CHAPTER 9 Chemical Bonding II: Molecular Geometry and Bonding Theories
Shapes of Molecules and Ions Molecules and ions have a three dimensional shape. This shape can be important in determining the chemical behavior of a substance. We will discuss two types of geometries: 1) electron domain geometry - The arrangement of electron containing regions about a central atom. This is sometimes called electron cloud geometry. 2) molecular geometry - The arrangement of atoms about a central atom. The number of electron containing regions about a central atom is equal to the number of lone pair regions + the number of covalent bonds. Note that in counting electron containing regions a single, double, or triple bond counts as one region.
Examples of Counting Electron Containing Regions How many electron containing regions are there for central atoms in each of the mole- cules at left?
N 3 regions (two bonds, one lone pair) C 3 regions (three bonds, no lone pairs) C at left 4 regions (four covalent bonds) C at right 3 regions (three covalent bonds) Note the bond order does not matter in counting electron containing regions.
VSEPR Theory We may predict both electron cloud geometry and molecular geometry using VSEPR (Valence Shell - Electron Pair Repulsion) theory. The idea behind this theory is that electron containing regions will arrange themselves about a central atom in such a way as to put those regions as far apart as possible. This is due to the repulsive force existing between particles of the same charge (in this case electrons). The various common cases for electron and molecular geometry are given in Figure 9.2 (page 368) or Table 9.2 (page 369).
Two Regions If we have two electron containing regions around a central atom, then placing them opposite one another keeps them as far apart as possible. In this case, both the electron geometry and the molecular geometry are linear.
Three Regions For three regions about a central atom the electron geometry is trigonal planar (120 angle between the regions). There are two possible molecular geometries: If all three regions are bonds - trigonal planar If two of the three regions are bonds, and one is a lone pair of electrons - nonlinear (bent)
Four Regions For four regions about a central atom the electron geometry is tetrahedral (109 angle between the regions). There are three possible molecular geometries: 4 bonds - tetrahedral2 bonds - nonlinear (bent) 3 bonds - trigonal pyramid
Five Regions For five regions about a central atom the electron geometry is trigonal bipyramid. In this case not all of the angles between electron containing regions are the same. Instead, we may divide the regions into equitorial regions and axial regions.
Five Regions There are four possible molecular geometries: 5 bonds - trigonal bipyramid3 bonds - T-shape 4 bonds - “see-saw”2 bonds - linear
Six Regions For six regions about a central atom the electron geometry is octahedral. The bond angles between adjacent regions are all 90 .
Six Regions There are three common molecular geometries: 6 bonds - octahedral5 bonds - square pyramid 4 bonds - square planar
Example: What are the electron geometries and molecular geometries around the central atom in BrF 3, POCl 3, and H 2 SO 3 ?
BrF 3 5 regions, so electron cloud geometry is trigonal bipyramid. 3 bonds, so molecular geometry is T-shape. POCl 3 4 regions, so electron cloud geometry is tetrahedral. 4 bonds, so molecular geometry is also tetrahedral. H 2 SO 3 4 regions, so electron cloud geometry is tetrahedral. 3 bonds, so molecular geometry is trigonal pyramid.
Summary electron cloud bonds electron molecular regions geometry geometry 2 2linear linear 3 3trigonal planar trigonal planar 2 nonlinear (bent) 4 4 tetrahedral tetrahedral 3 trigonal pyramid 2 nonlinear (bent)
Summary electron cloud bonds electron molecular regions geometry geometry 5 5trig. bipyramid trig. bipyramid 4 see-saw 3 T-shape 2 linear 6 6octahedral octahedral 5 square pyramid 4 square planar
Geometry in Large Molecules For large molecules we can discuss the electron cloud and molecular geometry around each one of the interior atoms. Example: Give the electron cloud and molecular geometry for each interior atom in the molecule glycine (NH 2 CH 2 COOH).
Example: Give the electron and molecular geometry for each interior atom in the molecule glycine (NH 2 CH 2 COOH). Atomelectron geometrymolecular geometry N atom tetrahedral trigonal pyramid Left C atom tetrahedral tetrahedral Right C atom trigonal planar trigonal planar O atom tetrahedral nonlinear (bent)
Deviations From “Pure” Geometries We have assumed that the angles observed in molecular geometries do not depend on how many bonds and lone pair regions there are. In fact, the number of regions containing lone pair electrons has a small effect on the observed bond angles. In general we may say the repulsive forces between electron containing regions in a molecule or ion are stronger for lone pair electrons than for bonding electrons. So lone pair - lone pair > lone pair - bonding > bonding - bonding This is due to the fact that bonding electrons are more localized than lone pair electrons, as they must appear between bonded atoms.
In the molecules at left (all of which have four electron containing regions around a central atom) the bond angle decreases from 109.5 in CH 4 (pure tetrahedral geometry) to 107.0 in NH 3 to 104.5 in H 2 O. In CH 2 O (below) all of the bond angles would be 120. ° in pure trigonal planar geometry.
Representing Three Dimensional Structure Molecules have a three dimensional structure. We need a systematic method for representing these structures in two dimensions. We do this as follows For convenience, we will sometimes used a dashed line to replace the hatched wedge for a bond going into the page. Example: Give the three dimensional structures for CH 3 Cl and PF 5.
Polar Molecule A polar molecule is a molecule where the center of positive and negative charge do not coincide. Two things are required for a molecule to be polar 1) The molecule must have at least one polar bond. 2) The contributions from the polar bonds cannot cancel.
For a polar covalent bond the difference in electronegativity between the bonded atoms should be about 0.5 or greater. This means that carbon-carbon bonds are completely nonpolar, and carbon-hydrogen bonds are only slightly polar. EN(C) = 2.5EN(H) = 2.1 The table of electronegativities and the molecular geometry for the molecule can be used to determine whether the molecule is polar or nonpolar. The polarity of a molecule is expressed in terms of the dipole moment of the molecule. The symbol for dipole moment is . Dipole moments are measured in units of Debye (D).
Example Consider the following molecules: H 2 O, CF 4, NH 3, and CH 3 COCH 3. Which of these molecules is expected to have a permanent dipole moment?
H 2 O = 1.85 D NH 3 = 1.47 D CF 4 = 0. D CH 3 COCH 3 = 2.88 D EN Values: H = 2.1; C = 2.5; N = 3.0; O = 3.5; F = 4.0 1 Debye = 3.336 x 10 -30 C. m
Theories For Molecular Bonding The Lewis dot structure method predates quantum mechanics. While it is a good qualitative description of covalent bonding it fails to work well in some cases (resonance structures are one example). There are two general methods that use quantum mechanics to improve on the Lewis dot structure method: Valence Bond theory - Discusses bond formation in terms of overlap of atomic orbitals (often hybrid orbitals). Molecular Orbital theory - Uses quantum mechanics to solve the Schrodinger equation for a molecule or ion. This is a very mathematical approach.
Valence Bond Theory For H 2 In valence bond theory bond formation is pictured as occurring due to the overlap of atomic orbitals of the atoms that are bonded together. Each of the orbitals contains one electron. When the orbitals overlap, the electron from each atomic orbital is shared by the two atoms. Notice the electrons need to be opposite spin. The covalent bond forms from the overlap of the two 1s atomic orbitals of the hydrogen atoms that are bonded together. This places the electrons between the two hydrogen nuclei, which holds the molecule together.
Bond Formation and Energy The formation of a covalent bond between two atoms occurs because it leads to a lower energy than exists for separate atoms. This can be seen in the bonding of two H atoms to form an H 2 molecule.
Shortcoming of Simple Valence Bond Theory The above picture breaks down when you need to form several different valence bonds for the same atom out of orbitals of different types. Example: Be in BeH 2 Be 1s 2 2s 2 H 1s 1 We want the beryllium atom to contribute one electron to each bond between Be and an H atom, but the 2s orbital of beryllium is full, with no unpaired electron. So what do we do?
Hybrid Orbitals In this case, before we form the valence bonds we first construct a new set of equivalent orbitals, called hybrid orbitals (in this case sp hybrid orbitals). We can envision the process taking place as indicated below. While the process of forming hybrid orbitals raises the energy of the electrons in Be, this is more than made up for when the two Be - H bonds are formed.
Formation of sp Hybrid Orbitals The sp hybrid orbitals are formed from combinations of the s and p x atomic orbitals. Since we begin with two atomic orbitals, we end up with two hybrid orbitals.
Use of sp Hybrid Orbitals For Bonding (BeH 2 ) The two sp hybrid orbitals formed in Be can now be used to form the two Be - H valence bonds.
sp 3 Hybrid Orbitals In methane (CH 4 ) we need the central carbon atom to have four equivalent hybrid orbitals to form the four C - H bonds. This is done using sp 3 hybridization. CH 4. C: 1s 2 2s 2 2p 2 As before, we start by “unpairing” the electrons in the carbon atom by promoting one electron from a 2s to a 2p orbital __ __ __ __ promote __ __ __ __ 2s 2p 2s 2p
sp 3 Hybrid Orbitals (Continued) Now that we have one electron in our 2s atomic orbital, and in each of the three 2p atomic orbitals, we combine the four orbitals to form our set of four sp 3 hybrid orbitals. Since we began with four atomic orbitals, we end up with four hybrid orbitals.
These sp 3 hybrid orbitals can now be used to form valence bonds or to hold lone pairs of electrons.
Naming and Use of Hybrid Orbitals We name hybrid orbitals by listing the type of atomic orbitals used to construct the hybrid orbitals (s, p, or d). If we use more than one of a particular type of orbital, we indicate the number of orbitals used by a superscript to the right of the symbol for the orbital. There is a simple relationship between the number of electron containing regions around a central atom and the type of hybrid orbitals that are required. Number of regionsHybrid orbitals Electron geometry 2 splinear 3 sp 2 trigonal planar 4 sp 3 tetrahedral 5 * sp 3 dtrigonal bipyramid 6 * sp 3 d 2 octahedral * Not possible for atoms from 2 nd row of periodic table
Why PF 5 Exists and NF 5 Does Not We can now return to an observation we made in the last chapter, that in looking at molecules made from a group 5 nonmetal and fluorine the molecule PF 5 exists, but NF 5 does not. We can see why this is the case by looking at the hybridization required for the central atom in these two molecules. N [He] 2s 2 2p 3 P [Ne] 3s 2 3p 3 3d 0 __ __ __ __ __ __ __ __ __ promote __ __ __ __ __ __ __ __ __ 3s 3p 3d Hybridize to get 5 sp 3 d hybrid orbitals. This is not possible for nitrogen because there are no 2d orbitals, and so hybrid orbitals requiring use of one or more d orbitals cannot be formed.
Appearance of Hybrid Orbitals Each particular type of hybrid orbital has its own geometry, which in all cases corresponds to the geometries predicted using VSEPR theory. Also notice that in all cases the number of atomic orbitals we begin with is equal to the number of hybrid orbitals we end up with.
Sigma ( ) and Pi ( ) Bonds The above description works well for single bonds between atoms. However, when we have a multiple bond (double or triple bond), the bonds can be divided into two types: sigma bond - Formed from the overlap of atomic or hybrid orbitals; places electrons directly between the bonded atoms. pi bond - Formed from the overlap of p type atomic orbitals; places electrons above and below the region between the bonded atoms. In general, a single bond will always be a sigma bond. For a multiple bond, one of the bonds will be a sigma bond and the other bonds will be pi bonds.
Example: C 2 H 4 (ethene) (C atoms are sp 2 hybridization)
Summary Total number Number ofNumber of bonds sigma bonds pi bonds 1 1 0 2 1 1 3 1 2 So the first bond is always a sigma bond, while any additional bonds are pi bonds.
Example How many sigma bonds and how many pi bonds are present in the molecule shown below?
There are seven sigma bonds. There are two pi bonds.
Pi Bonds and Free Rotation Because pi bonds are formed from the overlap of p orbitals, molecules that contain pi bonds (molecules with double or triple bonds) cannot rotate freely around those bonds, since to do so would mean breaking one or more pi bond. In ethane (C 2 H 6 ) rotation around the C - C bond does not affect the bond and so is allowed. In ethene (C 2 H 4 ) rotation around the C = C bond breaks the pi bond, and so will not occur (except at high energy).
Molecular Orbital Theory In molecular orbital theory we solve the Schrodinger equation to find information about molecules (energies, geometries, electron distribution, and so forth). Just as we find atomic orbitals for atoms, we find molecular orbitals for molecules or ions. This is a very mathematical theory, and so we will only discuss simple cases in a nonmathematical way. The usual way people do MO theory is called the LCAO-MO method. In this method, linear combinations of atomic orbitals are used to construct molecular orbitals. We also focus on the valence electrons, and generally ignore core electrons.
Molecular Orbital Theory for H 2 For H 2, we begin with the two 1s atomic orbitals on the two H atoms. There are two ways in which these can be combined, cor- responding to two molecular orbitals. One molecular orbital lowers the energy and therefore corresponds to a bonding orbital, while the other molecular orbital raises the energy and therefore corresponds to a * antibonding orbital (note we use a * to indicate an antibonding orbital). We often also indicate the starting atomic orbitals. 1s atomic orbitals 1s MO * 1s MO
MO Diagram In a molecular orbital diagram we indicate the starting atomic orbitals and the molecular orbitals made from them with the correct relative energies. The above diagram represents the MO picture for the H 2 molecule. As is the case for atoms, we can give an electron configuration for molecules as well. For the above we have H 2 : ( 1s ) 2
Rules for Adding Electrons The rules for filling molecular orbitals are the same as filling atomic orbitals. They are: Pauli principle. Aufbau principle Hund’s rule Just as for atoms, we can write electron configurations for molecules by listing the occupied orbitals in order of energy, and indicating the number of electrons in an orbital by a superscript to the right of the orbital name. We usually place each orbital in parentheses.
Example H 2 molecule H 2 - ion He 2 “molecule” So H 2 ( 1s ) 2 H 2 - ( 1s ) 2 ( 1s *) 1 He 2 ( 1s ) 2 ( 1s *) 2
Bond Order We may define the bond order (BO) as follows BO = (# bonding e - ) - (# antibonding e - ) 2 The higher the bond order the stronger the bond. Note that fractional bond orders are possible. H 2 ( 1s ) 2 BO = 1 H 2 - ( 1s ) 2 ( 1s *) 1 BO = 1 / 2 He 2 ( 1s ) 2 ( 1s *) 2 BO = 0 If the bond order is zero, then we don’t expect the molecule or ion to be stable.
Period 2 Homonuclear Diatomics We may apply the above procedure to the period 2 homonuclear diatomic molecules and ions. Note that we only look at he molecular orbitals involving atomic orbitals in the valence shell. The 2s atomic orbitals present in the valence shell of second row atoms can be used to form a bonding and an antibonding sigma orbital, as was the case with the 1s atomic orbitals. * 2s 2s 2s 2s AO MO AO
Molecular Orbitals From 2p Atomic Orbitals The 2p atomic orbitals present in second row atoms can be used to form two types of molecular orbitals - sigma orbitals (bonding and antibonding) and pi orbitals (bonding and antibonding). * 2p * 2p 2p 2p 2p 2p AO MO AO
Formation of Molecular Orbitals From p x Atomic Orbitals
Formation of Molecular Orbitals From p y and p z Atomic Orbitals
Period 2 Homonuclear Diatomics The molecular orbitals formed from the 2s and 2p atomic orbitals of second period atoms are shown below. The order of these orbitals in terms of energy depends on the particular type of homonuclear diatomic species being discussed. Order for Li 2 to N 2 Order for O 2, F 2
Example: Give the electron configuration and bond order for C 2, C 2 +, and C 2 -. C 2 (8 e - )( 2s ) 2 ( 2s *) 2 ( 2p ) 4 BO = (6-2)/2 = 2 C 2 + (7 e - ) ( 2s ) 2 ( 2s *) 2 ( 2p ) 3 BO = (5-2)/2 = 1 1 / 2 C 2 - (9 e - ) ( 2s ) 2 ( 2s *) 2 ( 2p ) 4 ( 2p ) 1 BO = (7-2)/2 = 2 1 / 2
Summary of Bonding Theories Lewis theory - Simple to use, useful in making qualitative predictions about bond lengths and bond strengths. Not directly useful for three dimensional structure of molecules, sometimes makes incorrect predictions concerning bond order, unpaired electron spins. Difficulties in use for some molecules (requiring resonance structures). VSEPR- Based on Lewis theory, and allows predictions of molecular geometries. However, some of the same weaknesses of Lewis theory. Valence Bond theory (with hybridization) - Explains the formation of covalent bonds in more detail than Lewis theory, and also why atoms in the third row and below can violate the octet rule. Fails in the prediction of some properties of molecules, such as paramagnetism in O 2. Molecular Orbital theory - Most rigorous theory for molecules, but also the most complicated and mathematical theory. Difficult to apply in a simple way for large molecules.
Multicenter Pi Bonding We may combine valence bond theory and MO theory to account for resonance structures in terms of multicenter pi bonds, that is, pi bonds among more than two atoms. NO 2 - 24 valence electrons (and so 4 covalent bonds) When there are resonance structures that is usually evidence that the bonding needs to be described in terms of multicentered pi bonds. A correct description of bonding in this case requires use of both valence bond theory and molecular orbital theory.
The N atom and three O atoms can each form sp 2 hybrid orbitals. These form the N - O sigma bonds, and also contain two sets of lone pair electrons for each oxygen atom. Formation of Sigma Bonds
The remaining p orbitals on each atom that are perpendicular to the plane of the molecule can be used to form a final, multicentered pi bond, along with two other multicentered molecular orbitals (not shown) for the additional two sets of lone pair electrons. Formation of Multicenter Pi Bonds 4 p z antibonding MO lone pair MOs bonding MOs (multicentered pi bond)
Benzene Benzene (C 6 H 6 ) is an important example of a molecule that gains stability due to the presence of multicentered pi bonds.
End of Chapter 9 “Physicists are notoriously scornful of scientists from other fields. When the wife of the great Austrian physicist Wolfgang Pauli left him for a chemist, he was staggered with disbelief. ‘Had she taken a bullfighter I would have understood,’ he remarked in wonder to a friend. ‘But a chemist…’” Bill Bryson, A Short History of Nearly Everything “The physicist's greatest tool is his wastebasket.” - Albert Einstein “Hofstadter's law: It always takes longer than you expect, even when you take into account Hofstadter's law.” - Douglas Hofstadter “Love hides in molecular structures.” - Jim Morrison