Теория молекулярных орбиталей Хюккеля

Theory of molecular orbitals by Erich Hückel
The Hückel method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear combinations of atomic orbitals. The theory predicts the molecular orbitals for π electrons in π delocalized molecules, such as ethylene, benzene, butadiene, and pyridine. It provides the theoretical basis for Hückel's rule that cyclic, planar molecules or ions with π electrons are aromatic. It was later extended to conjugated molecules such as pyridine, pyrrole and furan that contain atoms other than carbon and hydrogen (heteroatoms). A more dramatic extension of the method to include σ electrons, known as the extended Hückel method (EHM), was developed by Roald Hoffmann. The extended Hückel method gives some degree of quantitative accuracy for organic molecules in general (not just planar systems) and was used to provide computational justification for the Woodward–Hoffmann rules. To distinguish the original approach from Hoffmann's extension, the Hückel method is also known as the simple Hückel method (SHM). Although undeniably a cornerstone of organic chemistry, Hückel's concepts were undeservedly unrecognized for two decades. Pauling and Wheland characterized his approach as "cumbersome" at the time, and their competing resonance theory was relatively easier to understand for chemists without fundamental physics background, even if they couldn't grasp the concept of quantum superposition and confused it with tautomerism. His lack of communication skills contributed: when Robert Robinson sent him a friendly request, he responded arrogantly that he is not interested in organic chemistry. In spite of its simplicity, the Hückel method in its original form makes qualitatively accurate and chemically useful predictions for many common molecules and is therefore a powerful and widely taught educational tool. It is described in many introductory quantum chemistry and physical organic chemistry textbooks, and organic chemists in particular still routinely apply Hückel theory to obtain a very approximate, back of the envelope understanding of π bonding.

The value of α is the energy of an electron in a 2p orbital, relative to an unbound electron at infinity. This quantity is negative, since the electron is stabilized by being electrostatically bound to the positively charged nucleus. For carbon this value is known to be approximately –11.4 eV. Since Hückel theory is generally only interested in energies relative to a reference localized system, the value of α is often immaterial and can be set to zero without affecting any conclusions. Roughly speaking, β physically represents the energy of stabilization experienced by an electron allowed to delocalize in a π molecular orbital formed from the 2p orbitals of adjacent atoms, compared to being localized in an isolated 2p atomic orbital. As such, it is also a negative number, although it is often spoken of in terms of its absolute value. The value for |β| in Hückel theory is roughly constant for structurally similar compounds, but not surprisingly, structurally dissimilar compounds will give very different values for |β|. For example, using the π bond energy of ethylene (65 kcal/mole) and comparing the energy of a doubly occupied π orbital (2α + 2β) with the energy of electrons in two isolated p orbitals (2α), a value of |β| = 32.5 kcal/mole can be inferred. On the other hand, using the resonance energy of benzene (36 kcal/mole, derived from heats of hydrogenation) and comparing benzene (6α + 8β) with a hypothetical "non aromatic 1,3,5 cyclohexatriene" (6α + 6β), a much smaller value of |β| = 18 kcal/mole emerges. These differences are not surprising, given the substantially shorter bond length of ethylene (1.33 Å) compared to benzene (1.40 Å). The shorter distance between the interacting p orbitals accounts for the greater energy of interaction, which is reflected by a higher value of |β|. Nevertheless, heat of hydrogenation measurements of various polycyclic aromatic hydrocarbons like naphthalene and anthracene all imply values of |β| between 17 and 20 kcal/mol. However, even for the same compound, the correct assignment of |β| can be controversial. For instance, it is argued that the resonance energy measured experimentally via heats of hydrogenation is diminished by the distortions in bond lengths that must take place going from the single and double bonds of "non aromatic 1,3,5 cyclohexatriene" to the delocalized bonds of benzene. Taking this distortion energy into account, the value of |β| for delocalization without geometric change (called the "vertical resonance energy") for benzene is found to be around 37 kcal/mole. On the other hand, experimental measurements of electronic spectra have given a value of |β| (called the "spectroscopic resonance energy") as high as 3 eV (~70 kcal/mole) for benzene. Given these subtleties, qualifications, and ambiguities, Hückel theory should not be called upon to provide accurate quantitative predictions – only semi quantitative or qualitative trends and comparisons are reliable and robust.

The analysis of the optical activity of a molecule depends to a certain extent on the study of its chiral characteristics. However, for achiral molecules applying pesudoscalars to simplify the calculations of optical activity cannot be achieved due to the lack of spatial average. Instead of traditional chiroptical solution measurements, Hückel theory helps focus on oriented π systems by separating from σ electrons especially in the planar, symmetric cases. Transition dipole moments derived by multiplying each wavefunction of individual planar molecule one by one, contribute to the directions of the most optical activity, where sit at the bisectors of two orthogonal ones. Despite the zero value for the trace of the tensor, cis butadiene shows considerable off diagonal component which was computed as the first optical activity evaluation of achiral molecule. By using 3,5 dimethylene 1 cyclopentene as an example. Transition electric dipole, magnetic dipole and electric quadrupole moments interactions result in optical rotation(OR), which can be described by both tensor components and chemical geometries. The in phase overlap of two molecular orbitals yield negative charge while depleting charge out of phase. The movement can be interpreted quantitatively by corresponding π and π* orbitals coefficients.