Chapter 9 Hybrid Orbitals

1 Jeffrey Mack California State University, Sacramento Chapter 9 Bonding and Molecular Structure: Orbital Hybridization and Molecular Orbitals Orbitals & Theories of Chemical Bonding Chapter 6 told us that the location of the valence electrons in an atom is described by an orbital model. It should seem reasonable that an orbital model can also be used to describe electrons in molecules. In this chapter, you will explore two common approaches to rationalizing chemical bonding based on orbitals: Valence Bond (VB) theory and Molecular Orbital (MO) theory. Valence Bonding Theory Molecular Orbital Theory Developed by Linus Pauling Premise: Bonding involves valence electrons. Half-filled atomic orbitals on bonding atoms overlap to form bonds. Bonds are localized between atoms (or as lone pairs). Leads to prediction of molecular shape. Linus Pauling, 1901-1994 Developed by Robert S. Mullikan (1896-1986) Bonding electrons reside in Molecular Orbitals that arise from the original atomic orbitals of the bonding atoms. Bonding electrons are spread over the entire molecule. (delocalized) Explains paramagnetism and electronic spectroscopy in molecules. The Orbital Overlap Model of Bonding Overlap of two s orbitals In H a sigma () covalent bond that arises from the overlap of two half filled s orbitals, one from each atom. A sigma bond is defined as a bond in which electron density lies along the axis of the bond. Sigma Bond Formation Two s orbitals overlap Overlap of an s & p orbital Two p orbitals overlap

: : Chapter 9 Hybrid Orbitals Valence Bond Theory The main points of the valence bond approach to bonding are: Orbitals overlap to form a bond between two atoms. Overlapping orbitals hold two electrons of opposite spin. Usually, one electron is supplied by each of the two bonded atoms. The bonding electrons are localized with a higher probability of being found within a region of space between the bonding nuclei. Both electrons are simultaneously associated with both nuclei. Valence Bond Terminology Overlap: two orbitals existing in the same region of space lp: lone pair of electrons (non-bonding) bp: bonding pair of electrons (result of orbital overlap) Central atom: the atom of concern in a molecule hybridization: the linear combination of atomic orbitals hybrid orbital: bonding orbitals that arise from the mixing of AO s. -bond: (sigma bond) overlap of orbitals along the bond axis -bond: (pi bond) overlap of orbitals above and below the bond axis. single bond: one -bond double bond: one -bond & one -bond triple bond: one -bond & two -bonds Sigma (σ) Bonding When bonding occurs along a bond axis, it is referred to as a sigma bond: () Pi (π) Bonding When bonding occurs above and below a bond axis, it is referred to as a pi bond: () X : Y X Y The electrons occupy space between the nuclei. The electrons occupy space above and below the nuclei. Sigma (σ) Bonding & Pi (π) Bonding Sigma () bonding: When bonding occurs along a bond axis, it is referred to as a sigma bond. X Pi () bonding: When bonding occurs above and below a bond axis, it is referred to as a pi bond. A double bond is made up of a and a bond. : Y Hybridization of Atomic Orbitals The simple model of atomic orbital overlap in H, HF and F breaks down for more complicated molecules. Consider methane: VSEPR theory predicts bond angles of 109.5. These angles can t be achieved with the s, p x, p y & p z orbitals of the central carbon atoms.

3 Hybridization of Atomic Orbitals In order to attain the needed geometry, the atomic orbitals (AO s) mix or hybridize to form new valence bond orbitals. consider carbon as a central atom in a molecule: There are 4 valence electrons: s carbon The valence orbitals are the s & s Hybridization of Atomic Orbitals This hybridization determines by the electron pair geometry for the central atom. Each half-filled orbital is capable of forming a covalent bond. s carbon carbon The new orbitals are called sp 3 Valence bond orbitals The 4 valence electrons on carbon fill the orbitals by Hund s rule: Hybridization of Atomic Orbitals Bonding in CH 4 Bonding in methane involves the overlap of the new sp 3 hybrid orbitals in carbon with the orbitals in hydrogen. s p Carbon Each overlap contains two shared electrons, one from each bonding nuclei. Each overlap results in a bond H H H H sp 3 hybrid valence bond orbitals. sp 3 Hybridization Since there are four sp 3 hybrid orbitals, they must spread out to form a tetrahedron about a central atom to minimize repulsion. It follows then that an central atom that has a tetrahedral EPG must have sp 3 hybridization. sp 3 Hybridization Water must also bond via sp 3 hybrid valence bond orbitals.

4 Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals 4 C atom orbitals hybridize to form four equivalent sp 3 hybrid atomic orbitals. 4 C atom orbitals hybridize to form four equivalent sp 3 hybrid atomic orbitals. sp 3 Hybridization Conclusion: When the central atom in a molecule has combination of 4 total sigma (single) bonds and lone pairs, the hybridization at the central atom is sp 3. In order to attain the needed geometry, the atomic orbitals (AO s) mix or hybridize to form new valence bond orbitals. The s & two of the orbitals mix: The new hybrid obitals all have the same energy: sp Hybridization sp there is one p-orbital left over The new orbitals are called sp Valence bond orbitals sp Hybridization sp Hybridization The remaining p-orbital is perpendicular to the three sp valence bond orbitals that spread out in a plane.

5 sp Hybridization Bonding in BF 3 Bonding in BF 3 The atomic orbitals on the central B-atom can t accommodate 3 bonds! The 1 s orbital and p orbitals must mix to form 3 new sp hybrid orbitals. The 3 sp hybrid orbitals can now form sigma bonds with each half-filled p-orbital on each fluorine atom. This results in a Trigonal Planar molecular and electron pair geometry. Bonding in an sp hybridized atom is shown below: Each of the three sp orbitals can form a -bond with another atom. Two of the orbitals overlap along the bond axis: sp Hybridization end on overlap The left over p-orbital can form a -bond with another halffilled p-orbital. Bonding in an sp hybridized atom is shown below: Each of the three sp orbitals can form a -bond with another atom. Two of the orbitals overlap along the bond axis: sp Hybridization end on overlap The left over p-orbital can form a -bond with another halffilled p-orbital. Sideways overlap... results in a -bond! Sideways overlap... results in a -bond! An example of sp hybridization is given by C H 4 (ethene) s sp Hybridization Carbon H C H sp hybrid valence bond orbitals. The left over p-orbitals on each carbon overlap to form the - bond (second half of the double bond). Each sp orbital can form a -bond, two with each of the H s and one with the other carbon. C H H Trigonal planar EPG at each carbon: sp hybridizaton! An Example of sp Hybridization: C H 4

6 Multiple Bonding in C H 4 - Bonds in C H 4 -Bonding in C H 4 Consequences of Multiple Bonding There is restricted rotation around C=C bond. The unused p orbital on each C atom contains an electron and this p orbital overlaps the p orbital on the neighboring atom to form the π bond. Consequences of Multiple Bonding Other Examples of Molecules with sp : CH O Restricted rotation around C=C bond. Conclusion: When a central atom has a trigonal planar electronic geometry (EPG), it is most likely to bond through sp hybridization. Compounds containing double bonds ( + ) most often have have sp hybridization.

7 sp Hybridization The sp orbitals spread out to form a linear geometry (directed away from one another) leaving the p orbitals perpendicular to the molecular axis. The sp orbitals can form -bonds or hold lone pairs. The two p- orbitals can form the () -bonds in a triple bond. sp Hybridization Just as with sp hybridization, in sp hybridization, the left over p-orbitals can form -bonds (in this case ). In acetylene (C H ) there is a triple bond. (1, s) An example of sp hybridization is given by C H (acetylene) Carbon sp hybrid valence bond orbitals form. s and Bonding in C H sp Hybridization Other examples of molecules with sp hybridization are: N :NN: CN (cyanide anion) [:CN:] Conclusion: When a central atom has a linear electronic geometry (EPG) with no lone pairs, it is most likely to bond through sp hybridization. Compounds containing triple bonds ( + ) or adjacent double bonds (CO ) have sp hybridization. sp, sp, & sp 3 hybridization Bonding in Glycine

8 Bonding in Glycine Bonding in Glycine Bonding in Glycine Bonding in Glycine Valence Bond Theory (): Expanded Valence For elements beyond the second period, we found several examples where the central atom in a Lewis structure had greater than 8 electrons in the valence shell. At n = 3 l = 0 1 s-orbitals p-orbitals d-orbitals We ve seen that when four sp 3 hybrid orbitals form, a central atom can accommodate only up to 8 electrons in the valence (bp & lp). To place more electrons in the valence, we must bring the d orbitals into the mix. Consider a Molecule Like PCl 5 Phosphorous:valence electron configuration of 3s 3p 3. (5 electrons) Each of the five electrons forms a single bond with a chlorine atom. This means that central atom in the molecule needs 5 bonding orbitals to achieve the trigonal bipyramidal electronic geometry. 3s 3p mix or hybridize This cannot happen with sp 3 hybridization sp 3 hybrid valence bond orbitals.

9 Valence Bond Theory (): Expanded Additional example of sp 3 d hybrid Valence molecules: The only way to produce 5 half-filled orbitals on phosphorous is by adding a fifth atomic orbital SF 4 (sulfur tetrafluoride) ClF 3 (chlorine trifluoride) 3p 3s 3d mix the 3s, the three 3p and one 3d 3d new sp 3 d hybrid valence bond orbitals Each of these half filled sp 3 d orbitals can form a bond with a chlorine atom in PCl 5. EPG: Trigonal Bipyramidal MG: See Saw EPG: Trigonal Bipyramidal MG: T-shape Valence Bond Theory (): Expanded Valence What about molecules with 1 electrons in the valence? In order to achieve an expanded valence that can hold six electron pairs (bp & lp) we need to form 6 new hybrid orbitals. This requires the mixing of an s, three p s and two d atomic orbitals. sp 3 d Hybridization: SF 6 3s 3p 3d mix the 3s, the three 3p and two 3d s 3d new sp 3 d hybrid valence bond orbitals 3p 3s sulfur 3d mix the 3s, the three 3p and two 3d s 3d six new sp 3 d hybrid valence bond orbitals Each of these half filled sp 3 d orbitals can form a bond with a fluorine atom. sp 3 d Hybridization: SF 6 Sulfur has a valence electron configuration of 3s 3p 4 (6 electrons). Each of the six electrons forms a single bond with a fluorine atom forming an octahedral MG and EPG. The bonding can be described in terms of sp 3 d hybrid orbitals. SF 6 Predicting Hybridization 1. Start by drawing the Lewis structure (check formal charges). Use VSEPR theory the electron group geometry about the central atom. 3. Relate the central atom electron group geometry to the corresponding hybridization. 4. Identify and label the orbital overlap in each bond. 5. Label the bonds with and bonds.

10 Hybridization Practice Additional Examples of sp 3 d Indicate the central atom hybridization for the following. XeF 4 CH O BrF 5 SF 6 Br 3 BrF 5 (bromine pentafluoride) EPG: octahedral MG: Square Pyramidal XeF 4 (xenon tetra fluoride) EPG: octahedral MG: Square Planar Conclusion: Molecules with an octahedral EPG have sp 3 d hybridization at the central atom. Molecular Orbital Theory Molecular Orbital Theory (MO) approaches bonding between atoms from a different approach than Valence Bond Theory. In Valence Bond theory, the atomic orbitals of a bonding atom mix or hybridize to form localized bonds that take on the EPG s predicted by VSEPR theory. In MO theory, the atomic orbitals are treated like waves that constructively or destructively add to form new Molecular Orbitals. The electrons of the molecule are distributed over the entire molecule as a whole. (delocalized) Molecular Orbital Theory Molecular Orbital Theory has several advantages and differences over VESPR & VB theory: MO does a good job of predicting electron pair spectra and paramagnetism, where VSEPR and the VB theories don't. MO theory like VB theory, predicts the bond order of molecules, however it does not need resonance structures to describe molecules. The main drawback to our discussion of MO theory is that we are limited to talking about diatomic molecules (molecules that have only two atoms bonded together), or the theory gets very complex. MO Theory: Considered Hydrogen When two wave functions (orbitals) on different atoms add constructively they produce a new MO that promotes bonding given by: atomic orbitals new Molecular Orbital MO Theory: Considered Hydrogen When two wave functions (orbitals) on different atoms add destructively they produce a new MO that decreases bonding given by: atomic orbitals new Molecular Orbital () H(1) + () H() H-H () H(1) () H() H-H when two waves add, the amplitude increases: + constructive interference = increased amplitude when two waves subtract, the amplitude decreases: + destructive interference = no amplitude (a node)

Energy Chapter 9 Hybrid Orbitals 11 Molecular Orbital Theory Consider hydrogen atoms combining to form H. The individual atomic orbitals combine. Molecular Orbital Theory Bonding and antibonding sigma MO s are formed from orbitals on adjacent atoms. When they add, a lower energy -bonding MO forms. When they subtract, a higher energy -antibonding MO forms Molecular Orbital Diagrams Molecular Orbital Diagrams Molecular orbitals result when atomic orbitals on bonding atoms constructively and destructively combine: s Once again we consider the simplest molecule, H. When two hydrogen atoms combine the orbitals on each can add or subtract to form a bonding or anti-bonding orbital. H-atom H-atom When they add, lower energy bonding Molecular Orbitals (MO s) form, when they subtract, higher energy anti-bonding MO s form. Anti-bonding orbitals are designated by an asterisk () called a star. s Each H-atom has one electron that can contribute to the MO bonding and anti-bonding MO s. Just as in the electron configurations of atoms, the electron fill from the lowest energy MO first (Aufbau principle) only pairing when forced to (Hund s rule). Each MO can only hold two electrons of opposite spin (Pauli principle) Bond Order in Molecular Orbital # of Bonding electrons - # antibonding electrons BO = Electrons in bonding molecular orbitals add stability. Electrons in anti-bonding molecular orbitals reduce stability. Bond Order: The Bonding in H is described by H-atom H-atom electrons in a bonding MO # of Bonding electrons - # antibonding electrons BO = Bond Order = 1 (single bond) MO electron configuration of: 0 electrons in an anti-bonding MO ( s ) One also sees that the molecule (H ) is diamagnetic (no unpaired electrons) - 0 = = 1

1 Excited States Why Doesn t He Exist? What happens to a H molecule if one of the electrons is excited to the anti-bonding orbital? - 0 Original BO = = 1 H-atom ground state H H-atom He: electrons in AO s fill the MO s 1-1 New BO = = 0 excited state H The molecule falls apart! Photodissociation - BO = = 0 Molecular Orbital theory predicts that the molecule is unstable! Sigma Bonding from p-orbitals Molecular Orbitals from Atomic p- Orbitals Sideways overlap of atomic orbitals that lie in the same direction in space give bonding and antibonding MOs. The MO Correlation Diagram for the Atomic Orbitals The three orbitals on each side combine to form six new Molecular Orbitals that can accommodate up to 1 electrons. s The MO Correlation Diagram for the Atomic Orbitals The three orbitals on each side combine to form six new Molecular Orbitals that can accommodate up to 1 electrons. s p p s p The two and the This configuration is seen for B, C and N only two are degenerate. p s This configuration is seen for O and F only

13 The overall MO diagram for the, s and orbitals: MO s s MO s MO s Bonding in O Since the and s MO s are full, they do not contribute any net bonding Any net bonding will be determined by the MO s. Each O atom has four electrons: O - atom s p p O - atom The electrons fill the MO s fill by the Aufbau principle and Hund s rule. s Since the and s MO s are full, they do not contribute any net bonding Any net bonding will be determined by the MO s. Each O atom has four electrons: Bonding in O O - atom s p p s The electrons fill the MO s fill by the Aufbau principle and Hund s rule O - atom O - atom Bonding in O 6 - BO = = This agrees with the Lewis dot structure: s p p s double bond O - atom O=O However, VB theory did not tell us that the molecule is paramagnetic!

14 The Paramagnetism of O (a) Making liquid O. (b) Liquid O is a light blue color. (c) Paramagnetic liquid O clings to a magnet. (d) Diamagnetic liquid N is not attracted to a magnet.