Lone pair

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Lone pairs (shown as pairs of dots) in the Lewis structure of hydroxide Hydroxide lone pairs-2D.svg
Lone pairs (shown as pairs of dots) in the Lewis structure of hydroxide

In chemistry, a lone pair refers to a pair of valence electrons that are not shared with another atom in a covalent bond [1] 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 pairs are therefore considered lone pairs if two electrons are paired but are not used in chemical bonding. Thus, the number of electrons 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.

Lone pairs in ammonia (A), water (B), and hydrogen chloride (C) ParSolitario.png
Lone pairs in ammonia (A), water (B), and hydrogen chloride (C)

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 halogens 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. [2] [3] [4]

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 Laplacian 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). [5]

Angle changes

Tetrahedral structure of water Tetrahedral Structure of Water.png
Tetrahedral structure of water

The pairs often exhibit a negative polar character with their high charge density and are located closer to the atomic nucleus on average compared to the bonding pair of electrons. The presence of a lone pair decreases the bond angle between the bonding pair of electrons, due to their high electric charge, which causes great repulsion between the electrons. They are also involved in the formation of a dative bond. For example, the creation of the hydronium (H3O+) ion occurs when acids are dissolved in water and is due to the oxygen atom donating a lone pair to the hydrogen ion.

This can be seen more clearly when looked at it in two more common molecules. For example, in carbon dioxide (CO2), the oxygen atoms are on opposite sides of the carbon atom (linear molecular geometry), whereas in water (H2O) the angle between the hydrogen atoms is 104.5° (bent molecular geometry). The repulsive force of the oxygen atom's two lone pairs pushes 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.

Dipole moments

Lone pairs can contribute to a molecule's dipole moment. NH3 has a dipole moment of 1.42 D. As the electronegativity of nitrogen (3.04) is greater than that of hydrogen (2.2) the result is that the N-H bonds are polar with a net negative charge on the nitrogen atom and a smaller net positive charge on the hydrogen atoms. There is also a dipole associated with the lone pair and this reinforces the contribution made by the polar covalent N-H bonds to ammonia's dipole moment. In contrast to NH3, NF3 has a much lower dipole moment of 0.234 D. Fluorine is more electronegative than nitrogen and the polarity of the N-F bonds is opposite to that of the N-H bonds in ammonia, so that the dipole due to the lone pair opposes the N-F bond dipoles, resulting in a low molecular dipole moment. [6]

Stereogenic lone pairs

Amine R-N.svg   Amine N-R.svg
Inversion of a generic organic amine molecule at nitrogen

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 amines, phosphines, [7] sulfonium and oxonium ions, sulfoxides, and even carbanions.

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).

Unusual lone pairs

A stereochemically active lone pair is also expected for divalent lead and tin ions due to their formal electronic configuration of ns2. In the solid state this results in the distorted metal coordination observed in the tetragonal litharge structure adopted by both PbO and SnO. The formation of these heavy metal ns2 lone pairs which was previously attributed to intra-atomic hybridization of the metal s and p states [8] has recently been shown to have a strong anion dependence. [9] This dependence on the electronic states of the anion can explain why some divalent lead and tin materials such as PbS and SnTe show no stereochemical evidence of the lone pair and adopt the symmetric rocksalt crystal structure. [10] [11]

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. [12] 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"). [13] [14] [15]

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 inhibited.

In Group 14 elements (the carbon group), lone pairs can manifest themselves by shortening or lengthening single bond (bond order 1) lengths, [16] as well as in the effective order of triple bonds as well. [17] [18] The familiar alkynes have a carbon-carbon triple bond (bond order 3) and a linear geometry of 180° bond angles (figure A in reference [19] ). 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 [19] ) 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 [19] ). In the organogermanium compound (Scheme 1 in the reference), the effective bond order is also 1, with complexation of the acidic isonitrile (or isocyanide) C-N groups, based on interaction with germanium's empty 4p orbital. [19] [20]

Lone pair trends in group 14 triple bonds Digermina.png
Lone pair trends in group 14 triple bonds

Different descriptions for multiple lone pairs

The symmetry-adapted and hybridized lone pairs of H2O H2O lone pairs two descriptions.png
The symmetry-adapted and hybridized lone pairs of H2O

In elementary chemistry courses, the lone pairs of water are described as "rabbit ears": two equivalent electron pairs of approximately sp3 hybridization, while the HOH bond angle is 104.5°, slightly smaller than the ideal tetrahedral angle of arccos(–1/3) ≈ 109.47°. The smaller bond angle is rationalized by VSEPR theory by ascribing a larger space requirement for the two identical lone pairs compared to the two bonding pairs. In more advanced courses, an alternative explanation for this phenomenon considers the greater stability of orbitals with excess s character using the theory of isovalent hybridization, in which bonds and lone pairs can be constructed with spx hybrids wherein nonintegral values of x are allowed, so long as the total amount of s and p character is conserved (one s and three p orbitals in the case of second-row p-block elements).

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' by taking linear combinations h = c1σ(out) + c2p and h' = c1σ(out) – c2p for an appropriate choice of coefficients c1 and c2. 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 stereoelectronic requirement for the anomeric effect can be rationalized using equivalent lone pairs, since it is the overall donation of electron density into the antibonding orbital that matters. An alternative treatment using σ/π separated lone pairs is also valid, but it requires striking a balance between maximizing nO(π)-σ* overlap (maximum at 90° dihedral angle) and nO(σ)-σ* overlap (maximum at 0° dihedral angle), a compromise that leads to the conclusion that a gauche conformation (60° dihedral angle) is most favorable, the same conclusion that the equivalent lone pairs model rationalizes in a much more straightforward manner. [21] Similarly, the hydrogen bonds of water form along the directions of the "rabbit ears" lone pairs, as a reflection of the increased availability of electrons in these regions. This view is supported computationally. [5] However, because only the symmetry-adapted canonical orbitals have physically meaningful energies, phenomena that have to do with the energies of individual orbitals, such as photochemical reactivity or photoelectron spectroscopy, are most readily explained using σ and π lone pairs that respect the molecular symmetry. [21] [22]

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. [23] 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 [24] and supporting [25] the practice.

See also

Related Research Articles

<span class="mw-page-title-main">Chemical bond</span> Lasting attraction between atoms that enables the formation of chemical compounds

A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding. Strong chemical bonding arises from the sharing or transfer of electrons between the participating atoms.

<span class="mw-page-title-main">Covalent bond</span> Chemical bond that involves the sharing of electron pairs between atoms

A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding.

<span class="mw-page-title-main">Conjugated system</span> System of connected p-orbitals with delocalized electrons in a molecule

In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed. The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.

<span class="mw-page-title-main">Aromaticity</span> Phenomenon of chemical stability in resonance hybrids of cyclic organic compounds

In chemistry, aromaticity is a chemical property of cyclic (ring-shaped), typically planar (flat) molecular structures with pi bonds in resonance that gives increased stability compared to saturated compounds having single bonds, and other geometric or connective non-cyclic arrangements with the same set of atoms. Aromatic rings are very stable and do not break apart easily. Organic compounds that are not aromatic are classified as aliphatic compounds—they might be cyclic, but only aromatic rings have enhanced stability. The term aromaticity with this meaning is historically related to the concept of having an aroma, but is a distinct property from that meaning.

<span class="mw-page-title-main">Chemical polarity</span> Separation of electric charge in a molecule

In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end.

<span class="mw-page-title-main">Unsaturated hydrocarbon</span> Hydrocarbon with double or triple covalent bonds between adjacent carbon atoms

Unsaturated hydrocarbons are hydrocarbons that have double or triple covalent bonds between adjacent carbon atoms. The term "unsaturated" means more hydrogen atoms may be added to the hydrocarbon to make it saturated. The configuration of an unsaturated carbons include straight chain, such as alkenes and alkynes, as well as branched chains and aromatic compounds.

<span class="mw-page-title-main">VSEPR theory</span> Model for predicting molecular geometry

Valence shell electron pair repulsion (VSEPR) theory, is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm.

Ligand field theory (LFT) describes the bonding, orbital arrangement, and other characteristics of coordination complexes. It represents an application of molecular orbital theory to transition metal complexes. A transition metal ion has nine valence atomic orbitals - consisting of five nd, one (n+1)s, and three (n+1)p orbitals. These orbitals are of appropriate energy to form bonding interaction with ligands. The LFT analysis is highly dependent on the geometry of the complex, but most explanations begin by describing octahedral complexes, where six ligands coordinate to the metal. Other complexes can be described by reference to crystal field theory.

<span class="mw-page-title-main">Pi backbonding</span> Movement of electrons from one atoms orbital to a symmetric antibonding orbital on another

In chemistry, π backbonding, also called π backdonation, is when electrons move from an atomic orbital on one atom to an appropriate symmetry antibonding orbital on a π-acceptor ligand. It is especially common in the organometallic chemistry of transition metals with multi-atomic ligands such as carbon monoxide, ethylene or the nitrosonium cation. Electrons from the metal are used to bond to the ligand, in the process relieving the metal of excess negative charge. Compounds where π backbonding occurs include Ni(CO)4 and Zeise's salt. IUPAC offers the following definition for backbonding:

A description of the bonding of π-conjugated ligands to a transition metal which involves a synergic process with donation of electrons from the filled π-orbital or lone electron pair orbital of the ligand into an empty orbital of the metal (donor–acceptor bond), together with release (back donation) of electrons from an nd orbital of the metal (which is of π-symmetry with respect to the metal–ligand axis) into the empty π*-antibonding orbital of the ligand.

In chemistry, orbital hybridisation is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. For example, in a carbon atom which forms four single bonds the valence-shell s orbital combines with three valence-shell p orbitals to form four equivalent sp3 mixtures in a tetrahedral arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.

<span class="mw-page-title-main">Trigonal pyramidal molecular geometry</span> Molecular geometry with one atom at the apex and three atoms at the corners of a trigonal base

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, and the sulfite ion, SO2−
. In organic chemistry, molecules which have a trigonal pyramidal geometry are sometimes described as sp3 hybridized. The AXE method for VSEPR theory states that the classification is AX3E1.

In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol. Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.

<span class="mw-page-title-main">Bent's rule</span>

In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization of central atoms in molecules and the electronegativities of substituents. The rule was stated by Henry A. Bent as follows:

Atomic s character concentrates in orbitals directed toward electropositive substituents.

A molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.

<span class="mw-page-title-main">Linear molecular geometry</span> 3D shape of molecules in which all bond angles are 180°

In chemistry, the linear molecular geometry describes the geometry around a central atom bonded to two other atoms placed at a bond angle of 180°. Linear organic molecules, such as acetylene, are often described by invoking sp orbital hybridization for their carbon centers.

<span class="mw-page-title-main">Bent molecular geometry</span>

In chemistry, molecules with a non-collinear arrangement of two adjacent bonds have bent molecular geometry, also known as angular or V-shaped. Certain atoms, such as oxygen, will almost always set their two (or more) covalent bonds in non-collinear directions due to their electron configuration. Water (H2O) is an example of a bent molecule, as well as its analogues. The bond angle between the two hydrogen atoms is approximately 104.45°. Nonlinear geometry is commonly observed for other triatomic molecules and ions containing only main group elements, prominent examples being nitrogen dioxide (NO2), sulfur dichloride (SCl2), and methylene (CH2).

<span class="mw-page-title-main">Stereoelectronic effect</span>

In chemistry, primarily organic and computational chemistry, a stereoelectronic effect is an effect on molecular geometry, reactivity, or physical properties due to spatial relationships in the molecules' electronic structure, in particular the interaction between atomic and/or molecular orbitals. Phrased differently, stereoelectronic effects can also be defined as the geometric constraints placed on the ground and/or transition states of molecules that arise from considerations of orbital overlap. Thus, a stereoelectronic effect explains a particular molecular property or reactivity by invoking stabilizing or destabilizing interactions that depend on the relative orientations of electrons in space.

The σ-π model and equivalent-orbital model refer to two possible representations of molecules in valence bond theory. The σ-π model differentiates bonds and lone pairs of σ symmetry from those of π symmetry, while the equivalent-orbital model hybridizes them. The σ-π treatment takes into account molecular symmetry and is better suited to interpretation of aromatic molecules, although computational calculations of certain molecules tend to optimize better under the equivalent-orbital treatment. The two representations produce the same total electron density and are related by a unitary transformation of the occupied molecular orbitals; different localization procedures yield either of the two. Two equivalent orbitals h and h' can be constructed by taking linear combinations h = c1σ + c2π and h' = c1σ – c2π for an appropriate choice of coefficients c1 and c2.

<span class="mw-page-title-main">Chemical bonding of water</span>

Water is a simple triatomic bent molecule with C2v molecular symmetry and bond angle of 104.5° between the central oxygen atom and the hydrogen atoms. Despite being one of the simplest triatomic molecules, its chemical bonding scheme is nonetheless complex as many of its bonding properties such as bond angle, ionization energy, and electronic state energy cannot be explained by one unified bonding model. Instead, several traditional and advanced bonding models such as simple Lewis and VSEPR structure, valence bond theory, molecular orbital theory, isovalent hybridization, and Bent's rule are discussed below to provide a comprehensive bonding model for H
, explaining and rationalizing the various electronic and physical properties and features manifested by its peculiar bonding arrangements.

<span class="mw-page-title-main">Digermyne</span>

Digermynes are a class of compounds that are regarded as the heavier digermanium analogues of alkynes. The parent member of this entire class is HGeGeH, which has only been characterized computationally, but has revealed key features of the whole class. Because of the large interatomic repulsion between two Ge atoms, only kinetically stabilized digermyne molecules can be synthesized and characterized by utilizing bulky protecting groups and appropriate synthetic methods, for example, reductive coupling of germanium(II) halides.


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