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, backoftheenvelope understanding of πbonding.
 The Hückel method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a very simple linear combination of atomic orbitals molecular orbitals method for the determination of energies of molecular orbitals of πelectrons in πdelocalized molecules, such as ethylene, benzene, butadiene, and pyridine.[1][2] It is the theoretical basis for Hückel’s rule for the aromaticity of
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The method has several characteristics:
 It limits itself to conjugated hydrocarbons.
 Only π electron molecular orbitals are included because these determine much of the chemical and spectral properties of these molecules. The σ electrons are assumed to form the framework of the molecule and σ connectivity is used to determine whether two π orbitals interact. However, the orbitals formed by σ electrons are ignored and assumed not to interact with π electrons. This is referred to as σπ separability. It is justified by the orthogonality of σ and π orbitals in planar molecules. For this reason, the Hückel method is limited to systems that are planar or nearly so.
 The method is based on applying the variational method to linear combination of atomic orbitals and making simplifying assumptions regarding the overlap, resonance and Coulomb integrals of these atomic orbitals. It does not attempt to solve the Schrödinger equation, and neither the functional form of the basis atomic orbitals nor details of the Hamiltonian are involved.
 For hydrocarbons, the method takes atomic connectivity as the only input; empirical parameters are only needed when heteroatoms are introduced.
 The method predicts how many energy levels exist for a given molecule, which levels are degenerate and it expresses the molecular orbital energies in terms of two parameters, called α, the energy of an electron in a 2p orbital, and β, the interaction energy between two 2p orbitals (the extent to which an electron is stabilized by allowing it to delocalize between two orbitals). The usual sign convention is to let both α and β be negative numbers. To understand and compare systems in a qualitative or even semiquantitative sense, explicit numerical values for these parameters are typically not required.
 In addition the method also enables calculation of charge density for each atom in the π framework, the fractional bond order between any two atoms, and the overall molecular dipole moment.
The results for a few simple molecules are tabulated below:
The theory predicts two energy levels for ethylene with its two π electrons filling the lowenergy HOMO and the high energy LUMO remaining empty. In butadiene the 4 πelectrons occupy 2 low energy molecular orbitals, out of a total of 4, and for benzene 6 energy levels are predicted, two of them degenerate.
For linear and cyclic systems (with N atoms), general solutions exist:[7]

 Linear system (polyene/polyenyl):

 Cyclic system, Hückel topology (annulene/annulenyl):
 Cyclic system, Möbius topology (hypothetical for N [8]):
The energy levels for cyclic systems can be predicted using the Frost circle [de] mnemonic (named after the American chemist Arthur Atwater Frost [de]). A circle centered at α with radius 2β is inscribed with a regular Ngon with one vertex pointing down; the ycoordinate of the vertices of the polygon then represent the orbital energies of the [N]annulene/annulenyl system.[9] Related mnemonics exists for linear and Möbius systems.[10]
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