<P> However, an alternative description of water treats the lone pairs of water as energetically and geometrically distinct and possessing different symmetry (σ and π). In this model, one lone pair is represented by a lower energy σ - symmetry in - plane hybrid orbital that mixes s and p character (σ (out)), while the other lone pair is represented by a higher energy π - symmetry orbital perpendicular to the plane of the molecule of pure 2p character (p). In the fully delocalized canonical molecular orbital picture, these orbitals are given the Mulliken labels a and b, in which the "nonbonding" a orbital actually consists of σ (out) mixed with the in - phase symmetry - adapted linear combination of the H (1s) orbitals (the small back lobe of σ (out) is able to interact). Thus, a is actually weakly bonding in character while b is truly nonbonding . </P> <P> Both models are of value, but one must be careful of their applicability . Since only the canonical MOs (as opposed to any variety of localized MOs) are eigenfunctions of the effective Hamiltonian, one must look at inequivalent, fully delocalized lone pair orbitals when interpreting the photoelectron spectrum of water (Koopmans' theorem), which does indeed show two signals corresponding to different energy levels for the lone pairs . However, any set of orbitals obtained by taking linear combination of symmetry - adapted orbitals via unitary transformations, as the equivalent lone pair hybrid orbitals are, result in the same electron density as the original set of orbitals . In this case, we can construct the two equivalent lone pair hybrid orbitals h and h' by taking linear combinations h = c σ (out) + c p and h' = c σ (out)--c p for an appropriate choice of coefficients c and c . For chemical and physical properties of water that depend on the overall electron distribution of the molecule, the use of h and h' is just as valid as the use of σ (out) and p . In some cases, such a view is intuitively useful . For example, the hydrogen bonds of water form along the directions of the "rabbit ears" lone pairs, as a reflection of the high electron density in these regions . </P> <P> Because of the popularity of VSEPR theory, the treatment of the water lone pairs as equivalent is prevalent in introductory chemistry courses, and many practicing chemists continue to regard it as a useful model . A similar situation arises when describing the two lone pairs on the carbonyl oxygen of a ketone . However, the question of whether it is physically sound and conceptually useful to derive equivalent orbitals from symmetry - correct ones, from the standpoint of bonding theory and pedagogy and in light of modern experimental and computational data, is still a controversial one, with recent (2014 and 2015) articles opposing and supporting the practice . </P> <P> (See article on localized molecular orbitals and sigma - pi and equivalent - orbital models for more details .) </P>

Describe the difference between a shared pair and an unshared pair of electrons