Natural orbitals hypothesis

Natural bond orbital analysis of early and late TSs has been carried out to explore the factors involved in tt-selectivity of nucleophilic addition to carbonyls.209 Cieplak s o —r o hyperconjugation hypothesis (where o is the incipient bond) is not supported by the results for early TSs, and evidence in favour of Felkin-Anh s o er hypothesis is weak. Late TSs are devoid of o 7r(t=() interactions here, the Cieplak model may be applicable. 

However, if a hypothesis or set of hypotheses, based on an observation of a natural phenomenon, cannot be tested or experiments fail to show a direct conclusion, it is identified as a theory. A theory explains why something happens. For example, the atomic theory (see Lessons 9 and 10) of small electron particles orbiting around a dense nucleus containing protons and neutrons is based on indirect observations of the atom. This is only a possible explanation for the structure of an atom. A model is the description of the theory, such as the structure of an atom. 

Support for the reverse sequence hypothesis is derived from a comparative study on the photoelectron spectra of numerous a-substituted derivatives of furan, thiophene, selenophene, and tellurophene.33 The vertical ionization energies (I, and I2) of the two highest MOs (n2 and n ) are reported in Table XIV. An examination of the correlations obtained between the ionization energies of molecular orbitals of substituted furans, selenophenes, and tellurophenes vs. those of substituted thiophenes makes clear the diverse nature of the upper orbitals in tellurophenes. Slopes close to I, very high correlation coefficients and low standard deviations are obtained when I, and I2 values for substituted furans and selenophenes are plotted against the corresponding values for substituted thiophenes. On the contrary, slopes differing... 

Without this luxury Laplace set out to assess the natural stability of the system. When asked by Napoleon to clarify the role of God in this, he replied "I have no need of that hypothesis". The first important result, which he demonstrated mathematically, was that the irregularities in the eccentricities and inclinations of planetary orbits oscillate about fixed values, without amplification, and hence never deviate too far from the ideal orbits. He could therefore theorize that the solar system remains indefinitely stable. Like some self-correcting clockwork, driven by the universal force of gravitation, the solar system was concluded to be inherently stable and predictable. Laplace saw no reason why the whole universe should not be dynamically stable in the same sense. He claimed that ... 

Although the orbitals crossing shown above are not real, this diagram gives us a convenient way to treat electrocyclic reactions. We can determine the nature of the process conrotatory or disrotatory) by assuming that the ti-HOMO must be converted to the new a-MO. This was the hypothesis that was originally published by Woodward and Hoffmann. It means that, because the symmetry of the HOMO alternates as one more double bond (or two electrons) is added, the conrotatory or disrotatory nature of electrocyclic reactions also alternates. This can then be formulated as a set of rules, as shown in Table 4.1. 

The electrons in an atom also have an intrinsic angular momentum in addition to their orbital angular momentum about the nucleus. This is called the electron spin or sometimes just referred to as spin. Even an electron in the / = 0 orbital that has zero angular momentum will have an intrinsic spin. The intrinsic spin of the electron is not a classical mechanical effect hence, it is not a correct picture to view the electron spinning about one of its axes, as the classical mechanical picture would indicate. The term spin is more of a name for this phenomenon rather than an actual description of the electron. Though the intrinsic spin of the electron is real, there is no example in the macroscopic world to form a visual model. The electron spin arises naturally when relativistic mechanics is combined with quantum mechanics. Since this text is confined to quantum mechanics, the concept of electron spin must be introduced as a hypothesis. 

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