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According to R.H. Crabtree, Metal Dihydrogen and sigma-Bond Complexes is dihydrogen coordination and the study of its structure and general properties but. `The reactions of transition metals and metal complexes with hydrogen, and Bonding and Activation of Dihydrogen and σ Ligands: Theory versus Experiment.
Table of contents

It gives a simple orbital picture equivalent to Lewis structures. Hybridisation theory finds its use mainly in organic chemistry. Hybridisation theory is an integral part of organic chemistry. For drawing reaction mechanisms sometimes a classical bonding picture is needed with two atoms sharing two electrons.

Orbitals are a model representation of the behavior of electrons within molecules. In heavier atoms, like carbon, nitrogen, and oxygen, the atomic orbitals used are the 2s and 2p orbitals, similar to excited state orbitals for hydrogen. Hybrid orbitals are assumed to be mixtures of atomic orbitals, superimposed on each other in various proportions. In general, any two hybrid orbitals on the same atom must be mutually orthogonal. The bond directed towards a more electronegative substituent tends to have higher p -character as stated in Bent's rule.

In other words, sp 2 hybrids. For a tetrahedrally coordinated carbon e. Carbon's ground state configuration is 1s 2 2s 2 2p 2 or more easily read:. Note: The 1 s orbital is lower in energy than the 2 s orbital, and the 2 s orbital is lower in energy than the 2 p orbitals. The carbon atom can utilize its two singly occupied p-type orbitals, to form two covalent bonds with two hydrogen atoms, yielding the singlet methylene CH 2 , the simplest of the carbenes.

The carbon atom can also bond to four hydrogen atoms by an excitation of an electron from the doubly occupied 2s orbital to the empty 2p orbital, so that there are four singly occupied orbitals. The energy released by formation of two additional bonds more than compensates for the excitation energy required, energetically favouring the formation of four C-H bonds.

Quantum mechanically, the lowest energy is obtained if the four bonds are equivalent, which requires that they be formed from equivalent orbitals on the carbon. A set of four equivalent orbitals can be obtained that are linear combinations of the valence-shell core orbitals are almost never involved in bonding s and p wave functions, [8] which are the four sp 3 hybrids.


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Other carbon based compounds and other molecules may be explained in a similar way as methane. For example, ethene C 2 H 4 has a double bond between the carbons. The Lewis structure looks like this:. In sp 2 hybridisation the 2 s orbital is mixed with only two of the three available 2 p orbitals:. The hydrogen-carbon bonds are all of equal strength and length, which agrees with experimental data.

The chemical bonding in compounds such as alkynes with triple bonds is explained by sp hybridization. In this model, the 2 s orbital mixes with only one of the three p -orbitals,. Hybridisation helps to explain molecule shape, since the angles between bonds are approximately equal to the angles between hybrid orbitals, as explained above for the tetrahedral geometry of methane. Other examples are given in the table below. Nonetheless, molecules such as Ta CH 3 5 with sd 4 hybridisation adopt a square pyramidal shape.

In general chemistry courses and mainstream textbooks, hybridisation is often presented for main group AX5 and above, as well as for transition metal complexes, using the hybridisation scheme first proposed by Pauling. In , Magnusson published a seminal work definitively excluding the role of d-orbital hybridization in bonding in hypervalent compounds of second-row elements.

This had long been a point of contention and confusion in describing these molecules using molecular orbital theory. Part of the confusion here originates from the fact that one must include d-functions in the basis sets used to describe these compounds or else unreasonably high energies and distorted geometries result , and the contribution of the d-function to the molecular wavefunction is large.

These facts were historically interpreted to mean that d-orbitals must be involved in bonding. However, Magnusson concludes in his work that d-orbital involvement is not implicated in hypervalency. For transition metal centers, the d and s orbitals are the primary valence orbitals, which are only weakly supplemented by the p orbitals. In light of computational chemistry , a better treatment would be to invoke sigma resonance in addition to hybridisation, which implies that each resonance structure has its own hybridisation scheme.

Sigma bond - Wikiwand

For main group compounds, all resonance structures must obey the octet 8 rule. For transition metal compounds, the resonance structures that obey the duodectet 12 rule [15] suffice to describe bonding, with optional inclusion of d m sp n resonance structures. Although ideal hybrid orbitals can be useful, in reality most bonds require orbitals of intermediate character, analogous to intermediate ionic-covalent character.

This requires an extension to include flexible weightings of atomic orbitals of each type s, p, d and allows for a quantitative depiction of bond formation when the molecular geometry deviates from ideal bond angles.

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The amount of p-character is not restricted to integer values; i. The hybridisation of bond orbitals is determined by Bent's rule: "Atomic s character concentrates in orbitals directed toward electropositive substituents". For molecules with lone pairs, the bonding orbitals are isovalent sp x bond hybrids. For example, the two bond-forming hybrid orbitals of oxygen in water can be described as sp 4. The shapes of molecules with lone pairs are:.

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In such cases, there are two mathematically equivalent ways of representing lone pairs. They can be represented with orbitals of sigma and pi symmetry similar to molecular orbital theory or with equivalent orbitals similar to VSEPR theory. For hypervalent molecules with lone pairs, the bonding scheme can be split into a hypervalent component and a component consisting of isovalent sp x bond hybrids.

The hypervalent component consists of resonant bonds utilizing p orbitals.

Sigma bond

The table below shows how each shape is related to the two components and their respective descriptions. Hybridisation of s and p orbitals to form effective sp x hybrids requires that they have comparable radial extent. The hybridisation of atoms in chemical bonds can be analysed by considering localised molecular orbitals, for example using natural localised molecular orbitals in a natural bond orbital NBO scheme.

A similar trend is seen for the other 2p elements. The similar chemical behavior of different FLPs was proposed to originate from similarity of the electric field characteristics.

What Is Valence Bond Theory in Chemistry?

Based on both theoretical and experimental studies it was early agreed upon that secondary interactions play a prominent role in the mechanism, not only in the reactant state but also along the entire process including the transition state 9 , 27 , Also, the existence of a preorganized entity is now univocally accepted. According to simulations using an explicit solvation model, the encounter complex can be present in solvent in a small, but relevant concentration and accordingly, the reaction takes place by the intermediacy of this reactive species.

In an attempt to settle the debate on the H 2 cleavage mechanism, Camaioni et al. They revealed that the dominant stabilizing factor at the TS is a charge transfer interaction, and that the electric field clearly plays a role in the polarization of H 2 , but its contribution to the overall interaction energy is small compared to the orbital interactions. It was found that in the TSs, the base … H—H … acid fragment is actually not linear but has a characteristic bent arrangement, with a general tendency for end-on base … H 2 and side-on acid … H 2 interactions.

Actually, in TSs with relatively large base … acid distance the electric field EF strength in the interior is about 0. Thus, it was concluded that the EF generated by the FLP is not sufficient to account for the observed hydrogen splitting and that the EF model does not provide an explanation for the observed bent geometry of transition states either. Moreover, interaction energy decomposition and NOCV analyses clearly supported the earlier proposed lack of dative bond between donor and acceptor centers in FLPs.

In this study we focus on the reactivity of representative FLPs and CLPs towards molecular hydrogen using again a complementing set of in silico instruments to answer the simple but critical question that, as we believe, arises from the findings of earlier studies. To the best of our knowledge this controversy has not been addressed before. The quenching of the acid and base reactivities in CLPs via dative bond formation is a conceptually compelling explanation for the unreactive nature of CLPs.

Steric acceleration, in general, embodies two activation barrier lowering effects of bulky substituents: destabilization of the reactant state through steric repulsions between large groups and stabilization of the transition state by secondary interactions between these bulky substituents.

In this comprehensive computational study we systematically investigated the reaction of six Lewis pairs with molecular hydrogen, shown schematically in Fig.


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Definition of stationary points, activation- and reaction parameters on a general reaction profile for the heterolytic cleavage of H 2 by FLPs and CLPs, given together with the investigated systems top right and structure of lut and carb bottom left. Accordingly, these systems cover all possible types of scenarios, as well as they span a representative chemical space allowing us to investigate the effect of the donor atom and substituents of the Lewis base.

Most importantly, through these systems we can unambiguously demonstrate the operation of two distinct mechanisms of activation of H 2 by Lewis-pairs, which have clear manifestations in the energy-related activation parameters and in the geometry and electronic structure of transition states. With Fig. First, as Fig. FLPs and CLPs are not defined based on their relative stability but based on the lack or presence of a dative bond between the acid and base, respectively.

It is also clear from Fig. The quenching of acid and base reactivity, an appealing electronic structure-related concept for accounting for the reactivity difference of FLPs and CLPs, can be intuitively witnessed in the significantly more negative relative energy of stable Lewis pairs, such as Me 3 P—B C 6 F 5 3 Fig. In these cases the high stability of the Lewis pair inevitably manifests in a prohibiting activation barrier for H 2 splitting, which is Accordingly, these CLPs are also capable of activating H 2 , if they exhibit a low-energy transition state.

This simple observation strongly implies the operation of two different activation mechanisms through the two types of transition states. In line with these notions, a significantly stretched H—H bond of about 0.

General Properties

In addition, the computed base … H distances are characteristically longer by about 0. In fact, these H—H—B angles are more consistent with an end-on interaction of the acid with H 2 for these structures rather than with a side-on electron withdrawing process that was proposed earlier. These striking structural differences between transition states further support our notion of two distinct H 2 -activation mechanisms for systems with low-energy TSs and high-energy TSs. To our best knowledge, however, this geometry-based distinction of TSs has not been linked to an electronic structure and energy differentiation of transition states, however, it is crucial in understanding the feasibility of H 2 splitting by Lewis pairs.

In this context, it is critical to realize, however, that these transition states represent the highest-energy structure along the corresponding H—H splitting process and, accordingly the most critical electronic rearrangements are taking place at these specific geometries.