Infrared spectra and substituent effects in 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones

1983 ◽  
Vol 48 (2) ◽  
pp. 586-595 ◽  
Author(s):  
Alexander Perjéssy ◽  
Pavol Hrnčiar ◽  
Ján Šraga
Keyword(s):  
Substituent Effects ◽  
Phenyl Group ◽  
Wave Number ◽  
Vibrational Coupling ◽  
Wave Numbers ◽  
Stretching Vibration ◽  
Stretching Vibrations ◽  
The Relationship ◽  
Derivatives Of ◽  
Effect Of Structure

The wave numbers of the fundamental C=O and C=C stretching vibrations, as well as that of the first overtone of C=O stretching vibration of 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones and 1,3-cycloheptanedione were measured in tetrachloromethane and chloroform. The spectral data were correlated with σ+ constants of substituents attached to phenyl group and with wave number shifts of the C=O stretching vibration of substituted acetophenones. The slope of the linear dependence ν vs ν+ of the C=C stretching vibration of the ethylenic group was found to be more than two times higher than that of the analogous correlation of the C=O stretching vibration. Positive values of anharmonicity for asymmetric C=O stretching vibration can be considered as an evidence of the vibrational coupling in a cyclic 1,3-dicarbonyl system similarly, as with derivatives of 1,3-indanedione. The relationship between the wave numbers of the symmetric and asymmetric C=O stretching vibrations indicates that the effect of structure upon both vibrations is symmetric. The vibrational coupling in 1,3-cycloheptanediones and the application of Seth-Paul-Van-Duyse equation is discussed in relation to analogous results obtained for other cyclic 1,3-dicarbonyl compounds.

Structural and substituent effects on the ketene infrared stretching frequency

1994 ◽  
Vol 72 (3) ◽  
pp. 882-887 ◽  
Author(s):  
Michael A. McAllister ◽  
Thomas T. Tidwell
Keyword(s):  
Negative Charge ◽  
Substituent Effects ◽  
Resonance Structure ◽  
Stretching Vibration ◽  
Structure Formula ◽  
Negative Charge Density ◽  
The Relationship ◽  
Absorption Frequencies ◽  
Modest Correlation ◽  
Good Agreement

The frequencies and intensities of the ketene asymmetric stretching vibration near 2100 cm−1 for a series of substituted ketenes and fulvenones have been calculated using ab initio molecular orbital methods. Comparisons of the calculated values with experimentally determined results show reasonably good agreement in most cases, with a typical deviation of ± 10 cm−1 between the measured and calculated values. A test of a correlation proposed by Gano and Jacob (Spectrochim. Acta, 43A, 1023 (1987)) of the frequencies with substituent field and resonance parameters F and R shows a modest correlation coefficient of 0.86, with no significant dependence on R. These results are consistent with enhancements of ketene infrared absorption frequencies by interaction of substituents with the negative charge density at Cβ of ketenes, as indicated by the resonance structure [Formula: see text] The calculated intensities I (km/mol) for non-π acceptor substituents are correlated with the group electronegativities X by the relationship I = 1841.6 − 305.7X (r = 0.94). The π-acceptor substituents show exaltations of the intensities, and the results are interpreted as showing an enhancement of intensities by electropositive substituents increasing the normal ketene dipole directed towards oxygen, and an opposite effect by π-acceptor substituents delocalizing the negative charge at Cβ.

The wavenumbers of NO2 stretching vibrations and transmission of substituent effects in 2- and 4-substituted 3-nitropyridine series

1985 ◽  
Vol 50 (11) ◽  
pp. 2443-2452 ◽  
Author(s):  
Alexander Perjéssy ◽  
Danuta Rasala ◽  
Piotr Tomasik ◽  
Ryszard Gawinecki
Keyword(s):  
Nitro Group ◽  
Substituent Effect ◽  
Substituent Effects ◽  
Correlation Equations ◽  
Stretching Vibration ◽  
Stretching Vibrations ◽  
Transmission Factors

The wavenumbers of both the symmetric and asymmetric stretching vibrations of the nitro group were measured in chloroform for the series of 2-X- and 4-X-substituted 3-nitropyridines as well as for o-X-substituted nitrobenzenes. The νas(NO2) and νs(NO2) values of both nitropyridine series were compared with those of corresponding nitrobenzenes. It has been found that the substituent effects in pyridines are transmitted to the 3-nitro group more readily from the 4-position, than from the 2-position. This transmission in 2-X-substituted 3-nitropyridines is comparable with that in the series of o-substituted benzene analogues. The transmission factors, γ, were determined according to Charton's definition for both 2,3- and 4,3-disubstituted pyridine rings. The separation of overall substituent effect into its inductive (field), resonance and steric components is discussed in terms of multiparameter correlation equations for wavenumber of asymmetric NO2 stretching vibration.

Preparation of 3-cyano-4-(R-vinyl)-5,5-dimethyl-Δ3-butenolides and substituent effects on their infrared spectra

1989 ◽  
Vol 54 (6) ◽  
pp. 1666-1674 ◽  
Author(s):  
Alexander Perjéssy ◽  
Aida Avetisovna Avetisyan ◽  
Anna Alexandrovna Aknazaryan ◽  
Gagik Surenovich Melikyan
Keyword(s):  
Infrared Spectra ◽  
Substituent Effects ◽  
Aromatic Aldehydes ◽  
The Other ◽  
Wave Numbers ◽  
Different Types ◽  
Group A ◽  
Stretching Vibrations ◽  
Transmission Factors ◽  
Statistical Results

Twenty nine 3-cyano-4-(R-vinyl)-5,5-dimethyl-Δ3-butenolides were prepared by condensation of 3-cyano-4,5,5-trimethyl-Δ3-butenolide with aliphatic and aromatic aldehydes. The wave numbers of C=O, C=N and C=C stretching vibrations of synthesized compounds were measured in trichloro- and tetrachloromethane. The spectral data were correlated with substituent conotants using Hammett-Brown and the improved and extended Seth-Paul-Van Duyse equation. The statistical results of correlations were compared with those of ethyl α-cyanocinnamates, ethyl benzoates and benzonitriles. The transmission factors for one and two C=C bonds were determined in the regions of π' = 0.46-0.57 and 0.27-0.37, respectively. In 3-cyano-4-(arylvinyl)-5,5-dimethyl-Δ3-butenolides a considerable conjugation exists between the arylvinyl moiety and both the C=O and C=N groups. On the other hand, in 3-cyano-4-(alkylvinyl)-5,5-dimethyl-Δ3-butenolides probably only the endocyclic C=C bond takes part in a marked resonance interaction with alkylvinyl group. A generally valid relationship was found between the slopes of ν(C=O) vs σ+ and ν(C=N) vs σ+ correlations for different types of compounds measured in CHCl3 and CCl4.

Private and Public Law

2020 ◽  
pp. 574-592
Author(s):  
Thomas W. Merrill
Keyword(s):  
Law And Economics ◽  
Public Law ◽  
Private Law ◽  
General Criterion ◽  
The Public ◽  
Private Ordering ◽  
Public Rights ◽  
Private And Public ◽  
The Relationship ◽  
Derivatives Of

This chapter explores the relationship between private and public law. In civil law countries, the public-private distinction serves as an organizing principle of the entire legal system. In common law jurisdictions, the distinction is at best an implicit design principle and is used primarily as an informal device for categorizing different fields of law. Even if not explicitly recognized as an organizing principle, however, it is plausible that private and public law perform distinct functions. Private law supplies the tools that make private ordering possible—the discretionary decisions that individuals make in structuring their lives. Public law is concerned with providing public goods—broadly defined—that cannot be adequately supplied by private ordering. In the twentieth and twenty-first centuries, various schools of thought derived from utilitarianism have assimilated both private and public rights to the same general criterion of aggregate welfare analysis. This has left judges with no clear conception of the distinction between private and public law. Another problematic feature of modern legal thought is a curious inversion in which scholars who focus on fields of private law have turned increasingly to law and economics, one of the derivatives of utilitarianism, whereas scholars who concern themselves with public law are increasingly drawn to new versions of natural rights thinking, in the form of universal human rights.

On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability

2021 ◽  
pp. 1-19
Author(s):  
M. Miri Karbasaki ◽  
M. R. Balooch Shahriari ◽  
O. Sedaghatfar
Keyword(s):  
Linear Function ◽  
Level Set ◽  
Fuzzy Numbers ◽  
Sufficient Condition ◽  
Continuous Linear ◽  
Generalized Differentiability ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of ◽  
Dimensional Mapping

This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fréchet and Gâteaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fréchet and Gâteaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fréchet and Gâteaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fréchet and Gâteaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.

scholarly journals Permutation Matrices, Their Discrete Derivatives and Extremal Properties

2020 ◽  
Vol 48 (4) ◽  
pp. 719-740
Author(s):  
Richard A. Brualdi ◽  
Geir Dahl
Keyword(s):  
Permutation Matrix ◽  
Permutation Matrices ◽  
Discrete Derivative ◽  
The Relationship ◽  
Derivatives Of ◽  
Extremal Properties

AbstractFor a permutation π, and the corresponding permutation matrix, we introduce the notion of discrete derivative, obtained by taking differences of successive entries in π. We characterize the possible derivatives of permutations, and consider questions for permutations with certain properties satisfied by the derivative. For instance, we consider permutations with distinct derivatives, and the relationship to so-called Costas arrays.

Oxidation of Olefins Representing Some Structural Units of GR-S

1952 ◽  
Vol 25 (1) ◽  
pp. 21-32 ◽  
Author(s):  
W. C. Warner ◽  
J. Reid Shelton
Keyword(s):  
Phenyl Group ◽  
Kinetic Mechanism ◽  
Oxidation Reactions ◽  
Chain Reaction ◽  
Instantaneous Rate ◽  
Initial Oxygen ◽  
Oxidation Of Olefins ◽  
A Minor ◽  
The Relationship ◽  
Kinetics Of

Abstract Three olefins were oxidized in the liquid phase with molecular oxygen to determine the kinetics of the oxidation reactions and the relationship to oxidation of rubber. The instantaneous rate of oxidation was found to be related to the analytically determined olefin and peroxide concentrations by the equation : Rate=k (unreacted olefin)(peroxide), where rate equals moles of oxygen per mole of original olefin per hour and the parentheses represent molarities. Presence of a phenyl group was found to affect k, but only in a minor way, indicating that the same fundamental kinetic mechanism applies in both aromatic and aliphatic olefins. The data are consistent with the general kinetic mechanism of Bolland involving oxygen attack at the alpha-methylenic group. However, it appears probable that initial oxygen attack can also occur at the double bond, resulting in the formation of a peroxide biradical, which may then react with other olefin molecules, initiating the usual chain reaction mechanism.

Nuclear magnetic resonance characterization of the ring conformations of monosubstituted derivatives of 1,3-dioxa-5,6-benzocycloheptene

1983 ◽  
Vol 61 (1) ◽  
pp. 109-115 ◽  
Author(s):  
R. St-Amour ◽  
M. St-Jacques
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Substituent Effects ◽  
Steric Effects ◽  
Slow Exchange ◽  
Conformational Properties ◽  
Derivatives Of ◽  
Ring Conformations ◽  
Twist Boat

The conformational properties of 2-alkyl (Me, Et, i-Pr, and t-Bu) and 2-phenyl derivatives of 1,3-dioxa-5,6-benzocycloheptene (1) were studied by 13C dnmr. Analysis of slow exchange spectra at 100.6 MHz indicates that all derivatives except tert-butyl exist in an equilibrium of chair (major) and twist-boat (minor) conformations. Substituent effects on the position of the equilibrium are rationalized in terms of steric effects.

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