The bond valencemethod or mean method (or bond valence sum) (not to be mistaken for the valence bond theory in quantum chemistry) is a popular method in coordination chemistry to estimate the oxidation states of atoms. It is derived from the bond valence model, which is a simple yet robust model for validating chemical structures with localized bonds or used to predict some of their properties. This model is a development of Pauling's rules.
The basic method is that the valence V of an atom is the sum of the individual bond valences vi surrounding the atom:
The individual bond valences in turn are calculated from the observed bond lengths.
Ri is the observed bond length, R0 is a tabulated [1] parameter expressing the (ideal) bond length when the element i has exactly valence 1, and b is an empirical constant, typically 0.37 Å.
Another formula for has also been used: [2]
Although the bond valence model is mostly used for validating newly determined structures, it is capable of predicting many of the properties of those chemical structures that can be described by localized bonds [3]
In the bond valence model, the valence of an atom, V, is defined as the number of electrons the atom uses for bonding. This is equal to the number of electrons in its valence shell if all the valence shell electrons are used for bonding. If they are not, the remainder will form non-bonding electron pairs, usually known as lone pairs.
The valence of a bond, S, is defined as the number of electron pairs forming the bond. In general this is not an integral number. Since each of the terminal atoms contributes equal numbers of electrons to the bond, the bond valence is also equal to the number of valence electrons that each atom contributes. Further, since within each atom, the negatively charged valence shell is linked to the positively charged core by an electrostatic flux that is equal to the charge on the valence shell, it follows that the bond valence is also equal to the electrostatic flux that links the core to the electrons forming the bond. The bond valence is thus equal to three different quantities: the number of electrons each atom contributes to the bond, the number of electron pairs that form the bond, and the electrostatic flux linking each core to the bonding electron pair.
It follows from these definitions, that the valence of an atom is equal to the sum of the valences of all the bonds it forms. This is known as the valence sum rule, Eq. 1, which is central to the bond valence model.
A bond is formed when the valence shells of two atoms overlap. It is apparent that the closer two atoms approach each other, the larger the overlap region and the more electrons are associated with the bond. We therefore expect a correlation between the bond valence and the bond length and find empirically that for most bonds it can be described by Eq. 2: [4]
where S is the valence and R is the length of the bond, and Ro and b are parameters that are empirically determined for each bond type. For many bond types (but not all), b is found to be close to 0.37 Å. [5] A list of bond valence parameters for different bond types (i.e. for different pairs of cation and anion in given oxidation states) can be found at the web site. [1] It is this empirical relation that links the formal theorems of the bond valence model to the real world and allows the bond valence model to be used to predict the real structure, geometry and properties of a compound.
If the structure of a compound is known, the empirical bond valence - bond length correlation of Eq. 2 can be used to estimate the bond valences from their observed bond lengths. Eq. 1 can then be used to check that the structure is chemically valid; any deviation between the atomic valence and the bond valence sum needs to be accounted for.
Eq. 2 is used to derive the distortion theorem which states that the more the individual bond lengths in a coordination sphere deviate from their average, the more the average bond length increases provided the valence sum is kept constant. Alternatively if the average bond length is kept constant, the more the bond valence sum increases [6]
If the structure is not known, the average bond valence, Sa can be calculated from the atomic valence, V, if the coordination number, N, of the atom is known using Eq. 3.
If the coordination number is not known, a typical coordination number for the atom can be used instead. Some atoms, such as sulfur(VI), are only found with one coordination number with oxygen, in this case 4, but others, such as sodium, are found with a range of coordination numbers, though most lie close to the average, which for sodium is 6.2. In the absence of any better information, the average coordination number observed with oxygen is a convenient approximation, and when this number is used in Eq. 3, the resulting average bond valence is known as the bonding strength of the atom.
Since the bonding strength of an atom is the valence expected for a bond formed by that atom, it follows that the most stable bonds will be formed between atoms with the same bonding strengths. In practice some tolerance is allowed, but bonds are rarely formed if the ratio of the bonding strengths of the two atoms exceeds two, a condition expressed by the inequality shown in Eq. 4. This is known and the valence matching rule. [3]
Atoms with non-bonding valence electrons, i.e., with lone pairs, have more flexibility in their bonding strength than those without lone pairs depending on whether the lone pairs are stereoactive or not. If the lone pairs are not stereoactive, they are spread uniformly around the valence shell, if they are stereoactive they are concentrated in one portion of the coordination sphere preventing that portion from forming bonds. This results in the atom having a smaller coordination number, hence a higher bonding strength, when the lone pair is stereoactive. Ions with lone pairs have a greater ability to adapt their bonding strength to match that of the counter-ion. The lone pairs become stereoactive when the bonding strength of the counter-ion exceeds twice the bonding strength of the ion when its lone pairs are inactive. [7]
Compounds that do not satisfy Eq. 4 are difficult, if not impossible, to prepare, and chemical reactions tend to favour the compounds that provide the best valence match. For example, the aqueous solubility of a compound depends on whether its ions are better matched to water than they are to each other. [3]
Several factors influence the coordination number of an atom, but the most important of these is its size; larger atoms have larger coordination numbers. The coordination number depends on the surface area of the atom, and so is proportional to r2. If VE is the charge on the atomic core (which is the same as the valence of the atom when all the electrons in the valence shell are bonding), and NE is the corresponding average coordination number, VE/NE is proportional to the electric field at the surface of the core, represented by SE in Eq. 5:
Not surprisingly, SE gives the same ordering of the main group elements as the electronegativity, though it differs in its numerical value from traditional electronegativity scales. Because it is defined in structural terms, SE is the preferred measure of electronegativity in the bond valence model, [8]
The bond valence model can be reduced to the traditional ionic model if certain conditions are satisfied. These conditions require that atoms be divided into cations and anions in such a way that (a) the electronegativity of every anion is equal to, or greater than, the electronegativity of any of the cations, (b) that the structure is electroneutral when the ions carry charges equal to their valence, and (c) that all the bonds have a cation at one end and an anion at the other. If these conditions are satisfied, as they are in many ionic and covalent compounds, the electrons forming a bond can all be formally assigned to the anion. The anion thus acquires a formal negative charge and the cation a formal positive charge, which is the picture on which the ionic model is based. The electrostatic flux that links the cation core to its bonding electrons now links the cation core to the anion. In this picture, a cation and anion are bonded to each other if they are linked by electrostatic flux, with the flux being equal to the valence of the bond. [7] In a representative set of compounds Preiser et al. [4] have confirmed that the electrostatic flux is the same as the bond valence determined from the bond lengths using Eq. 2.
The association of the cation bonding electrons with the anion in the ionic model is purely formal. There is no change in physical locations of any electrons, and there is no change in the bond valence. The terms "anion" and "cation" in the bond valence model are defined in terms of the bond topology, not the chemical properties of the atoms. This extends the scope of the ionic model well beyond compounds in which the bonding would normally be considered as "ionic". For example, methane, CH4, obeys the conditions for the ionic model with carbon as the cation and hydrogen as the anion (or vice versa, since carbon and hydrogen have the same electronegativity).
For compounds that contain cation-cation or anion-anion bonds it is usually possible to transform these homoionic bonds into cation-anion bonds either by treating the atoms linked by the homoionic bond as a single complex cation (e.g., Hg22+), or by treating the bonding electrons in the homoionic bond as a pseudo-anion to transform a cation-cation bond into two cation - pseudo-anion bonds, e.g., Hg2+-e2−-Hg2+.
Structures containing covalent bonds can be treated using the ionic model providing they satisfy the topological conditions given above, but a special situation applies to hydrocarbons which allows the bond valence model to be reduced to the traditional bond model of organic chemistry. If an atom has a valence, V, that is equal to its coordination number, N, its bonding strength according to Eq. 3 is exactly 1.0 vu (valence units), a condition that greatly simplifies the model. This condition is obeyed by carbon, hydrogen and silicon. Since these atoms all have bonding strengths of 1.0 vu the bonds between them are all predicted to have integral valences with carbon forming four single bonds and hydrogen one. Under these conditions, the bonds are all single bonds (or multiples of single bonds). Compounds can be constructed by linking carbon and hydrogen atoms with bonds that are all exactly equivalent. Under certain conditions, nitrogen can form three bonds and oxygen two, but since nitrogen and oxygen typically also form hydrogen bonds, the resulting N-H and O-H bonds have valences less than 1.0 vu, leading through the application of Eq. 1, to the C-C and C-H bonds having valences that differ from 1.0 vu. Nevertheless, the simple bonding rules of organic chemistry are still good approximations, though the rules of the bond valence model are better.
A chemical structure can be represented by a bond network of the kind familiar in molecular diagrams. The infinitely connected bond networks found in crystals can be simplified into finite networks by extracting one formula unit and reconnecting any broken bonds to each other. If the bond network is not known, a plausible network can be created by connecting well matched cations and anions that satisfy Eq. 4. If the finite network contains only cation-anion bonds, every bond can be treated as an electric capacitor (two equal and opposite charges linked by electrostatic flux). The bond network is thus equivalent to a capacitive electrical circuit with the charge on each capacitor being equivalent to the bond valence. The individual bond capacitors are not initially known, but in the absence of any information to the contrary we assume that they are all equal. In this case the circuit can be solved using the Kirchhoff equations, yielding the valences of each bond. Eq. 2 can then be used to calculate bond lengths which are found to lie within a few picometres of the observed bond lengths if no additional constraints are present. Additional constraints include electronic anisotropies (lone pairs and Jahn-Teller distortions) or steric constraints, (bonds stretched or compressed in order to fit them into three-dimensional space). Hydrogen bonds are an example of a steric constraint. The repulsion resulting from the close approach of the donor and acceptor atoms causes the bonds to be stretched, and under this constraint the distortion theorem predicts that the hydrogen atom will move off-center. [3]
The bond valence is a vector directed along the bond since it represents the electrostatic field linking the ions. If the atom is unconstrained, the sum of the bond valence vectors around an atom is expected to be zero, a condition that limits the range of possible bond angles. [9]
The bond valence model is an extension of the electron counting rules and its strength lies in its simplicity and robustness. Unlike most models of chemical bonding, it does not require a prior knowledge of the atomic positions and so can be used to construct chemically plausible structures given only the composition. The empirical parameters of the model are tabulated and are readily transferable between bonds of the same type. The concepts used are familiar to chemists and provide ready insight into the chemical restraints acting on the structure. The bond valence model uses mostly classical physics, and with little more than a pocket calculator, it gives quantitative predictions of bond lengths and places limits on what structures can be formed.
However, like all models, the bond valence model has its limitations. It is restricted to compounds with localized bonds; it does not, in general, apply to metals or aromatic compounds where the electrons are delocalized. It cannot in principle predict electron density distributions or energies since these require the solution of the Schoedinger equation using the long-range Coulomb potential which is incompatible with the concept of a localized bond.
The bond valence method is a development of Pauling's rules. In 1930, Lawrence Bragg [10] showed that Pauling's electrostatic valence rule could be represented by electrostatic lines of force emanating from cations in proportion to the cation charge and ending on anions. The lines of force are divided equally between the bonds to the corners of the coordination polyhedron.
Starting with Pauling in 1947 [11] a correlation between cation–anion bond length and bond strength was noted. It was shown later [12] that if bond lengths were included in the calculation of bond strength, its accuracy was improved, and this revised method of calculation was termed the bond valence. These new insights were developed by later workers culminating in the set of rules termed the bond valence model. [3]
It is possible by bond valence calculations [13] to estimate how great a contribution a given oxygen atom is making to the assumed valence of uranium. Zachariasen [14] lists the parameters to allow such calculations to be done for many of the actinides. Bond valence calculations use parameters which are estimated after examining a large number of crystal structures of uranium oxides (and related uranium compounds); note that the oxidation states which this method provides are only a guide which assists in the understanding of a crystal structure.
For uranium binding to oxygen the constants R0 and B are tabulated in the table below. For each oxidation state use the parameters from the table shown below.
| Oxidation state | R0 | B |
|---|---|---|
| U(VI) | 2.08Å | 0.35 |
| U(V) | 2.10Å | 0.35 |
| U(IV) | 2.13Å | 0.35 |
It is possible to do these simple calculations on paper or to use software. A program which does it can be obtained free of charge. [15] [16] In 2020 David Brown published a nearly comprehensive set of bond valence parameters on the IuCr web site. [17]
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.
Electronegativity, symbolized as χ, is the tendency for an atom of a given chemical element to attract shared electrons when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity, the more an atom or a substituent group attracts electrons. Electronegativity serves as a simple way to quantitatively estimate the bond energy, and the sign and magnitude of a bond's chemical polarity, which characterizes a bond along the continuous scale from covalent to ionic bonding. The loosely defined term electropositivity is the opposite of electronegativity: it characterizes an element's tendency to donate valence electrons.
Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be of a more complex nature, e.g. molecular ions like NH+
4 or SO2−
4. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal in order to obtain a full valence shell for both atoms.
In chemistry, an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding. The compound is neutral overall, but consists of positively charged ions called cations and negatively charged ions called anions. These can be simple ions such as the sodium (Na+) and chloride (Cl−) in sodium chloride, or polyatomic species such as the ammonium (NH+
4) and carbonate (CO2−
3) ions in ammonium carbonate. Individual ions within an ionic compound usually have multiple nearest neighbours, so are not considered to be part of molecules, but instead part of a continuous three-dimensional network. Ionic compounds usually form crystalline structures when solid.
A Lewis acid (named for the American physical chemist Gilbert N. Lewis) is a chemical species that contains an empty orbital which is capable of accepting an electron pair from a Lewis base to form a Lewis adduct. A Lewis base, then, is any species that has a filled orbital containing an electron pair which is not involved in bonding but may form a dative bond with a Lewis acid to form a Lewis adduct. For example, NH3 is a Lewis base, because it can donate its lone pair of electrons. Trimethylborane (Me3B) is a Lewis acid as it is capable of accepting a lone pair. In a Lewis adduct, the Lewis acid and base share an electron pair furnished by the Lewis base, forming a dative bond. In the context of a specific chemical reaction between NH3 and Me3B, a lone pair from NH3 will form a dative bond with the empty orbital of Me3B to form an adduct NH3•BMe3. The terminology refers to the contributions of Gilbert N. Lewis.
The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule is especially applicable to carbon, nitrogen, oxygen, and the halogens; although more generally the rule is applicable for the s-block and p-block of the periodic table. Other rules exist for other elements, such as the duplet rule for hydrogen and helium, or the 18-electron rule for transition metals.
In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures into a resonance hybrid in valence bond theory. It has particular value for analyzing delocalized electrons where the bonding cannot be expressed by one single Lewis structure.
In chemistry, a lone pair refers to a pair of valence electrons that are not shared with another atom in a covalent bond 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.
Lewis structures, also known as Lewis dot formulas,Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds. The Lewis structure was named after Gilbert N. Lewis, who introduced it in his 1916 article The Atom and the Molecule. Lewis structures extend the concept of the electron dot diagram by adding lines between atoms to represent shared pairs in a chemical bond.
In chemistry, a hypervalent molecule is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells. Phosphorus pentachloride, sulfur hexafluoride, chlorine trifluoride, the chlorite ion, and the triiodide ion are examples of hypervalent molecules.
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.
In chemistry, the valence or valency of an element is the measure of its combining capacity with other atoms when it forms chemical compounds or molecules.
In chemistry, a formal charge, in the covalent view of chemical bonding, is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity. In simple terms, formal charge is the difference between the number of valence electrons of an atom in a neutral free state and the number assigned to that atom in a Lewis structure. When determining the best Lewis structure for a molecule, the structure is chosen such that the formal charge on each of the atoms is as close to zero as possible.
The 3-center 4-electron (3c–4e) bond is a model used to explain bonding in certain hypervalent molecules such as tetratomic and hexatomic interhalogen compounds, sulfur tetrafluoride, the xenon fluorides, and the bifluoride ion. It is also known as the Pimentel–Rundle three-center model after the work published by George C. Pimentel in 1951, which built on concepts developed earlier by Robert E. Rundle for electron-deficient bonding. An extended version of this model is used to describe the whole class of hypervalent molecules such as phosphorus pentafluoride and sulfur hexafluoride as well as multi-center π-bonding such as ozone and sulfur trioxide.
An intramolecular force is any force that binds together the atoms making up a molecule or compound, not to be confused with intermolecular forces, which are the forces present between molecules. The subtle difference in the name comes from the Latin roots of English with inter meaning between or among and intra meaning inside. Chemical bonds are considered to be intramolecular forces which are often stronger than intermolecular forces present between non-bonding atoms or molecules.
A carbon–oxygen bond is a polar covalent bond between atoms of carbon and oxygen. Carbon–oxygen bonds are found in many inorganic compounds such as carbon oxides and oxohalides, carbonates and metal carbonyls, and in organic compounds such as alcohols, ethers, carbonyl compounds and oxalates. Oxygen has 6 valence electrons of its own and tends to fill its outer shell with 8 electrons by sharing electrons with other atoms to form covalent bonds, accepting electrons to form an anion, or a combination of the two. In neutral compounds, an oxygen atom can form up to two single bonds or one double bond with carbon, while a carbon atom can form up to four single bonds or two double bonds with oxygen.
An ion is an atom or molecule with a net electrical charge.
A chemical compound is a chemical substance composed of many identical molecules containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound. A compound can be transformed into a different substance by a chemical reaction, which may involve interactions with other substances. In this process, bonds between atoms may be broken and/or new bonds formed.
Solids can be classified according to the nature of the bonding between their atomic or molecular components. The traditional classification distinguishes four kinds of bonding:
In theoretical chemistry, the charge-shift bond is a proposed new class of chemical bonds that sits alongside the three familiar families of covalent, ionic, and metallic bonds where electrons are shared or transferred respectively. The charge shift bond derives its stability from the resonance of ionic forms rather than the covalent sharing of electrons which are often depicted as having electron density between the bonded atoms. A feature of the charge shift bond is that the predicted electron density between the bonded atoms is low. It has long been known from experiment that the accumulation of electric charge between the bonded atoms is not necessarily a feature of covalent bonds.
