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In chemistry, a lone pair refers to a pair of that are not shared with another atom in a covalent bondIUPAC Gold Book definition: lone (electron) pair and is sometimes called an unshared pair or non-bonding pair. Lone pairs are found in the outermost electron shell of atoms. They can be identified by using a Lewis structure. Electron pair are therefore considered lone pairs if two electrons are paired but are not used in chemical bonding. Thus, the number of in lone pairs plus the number of electrons in bonds equals the number of valence electrons around an atom.
Lone pair is a concept used in valence shell electron pair repulsion theory (VSEPR theory) which explains the shapes of molecules. They are also referred to in the chemistry of Lewis acids and bases. However, not all non-bonding pairs of electrons are considered by chemists to be lone pairs. Examples are the transition metals where the non-bonding pairs do not influence molecular geometry and are said to be stereochemically inactive. In molecular orbital theory (fully delocalized canonical orbitals or localized in some form), the concept of a lone pair is less distinct, as the correspondence between an orbital and components of a Lewis structure is often not straightforward. Nevertheless, occupied non-bonding orbitals (or orbitals of mostly nonbonding character) are frequently identified as lone pairs.
A single lone pair can be found with atoms in the nitrogen group, such as nitrogen in ammonia. Two lone pairs can be found with atoms in the chalcogen group, such as oxygen in water. The can carry three lone pairs, such as in hydrogen chloride.
In VSEPR theory the electron pairs on the oxygen atom in water form the vertices of a tetrahedron with the lone pairs on two of the four vertices. The H–O–H bond angle is 104.5°, less than the 109° predicted for a tetrahedral angle, and this can be explained by a repulsive interaction between the lone pairs.
Various computational criteria for the presence of lone pairs have been proposed. While electron density ρ( r) itself generally does not provide useful guidance in this regard, the Laplace operator of the electron density is revealing, and one criterion for the location of the lone pair is where L( r) = –∇2ρ( r) is a local maximum. The minima of the electrostatic potential V( r) is another proposed criterion. Yet another considers the electron localization function (ELF).
This can be seen more clearly when looked at it in two more common . For example, in carbon dioxide (CO2), which does not have a lone pair, the oxygen atoms are on opposite sides of the carbon atom (linear molecular geometry), whereas in water (H2O) which has two lone pairs, the angle between the hydrogen atoms is 104.5° (bent molecular geometry). This is caused by the repulsive force of the oxygen atom's two lone pairs pushing the hydrogen atoms further apart, until the forces of all electrons on the hydrogen atom are in equilibrium. This is an illustration of the VSEPR theory.
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A lone pair can contribute to the existence of chirality in a molecule, when three other groups attached to an atom all differ. The effect is seen in certain , ,Quin, L. D. (2000). A Guide to Organophosphorus Chemistry, LOCATION: John Wiley & Sons. . sulfonium and , , and even .
The resolution of enantiomers where the stereogenic center is an amine is usually precluded because the energy barrier for nitrogen inversion at the stereo center is low, which allow the two stereoisomers to rapidly interconvert at room temperature. As a result, such chiral amines cannot be resolved, unless the amine's groups are constrained in a cyclic structure (such as in Tröger's base).
In molecular systems the lone pair can also result in a distortion in the coordination of ligands around the metal ion. The lone-pair effect of lead can be observed in supramolecular complexes of lead(II) nitrate, and in 2007 a study linked the lone pair to lead poisoning. Lead ions can replace the native metal ions in several key enzymes, such as zinc cations in the ALAD enzyme, which is also known as porphobilinogen synthase, and is important in the synthesis of heme, a key component of the oxygen-carrying molecule hemoglobin. This inhibition of heme synthesis appears to be the molecular basis of lead poisoning (also called "saturnism" or "plumbism").
Computational experiments reveal that although the coordination number does not change upon substitution in calcium-binding proteins, the introduction of lead distorts the way the ligands organize themselves to accommodate such an emerging lone pair: consequently, these proteins are perturbed. This lone-pair effect becomes dramatic for zinc-binding proteins, such as the above-mentioned porphobilinogen synthase, as the natural substrate cannot bind anymore – in those cases the protein is enzyme inhibitor.
In Group 14 elements (the carbon group), lone pairs can manifest themselves by shortening or lengthening single bond (bond order 1) lengths, as well as in the effective order of as well. The familiar have a carbon-carbon triple bond (bond order 3) and a linear geometry of 180° bond angles (figure A in reference ). However, further down in the group (silicon, germanium, and tin), formal triple bonds have an effective bond order 2 with one lone pair (figure B) and trans-bent geometries. In lead, the effective bond order is reduced even further to a single bond, with two lone pairs for each lead atom (figure C). In the organogermanium compound ( Scheme 1 in the reference), the effective bond order is also 1, with complexation of the Lewis acid isonitrile (or isocyanide) C-N groups, based on interaction with germanium's empty 4p orbital.
To determine the hybridization of oxygen orbitals used to form the bonding pairs and lone pairs of water in this picture, we use the formula 1 + x cos θ = 0, which relates bond angle θ with the hybridization index x. According to this formula, the O–H bonds are considered to be constructed from O bonding orbitals of ~sp4.0 hybridization (~80% p character, ~20% s character), which leaves behind O lone pairs orbitals of ~sp2.3 hybridization (~70% p character, ~30% s character). These deviations from idealized sp3 hybridization (75% p character, 25% s character) for tetrahedral geometry are consistent with Bent's rule: lone pairs localize more electron density closer to the central atom compared to bonding pairs; hence, the use of orbitals with excess s character to form lone pairs (and, consequently, those with excess p character to form bonding pairs) is energetically favorable.
However, theoreticians often prefer an alternative description of water that separates the lone pairs of water according to symmetry with respect to the molecular plane. In this model, there are two energetically and geometrically distinct lone pairs of water possessing different symmetry: one (σ) in-plane and symmetric with respect to the molecular plane and the other (π) perpendicular and anti-symmetric with respect to the molecular plane. The σ-symmetry lone pair (σ(out)) is formed from a hybrid orbital that mixes 2s and 2p character, while the π-symmetry lone pair (p) is of exclusive 2p orbital parentage. The s character rich O σ(out) lone pair orbital (also notated nO(σ)) is an ~sp0.7 hybrid (~40% p character, 60% s character), while the p lone pair orbital (also notated nO(π)) consists of 100% p character.
Both models are of value and represent the same total electron density, with the orbitals related by a unitary transformation. In this case, we can construct the two equivalent lone pair hybrid orbitals h and h
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 atom of a ketone. However, the question of whether it is conceptually useful to derive equivalent orbitals from symmetry-adapted ones, from the standpoint of bonding theory and pedagogy, is still a controversial one, with recent (2014 and 2015) articles opposing and supporting the practice.
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