problem ◽  
Old Order ◽  
Reinforcing Factors ◽  
The Right

This chapter elaborates the shifting case law over the 24 year period from 1982 to 2006 in regard to the right of private individuals and organisations to establish educational institutions, the regulation of admissions to private-unaided institutions (self-financing institutions), and the regulatory power of AICTE. It offers a theoretical explanation of these shifts by elaborating two major reinforcing factors. The first is the adoption of an interpretational philosophy that legitimates judges going beyond the express wording and original intent of Constitution makers, discerning the purpose underlying a constitutional provision, and applying the purpose so discovered to rectify failures of public policy and governance types. The second factor is the inbuilt trait to expand as a result of a generous policy of admitting appeals. Given that judges differ considerably in the judicial philosophy they hold, and their perception of policy problem and solutions case law has bene fluid, creating uncertainty for institutions which are regulated as well as regulators like the AICTE.

scholarly journals The thermochemistry of carbon: valence states, heats of sublimation and energies of linkage

1946 ◽  
Vol 187 (1010) ◽  
pp. 337-357 ◽  
Keyword(s):  
Ground State ◽  
Electronic Configuration ◽  
Dissociation Energies ◽  
True Value ◽  
Valence States ◽  
Chemical Combination ◽  
The Right ◽  
Right Order ◽  
Unambiguous Assignment ◽  
Apparent Conflict

The controversy which exists at the present time between the figures 125 and 170 kcal./g.- atom for the latent heat of sublimation of carbon into monatomic vapour in the ground state originates largely from the neglect to take into consideration the energy required to raise the carbon atoms from the ground ( 3 P ) state to the lowest tetravalent ( 5 S ) electronic configuration corresponding to that in which it is normally found in chemical combination. Consideration of the energies of removal of a hydrogen atom from the methane and ethane molecules and of the energies of reorganization of the resulting radicals leads to the figure 190 ± about 10 kcal. for L 2 , the heat of sublimation into free atoms in the 5 S state. This in turn leads to a satisfactory and unambiguous assignment of values to bond energies (as distinct from dissociation energies) which can now be expressed with an uncertainty of not more than a few kcal. In the light of the valency distinction there remains no sound evidence to maintain the higher value put forward for L 1 and 125 kcal. is unquestionably of the right order. There are strong indications that an earlier estimate of 100 kcal. for the energy level of the 5 S state above the 3 P (ground) state is about 50 % in excess of the true value. The necessity for establishing this branch of thermochemistry on a sound theoretical and experimental footing has long been a very obvious need. The scheme here suggested reconciles points hitherto in apparent conflict, and brings virtually all established experimental knowledge into alignment.

scholarly journals Chronicle of the discovery of the back-bending phenomenon in atomic nuclei: a personal recollection 50 years on

2021 ◽  
Vol 46 (1) ◽  
Author(s):  
Hans Ryde
Keyword(s):  
Nuclear Structure ◽  
Ground State ◽  
Energy Levels ◽  
Historical Context ◽  
Rotational Frequency ◽  
Heavy Nuclei ◽  
Atomic Nuclei ◽  
Key Points ◽  
The Moment ◽  
The Right

AbstractA chronicle describing the historical context and the development of ideas and experiments leading to the discovery of the back-bending phenomenon in rapidly rotating atomic nuclei some 50 years ago is presented. The moment of inertia of some atomic nuclei increases anomalously at a certain rotational frequency, revealing important clues to our understanding of nuclear structure. I highlight the decisive interactions and contacts between experimentalists and theorists, which created the right environment, allowing for the revelation of an undetected phenomenon in Nature. Finally, I reflect on the key points allowing for the discovery and particularly point to the importance of systematic surveys, which in this case investigated the energy levels in heavy nuclei of a large sample of elements, as well as to the accuracy of the measurements of the ground state levels made at the time.

scholarly journals Computing Superior Counter-Examples for Conformant Planning

2020 ◽  
Vol 34 (06) ◽  
pp. 10017-10024
Author(s):  
Xiaodi Zhang ◽  
Alban Grastien ◽  
Enrico Scala
Keyword(s):  
Theoretical Explanation ◽  
Improve Performance ◽  
Conformant Planning ◽  
Counter Example ◽  
The Right

In a counter-example based approach to conformant planning, choosing the right counter-example can improve performance. We formalise this observation by introducing the notion of “superiority” of a counter-example over another one, that holds whenever the superior counter-example exhibits more tags than the latter. We provide a theoretical explanation that supports the strategy of searching for maximally superior counter-examples, and we show how this strategy can be implemented. The empirical experiments validate our approach.

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