Approximate Molecular Orbital Theory: The Hückel/Tight-binding Model

Huckel molecular orbital (HMO) theory is a simple approximate parameterized molecular orbital (MO) theory that has been very successful in organic chemistry and other fields. This chapter introduces the approximations made in HMO theory, and then treats as examples ethane, hetratriene and other linear polyenes, and benzene and other cyclic polyenes. The pi binding energy of benzene is particularly large according to HMO theory, rationalizing the special ‘aromatic’ behaviour of benzene. But there is a lot more to benzene than that. It is shown that the pi bond framework of benzene would rather prefer a structure with alternating single and double C-C bonds, rather than the actually observed 6-fold symmetric structure where all C-C bonds are equivalent. The observed benzene structure is a result of a delicate balance between the tendencies of the pi framework to create bond length alternation, and the sigma framework to resist bond length alternation.

Reduced bond length alternation and helical molecular orbitals in donor and acceptor substituted linear carbon chains

Increasing chain length and end group substitution of polyynes play a crucial role in molecular electronics and nanomaterials. The studies on linear carbon chains are lesser when compared to other carbon allotropes like graphene, fullerenes, nanotube, etc. This prompted us to study the linear carbon chains of different lengths and substitutions. The electronic and optical properties of X–C[Formula: see text]–X ([Formula: see text]–15 and [Formula: see text], NH2, CN, OH) molecules have been studied by using CAM-B3LYP/6-31G* level of theory of DFT methods. Linear carbon chains with odd values of n show lower bond length alternation (BLA) values similar to that of cumulenes and may have metallic property, but the substitution of donor/acceptor molecules does not decrease the BLA significantly. Molecular orbital analysis of linear carbon chains shows that NH2 or NO2 substituted polyynes have helical molecular orbitals for smaller chain lengths which may make a good candidate for molecular wires in molecular devices. As the chain length increases, the helicity decreases and finally disappears. Also, it is seen that for smaller odd values of [Formula: see text] for donor, substituted polyynes have a singlet ground, whereas all the odd [Formula: see text] values of acceptor substitution have triplet ground state.