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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. Only valence electrons are used for bonding: n s, n p, n d “Core” electrons are held too tightly (too low in energy)

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Bonding in Molecules Covalent Bonding

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  1. Bonding in Molecules Covalent Bonding The term covalent implies sharing of electrons between atoms. Valence electrons and valence shell orbitals • Only 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. C* E.g. C 2s2 2p2 2s1 2p3 valence state ground state

  2. ns np Localized Bonding Models Localized implies that electrons are confined to a particular bond or atom. 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. G.N. Lewis Octet rule: most main group atoms will tend to end up with an ns2np6 electron configuration. This is mostly true for the molecules of organic chemistry not necessarily for inorganic compounds.

  3. 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. • - Oxygen is often terminal and hydrogen almost always is. • - Often the formula is written with the central atom first. • (Sometimes there may be more than one central atom.) • 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. • 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: • 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.)

  4. 1s 1s 1s 1s 1s 1s 1s Typical Lewis structural types: Molecules that conform to the “Octet Rule”: saturated molecules NH3 CH4 2s 2p 2s 2p C ground state N C* valence state 3 H 4 H These are typical of the molecules of organic chemistry.

  5. Molecules that conform to the “Octet Rule”: unsaturated molecules. NO3- ClNO 2s 2p 2s 2p N N N+ O Cl O 2s 2p 3s 3p 2s 2p O- 2s 2p O- 2s 2p

  6. 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. 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. I expect you to be able to: Draw Lewis structures (including resonance structures when necessary), determine bond orders, determine and place formal charges. Less favourable canonical structure

  7. 1s 1s 1s Molecules that don’t conform to the “Octet Rule”: Electron-deficient molecules Expanded valence shell molecules ClF3 BH3 3s 3p 2s Cl 2p 3d B Cl* B* F 2s 2p 3 H F 2s 2p F 2s 2p “Hypervalent molecules” “Lewis acids”

  8. 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. Objects 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.

  9. The geometry around an atom is described by the general formula: AXmEn 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.

  10. Less common geometries Xe- F F F F F Xe is described as AX5E2 and has a pentagonal planar shape derived from the pentagonal bipyramidal geometry. XeF5- NMe4+

  11. 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. CH4 Lone pair of electrons 109.5° Multiple bond polarized toward central atom NH3 Increasing steric demand 106.6° Normal single bond OH2 Long single bond polarized away from central atom 104.5°

  12. 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.  bonds: have a node on the inter-nuclear axis and the sign of the lobes changes across the axis.  bonds: symmetric about the internuclear axis

  13. Valence Bond Theory Detailed valence bond theory treatment of bonding in H2. VBT considers the interactions between separate atoms as they are brought together to form molecules. HA 1s1 HB 1s1 electron B (2) A (1) Atomic wavefunction on atom B 1 = A(1) B(2) Quantum mechanics demands that electrons can be interchangeable so we must use a linear combination of 1 and 2. 2 = A(2) B(1) + = N (1 + 2) (bonding, H-H) 3 = A(1) A(2) (ionic H- H+) - = N (1 - 2) (anti-bonding) 4 = B(1) B(2) (ionic H+ H-) molecule = N [1 + 2] + (C [3 + 4]) molecule = N [covalent + (C ionic)] N is a normalizing coefficient C is a coefficient related to the amount of ionic character

  14. Valence Bond Theory Valence bond theory treatment of bonding in H2 and F2 – the way it is generally used. F 2s 2p HA 1s1 HB 1s1 F Aa Bb 2s 2p Z axis 2pz 2pz This gives a 2p-2p  bond between the two F atoms. This gives a 1s-1s  bond between the two H atoms. For VBT treatment of bonding, people generally ignore the anti-bonding combinations and the ionic contributions.

  15. O 2s 2p O 2s 2p The Lewis approach and VBT predict that O2 is diamagnetic – this is wrong! Lewis structure Valence bond theory treatment of bonding in O2 Z axis 2pz 2pz This gives a 2p-2p  bond between the two O atoms. Z axis 2py (the choice of 2py is arbitrary) 2py Double bond:  bond +  bond Triple bond:  bond + 2  bond This gives a 2p-2p  bond between the two O atoms. In VBT,  bonds are predicted to be weaker than  bonds because there is less overlap.

  16. 1s 1s 1s 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: 2s 2p N The 2p orbitals on N are oriented along the X, Y, and Z axes so we would predict that the angles between the 2p-1s  bonds in NH3 would be 90°. We know that this is not the case. 3 H 106.6°

  17. Hybridization The problem of accounting for the true geometry of molecules and the directionality of orbitals is handled using the concept of hybrid orbitals. Hybrid 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 2s orbital superimposed on a 2px orbital The two resultant sp hybrid orbitals that are directed along the X-axis (in this case) The 1/2 are normalization coefficients.

  18. Orthogonality 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. Orthogonal means that the integral of the product of an orbital with any other orbital is equal to 0, i.e.: where n  m and dt 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 1, i.e.: This means that we must find normalization coefficients that satisfy these conditions. Note that the atomic orbitals () we use can be considered to be both orthogonal and normal or “orthonormal”.

  19. Example of the orthogonality of 1 and 2 Thus our hybrid sp orbitals are orthogonal to each other, as required.

  20. 1s 1s Hybridization Valence bond theory treatment of a linear molecule: the bonding in BeH2 BeH2 The promotion energy can be considered a part of the energy required to form hybrid orbitals. 2s 2p Be Be* sp 2p Be* (sp) 2 H The overlap of the hybrid orbitals on Be with the 1s orbitals on the H atoms gives two Be-H (sp)-1s  bonds oriented 180° from each other. This agrees with the VSEPR theory prediction.

  21. Valence bond theory treatment of a trigonal planar molecule: the bonding in BH3 2s 2p B B* sp2 2p B* (sp2) This gives three sp2 orbitals that are oriented 120° apart in the xy plane – be careful: the choice of axes in this example determines the set of coefficients.

  22. 1s 1s 1s Valence bond theory treatment of a trigonal planar molecule: the bonding in BH3 sp2 2p B* 3 H The overlap of the sp2 hybrid orbitals on B with the 1s orbitals on the H atoms gives three B-H (sp2)-1s  bonds oriented 120° from each other. This agrees with the VSEPR theory prediction.

  23. Valence bond theory treatment of a tetrahedral molecule: the bonding in CH4 2p 2s C C* sp3 C* (sp3) This gives four sp3 orbitals that are oriented in a tetrahedral fashion.

  24. 1s 1s 1s 1s Valence bond theory treatment of a tetrahedral molecule: the bonding in CH4 2p 2s C C* sp3 C* (sp3) 4 H The overlap of the sp3 hybrid orbitals on C with the 1s orbitals on the H atoms gives four C-H (sp3)-1s  bonds oriented 109.47° from each other. This provides the tetrahedral geometry predicted by VSEPR theory.

  25. Valence bond theory treatment of a trigonal bipyramidal molecule: the bonding in PF5 3s 3p PF5 has an VSEPR theory AX5 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). P 3d P* P* (sp3d) 3d 3s 3pz 3py 3px 3dz2 sp3dz2 The appropriate mixture to form a trigonal bipyramidal arrangement of hybrids involves all the ns and np orbitals as well as the ndz2 orbital.

  26. Valence bond theory treatment of a trigonal bipyramidal molecule The orbitals are treated in two different sets. These coefficients are exactly the same as the result for the trigonal planar molecules because they are derived from the same orbitals (sp2) 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.

  27. Valence bond theory treatment of a trigonal bipyramidal molecule: the bonding in PF5 P* (sp3d) 3d F 2s 2p F F 2s 2p 2s 2p F 2s 2p F 2s 2p The overlap of the sp3d hybrid orbitals on P with the 2p orbitals on the F atoms gives five P-F (sp3d)-2p  bonds in two sets: the two axial bonds along the z-axis (180° from each other) and three equatorial bonds in the xy plane (120° from each other and 90° from each axial bond). This means that the 5 bonds are not equivalent!

  28. 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 (sp2) hybrids and the axial bonds come from an MO interaction between the two ligand orbitals and the pz orbital on the central atom.

  29. The square pyramidal AX5 geometry requires mixing with a different d orbital than in the trigonal bipyramidal case. Sb(C6H5)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.

  30. Valence bond theory treatment of an octahedral molecule: the bonding in SF6 3s 3p S 3d S* S* (sp3d2) 3d F F F F F F 3s 3pz 3py 3px 3dx2-y2 sp3d2 3dz2 The overlap of the sp3d2 hybrid orbitals on S with the 2p orbitals on the F atoms gives six S-F (sp3d2)-2p  bonds 90° from each otherthat are equivalent. You can figure out the normalization coefficients. As in the case of the TBP, there is also an MO approach that does not require d orbitals.

  31. Valence bond theory treatment of p-bonding: the bonding in ClNO 2s 2p N sp2 2p There are three “objects” around N so the geometry is trigonal planar. The shape is given by AX2E (angular or bent). N*(sp2)    Cl O 3s 3p 2s 2p A drawing of the VBT p bond in ClNO. The overlap of the sp2 hybrid orbitals on N with the 3p orbital on Cl and the 2p orbital on O give the two  bonds and it is the overlap of the “left over” p orbital on N with the appropriate orbital on O that forms the (2p-2p) p bond between the two atoms.

  32. Valence bond theory treatment of p-bonding: the bonding in the nitrate anion 2s 2p N N+ sp2 2p There are three “objects” around N so the geometry is trigonal planar. The shape is given by AX3 (trigonal planar). N+*(sp2)  O-    2s 2p O- 2s 2p O VBT gives only one of the canonical structures at a time. 2s 2p The overlap of the sp2 hybrid orbitals on N with the the 2p orbitals on the O give the three (sp2-2p)  bonds and it is the overlap of the “left over” p orbital on N with the appropriate orbital on the uncharged O atom that forms the (2p-2p) p bond.

  33. 1s 1s 1s 1s Valence bond theory treatment of p-bonding: the bonding in ethene 2s 2p Each C Each C* There are three “objects” around each C so the geometry is trigonal planar at each carbon. The shape is given by AX3 for each carbon. sp2 2p C*(sp2)  2p sp2     C*(sp2)  4 H The overlap of the sp2 hybrid orbitals on C with the the 1s orbitals on each H give the four terminal (sp2-1s)  bonds. The double bond between the C atoms is formed by a (sp2- sp2)  bond and the (2p-2p) p bond.

  34. Valence bond theory treatment of p-bonding: the bonding in SOCl2 3s 3p S 3d S* There are four “objects” around S so the geometry is tetrahedral and the shape is given by AX3E (pyramidal). sp3 3d S*(sp3)     O Cl Cl 2s 2p The overlap of the sp3 hybrid orbitals on S with the 3p orbitals on Cl and the 2p orbital on O give the three  bonds and, because the lone pair is located in the final sp3 hybrid, it is the overlap of the “left over” d orbital on S with an appropriate p orbital on O that forms the (3d-2p) p bond in the molecule.

  35. Valence bond theory treatment of bonding: a hypervalent molecule, ClF3 3s 3p Cl 3d Cl* There are five “objects” around Cl so the geometry is trigonal bipyramidal and the shape is given by AX3E2 (T-shaped). Consider this: Why are such molecules T-shaped instead of pyramidal? Cl* (sp3d) 3d F F F The overlap of the sp3d hybrid orbitals on Cl with the 2p orbitals on the F atoms gives three P-F (sp3d)-2p  bonds in two sets: the two axial bonds along the z-axis (less than 180° 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.

  36. Summary of Valence Bond Theory • Write an acceptable Lewis structure for the molecule. • Determine the number of VSEPR objects around all central atoms and determine the geometry around the atom. • Construct hybrid orbitals suitable for the predicted bonding. • Link orbitals together to make bonds. • 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 AX2 (linear) Two orbitals pointing 180° from each other needed, so use two sp hybrids 1s sp Two (sp-1s) Be-H  bonds.

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