Bonding in Molecules Covalent Bonding

Bonding in Molecules Covalent Bonding The term covalent implies sharing of electrons between atoms. Valence electrons and valence shell orbitals - nly valence electrons are used for bonding: ns, np, nd - Core electrons are held too tightly (too low in energy) - Filled nd orbitals are considered core electrons Valence state electron configurations and Promotion Energies -The promotion energy is the energy required to promote electrons from the ground state to a valence state, which is one type of excited state configuration that is used for bonding. E.g. C s ground state s 3 valence state C*

Localized Bonding Models Localized implies that electrons are confined to a particular bond or atom. G.N. Lewis The Lewis approach to bonding Pairs of electrons are localized in bonds or as non-bonding lone pairs on atoms. Each bond is formed by a pair of electrons shared by two atoms. ctet rule: most main group atoms will tend to end up with an ns np 6 electron configuration. ns This is mostly true for the molecules of organic chemistry not necessarily for inorganic compounds. np

Rules for drawing Lewis diagrams a. Pick the central atom. - Atoms that are present only once in the formula, especially heavy elements and metals, tend to be at the center of the structure. - xygen is often terminal and hydrogen almost always is. - ften the formula is written with the central atom first. (Sometimes there may be more than one central atom.) b. Write out the valence shell electron configurations for the neutral central atom and the "terminal" atoms in their ground states. c. If there is a negative charge distribute it among the terminal atoms in the first instance. Bear in mind that all the terminal atoms must make at least one covalent bond with the central atom, so do not create any noble gas configurations on them. Positive charge is best initially assigned by removing electrons from the central atom. d. The total number of unpaired electrons on the terminal atoms will have to match the number of unpaired electrons on the central atom to account for the bonds and leave no unpaired electrons. If this is not the case, once the first three steps have been carried out, there are two strategies available: e. Move electrons between the central atom and the terminal atoms as necessary. Make sure you keep track of the formal charges because you must be specific about their location. Enclosing a Lewis structure in brackets with the charge outside is not acceptable. f. If and only if the central atom comes from the second period or below (Na onwards, n=3 and up), electrons can be placed into the nd subshell. (Whether the d orbitals play a significant role in bonding in main group compounds is debatable, but they do help to predict correct structure without invoking canonical structures with unreasonable charge separations.)

Typical Lewis structural types: Molecules that conform to the ctet Rule : saturated molecules N 3 C 4 N s C s ground state C* valence state 3 s s s 4 s s s s N C These are typical of the molecules of organic chemistry.

Molecules that conform to the ctet Rule : unsaturated molecules. N s ClN N s N 3 - N + Cl 3s 3p s s - s Cl N - s N

Resonance Resonance implies that there is more than one possible way to distribute the valence electrons in a Lewis structure. For an adequate description, each canonical structure must be drawn. N If different equivalent resonance structures are possible, the molecule tends to be more stable than one would otherwise expect. This is a quantum mechanical effect that we will talk about later. N N N Less favourable canonical structure I expect you to be able to: Draw Lewis structures (including resonance structures when necessary), determine bond orders, determine and place formal charges.

Molecules that don t conform to the ctet Rule : Electron-deficient molecules Expanded valence shell molecules B B* s B 3 Cl Cl* 3s 3p ClF 3 3d F 3 s s s B s F F s F s F Cl Lewis acids F ypervalent molecules

Valence Shell Electron Pair Repulsion Theory A basic geometry can be assigned to each non-terminal atom based on the number of objects attached to it. bjects include bonded atoms (single, double, triple, partial bonds) and lone pairs of electrons. VSEPR theory lets us predict the shape of a molecule based on the electron configurations of the constituent atoms. It is based on maximizing the distance between points on a spherical surface. Number of 3 4 5 6 bjects Geometry linear trigonal planar tetrahedral trigonal bipyramidal* ctahedral

The geometry around an atom is described by the general formula: AX m E n Where X is a bonded atom, E is a lone pair and (m+n) is the number of objects (sometimes called the steric number, SN) around the central atom A. Number of bjects 3 4 5 6 Geometry linear trigonal planar tetrahedral trigonal bipyramidal ctahedral Formula (Shape) AX AX 3 (trig. planar) AX E (bent) AX 4 (tetrahedral) AX 3 E (pyramidal) AX E (bent) AX 5 (t.b.p. or square pyramidal) AX 4 E (seesaw) AX 6 (octahedral) AX 5 E (square pyramidal) AX 4 E (square planar) AX 3 E (T-shaped) AX 3 E 3 (T-shaped) AX E 3 (linear)

Less common geometries Number of bjects Geometry 7 pentagonal bipyramidal 8 square anti-prismatic Xe - F F F F F XeF 5 - NMe 4 + Xe is described as AX 5 E and has a pentagonal planar shape derived from the pentagonal bipyramidal geometry.

Refinement of VSEPR theory predicted geometries The relative steric demand of objects is different and amount of repulsion caused by the object will alter the arrangement of the atoms around the central atom. Increasing steric demand Lone pair of electrons Multiple bond polarized toward central atom Normal single bond Long single bond polarized away from central atom 09.5 06.6 04.5 C 4 N 3

Valence Bond Theory Valence bond theory (VBT) is a localized quantum mechanical approach to describe the bonding in molecules. VBT provides a mathematical justification for the Lewis interpretation of electron pairs making bonds between atoms. VBT asserts that electron pairs occupy directed orbitals localized on a particular atom. The directionality of the orbitals is determined by the geometry around the atom which is obtained from the predictions of VSEPR theory. In VBT, a bond will be formed if there is overlap of appropriate orbitals on two atoms and these orbitals are populated by a maximum of two electrons. σ bonds: symmetric about the internuclear axis π bonds: have a node on the inter-nuclear axis and the sign of the lobes changes across the axis.

Valence Bond Theory Detailed valence bond theory treatment of bonding in. A s B s φ A () φ B () electron VBT considers the interactions between separate atoms as they are brought together to form molecules. Atomic wavefunction on atom B Ψ = φ A () φ B () Ψ = φ A () φ B () Quantum mechanics demands that electrons can be interchangeable so we must use a linear combination of Ψ and Ψ. Ψ + = N (Ψ + Ψ ) (bonding, -) Ψ - = N (Ψ - Ψ ) (anti-bonding) Ψ 3 = φ A () φ A () (ionic - + ) Ψ 4 = φ B () φ B () (ionic + - ) N is a normalizing coefficient C is a coefficient related to the amount of ionic character Ψ molecule = N [Ψ + Ψ ] + (C [Ψ 3 + Ψ 4 ]) Ψ molecule = N [Ψ covalent + (C Ψ ionic )]

Valence Bond Theory Valence bond theory treatment of bonding in and F the way it is generally used. F s A s B s φ A α φ B β F s Z axis z z This gives a s-s σ bond between the two atoms. This gives a - σ bond between the two F atoms. For VBT treatment of bonding, people generally ignore the antibonding combinations and the ionic contributions.

Valence bond theory treatment of bonding in z z This gives a - σ bond between the two atoms. Z axis s s y y Z axis (the choice of y is arbitrary) This gives a - π bond between the two atoms. In VBT, π bonds are predicted to be weaker than σ bonds because there is less overlap. Lewis structure Double bond: σ bond + π bond Triple bond: σ bond + π bond The Lewis approach and VBT predict that is diamagnetic this is wrong!

Directionality The bonding in diatomic molecules is adequately described by combinations of pure atomic orbitals on each atom. The only direction that exists in such molecules is the inter-nuclear axis and the geometry of each atom is undefined in terms of VSEPR theory (both atoms are terminal). This is not the case with polyatomic molecules and the orientation of orbitals is important for an accurate description of the bonding and the molecular geometry. Examine the predicted bonding in ammonia using pure atomic orbitals: N s 3 s N s s The orbitals on N are oriented along the X, Y, and Z axes so we would predict that the angles between the -s σ bonds in N 3 would be 90. We know that this is not the case. 06.6

ybridization The problem of accounting for the true geometry of molecules and the directionality of orbitals is handled using the concept of hybrid orbitals. ybrid orbitals are mixtures of atomic orbitals and are treated mathematically as linear combinations of the appropriate s, p and d atomic orbitals. Linear sp hybrid orbitals A s orbital superimposed on a x orbital Ψ = φs + Ψ = φs φ φ p p The two resultant sp hybrid orbitals that are directed along the X-axis (in this case) The / are normalization coefficients.

rthogonality and Normalization Two properties of acceptable orbitals (wavefunctions) that we have not yet considered are that they must be orthogonal to every other orbital and they must be normalized. These conditions are related to the probability of finding an electron in a given space. rthogonal means that the integral of the product of an orbital with any other orbital is equal to 0, i.e.: ΨΨ n m τ = 0 where n m and δτ means that the integral is taken over all of space (everywhere). Normal means that the integral of the product of an orbital with itself is equal to, i.e.: ΨΨ n n τ = This means that we must find normalization coefficients that satisfy these conditions. Note that the atomic orbitals (φ) we use can be considered to be both orthogonal and normal or orthonormal.

Example of the orthogonality of Ψ and Ψ Ψ = φs + φp Ψ = φs φ p ΨΨ τ = φs + φp φs φ τ p ( ) ( ) ΨΨ ( ) ( ) τ = φsφs τ φ φ τ φ φ τ φ φ τ s p + s p p p () ( ) ( ) () ΨΨ 0 0 τ = + ΨΨ τ = = 0 Thus our hybrid sp orbitals are orthogonal to each other, as required.

ybridization Valence bond theory treatment of a linear molecule: the bonding in Be Be s Be The promotion energy can be considered a part of the energy required to form hybrid orbitals. Be* Be* (sp) sp s s Be The overlap of the hybrid orbitals on Be with the s orbitals on the atoms gives two Be- (sp)-s σ bonds oriented 80 from each other. This agrees with the VSEPR theory prediction.

Valence bond theory treatment of a trigonal planar molecule: the bonding in B 3 B B* s B* (sp ) sp B This gives three sp orbitals that are oriented 0 apart in the xy plane be careful: the choice of axes in this example determines the set of coefficients. Ψ = φ φ + φ x 3 6 s p p Ψ = φ φ φ x 3 6 Ψ 3 = φs + φ 3 6 s p p p x y y

Valence bond theory treatment of a trigonal planar molecule: the bonding in B 3 B* sp 3 s s s B The overlap of the sp hybrid orbitals on B with the s orbitals on the atoms gives three B- (sp )-s σ bonds oriented 0 from each other. This agrees with the VSEPR theory prediction.

Valence bond theory treatment of a tetrahedral molecule: the bonding in C 4 C C* s C* (sp 3 ) sp 3 C This gives four sp 3 orbitals that are oriented in a tetrahedral fashion. Ψ = φ + φ + φ + φ 4 4 4 4 Ψ = φ + φ φ φ 4 4 4 4 Ψ 3 = φ φ φ + φ 4 4 4 4 Ψ 4 = φ φ + φ φ 4 4 4 4 s p p p x y z s p p p x y z s p p p x y z s p p p x y z

Valence bond theory treatment of a tetrahedral molecule: the bonding in C 4 C C* s C* (sp 3 ) sp 3 4 s s s s C The overlap of the sp 3 hybrid orbitals on C with the s orbitals on the atoms gives four C- (sp 3 )-s σ bonds oriented 09.47 from each other. This provides the tetrahedral geometry predicted by VSEPR theory.

Valence bond theory treatment of a trigonal bipyramidal molecule: P P* 3s 3p the bonding in PF 5 P* (sp 3 d) 3d 3d PF 5 has an VSEPR theory AX 5 geometry so we need hybrid orbitals suitable for bonds to 5 atoms. ns and np combinations can only provide four, so we need to use nd orbitals (if they are available). 3s 3p z 3p y 3p x 3d z sp 3 d z The appropriate mixture to form a trigonal bipyramidal arrangement of hybrids involves all the ns and np orbitals as well as the nd z orbital.

Valence bond theory treatment of a trigonal bipyramidal molecule The orbitals are treated in two different sets. Ψ = φ + φ + φ x 3 6 s p p Ψ = φ + φ φ x 3 6 Ψ 3 = φs φ 3 6 s p p p x y y These coefficients are exactly the same as the result for the trigonal planar molecules because they are derived from the same orbitals (sp ) Ψ 4 = φp + z Ψ 5 = φp + z φ d φ z d z These coefficients are similar to those for the sp hybrids because they are formed from a combination of two orbitals (pd). Remember that d orbitals are more diffuse than s or p orbitals so VBT predicts that the bonds formed by hybrids involving d orbitals will be longer than those formed by s and p hybrids.

Valence bond theory treatment of a trigonal bipyramidal molecule: the bonding in PF 5 P* (sp 3 d) 3d F s F s F s F s F s The overlap of the sp 3 d hybrid orbitals on P with the orbitals on the F atoms gives five P-F (sp 3 d)- σ bonds in two sets: the two axial bonds along the z-axis (80 from each other) and three equatorial bonds in the xy plane (0 from each other and 90 from each axial bond). This means that the 5 bonds are not equivalent!

An alternative, and maybe more reasonable, version of VBT treatment of a trigonal bipyramidal molecule: The d orbitals are too high in energy to mix effectively with the s and p orbitals, so the trigonal bipyramidal molecule is actually composed of an equatorial set of trigonal (sp ) hybrids and the axial bonds come from an M interaction between the two ligand orbitals and the p z orbital on the central atom. Ψ = φp + zfa Ψ = φp zfa φ φ p zfb p zfb σ = Ψ + φ 3 p zp σ* = Ψ φ 3 p zp

The square pyramidal AX 5 geometry requires mixing with a different d orbital than in the trigonal bipyramidal case. Sb(C 6 5 ) 5 d orbitals You should consider what orbital(s) would be useful for such a geometry and we will see a way to figure it out unambiguously when we examine the symmetry of molecules.

Valence bond theory treatment of an octahedral molecule: S S* 3s 3p the bonding in SF 6 3d S* (sp 3 d ) 3d F F F F F F 3s 3p z 3p y 3p x 3d z 3d sp 3 d x -y The overlap of the sp 3 d hybrid orbitals on S with the orbitals on the F atoms gives six S-F (sp 3 d )- σ bonds 90 from each other that are equivalent. You can figure out the normalization coefficients. As in the case of the TBP, there is also an M approach that does not require d orbitals.

Valence bond theory treatment of π-bonding: the bonding in ClN N s Cl N N*(sp ) sp σ σ π There are three objects around N so the geometry is trigonal planar. The shape is given by AX E (angular or bent). Cl 3s 3p s Cl N A drawing of the VBT π bond in ClN. The overlap of the sp hybrid orbitals on N with the 3p orbital on Cl and the orbital on give the two σ bonds and it is the overlap of the left over p orbital on N with the appropriate orbital on that forms the (- ) π bond between the two atoms.

Valence bond theory treatment of π-bonding: the bonding in the nitrate anion N N + N + *(sp ) s σ - s sp - s σ σ s π N There are three objects around N so the geometry is trigonal planar. The shape is given by AX 3 (trigonal planar). The overlap of the sp hybrid orbitals on N with the the orbitals on the give the three (sp -) σ bonds and it is the overlap of the left over p orbital on N with the appropriate orbital on the uncharged atom that forms the (-) π bond. N VBT gives only one of the canonical structures at a time.

C*(sp ) Chem 59-65 4 Valence bond theory treatment of π-bonding: the bonding in ethene Each C Each C* σ sp σ σ s σ s s s s sp σ π C*(sp ) C C There are three objects around each C so the geometry is trigonal planar at each carbon. The shape is given by AX 3 for each carbon. The overlap of the sp hybrid orbitals on C with the the s orbitals on each give the four terminal (sp -s) σ bonds. The double bond between the C atoms is formed by a (sp -sp ) σ bond and the (-) π bond. C C

Valence bond theory treatment of π-bonding: the bonding in SCl 3s 3p Cl S S* 3d S Cl S*(sp 3 ) σ sp 3 σ σ 3d π There are four objects around S so the geometry is tetrahedral and the shape is given by AX 3 E (pyramidal). Cl Cl s Cl Cl S The overlap of the sp 3 hybrid orbitals on S with the 3p orbitals on Cl and the orbital on give the three σ bonds and, because the lone pair is located in the final sp 3 hybrid, it is the overlap of the left over d orbital on S with an appropriate p orbital on that forms the (3d-) π bond in the molecule.

Cl Cl* Valence bond theory treatment of bonding: a hypervalent molecule, ClF 3 3s 3p 3d F F Cl F Cl* (sp 3 d) F F F 3d There are five objects around Cl so the geometry is trigonal bipyramidal and the shape is given by AX 3 E (T-shaped). Consider this: Why are such molecules T-shaped instead of pyramidal? The overlap of the sp 3 d hybrid orbitals on Cl with the orbitals on the F atoms gives three P-F (sp 3 d)- σ bonds in two sets: the two axial bonds along the z-axis (less than 80 from each other because of the repulsion from the lone pairs) and the one equatorial bond halfway between the other Cl bonds. Again, the bond lengths will not be the same because there is more d contribution to the axial hybrid orbitals.

Summary of Valence Bond Theory. Write an acceptable Lewis structure for the molecule. Be. Determine the number of VSEPR objects around all central atoms and determine the geometry around the atom. 3. Construct hybrid orbitals suitable for the predicted bonding. 4. Link orbitals together to make bonds. 5. Describe the bonding. Include the names of the orbitals involved in each bond. Draw pictures of the bonds formed by the overlap of these orbitals. Two objects around Be, so AX (linear) Two orbitals pointing 80 from each other needed, so use two sp hybrids sp Be Two (sp-s) Be- σ bonds. s