Orbitals hybrid atomic orbital

Orbital hybridization A mathematical approach that involves the combining of individual wave functions for s and p orbitals to obtain wave functions for new orbitals => hybrid atomic orbitals... 

The remaining p-orbitals (one on each carbon) form the pi orbital. In ethyne, sp hybridization occurs to give two hybrid orbitals on each atom with lobes pointing along the axis. The two remaining p-orbitals on each carbon form two pi orbitals. Hybrid atomic orbitals can also involve d-orbitals. For instance, square-planar complexes use sp d hybrids octahedral complexes use sp if. 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

We are now ready to account for the bonding in methane. In the promoted, hybridized atom each of the electrons in the four sp3 hybrid orbitals can pair with an electron in a hydrogen ls-orbital. Their overlapping orbitals form four o-bonds that point toward the corners of a tetrahedron (Fig. 3.14). The valence-bond description is now consistent with experimental data on molecular geometry. 

Noting that the bond angle of an sp hybridized atom is 109.5° and that of an sp1 hybridized atom is 120°, do you expect the bond angle between two hybrid orbitals to increase or decrease as the s-character of the hybrids is increased ... 

In the molecule Li2 the bond involves a hybrid atomic orbital as+bp formed from the 2s orbital and one of the much less stable 2p orbitals. It is shown below that the amount of p character of this bond orbital (equal to b2, with a2 + b2 = 1) is small, being about 8%. On the other hand, if each of the atoms in metallic lithium requires a bond orbital and a metallic orbital and the two are equivalent they will be 2- -p) and 2 t(s —p), with 50 % p character. The analysis of energy quantities supports this conclusion. 

To truly understand the geometry of bonds, we need to understand the geometry of these three different hybridization states. The hybridization state of an atom describes the type of hybridized atomic orbitals (ip, sp, or sp) that contain the valence electrons. Each hybridized orbital can be used either to form a bond with another atom or to hold a lone pair. 

Similarly, in H2O, the oxygen atom is sp hybridized. So all four orbitals are in a tetrahedral arrangement, just as we would expect for an sp hybridized atom. But only two of the orbitals are being used for bonds. So if we look just at the atoms that are connected, we do not see a tetrahedron. Rather, we see a bent arrangement ... 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

P n s p hybridized atom has three coplanar hybrid orbitals separated by 120° angles. One unchanged p orbital is perpendicular to the plane of the hybrids. 

An sp-hybridized atom has two hybrid orbitals separated by 180°. The remaining two atomic p orbitals are perpendicular to the hybrids and perpendicular to each other. 

The Lewis stmcture of moiecuiar oxygen shows the two atoms connected by a double bond, with two nonbonding electron pairs on each oxygen atom. Both atoms in O2 are outer atoms, so there are no constraining bond angles and no need for hybridization. Atomic valence 2. S and 2 p orbitals can be used to describe the bonding in this molecule. 

CS INDO [10] (as well as the parent C INDO [9]) shares the same basic idea as the PCILO scheme [29,30] to exploit the conceptual and computational advantages of using a basis set of hybrid atomic orbitals (AOs) directed along, or nearly, the chemical bonds. 

A carbon atom combining with four other atoms clearly does not use the one 2s and the three 2p atomic orbitals that would now be available, for this would lead to the formation of three directed bonds, mutually at right angles (with the three 2p orbitals), and one different, non-directed bond (with the spherical 2s orbital). Whereas in fact, the four C—H bonds in, for example, methane are known to be identical and symmetrically (tetrahedrally) disposed at an angle of 109° 28 to each other. This may be accounted for on the basis of redeploying the 2s and the three 2p atomic orbitals so as to yield four new (identical) orbitals, which are capable of forming stronger bonds (cf. p. 5). These new orbitals are known as sp3 hybrid atomic orbitals, and the process by which they are obtained as hybridisation ... 

Similar, but different, redeployment is envisaged when a carbon atom combines with three other atoms, e.g. in ethene (ethylene) (p. 8) three sp2 hybrid atomic orbitals disposed at 120° to each other in the same plane (plane trigonal hybridisation) are then employed. Finally, when carbon combines with two other atoms, e.g. in ethyne (acetylene) (p. 9) two sp1 hybrid atomic orbitals disposed at 180° to each other (idigonal hybridisation) are employed. In each case the s orbital is always involved as it is the one of lowest energy level. 

Figure 1.5 The shapes of some s and p orbitals. Pure, unhybridized p orbitals are almost-touching spheres. The p orbitals in hybridized atoms are lobe-shaped (Section 1.14).

The use of MO theory to find deep minima in the So surface, or geometries of stable molecules, is well known. A simplified rule would be to choose the geometry so as to allow efficient overlap of valence orbitals of the constituent atoms in a way giving bonding orbitals for all available electrons from pairs or larger sets of suitably hybridized atomic orbitals. No atomic orbitals occupied by one electron should be left over dangling free and unable to interact with others, since that would give radicals, biradicals, etc. Chemical intuition allows one to proceed almost automatically in cases of molecules of familiar types. 

A set of hybridized atomic orbitals holds the same maximum number of electrons as the set of atomic orbitals from which the hybridized atomic orbitals were formed. A hybridized atomic orbital can hold a maximum of 2 electrons having opposite spin. 

The central carbon is surrounded by three electron groups and is sp2 hybridized. The orbital diagrams for the un-hybridized atoms are ... 

Sigma (O) bond A bond formed by the end to end overlap of pure or hybridized atomic orbitals. 

The use of the Lbwdin orthogonalisation technique (or any other method of or-thogonalisation) means inevitably that the final basis of orthogonalised hybrid atomic orbitals (OHAOs) does contain many-centre orbitals in the sense that each OHAO is mainly its HAO parent but necessarily contains (minimal) contributions from overlapping HAOs. 

The use of hybrid atomic orbitals in qualitative valence theory has, in the past, rested on two points (i) an empirical justification of their use involving the concept of the valence state of an atom and (ii) a simple linear transformation technique for the construction of the explicit forms of the orbitals. In this section we show that both of these points can be replaced. The justification can be replaced by a derivation and this derivation can be used to suggest variational forms which render the linear transformation technique redundant. 

Intermediate values of R have eigenfunctions which are Unear combinations of the usual (complex) hydrogenic orbitals with the same values of n and m hybrid atomic orbitals. The actual values of the linear combination coefficients determining the expUcit form of the hybrids depend on R in the case of n = 2 m = 0 we get an inequivalent pair of hybrids pointing in opposite directions of the general form... 

The trigonal bond orbitals in the ten valence electron system as well as the two sets of trigonal lone pair orbitals in the 14 valence electron system are superpositions of it orbitals and o orbitals. The formation of such trigonally symmetric molecular orbitals from a-type and w-type molecular orbitals is entirely analogous in character to the formation of the three (sp2) hybrid atomic orbitals from one (s) and two ip) atomic orbitals which was discussed in the preceding section. This can be visualized by looking at the diatomic molecule... 

A second common type of orbital hybridization involves the 2s orbital and only two of the three 2p orbitals (2a). This process is therefore referred to as sp hybridization. The result is three equivalent sp hybrid orbitals lying in one plane at an angle of 120° to one another. The remaining 2px orbital is oriented perpendicular to this plane. In contrast to their sp counterparts, sp -hybridized atoms form two different types of bond when they combine into molecular orbitals (2b). The three sp orbitals enter into a bonds, as described above. In addition, the electrons in the two 2px orbitals, known as n electrons, combine to give an additional, elongated n molecular orbital, which is located above and below the plane of the a bonds. Bonds of this type are called double bonds. They consist of a a bond and a n bond, and arise only when both of the atoms involved are capable of sp hybridization. In contrast to single bonds, double bonds are not freely ro-... 

Fig. 6. The radially orientated sp hybrid atomic orbital (AO) and tangentially orientated p AO s that a BH unit can supply for skeletal bonding.

We start with Salem s treatment of the Walden inversion Frontier orbital approximation is assumed the major interaction is supposed to be that between the nucleophile s HOMO and the substrate s LUMO. Now, according to ab initio calculations, the latter is essentially an out-of-phase combination of a carbon hybrid atomic orbital 0c with a leaving group hybrid atomic orbital 0x- In the first approximation, the LUMO wave function may be written as ... 

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