3. Molecular structure

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1 3. Molecular structure 1. Molecular structure and covalent bonding theories Valance shell electron pair repulsion (VSEPR) Theory In a molecule composed of a central atom bonded covalently to several peripheral atoms the bonding and lone pairs are oriented so that electron-electron repulsions are minimized while electronnucleus attractions are maximized. The method of determining this orientation is called the valence-shell electron-pair repulsion or VSEPR method. The assumptions behind the method are: 1. Electron pairs in the valence shell of an atom tend to orient themselves so that their total energy is minimized. This means that they approach the nucleus as closely as possible, while at the same time staying as far away from each other as possible, thus minimizing interelectronic repulsions. 2. Because lone pairs are spread out more broadly than are bonding pairs, repulsions are greatest between two lone pairs, intermediate between a lone pair and a bonding pair, and Chapter 3: Molecular structure Page 57

2 weakest between two bonding pairs. This order of repulsion is shown as in figure 3-1 Figure 3-1 Order of repulsion between electron pairs 3. Repulsive forces decrease sharply with increasing interpair angle. They are strong at 90, much weaker at 120, and very weak at 180. Figure 3-2 Steric number 4: Two possible orientation Chapter 3: Molecular structure Page 58

3 Steric number and electron-pair orientation: The first step in the VSEPR method for determining the shape of a molecule is to draw its Lewis structure in order to find out how many electron pairs are located around the central atom. Consider arsenic trichloride, AsCl 3, and sulfur tetrafluoride, SF 4, as examples. Their Lewis structures are, respectively. The steric number is defined as the total number of electron pairs (lone and bonding) around the central atom. As can be seen from the above Lewis structures, arsenic has a steric number of 4 in AsCl 3, while in SF 4 ; the steric number of sulfur is 5. (The valence shell of sulfur has been expanded to 10 electrons.) The steric number determines the orientation in space of the valence-shell pairs. Table 3-1 shows the orientations expected for steric numbers of 2, 3, 4, 5, and 6. Each of the orientations is the one which minimizes electron-pair repulsion for that steric number. For example, for a steric number of 4, we might consider a square planar orientation, as shown in Fig.3-2. But in this orientation the interpair angle is 90, which produces a greater interpair repulsion than the tetrahedral orientation does. (That is, the pairs are closer Chapter 3: Molecular structure Page 59

around the As atom is predicted to be tetrahedral.

4 together.) Thus, for a steric number of 4, tetrahedral geometry is preferred over square-planar geometry. In AsCl 3 the steric number is 4, and so the orientation of valence-shell electron pairs around the As atom is predicted to be tetrahedral. In SF 4, with steric number of 5, the orientation is trigonal bipyramidal, as Table 3-1 shows. Table 3-1 Special orientations of electrons pairs around a central atom Steric number orientation Angles 2 Linear 180 O 3 Triangular planar 120 O 4 Tetrahedral o Chapter 3: Molecular structure Page 60

5 Trigonal Bipyramidal 90 o -120 o 6 90 o Octahedral Lone pairs and molecular geometry: The second step is to determine the number and location of lone pairs.

5 5 Trigonal Bipyramidal 90 o -120 o 6 90 o Octahedral Lone pairs and molecular geometry: The second step is to determine the number and location of lone pairs. This is really no problem in the case of AsCl 3. The Lewis structure shows that only one pair of electron; is a lone pair. Since all corners of a regular tetrahedron are equivalent, all we need to say is that the Ions pair is at a corner. (See Fig. 3-3) The resulting molecular shape is denned by the location of the four atoms aria is called a trigonal pyramid. Figure 3-3 The AsCl 4 molecule: Trigonal pyramid Chapter 3: Molecular structure Page 61

6 Example 3-1: Predict the shape of the chloride trifluoride molecule CLF 3 Fig 3-4 Possible orientation of ClF 3 The steric number is 5, so interpair repulsion is least when the five pairs occupy the corners of a trigonal bipyranids (Table 3-1). Because the molecule has two lone pairs, these have three possible orientations, as is shown in Fig Structure II in the illustration can be ruled out, because I and III each have fewer lone pair-lone pair repulsions at 90. Structure III is favored over I, because it has fewer lone pair-bonding pair repulsion at 90. Therefore, we predict III, a "T-shape," for GIF. Experiments show that the CIFs, molecule does indeed 3 hove This Shape but it is Slightly distorted the distortion is a accounted for by the repulsion between the two lone pairs and the axial bonding pairs. Table 3-2 summarizes the molecule geometries predicted for steric numbers 2 through 7. Chapter 3: Molecular structure Page 62

7 Table 3-2 Molecular geometry according to the VSER method: Chapter 3: Molecular structure Page 63

8 Valence-Bond Theory and Orbital Overlap Two approaches have been used for the purpose of describing the covalent bond and the electronic structures of molecules. At its most sophisticated level each approach employs quantum mechanics, but the basic assumptions of the two methods are quite different. The first approach, called valencebond (VB) theory, considers that when a pair of atoms forms a bond, the atomic orbitals of each atom remain essentially unchanged and that a pair of electrons occupies an orbital in. each of the atoms simultaneously. The second method, molecular-orbital (MO) " theory, assumes that the atomic orbitals of the original unbonded atoms become replaced by a new set of molecular energy levels, called molecular orbitals, and that the occupancy of these orbitals determines properties of the resulting molecule. Although the VB and MO methods appear to be quite different, it turns out that rigorous calculations using each method yield similar results. With the advent of sophisticated electronic computers many such calculations have been successfully completed, and the results support the usefulness of both the VB and MO models for covalent bonding. The hydrogen molecule Let us now reconsider the H 2 molecule and once more picture its formation from two isolated, ground-state H atoms. Each H atom has at the start a single electron in is atomic orbital. For identification purposes we will call the two H atoms A and B. After the covalent Chapter 3: Molecular structure Page 64

9 bond has been formed, we find that each electron now exists in the I s orbitals of both atoms. This can be shown schematically as It should be emphasized that we are not showing four electrons here, but only two occupying both orbitals at the same time. According to valence-bond theory simultanious occupaucy of orbitals of two atoms by a pair of electrons is possible if the orbitals overlap each other to an appreciable extent. Figure 3-5 Overlap of Is orbitals in H 2 (σ bond). Figure. 3-5 shows the boundary surfaces of the 1s orbitals of two bonded hydrogen atoms. The orbital overlap produces a region of enhanced electron probability density located directly between the nuclei. Note that the bond axis (the line connecting the two nuclei) passes through the middle of this region. Furthermore, the overlap region is symmetrical around the bond axis, because each atomic orbital is spherical. Chapter 3: Molecular structure Page 65

10 At this point we will borrow a term from MO theory. The bond in H 2 is a sigma (σ) bond, one in which the charge-cloud of the shared pair is centered on and is symmetrical around the bond axis. Such a charge cloud is said to have axial, or cylindrical, symmetry, The hydrogen fluoride molecule A sigma bond can also be formed as a result of the overlap of an s and a p orbital. Consider hydrogen fluoride, HF. Before bonding, a fluorine atom has the following ground-state electronic configuration: F 1s 2s 2p Two of the three 2p orbitals are filled. Assume that the unpaired electron is in the 2p x of a hydrogen atom overlaps one of these lobes end-on (Fig. 3-6), then the shared electron pair spends most of its time in a region which is centered on and symmetrical around the bond axis. The bond in HF is therefore a sigma bond. A σ bond can also be formed as the result of the overlap of two p orbitals, but the overlap must be end-to-end as in the fluorine molecule, F 2. Here the 2p : orbital of one F atom overlaps the 2p 2 orbital of the second as is shown in Fig Chapter 3: Molecular structure Page 66

11 Pi- bonding When p orbitals overlap sideways, the results are different. If we assume as before that the bond axis is the x axis and choose the 2p : orbitals for overlap (Fig. 3-8) the resulting sidc-to-side overlap produces enhanced electron probability density in two regions which are on opposite sides of the bond axis. This is characteristic of a pi (Π) bond, another term borrowed from MO theory. Multiple bonds In a double or triple bond one bond is always a σ bond, and the remaining bonds are π bonds. The nitrogen molecule N 2 provides an example of a triple bond. The ground-state electronic configuration of a nitrogen atom is N 1s 2s 2p Here the three unpaired electrons are in the 2p 6 2p y and 1p-, orbitals. Respectively. Each of these orbitels overlaps the corresponding orbital of the other atoms, the two p z orbitals overlap end-to-end to form a σ bond, the two 2p y orbitals, side-to-side to form a π bond, and the two 2p : orbitals, side-to-side to form a second π bond. Chapter 3: Molecular structure Page 67

12 Chapter 3: Molecular structure Page 68

13 These three bonds are shown separately as overlapping boundary surfaces in Fig. 3-9 The three overlaps together constitute the triple bond. Compare this with the simple Lewis structure Hybrid orbitals Carbon forms countless compounds in which its atoms bond covalently to four other atoms. The simplest of these is methane, CH 4. How can we describe the four covalent bonds in this molecule in terms of orbital overlap? The ground state electronic, configuration of C is C 1s 2s 2p Carbon thus appears to be able to form only two covalent bonds by contributing each of its two unpaired electrons to a shared pair. But the short-lived methylene (CH 2 ) molecule is much less stable than CH 4 In the methane molecule (Fig. 3-10) each H atom is located at the corner of a regular tetrahedron, shown inscribed in a cube in the drawing, so that the relationship between these two regular solids can be seen. In CH 4, all bond lengths are the same and the angle between each C H bond and any of the other three is the tetrahedral angle, The observed tetrahedral structure of methane is what we expect after applying VSEPR theory to this molecule. According to the Lewis structure for methane the carbon evidently uses all four of its valence electrons Chapter 3: Molecular structure Page 69

14 so that four C H bonds can be formed. It is not too difficult to see how carbon can form four bonds. Suppose that one of the 2S electrons is promoted to the vacant, but higher energy, 2p orbital. C 1s 2s 2p Now the C atom appears to be ready to form four σ bonds by overlap of its 2s and 2p orbitals with the 1s orbitals of four H atoms. The difficulty here is that if the bonding occurred this way, the CH 4 molecule would not be tetrahedral. Instead, its shape would be like that shown in Fig In Fig 3-11 a through c are shown the three C H bonds which would result from overlap of the three 1p orbitals of C with the Is orbitals of three H atoms. The fourth bond might go almost anywhere, because an s orbital is spherically symmetrical and good overlap is possible from any direction. If the last H is located as far away as possible from the other H atoms in order to minimize inter electronic repulsion, then it goes in the position indicated in d. The entire proposed CH 4 structure is shown in Fig If these orbitals were used in bonding, methane would evidently have the shape of a trigonal pyramid, but it does not. In CH 4 all bond angles are equal and all H atoms are equivalent. The experimentally determined structure of methane is tetrahedral. How can we account for it using the s and p orbitals of carbon? The answer is that the ground-state set of s and p orbitals of carbon is replaced by a new set which is suitable for forming four equivalent bonds, each at the tetrahedral angle from each of the others. This may sound like a kind of orbital sleight of hand, and so in order to aid understanding of this replacement we will Chapter 3: Molecular structure Page 70

15 pause to consider first two simpler cases, the bonding of beryllium and boron. sp Hybrid orbitals Beryllium (Z =4) forms a hydrogen compound which at high temperatures exists as discrete BeH 2 molecules. The ground-state electronic configuration of a Be atom is B 1s 2s 2p The two bonds in BeH 2 are found to be oriented at 180 from each other; that is, the molecule is linear. How does this come about? When a Be atom forms its two bonds, its 2S and one of its 2p orbitals are replaced by a pair of new orbitals, and these new orbitals, hybrid orbitals, are used for bonding, that each orbital corresponds to a solution, a wave function, to the Schrodinger wave equation. Because the wave equation is a differential equation, any set of its solutions can be combined mathematically to form a new set of wave functions which are also solutions. These new wave functions are said to be hybrids of the original ones and correspond to a set of hybrid orbitals.) Perhaps some pictures will help. At the left of Fig are shown an s and a p orbital. In the illustration the plus and minus signs are not charges. Each is the algebraic sign of the wave function in the designated lobe of the orbital. Now we will Chapter 3: Molecular structure Page 71

16 combine or mix the orbitals, first (upper-right drawing) by adding the p to the s. The result is a hybrid orbital, in which the density of electronic charge has increased where the original wave functions had the same sign and has decreased where they had opposite signs. This hybrid orbital, called an sp orbital, is highly directional; overlap is favored in the direction of its large major lobe. Subtraction of the original s and p orbitals (lower-right drawing) yields the second hybrid orbital. It is equivalent to the first, but points 180 away. Thus by combining or mixing two nonequivalent orbitals (one is an s and the other, a p) we have obtained two equivalent sp hybrid orbitals. Chapter 3: Molecular structure Page 72

Covalent Compounds: Bonding Theories and Molecular Structure

CHM 123 Chapter 8 Covalent Compounds: Bonding Theories and Molecular Structure 8.1 Molecular shapes and VSEPR theory VSEPR theory proposes that the geometric arrangement of terminal atoms, or groups of