On the extension of the Hückel rule to polycyclic non-alternant conjugated hydrocarbons

1976 ◽  
Vol 54 (11) ◽  
pp. 1789-1794 ◽  
Author(s):  
I. Gutman ◽  
N. Trinajstić
Keyword(s):  
Electron System ◽  
The Other ◽  
Conjugated Hydrocarbons ◽  
General Rules ◽  
Stabilizing Effect ◽  
Hückel Rule ◽  
Polycyclic Conjugated Hydrocarbons ◽  
Theoretical Considerations ◽  
Conjugated Molecule

General rules for aromatic stability of non-alternant polycyclic conjugated hydrocarbons are obtained using graph–theoretical considerations. Every pair of odd-membered rings contained in the conjugated molecule has a stabilizing effect if one ring is of the size 4N + 1 and the other of the size 4N + 3. If both rings are of the size 4N + 1 or 4N + 3, a destabilizing effect occurs. This conclusion holds both for fused and disjointed rings. The π-electron System is said to be relatively more stable if the number of (4N + l)-membered rings is equal to the number of (4N + 3)-rings.

An Extension of the Hückel 4N + 2 Rule to Polycyclic Non-alternant Conjugated Hydrocarbons

1975 ◽  
Vol 53 (6) ◽  
pp. 945-951 ◽  
Author(s):  
Jerzy Kruszewski ◽  
Tadeusz Marek Krygowski
Keyword(s):  
Substituent Effects ◽  
General Rule ◽  
Electron System ◽  
Ionic Form ◽  
Conjugated Hydrocarbons ◽  
Benzene Rings ◽  
The Difference ◽  
Polycyclic Conjugated Hydrocarbons ◽  
Prediction Of Substituent Effects ◽  
Stability Indices

A general rule of aromatic stability of non-alternant polycyclic conjugated hydrocarbons has been detailed and using aromatic stability indices, corroborated. The π-electron system is said to be relatively more stable if the difference between number of 4N + 3-type rings minus number of 4N + 1-type rings is 0 or divisible by 4. If not, the system is assumed to be relatively unstable. The presence of benzene rings does not affect the rule. A further extension for intramolecular H-bonded systems is also suggested. The rule suggested permits prediction of substituent effects on stability as well as the ionic form being most stable if the rule is not fulfilled.

scholarly journals Verifying the PCP-rule by five-center bond indices

2009 ◽  
Vol 74 (5) ◽  
pp. 549-554 ◽  
Author(s):  
Jelena Djurdjevic ◽  
Ivan Gutman ◽  
Robert Ponec
Keyword(s):  
Membered Ring ◽  
Energy Effect ◽  
Conjugated Hydrocarbons ◽  
Cyclic Conjugation ◽  
Bond Indices ◽  
Polycyclic Conjugated Hydrocarbons

According to the recently discovered PCP-rule, the (stabilizing) energy- effect of the cyclic conjugation in the 5-membered ring of acenaphthyleneand fluoranthene-type polycyclic conjugated hydrocarbons increases with the number of phenyl-cyclopentadienyl (PCP) fragments present in the molecule. It is now shown that the validity of the PCP-rule is also supported by the 5-center bond indices, an independent quantitative theoretical measure of cyclic conjugation in 5-membered rings.

A theoretical study on a series of polycyclic conjugated hydrocarbons—dinaphthobenzo[1,2:4,5]dicyclobutadienes with tunable charge transport properties by controlling [N]phenylenes and (anti)aromaticity

2019 ◽  
Vol 7 (22) ◽  
pp. 6721-6727
Author(s):  
Hang Yin ◽  
Daoyuan Zheng ◽  
Yan Qiao ◽  
Xiaofang Chen
Keyword(s):  
Charge Transport ◽  
Transport Properties ◽  
Theoretical Study ◽  
Energy Gap ◽  
Conjugated Hydrocarbons ◽  
Polycyclic Conjugated Hydrocarbons

A multi-dimensional relationship founded on the targeted [N] number, the energy gap (Eg) and the aromatic degree was constructed for predicting cyclobutadienoid-containing dinaphthobenzo[1,2:4,5]dicyclobutadienes (DNBDCs) with better charge transport properties.

Aromaticity of Polycyclic Conjugated Hydrocarbons

ChemInform ◽  
2003 ◽  
Vol 34 (48) ◽  
Author(s):  
Milan Randic
Keyword(s):  
Conjugated Hydrocarbons ◽  
Polycyclic Conjugated Hydrocarbons

Are There Different Kinds of Rogue Waves?

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Paul C. Liu ◽  
Keith R. MacHutchon
Keyword(s):  
Rogue Wave ◽  
Rogue Waves ◽  
Rayleigh Distribution ◽  
The Other ◽  
South Indian Ocean ◽  
Gas Drilling ◽  
Wave Measurements ◽  
South Indian ◽  
Theoretical Considerations

There is clearly no immediate answer to the question posted by the title of this paper. Inasmuch as that there are not much definitively known about rogue waves and that there is still no universally accepted definition for rogue waves in the ocean, we think there might just be even more than one kind of rogue waves to contend with. While the conventional approach has generally designated waves with Hmax∕Hs greater than 2.2 as possible rogue waves, based on Rayleigh distribution considerations, there is conspicuously no provision as to how high the ratio of Hmax∕Hs can be and thus not known how high can a rogue wave be. In our analysis of wave measurements made from a gas-drilling platform in South Indian Ocean, offshore from Mossel Bay, South Africa, we found a number of cases that indicated Hmax∕Hs could be valued in the range between 4 and 10. If this were to be the case, then these records could be considered to be “uncommon” rogue waves, whereas a record of Hmax∕Hs in the range between 2 and 4 could be considered to comprise “typical” rogue waves. On the other hand, the spikes in the Hmax data could have been caused by equipment malfunction or some other phenomenon. Clearly, the question of whether or not there are different kinds of rogue waves cannot be readily answered by theoretical considerations alone and there is a crucial need for long-term wave time-series measurements for studying rogue waves.

Effect of hemoglobin type on the cardiorespiratory system of sheep

1965 ◽  
Vol 209 (3) ◽  
pp. 593-598 ◽  
Author(s):  
T. J. Dawson ◽  
J. V. Evans
Keyword(s):  
Oxygen Affinity ◽  
The Other ◽  
Domestic Sheep ◽  
Cardiorespiratory System ◽  
Hemoglobin Type ◽  
Lower Oxygen ◽  
Respiratory Systems ◽  
Genetically Determined ◽  
Theoretical Considerations

In domestic sheep there exist two genetically determined types of hemoglobin which have considerably different oxygen affinities. Under most conditions sheep with either of these hemoglobins exist together, apparently sheep with one type being at no gross disadvantage compared to those with the other. Theoretical considerations suggested that the tissues of sheep with the higher oxygen affinity hemoglobin (Hb-A) should be hypoxic relative to those of sheep with the lower oxygen affinity hemoglobin (Hb-B). The data obtained showed that the cardiovascular and respiratory systems of animals with different hemoglobins differed in many respects. It was concluded that the nature of these differences was such that they could be viewed as being due to adjustments by animals with Hb-A to alleviate the potential hypoxia of their tissues relative to the tissues of animals with Hb-B.

Are There Different Kinds of Rogue Waves?

2006 ◽  
Author(s):  
Paul C. Liu ◽  
Keith R. MacHutchon
Keyword(s):  
Time Series ◽  
Rogue Waves ◽  
Rayleigh Distribution ◽  
The Other ◽  
South Indian Ocean ◽  
Gas Drilling ◽  
Wave Measurements ◽  
South Indian ◽  
Theoretical Considerations

Inasmuch as there is as yet still no universally accepted definition for rogue waves in the ocean, we think there might just be more than one kind of rogue waves to contend with. While the conventional approach has generally designated waves with Hmax/Hs greater than 2.2 as possible rogue waves, based on Rayleigh distribution considerations, there is conspicuously no provision as to how high the ratio of Hmax/Hs can be. In our analysis of wave measurements made from a gas-drilling platform in South Indian Ocean, offshore from Mossel Bay, South Africa, we found a number of cases that indicated Hmax/Hs could be valued in the range between 4 and 10. If this were to be the case these records could be considered to be “uncommon” rogue waves, whereas a record of Hmax/Hs in the range between 2 and 4 could be considered to comprise “typical” rogue waves. On the other hand the spikes in the Hmax data could have been caused by equipment malfunction or some other phenomenon. Clearly the question of whether or not there are different kinds of rogue waves can not be readily answered by theoretical considerations alone and there is a crucial need for long-term wave time series measurements for studying rogue waves.

Effect of Naphthalene Compounded Superplasticizer on Strength and Shrinkage of Ready-Mixed Concrete

2012 ◽  
Vol 174-177 ◽  
pp. 488-495
Author(s):  
Yu Fei Wang ◽  
Han Dong Yan
Keyword(s):  
Cement Paste ◽  
Test Data ◽  
Concrete Strength ◽  
Reducing Agent ◽  
The Other ◽  
General Rules ◽  
Early Strength ◽  
Ready Mixed Concrete ◽  
Mixed Concrete

Superplasticizer is widespread applied in the ready-mixed concrete in China. In the specific engineering, it is not only has the requirement of water-reducing ratio for superplasticizer, but also the superplasticizer has to meet the demand such as early-strength, air-entraining, retarding and so on. In current, the naphthalene compounded superplasticizer is conducted on the basis of the FDN modification. This paper selects two kinds of representative naphthalene compounded superplasticizers, one is the setretarder superplasticizer (WRA1), and the other one is the early strength-air entraining-retarding superplasticizer (WRA2). The effect of performance on neat cement paste, mortar and concrete which mixed with the two admixtures are compared with the benchmarks (not mixed with water reducing agent) and mixed with FDN. Through the analysis and comparison of the test data, the general rules of the naphthalene compounded superplasticizer to concrete strength and shrinkage are put forward in this paper. Also, according to those rules, it poses the concrete problems to be noted in the production. This may have guidance for reducing the early cracks of ready-mixed concrete.

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