A sextuple bond is a type of covalent bond involving 12 bonding electrons and in which the bond order is 6. The only known molecules with true sextuple bonds are the diatomic dimolybdenum (Mo 2) and ditungsten (W 2), which exist in the gaseous phase and have boiling points of 4,639 °C (8,382 °F) and 5,930 °C (10,710 °F) respectively.
Roos et al argue that no stable element can form bonds of higher order than a sextuple bond, because the latter corresponds to a hybrid of the s orbital and all five d orbitals, and f orbitals contract too close to the nucleus to bond in the lanthanides. [1] Indeed, quantum mechanical calculations have revealed that the dimolybdenum bond is formed by a combination of two σ bonds, two π bonds and two δ bonds. (Also, the σ and π bonds contribute much more significantly to the sextuple bond than the δ bonds.) [2]
Although no φ bonding has been reported for transition metal dimers, it is predicted that if any sextuply-bonded actinides were to exist, at least one of the bonds would likely be a φ bond as in quintuply-bonded diuranium and dineptunium. [3] No sextuple bond has been observed in lanthanides or actinides. [1]
For the majority of elements, even the possibility of a sextuple bond is foreclosed, because the d electrons ferromagnetically couple, instead of bonding. The only known exceptions are dimolybdenum and ditungsten. [1]
The formal bond order of a molecule is half the number of bonding electrons surplus to antibonding electrons; for a typical molecule, it attains exclusively integer values. A full quantum treatment requires a more nuanced picture, in which electrons may exist in a superposition, contributing fractionally to both bonding and antibonding orbitals. In a formal sextuple bond, there would be P = 6 different electron pairs; an effective sextuple bond would then have all six contributing almost entirely to bonding orbitals.
| Molecule | FBO | EBO [1] |
|---|---|---|
| Cr2 | 6 | 3.5 |
| [PhCrCrPh] | 5 | 3.5 |
| Cr2(O2CCH3)4 | 4 | 2.0 |
| Mo2 | 6 | 5.2 |
| W2 | 6 | 5.2 |
| Ac2 | 3 | 1.7 |
| Th2 | 4 | 3.7 |
| Pa2 | 5 | 4.5 |
| U2 | 6 | 3.8 [4] |
| [PhUUPh] | 5 | 3.7 |
| [Re2Cl8]2- | 4 | 3.2 |
In Roos et al's calculations, the effective bond order could be determined by the formula
where ηb is the proportion of formal bonding orbital occupation for an electron pair p, ηab is the proportion of the formal antibonding orbital occupation, and c is a correction factor accounting for deviations from equilibrium geometry. [1] Several metal-metal bonds' EBOs are given in the table at right, compared to their formal bond orders.
Dimolybdenum and ditungsten are the only molecules with effective bond orders above 5, with a quintuple bond and a partially formed sixth covalent bond. Dichromium, while formally described as having a sextuple bond, is best described as a pair of chromium atoms with all electron spins exchange-coupled to each other. [5]
While diuranium is also formally described as having a sextuple bond, relativistic quantum mechanical calculations have determined it to be a quadruple bond with four electrons ferromagnetically coupled to each other rather than in two formal bonds. [4] Previous calculations on diuranium did not treat the electronic molecular Hamiltonian relativistically and produced higher bond orders of 4.2 with two ferromagnetically coupled electrons. [6]
Laser evaporation of a molybdenum sheet at low temperatures (7 K) produces gaseous dimolybdenum (Mo2). The resulting molecules can then be imaged with, for instance, near-infrared spectroscopy or UV spectroscopy. [7]
Both ditungsten and dimolybdenum have very short bond lengths compared to neighboring metal dimers. [1] For example, sextuply-bonded dimolybdenum has an equilibrium bond length of 1.93 Å. This equilibrium internuclear distance is significantly lower than in the dimer of any neighboring 4d transition metal, and suggestive of higher bond orders. [8] [9] [10] However, the bond dissociation energies of ditungsten and dimolybdenum are rather low, because the short internuclear distance introduces geometric strain. [1] [11]
| Dimer | Force constant (Å) [10] | EBO [10] |
|---|---|---|
| Cu2 | 1.13 | 1.00 |
| Ag2 | 1.18 | 1.00 |
| Au2 | 2.12 | 1.00 |
| Zn2 | 0.01 | 0.01 |
| Cd2 | 0.02 | 0.02 |
| Hg2 | 0.02 | 0.02 |
| Mn2 | 0.09 | 0.07 |
| Mo2 | 6.33 | 5.38 |
One empirical technique to determine bond order is spectroscopic examination of bond force constants. Pauling's formula predicts that bond order is roughly [12] proportional to the force constant; that is,
where n is the bond order, ke is the force constant of the interatomic interaction and ke(1) is the force constant of a single bond between the atoms. [13]
The table at right shows some select force constants for metal-metal dimers compared to their EBOs; consistent with a sextuple bond, molybdenum's summed force constant is substantially more than quintuple the single-bond force constant.
Like dichromium, dimolybdenum and ditungsten are expected to exhibit a 1Σg+ singlet ground state. [14] [15] However, in tungsten, this ground state arises from a hybrid of either two 5D0 ground states or two 7S3 excited states. Only the latter corresponds to the formation of a stable, sextuply-bonded ditungsten dimer. [8]
Although sextuple bonding in homodimers is rare, it remains a possibility in larger molecules.
Theoretical computations suggest that bent dimetallocenes have a higher bond order than their linear counterparts. [16] For this reason, the Schaefer lab has investigated dimetallocenes for natural sextuple bonds. However, such compounds tend to exhibit Jahn-Teller distortion, rather than a true sextuple bond.
For example, dirhenocene is bent. Calculating its frontier molecular orbitals suggests the existence of relatively stable singlet and triplet states, with a sextuple bond in the singlet state. But that state is the excited one; the triplet ground state should exhibit a formal pentuple bond. [16] Similarly, for the dibenzene complexes Cr2(C6H6)2, Mo2(C6H6)2, and W2(C6H6)2, molecular bonding orbitals for the triplet states with symmetries D6h and D6d indicate the possibility of an intermetallic sextuple bond. Quantum chemistry calculations reveal, however, that the corresponding D2h singlet geometry is stabler than the D6h triplet state by 3–39 kcal/mol, depending on the central metal. [17]
Both quantum mechanical calculations and photoelectron spectroscopy of the tungsten oxide clusters W2On (n = 1-6) indicate that increased oxidation state reduces the bond order in ditungsten. At first, the weak δ bonds break to yield a quadruply-bonded W2O; further oxidation generates the ditungsten complex W2O6 with two bridging oxo ligands and no direct W-W bonds. [18]
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.
In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.
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.
A triple bond in chemistry is a chemical bond between two atoms involving six bonding electrons instead of the usual two in a covalent single bond. Triple bonds are stronger than the equivalent single bonds or double bonds, with a bond order of three. The most common triple bond, that between two carbon atoms, can be found in alkynes. Other functional groups containing a triple bond are cyanides and isocyanides. Some diatomic molecules, such as dinitrogen and carbon monoxide, are also triple bonded. In skeletal formulae the triple bond is drawn as three parallel lines (≡) between the two connected atoms.
In chemistry, molecular orbital theory is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century.
In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.
In chemistry, bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds.
In chemistry, delta bonds are covalent chemical bonds, where four lobes of one involved atomic orbital overlap four lobes of the other involved atomic orbital. This overlap leads to the formation of a bonding molecular orbital with two nodal planes which contain the internuclear axis and go through both atoms.
In organic chemistry, hyperconjugation refers to the delocalization of electrons with the participation of bonds of primarily σ-character. Usually, hyperconjugation involves the interaction of the electrons in a sigma (σ) orbital with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals. However, sometimes, low-lying antibonding σ* orbitals may also interact with filled orbitals of lone pair character (n) in what is termed negative hyperconjugation. Increased electron delocalization associated with hyperconjugation increases the stability of the system. In particular, the new orbital with bonding character is stabilized, resulting in an overall stabilization of the molecule. Only electrons in bonds that are in the β position can have this sort of direct stabilizing effect — donating from a sigma bond on an atom to an orbital in another atom directly attached to it. However, extended versions of hyperconjugation can be important as well. The Baker–Nathan effect, sometimes used synonymously for hyperconjugation, is a specific application of it to certain chemical reactions or types of structures.
A quintuple bond in chemistry is an unusual type of chemical bond, first reported in 2005 for a dichromium compound. Single bonds, double bonds, and triple bonds are commonplace in chemistry. Quadruple bonds are rarer but are currently known only among the transition metals, especially for Cr, Mo, W, and Re, e.g. [Mo2Cl8]4− and [Re2Cl8]2−. In a quintuple bond, ten electrons participate in bonding between the two metal centers, allocated as σ2π4δ4.
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.
In chemical bonding theory, an antibonding orbital is a type of molecular orbital that weakens the chemical bond between two atoms and helps to raise the energy of the molecule relative to the separated atoms. Such an orbital has one or more nodes in the bonding region between the nuclei. The density of the electrons in the orbital is concentrated outside the bonding region and acts to pull one nucleus away from the other and tends to cause mutual repulsion between the two atoms. This is in contrast to a bonding molecular orbital, which has a lower energy than that of the separate atoms, and is responsible for chemical bonds.
A quadruple bond is a type of chemical bond between two atoms involving eight electrons. This bond is an extension of the more familiar types double bonds and triple bonds. Stable quadruple bonds are most common among the transition metals in the middle of the d-block, such as rhenium, tungsten, technetium, molybdenum and chromium. Typically the ligands that support quadruple bonds are π-donors, not π-acceptors.
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.
Localized molecular orbitals are molecular orbitals which are concentrated in a limited spatial region of a molecule, such as a specific bond or lone pair on a specific atom. They can be used to relate molecular orbital calculations to simple bonding theories, and also to speed up post-Hartree–Fock electronic structure calculations by taking advantage of the local nature of electron correlation. Localized orbitals in systems with periodic boundary conditions are known as Wannier functions.
In chemistry, phi bonds are covalent chemical bonds, where six lobes of one involved atomic orbital overlap six lobes of the other involved atomic orbital. This overlap leads to the formation of a bonding molecular orbital with three nodal planes which contain the internuclear axis and go through both atoms.
Molybdenum(II) acetate is a coordination compound with the formula Mo2(O2CCH3)4. It is a yellow, diamagnetic, air-stable solid that is slightly soluble in organic solvents. Molybdenum(II) acetate is an iconic example of a compound with a metal-metal quadruple bond.
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
2O, explaining and rationalizing the various electronic and physical properties and features manifested by its peculiar bonding arrangements.
In theoretical chemistry, the bonding orbital is used in molecular orbital (MO) theory to describe the attractive interactions between the atomic orbitals of two or more atoms in a molecule. In MO theory, electrons are portrayed to move in waves. When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’ constructive interference causes the density of the electrons to be found within the binding region, creating a stable bond between the two species.
Hexa(tert-butoxy)dimolybdenum(III) is a coordination complex of molybdenum(III). It is one of the homoleptic alkoxides of molybdenum. An orange, air-sensitive solid, the complex has attracted academic attention as the precursor to many organomolybdenum derivatives. It an example of a charge-neutral complex featuring a molybdenum to molybdenum triple bond (Mo≡Mo), arising from the coupling of a pair of d3 metal centers. It can be prepared by a salt metathesis reaction from the THF complex of molybdenum trichloride and lithium tert-butoxide:
Pauling showed that the force constant is approximately proportional to the bond order...Note that the term 'bond order' as used here is not the same as the usual chemical definition [i.e., 1/2(no. of bonding electrons - no. of antibonding electrons) or better a function of the electron density]. This might more accurately be termed the 'vibrational bond order' since it is experimentally determined.
