TOPICS
3.8 Chiral molecules
A molecule is chiral if it is non-superposable on its mirror image.†
Helical chains such as Se1(Figure 3.16a) may be right- or left-handed and are chiral. Six-coordinate complexes such as [Cr(acac)3] ([acac], see Table 6.7) in which there are three didentate chelating ligands also possess non-super-posable mirror images (Figure 3.16b). Chiral molecules can rotate the plane of plane-polarized light (Figure 3.17). This property is known as optical activity and the two mirror images are known as optical isomers or enantiomers.
Enantiomers rotate the light to equal extents, but in opposite directions, the dextrorotatory (d) enantiomer to the right and the laevorotatory (l) to the left (see Box 3.2). The Fig. 3.16 A pair of enantiomers consists of two molecular species which are mirror images of each other and are non-superposable. (a) Helical Se1 has either a right- or left-handedness. (b) The six-coordinate complex [Cr(acac)3] contains three identical didentate, chelating ligands; the labels and describe the absolute configuration of the molecule (seeBox 3.2).
†This definition is taken from Basic Terminology of Stereochemistry:
IUPAC Recommendations 1996 (1996) Pure and Applied Chemistry, vol. 68, p. 2193.
Chapter 3 . Chiral molecules 95
amount of rotation and its sign depend upon the wavelength of the incident light. At this point, we note that the observa-tion of optical activity depends upon chemical properties of the chiral molecule; if the two enantiomers interconvert rapidly to give an equilibrium mixture containing equal amounts of the two forms, no overall rotation occurs. A mixture of equal amounts of two enantiomers is called a racemate or racemic mixture. Chiral complexes and the separation of enantiomers are discussed further in Section 19.8.
The rotation, , may be measured in an instrument called a polarimeter(Figure 3.17). In practice, the amount of rotation depends upon the wavelength of the light, temperature and the concentration of compound present in solution. The speci-fic rotation, [], for a chiral compound in solution is given by equation 3.7. Light of a single frequency is used for specific rotation measurements and a common choice is the sodium D-linein the emission spectrum of atomic sodium; the specific rotation at this wavelength is denoted as½D.
½ ¼
c ‘ ð3:7Þ
in which ¼ observed rotation, ‘ ¼ path length of solution in the polarimeter (in dm) and c¼ concentration (in g cm3).
Fig. 3.17 One enantiomer of a chiral compound rotates the plane of polarized light through a characteristic angle, 8; the instrument used to measure this rotation is called a
polarimeter. The direction indicated (a clockwise rotation as we view the light as it emerges from the polarimeter) is designated asþ8. The other enantiomer of the same compound would rotate the plane of polarized light through an angle8.
CHEMICAL AND THEORETICAL BACKGROUND Box 3.2 Nomenclature of chiral compounds The nomenclature of chiral compounds is complicated.
Historically, compounds were described in terms of the sign of the rotation of plane-polarized light; the rotation was denoted (þ) or d for dextrorotatory, and () or l for laevorotatory. The sign and magnitude of rotation are often dependent on the wavelength of light and this was incorporated in the descriptor: ()589 or ()D (where D stands for the sodium D-line at a wavelength of 589 nm).
Whilst this system is useful provided that the wavelength is specified, it is purely defined in terms of an observable (the rotation); there is no direct relationship with the absolute configuration of the molecule.
This problem was first addressed in organic chemistry where a chosen reference compound, glyceraldehyde, was arbitrarily assigned, one absolute configuration to the (þ) and the other to the () enantiomer. The (þ) form was assigned aDabsolute configuration and the () form, anL
configuration. Chemical transformations between organic molecules then allowed the assignment of D or L absolute configurations to be related to the arbitrarily assigned glycer-aldehyde configuration. A consequence is that, for many organic molecules, the () enantiomer may possess aD(not an L) configuration! Additionally, it is not always easy to relate aDorLconfiguration of a highly complicated organic molecule back to the configuration of glyceraldehyde. As a matter of interest, the original arbitrarily assigned configura-tion to (þ)-(D) glyceraldehyde has been shown to be correct by anomalous dispersion X-ray experiments.
In order to describe the absolute configuration of an organic molecule, the Cahn–Ingold–Prelog system was introduced.
The descriptors R and S refer to the absolute arrangement of the groups about a centre. A complete description of a molecule will include both the sign of the rotation and the absolute configuration, e.g. (þ)589-(R).
Unfortunately, the Cahn–Ingold–Prelog rules are not directly applicable to most inorganic systems. For example, the three chelating ligands in [Cr(en)3]3þ (en ¼ H2NCH2CH2NH2) are identical and ‘priorities’ (an integral part of the Cahn–Ingold–Prelog rules) cannot be assigned to individual nitrogen-donor atoms. Descriptions based upon the observable rotation are, of course, useful, for example, (þ)589-[Cr(en)3]3þ and ()589-[Cr(en)3]3þ. However, these convey no information about the absolute configurations of the complexes.
A number of schemes have been introduced to describe the configurations of such compounds, the most useful of which is the IUPAC recommended and system. This is exemplified in Figure 3.16b with the structures of the enantiomers of [Cr(acac)3].
For further discussion: see Box 19.2 and Section 19.8.
Further reading
Basic Terminology of Stereochemistry: IUPAC Recommenda-tions 1996 (1996) Pure and Applied Chemistry, vol. 68, p. 2193.
The importance of chirality is clearly seen in, for example, dramatic differences in the activities of different enantiomers of chiral drugs.†
A helical chain such as Se1is easy to recognize, but it is not always such a facile task to identify a chiral compound by attempting to convince oneself that it is, or is not, non-superposable on its mirror image. Symmetry considerations come to our aid: a chiral molecular species must lack an improper (Sn) axis of symmetry.
A chiral molecule lacks an improper (Sn) axis of symmetry.
Another commonly used criterion for identifying a chiral species is the lack of an inversion centre, i, and plane of symmetry, . However, both of these properties are compatible with the criterion given above, since we can rewrite the symmetry operations i and in terms of the improper rotations S2 and S1 respectively. (See problem 3.25 at the end of the chapter.) However, a word of caution: there are a few species that are non-chiral (achiral) despite lacking an inversion centre, i, and plane of symmetry, .
Worked example 3.9 Chiral species
The oxalate ligand, [C2O4]2, is a didentate ligand and the structure of the complex ion [Fe(ox)3]3is shown below. The view in the right-hand diagram is along one OFeO axis.
Confirm that the point group to which the ion belongs is D3 and that members of this point group are chiral.
(a) (b)
Using the scheme in Figure 3.10:
START
Is the molecular ion linear? No Does it have Td, Oh or Ih
symmetry? No
Is there a Cnaxis? Yes; a C3axis;
perpendicular to the plane of the paper in diagram (a)
Are there 3 C2axes
perpendicular to the principal axis?
Yes; one runs vertically through the Fe centre in diagram (b)
Is there a h plane (perpendicular to the
principal axis)? No
Are there n dplanes (containing the principal
axis)? No
STOP The point group is D3.
No centre of symmetry or planes of symmetry have been identified and this alone is sufficient to confirm that molecular species in the D3point group are chiral.
Self-study exercise
By referring to the character table (Appendix 3) for the D3point group, confirm that the symmetry elements of the D3point group do not include i, or Snaxis.
Glossary
The following terms have been introduced in this chapter.
Do you know what they mean?
q symmetry element q symmetry operator q identity operator (E) q rotation axis (Cn)
q plane of reflection (h, vor d)
q centre of symmetry or inversion centre (i) q improper rotation axis (Sn)
q point group
q translational degrees of freedom q rotational degrees of freedom q vibrational degrees of freedom q normal mode of vibration q degenerate modes of vibration q selection rule (for an IR-active mode) q fundamental absorption
q chiral species
q enantiomer (optical isomer) q racemic mixture
q specific rotation
Further reading
Symmetry and group theory
P.W. Atkins, M.S. Child and C.S.G. Phillips (1970) Tables for Group Theory, Oxford University Press, Oxford – A set of
†A relevant article is: E. Thall (1996) Journal of Chemical Education, vol. 73, p. 481 – ‘When drug molecules look in the mirror’.
Chapter 3 . Glossary 97
character tables with useful additional notes and symmetry diagrams.
R.L. Carter (1998) Molecular Symmetry and Group Theory, Wiley, New York – An introduction to molecular symmetry and group theory as applied to chemical problems including vibrational spectroscopy.
F.A. Cotton (1990) Chemical Applications of Group Theory, 3rd edn, Wiley, New York – A more mathematical treatment of symmetry and its importance in chemistry.
G. Davidson (1991) Group Theory for Chemists, Macmillan, London – An excellent introduction to group theory with examples and exercises.
J.E. Huheey, E.A. Keiter and R.L. Keiter (1993) Inorganic Chem-istry: Principles of Structure and Reactivity, 4th edn, Harper Collins, New York – Chapter 3 provides a useful, and readable, introduction to symmetry and group theory.
S.F.A. Kettle (1985) Symmetry and Structure, Wiley, Chichester – A detailed, but readable, account of symmetry and group theory.
J.S. Ogden (2001) Introduction to Molecular Symmetry, Oxford University Press, Oxford – An Oxford Chemistry Primer that provides a concise introduction to group theory and its applications.
A. Rodger and P.M. Rodger (1995) Molecular Geometry, Butterworth-Heinemann, Oxford – A useful, clear text for student use.
D.F. Shriver and P.W. Atkins (1999) Inorganic Chemistry, 3rd edn, Oxford University Press, Oxford – Contains a clear and concise introduction to symmetry and symmetry-related topics.
A.F. Wells (1984) Structural Inorganic Chemistry, 5th edn, Oxford University Press, Oxford – A definitive work on structural inorganic chemistry; Chapter 2 gives a concise introduction to crystal symmetry.
Infrared spectroscopy
E.A.V. Ebsworth, D.W.H. Rankin and S. Cradock (1991) Structural Methods in Inorganic Chemistry, 2nd edn, Black-well Scientific Publications, Oxford – Chapter 5 deals with vibrational spectroscopy in detail.
S.F.A. Kettle (1985) Symmetry and Structure, Wiley, Chichester – Chapter 9 deals with the relationship between molecular symmetry and molecular vibrations.
K. Nakamoto (1997) Infrared and Raman Spectra of Inorganic and Coordination Compounds, 5th edn, Wiley, New York – Part A: Theory and Applications in Inorganic Chemistry – An invaluable reference book for all practising experimental inorganic chemists, and including details of normal coordi-nate analysis.
Problems
Some of these questions require the use of Figure 3.10
3.1 Give the structures of the following molecules: (a) BCl3; (b) SO2; (c) PBr3; (d) CS2; (e) CHF3. Which molecules are polar?
3.2 In group theory, what is meant by the symbols (a) E, (b) , (c) Cnand (d) Sn? What is the distinction between planes labelled h, v, v’ and d?
3.3 For each of the following two-dimensional shapes, determine the highest order rotation axis of symmetry.
(a)
(b)
(c) (d)
3.4 Draw the structure of SO2and identify its symmetry properties.
3.5 The structure of H2O2was shown in Figure 1.16. Apart from the operator E, H2O2possesses only one other symmetry operator. What is it?
3.6 By drawing appropriate diagrams, illustrate the fact that BF3possesses a 3-fold axis, three 2-fold axes, and four
planes of symmetry. Give appropriate labels to these symmetry elements.
3.7 Using the answer to problem 3.6 to help you, deduce which symmetry elements are lost on going from (a) BF3to BClF2and (b) BClF2to BBrClF. (c) Which symmetry element (apart from E) is common to all three molecules?
3.8 Which of the following molecules or ions contain (a) a C3 axis but no hplane, and (b) a C3axis and a hplane: NH3; SO3; PBr3; AlCl3; [SO4]2; [NO3]?
3.9 Which of the following molecules contains a C4axis and a
hplane: CCl4; [ICl4]; [SO4]2; SiF4; XeF4? 3.10 How many mirror planes do each of the following
molecules contain: (a) SF4; (b) H2S; (c) SF6; (d) SOF4; (e) SO2; (f ) SO3?
3.11 (a) What structure would you expect Si2H6to possess?
(b) Draw the structure of the conformer most favoured in terms of steric energy. (c) Does this conformer possess an inversion centre? (d) Draw the structure of the conformer least favoured in terms of steric energy. (e) Does this conformer possess an inversion centre?
3.12 Which of the following species contain inversion centres?
(a) BF3; (b) SiF4; (c) XeF4; (d) PF5; (e) [XeF5]; (f ) SF6; (g) C2F4; (h) H2C¼C¼CH2.
3.13 Explain what is meant by an1-fold axis of rotation.
3.14 To which point group does NF3belong?
3.15 The point group of [AuCl2]is D1h. What shape is this ion?
3.16 Determine the point group of SF5Cl.
3.17 The point group of BrF3is C2v. Draw the structure of BrF3 and compare your answer with the predictions of VSEPR theory.
3.18 In worked example 1.14, we predicted the structure of the [XeF5]ion. Confirm that this structure is consistent with D5hsymmetry.
3.19 Assign a point group to each member in the series (a) CCl4, (b) CCl3F, (c) CCl2F2, (d) CClF3and (e) CF4.
3.20 (a) Deduce the point group of SF4. (b) Is SOF4in the same point group?
3.21 Which of the following point groups possesses the highest number of symmetry elements: (a) Oh; (b) Td; (c) Ih? 3.22 Determine the number of degrees of vibrational freedom
for each of the following: (a) SO2; (b) SiH4; (c) HCN; (d) H2O; (e) BF3.
3.23 How many normal modes of vibration are IR active for (a) H2O, (b) SiF4, (c) PCl3, (d) AlCl3, (e) CS2and (f ) HCN?
3.24 Explain what is meant by the terms (a) chiral;
(b) enantiomer; (c) helical chain.
3.25 Confirm that the symmetry operation of (a) inversion is equivalent to an S2improper rotation, and (b) reflection through a plane is equivalent to an S1improper rotation.
Web-based problems
These problems are designed to introduce you to the website that accompanies this book. Visit the website:
www.pearsoned.co.uk/housecroft
and then navigate to the Student Resources site for Chapter 3 of the 2nd edition of Inorganic Chemistry by Housecroft and Sharpe.
3.26 Open the structure file for problem 3.26: this is the structure of PF5. (a) Orientate the structure so that you are looking down the C3axis. Where is the hplane with respect to this axis? (b) Locate three C2axes in PF5.
(c) Locate three vplanes in PF5. (d) To what point group does PF5belong?
3.27 Open the structure file for problem 3.27 which shows the structure of NH2Cl. (a) How many planes of symmetry does NH2Cl possess? (b) Does NH2Cl possess any axes of rotation? (c) Confirm that NH2Cl belongs to the Cspoint group. (d) Detail what is meant by the statement: ‘On going from NH3to NH2Cl, the symmetry is lowered’.
3.28 Open the structure file for problem 3.28: this shows the structure of OsO4, which has Tdsymmetry. (a) Orientate the molecule so that you are looking down an O–Os bond, O atom towards you. What rotation axis runs along this bond? (b) The character table for the Tdpoint group shows the notation ‘8C3’. What does this mean? By manipulating the structure, perform the corresponding symmetry operations on OsO4.
3.29 Open the structure file for problem 3.29: this shows the structure of [Co(en)3]3þwhere en stands for the didentate ligand H2NCH2CH2NH2; the H atoms are omitted from the structure. The complex [Co(en)3]3þis generally described as being octahedral. Look at the character table for the Ohpoint group. Why does [Co(en)3]3þnot possess Ohsymmetry? What does this tell you about the use of the word ‘octahedral’ when used a description of a complex such as [Co(en)3]3þ?
3.30 Open the structure file for problem 3.30: this shows the structure of C2Cl6in the preferred staggered
conformation. (a) Orientate the structure so you are looking along the C–C bond. You should be able to see six Cl atoms forming an apparent hexagon around two superimposed C atoms. Why is the principal axis a C3axis and not a C6axis? (b) Explain why an S6axis is coincident with the C3axis. (c) By referring to the appropriate character table inAppendix 3, confirm that C2Cl6has D3d symmetry.
3.31 Open the structure file for problem 3.31: this shows the structure of -P4S3. (a) Orientate the structure so that the unique P atom is closest to you and the P3triangle coincides with the plane of the screen. You are looking down the principal axis of -P4S3. What type of axis is it?
(b) Show that the molecule does not have any other axes of rotation. (c) How many planes of symmetry does the molecule possess? Are they v, hor dplanes?
(d) Confirm that -P4S3belongs to the C3vpoint group.
Chapter 3 . Problems 99