Hybridization of Atomic Orbitals

• As two hydrogen atoms draw closer, their 1s orbitals begin to interact, and each electron experiences the attraction of the other proton
• Electron density concentrates in the region between the two nuclei, indicated by the red color
• A stable H2 molecule forms when the internuclear distance reaches 74 picometers

Hybridization of Atomic Orbitals

• Atomic orbital overlap applies to both polyatomic molecules
• A sufficient bonding scheme accounts for molecular geometry, which is exemplified in VB treatment of bonding in polyatomic molecules

sp3 Hybridization

• Consider methane (CH4), where carbon's valence electrons determine bonding

• In its ground state, carbon has two unpaired electrons within the 2p orbitals, limiting it to forming two bonds with hydrogen atoms

• The CH2 species is very unstable

• To account for the four C-H bonds in methane, promote an electron from the 2s to the 2p orbital.

• Four unpaired electrons on C can form four C-H bonds

• The geometry is incorrect, as three HCH bond angles would be 90° (the three 2p orbitals on carbon are perpendicular), yet all HCH angles are 109.5°

• VB theory explains methane's bonding by using hybrid orbitals, which result from combining two or more nonequivalent orbitals

• Hybridization mixes atomic orbitals in an atom (usually a central atom) to generate hybrid orbitals

• Equivalent hybrid orbitals for carbon are generated by mixing the 2s orbital and the three 2p orbitals

• The new orbitals, formed from one s and three p orbitals.

• These four hybrid orbitals are directed toward the four corners of a regular tetrahedron.

• The four covalent bonds form between the carbon sp3 hybrid orbitals and the hydrogen 1s orbitals in CH4.

• CH4 has a tetrahedral shape, with HCH angles at 109.5°

• Input is more than compensated for by the energy released upon the formation of C-H bonds

• Bond formation is an exothermic process.

• Red solution corresponds to one 2s orbital, the blue solutions represent three 2p orbitals, and the four equal volumes symbolize four separate orbitals

• By mixing the solutions, 200 mL of a purple solution is obtained and divided into four and sp3 hybrid orbitals

• Ammonia (NH3) is another example of sp3 hybridization

• The arrangement of four electron pairs is tetrahedral; N is sp3 hybridized.

• N's ground-state electron configuration is 1s22s22p3, so the orbital diagram for the sp3 hybridized N atom is:

• Three hybrid orbitals form covalent N-H bonds, and the fourth hybrid orbital accommodates nitrogen's lone pair

• Repulsion between lone-pair electrons and electrons in the bonding orbitals decreases the HNH bond angles from 109.5° to 107.3°

• Hybridization describes bonding schemes only when VSEPR predicts electron pair arrangement

• A tetrahedral arrangement of electron pairs indicates that one s and three p orbitals are hybridized to form four sp3 hybrid orbitals

sp Hybridization

• Beryllium chloride (BeCl2) molecule is predicted to be linear by VSEPR

• Be's orbital diagram, focusing only on valence electrons:

• In its ground state, Be does not form covalent bonds with Cl because its electrons are paired in the 2s orbital

• Through hybridization, a 2s electron is promoted to a 2p orbital

• Two Be orbitals, 2s and 2p, are available for bonding

• If two Cl atoms were to combine with Be in this excited state, one Cl atom would share a 2s electron and the other Cl would share a 2p electron, forming two non-equivalent BeCl bonds

• The 2s and 2p orbitals are mixed, or hybridized, to form two equivalent sp hybrid orbitals

• The shape and orientation of the sp orbitals on the x-axis, set the angle between them to 180°

• Each of the BeCl bonds forms by the overlap of a Be sp hybrid orbital and a Cl 3p orbital

• Resulting BeCl2 molecule has a linear geometry

sp2 Hybridization

• Boron trifluoride (BF3) molecule has planar geometry based on VSEPR

• Only the valence electrons are considered; the orbital diagram of B:

• A 2s electron is promoted to an empty 2p orbital

• Mixing the 2s orbital with the two 2p orbitals generates three sp2 hybrid orbitals

• These three sp2 *orbitals lie in the same plane, and the angle between any two of them is 120°

• Each of the BF bonds forms by the overlap of a boron sp2* hybrid orbital and a fluorine 2p orbital

• The BF3 molecule is planar with all the FBF angles equal to 120°

• This result conforms to experimental findings and VSEPR predictions

• Atoms starting with one s and three p orbitals still possess four orbitals, enough to accommodate eight electrons in a compound

• For elements in the second period of the periodic table, eight is the maximum number of electrons that an atom of any of these elements can accommodate in the valence shell

• This is the reason that the octet rule is usually obeyed by the second-period elements

• The situation is different for an atom of a third-period element

• If we use only the 3s and 3p orbitals of the atom to form hybrid orbitals in a molecule, then the octet rule applies

• The same atom may use one or more 3d orbitals in addition to the 3s and 3p orbitals to form hybrid orbitals

• Then the octet rule does not hold

• Not applied to isolated atoms — a theoretical model used to explain covalent bonding

• Hybridization mixes at least two nonequivalent atomic orbitals, for example, s and p orbitals — a hybrid orbital is not a pure atomic orbital

• Hybrid orbitals and pure atomic orbitals have very different shapes

• The number of hybrid orbitals generated is equal to the number of pure atomic orbitals that participate in the hybridization process

• Requires an input of energy; however, the system more than recovers this energy during bond formation

• Covalent bonds in polyatomic molecules and ions form by the overlap of hybrid orbitals, or of hybrid orbitals with unhybridized ones

• The hybridization bonding scheme is within the framework of valence bond theory, and electrons in a molecule occupy hybrid orbitals of individual atoms

Hybridization of s, p, and d Orbitals

• Hybridization explains bonding that involves s and p orbitals

• With elements in the third period and beyond, we cannot always account for molecular geometry by assuming that only s and p orbitals hybridize

• Formation of molecules requires including d orbitals in the hybridization concept

• Sulfur hexafluoride (SF6) is an example — the molecule has octahedral geometry

• Table 10.4 shows that the S atom is sp3d2-hybridized in SF6 and has a ground-state electron configuration of [Ne]3s23p4

• The 3d level is quite close in energy to the 3s and 3p levels, so 3s and 3p electrons can be promoted to two of the 3d orbitals

• Mixing the 3s, three 3p, and two 3d orbitals generates six sp3d2 hybrid orbitals

• The six S-F bonds form by the overlap of the hybrid orbitals of the S atom with the 2p orbitals of the F atoms

• Because there are 12 electrons around the S atom, the octet rule is violated

• The use of d orbitals in addition to s and p orbitals to form an expanded octet

• No suitable 2d energy levels — they can never expand their valence shells

• There are only 2s and 2p orbitals.

• Atoms of second-period elements can never be surrounded by more than eight electrons in any of their compounds

• Phosphorus in phosphorus pentabromide (PBr5) has five valence electrons, with each P atom has five valence electrons and trigonal bipyramidal arrangement.

• The 3d hybrid orbitals bond to Br, with one 3s, three 3p, and one 3d orbitals generates five sp3d hybrid orbitals

• A trigonal bipyramidal geometry forms and similar to previous diagrams, is presented in Figure 10.18

Hybridization in Molecules Containing Double and Triple Bonds

• Concept of hybridization extends to molecules with double and triple bonds

• The concept of hybridization is useful also for molecules with double and triple bonds.

• Consider the ethylene molecule, C2H4, where it contains a carbon-carbon double bond with planar geometry

• Geometry and bonding can be understood if each carbon atom is sp2-hybridized

• only the 2px and 2py orbitals combine with the 2s orbital, and that the 2pz orbital remains unchanged and perpendicular to the plane of the hybrid orbitals

• Each carbon atom uses the three sp2 hybrid orbitals to form two bonds with the two hydrogen 1s orbitals and one bond with the sp2 hybrid orbital of the adjacent C atom

• The two unhybridized 2pz orbitals of the C atoms form another bond by overlapping sideways

• bonds formed by orbitals overlapping end-to-end, with electron density concentrated between the nuclei

• called a pi bond (π bond), which is a covalent bond formed by sideways overlapping orbitals with electron density concentrated above and below the plane of the nuclei

• Acetylene molecule (C2H2) contains a carbon-carbon triple bond and linear geometry, assuming that each C atom is sp-hybridized

• If the central atom forms a double bond, it is sp2-hybridized

• If it forms two double bonds or a triple bond, it is sp-hybridized

• Applies only to atoms of the second-period elements

• Atoms of third-period elements and beyond that form multiple bonds present a more complicated picture

• Formaldehyde molecule bonding and using carbon and oxygen as example — there are three pairs of electrons around the C atom; therefore, the electron pair arrangement is trigonal planar