Chemistry 3820 Lecture tes Dr.R.T.Boeré Page 14 2 Lewis dot diagrams and VSEPR structures Review Lewis structures and VSEPR from General Chemistry texts, and consult S-A-L: 3.1-3.3 One of the basic distinctions you must learn to make is between ionic and covalent compounds. You will do much better in this course, as well as in all other chemistry courses, if you know instinctively whether the material being discussed is one or the other. So how can you learn this? Short of sheer memory work for millions of compounds, it is very possible to learn this intuitive knowledge simply by developing the habit of asking yourself: Is this compound covalent (i.e. a molecule) or ionic (i.e. composed of two or more ions)? Even if the answer is not obvious, it can usually be deduced from the information given. Often it becomes very obvious if you stop and think about it. We start by considering simple binary compounds, for which this distinction is simple. A compound A B is generally considered ionic if the difference in electronegativity between A and B is 2 units. Thus for H-F, χ = (3.9 2.2) = 1.7, and HF is considered to be a (polar) covalent molecule. But Li F, 6c = (3.9 1.0) = 2.9, and thus LiF is ionic. te however that the ionic character of LiF is predominantly observed in the bulk solid - gaseous LiF (at very high temperature) will contain some Li-F molecules. We now focus on the structure and symmetry of the common covalent molecules, including common covalent or molecular ions (also known as complex ions), for which there are chemical bonds within the ionic unit. An example of the latter is an ion such as the sulfate ion, SO 4 2-, which has covalent S-O bonds. 2.1 Valence and Lewis diagrams In Chem. 1000 you learned how to write Lewis structures. The number of valence electrons is taken directly off the periodic table, and can be had from the group numbers directly. (Using the new numbering sequence, for p-block elements, subtract 10.) The number of valence electrons includes all s electrons since the last noble gas configuration plus the electrons of the block in which the element finds itself. Completely filled orbitals (except s orbitals) sink to much lower energy, becoming unavailable for bonding to elements in the subsequent block. Although Lewis diagrams are not 100% reliable, they have the advantage of organizing thousands of varied chemical compounds into a fast, easily understood diagrams which give a lot of useful information about the structure and reactivity of the compound. The essential postulate of this theory, first postulated in 1916 and still used today, is that bonds between atoms are due to shared electron pairs. Unshared electrons form lone pairs. Multiple bonds form between elements short of electrons. Double bonds have four shared electrons, triple bonds six. To write Lewis structures, follow the step-by-step guidelines given in the text (S-A-L) on p. 51-52. 1. Decide how many electrons are to be included in the diagram by adding together all the valence electrons provided by the atoms. Adjust for the ionic charge, if any. 2. Write the chemical symbols with the right connectivity (this cannot be deduced from the Lewis theory). 3. Distribute the electrons in pairs so that there is one pair of electrons between each pair of bonded atoms, and then supply electron pairs (to form multiple bonds or lone pairs) until each atom has an octet. 4. The formal charge gives some indication of the electron distribution in the molecule, where this is not even. For each atom, count the sum of the number of lone pair electrons and one from each bond-pair. The difference between this count and the valence of the atom is its formal charge. 5. Resonance is invoked whenever there is more than one way to distribute the electrons according to the above rules. The true structure is said to be a blend or hybrid of the various resonance isomers. 6. Finally, there are some elements for which exceptions to the octet rule occur. These include Be (4), B and Al (6 in some cases), as well as the "heavy" elements of period three and beyond, which may have 10 or 12 valence electrons about them. My rule of thumb in all such cases is to start from the outside and provide octets for the ligands first. If there are deficient or excess electrons at the central atom, verify that the atom is one of the ones mentioned here, and leave the diagram as produced.. Let's do some examples: CO 2, NO 3 -, SO 3 2-, NSF 3, XeF 4, IF 5, PF 5, SF 6. You were wondering Why can we ignore previous shells when counting the number of valence electrons?
Chemistry 3820 Lecture tes Dr.R.T.Boeré Page 15 2.2 VSEPR theory Just as Lewis structures give us a fast road to mapping the electrons of molecules, the Valence Shell Electron Pair Repulsion theory gives us a quick approach to determining molecular structure for many common main-group compounds. It is not much use for transition metal complexes, except those of the metals in their highest possible oxidation states. This concept, which is especially due to Prof. Ronald Gillespie of McMaster University (along with Prof. Nyholm of the U.K.), considers the electron pairs in molecules to be bound regions of negative charge, which naturally repel each other. The basic arrangements which minimize electron pair repulsions are: # of pairs basic shape hybridization of the central atom 2 linear sp 3 trigonal planar sp 2 4 tetrahedral sp 3 5 trigonal bipyramidal dsp 3 6 octahedral d 2 sp 3 But since the central atom may have lone pairs, which do not contribute to the description of the shape of the molecule, there are several derivatives of the above. Within the derivatives, the choice of structure is such as to minimize 90 interactions in the order: LP/LP repulsions stronger than LB/BP repulsions, than BP/BP repulsions. The logic behind this is that LP are less constrained than BP, therefore are larger. This also accounts for deviations in bond angle in structures such as water and ammonia. Hybridization can also be used to re-configure the atomic orbitals of the atoms in the molecule according to the observed geometry. te that when angles deviate from the ideal values, the extent of hybridization also changes. thus while CH 4 has four sp 3 hybrid orbitals on carbon, the two orbitals bonding to H in OH 2 are not exactly sp 3. They have marginally more "p" character, and less "s". The associated lone pair orbitals have correspondingly more "s" character. Quantum chemistry texts have formulae which express hybridization functions for given values of angles. These ideas on molecular structure are at best imprecise. A much more exact and extremely powerful approach to describing molecular shape exists, using symmetry and point group labels. We start by considering symmetry operations and elements. The following table summarizes the VSEPR structure method, and includes some common examples of the different structures that are encountered. The precise names of the structures are problematic, and indeed we need a better system. This can be done much more systematically using symmetry labels, and that will be the next topic we turn to. # of electron pairs at central atom* shape family hybridization of the central atom # of bond pairs 2 linear sp 2 0 # of lone pairs actual molecule shape linear 2 linear sp 1 1 linear (e.g. BeH + ) 3 triangular-planar sp 2 3 0 3 triangular-planar sp 2 2 1 triangular-planar angular 3 triangular-planar sp 2 1 2 linear (e.g. AlCl + 2 ) 4 tetrahedral sp 3 4 0 4 tetrahedral sp 3 3 1 tetrahedral triangular-pyramidal
Chemistry 3820 Lecture tes Dr.R.T.Boeré Page 16 4 tetrahedral sp 3 2 2 angular 4 tetrahedral sp 3 1 3 linear (e.g. H Cl) 5 triangular-bipyramidal dsp 3 5 0 5 triangular-bipyramidal dsp 3 4 1 triangular-bipyramidal 5 triangular-bipyramidal dsp 3 3 2 seesaw 5 triangular-bipyramidal dsp 3 2 3 T-shaped 6 octahedral d 2 sp 3 6 0 linear 6 octahedral d 2 sp 3 5 1 octahedral 6 octahedral d 2 sp 3 4 2 square-pyramidal * using any resonance isomer; double and triple bonds count as a single pair! square-planar
Chemistry 3820 Lecture tes Dr.R.T.Boeré Page 17 3 Molecular symmetry 3.1 Symmetry operations and elements Symmetry operation: The movement of a molecule relative to some symmetry element which generates an orientation of the molecule indistinguishable from the original. Symmetry element: A line, point or plane, with respect to which one or more symmetry operations may be performed. We designate the symmetry elements by their Schönflies symbols. The following symmetry elements are found in molecules: a) Identity Symbol: E This means do nothing. It represents the lowest order of symmetry. All molecules posses the identity symmetry element. The inclusion of this element may seem silly, but it is vital to the correct mathematical description of symmetry by group theory. te that the C 1 rotation axis, i.e. rotation by 360, is the same as the identity, so C 1 is never used. b) Proper rotation axes Symbol: C n (n = 2, 3, 4, 5, 6, 7, ) An axis about which the molecule may be rotated 2π/n radians. A two-fold rotation axis means rotation by π radians, or 180. A three-fold axis means rotation by 120, etc. A molecule may have more than one order of axis; that axis with the largest value of n (highest order) is called the principal rotation axis. The graphics show a molecule possessing a C 2 axis at right, and a C 3 axis below. To discover if a molecule has a given symmetry element, we perform the corresponding operation. If the new orientation is indistinguishable from the original, then the molecule is said to posses that symmetry operation. c) Mirror planes Symbol: s, s v, s h, s d σ σ v σ h σ d A non-specific mirror plane (possible only if this is the only symmetry element the molecule possesses. Vertical mirror plane is a plane of reflection containing the principle rotation axis. Horizontal mirror plane is a plane of reflection normal to the principle rotation axis. Dihedral mirror plane is a plane of reflection containing the principle rotation axis which also bisects two adjacent C 2 axes perpendicular to the principle rotation axis. d) Centre of symmetry Symbol: i Also called an inversion, it means simply that: invert the position of all the atoms with respect to the centre of symmetry of the molecule. In coordinate language, this means converting x, y, z to -x, -y, -z.
Chemistry 3820 Lecture tes Dr.R.T.Boeré Page 18 e) Improper rotation axes Symbol: S n (n = 3, 4, 5, 6, 7 ) Also called rotation-reflection axes, which accurately describes this type of element. One rotates by 2π/n radians, then reflects through σ h to get the new representation. The lower orders of S n are redundant. Thus S 1 = mirror plane, while S 2 = centre of symmetry, so that these are never used. Also, when a molecule possesses a proper axis and σ h, it is also considered to contain the corresponding improper axis. The first graphic shows the presence of an S 4 axis in a true tetrahedral molecule, which lies along the line of the C 2 axis (there are 3 of each in a tetrahedral molecule). The second figure depicts the redundancy and hence non-use of S 1 and S 2. 3.2 Point Groups Point groups is short for point symmetry groups. They are collections of symmetry elements which isolated real objects may possess. Clearly only certain symmetry elements will coexist in the same object. The names of the point groups are related to the names of the symmetry operations, and in some cases the same symbol does for both. Be careful to distinguish the two! With some practice, it is easy to assign the point groups of all but the most difficult cases. The flowchart shown at the right will help you is assigning the point groups. Be sure to know how to correctly interpret each question along the path to the correct assignment. te that the questions often prompt you to look for symmetry that you may have missed. Therefore whenever a question is asked that you have not yet considered, always go back to your picture or model and try to see if the indicated symmetry element may be present. 3.3 Polarity In order to have a permanent dipole moment, a molecule must not belong to a D group of any kind, nor T d, O h or I h. 3.4 Chirality In order to be chiral, a molecule must not posses an S n axis, nor a mirror plane, nor an inversion axis. (The latter two are equivalent to S 1 and S 2 ).
Chemistry 3820 Lecture tes Dr.R.T.Boeré Page 19 3.5 Examples of point groups C?v H-Cl Linear, unsymmetrical D?h O=C=O Linear, symmetrical T d GeH 4 Tetrahedral (but not CH 3 F!) O h SF 6 Octahedral (but not SF 5 Cl) I h [B 12 H 12 ] 2- Icosahedral (rare) C 1 CHFClBr symmetry elements except E C s NHF 2 Only a plane C i no examples Only an inversion centre C n H 2 O 2, S 2 Cl 2 Only an n fold rotation axis C nv H 2 O, SF 4, NH 3, XeOF 4, BrF 5 C nh B(OH) 3 D n [Cr(en) 3 ] 3+ D nd Mn 2 (CO) 10, Cp 2 Fe staggered D nh BF 3, XeF 4 Shortened Flowchart to Determine Point Group C v, D h, T d, O h, or I h? C n? n = principal axis σ? C s C 1 C i nc 2 C n? σ h? nσ v? C n nσ v? D n C nh C nv σ h? D nh D nd
Chemistry 3820 Lecture tes Dr.R.T.Boeré Page 20 Extended Flowchart To Determine Point Group Symmetry Linear? D v C v I Unique Cn? n = principal axis 6C5? Ih S2n 4C3? 3C4? O Oh S2n Cn? nσ d? 3S4? T Th Td Dnd 3C2? σ? C1 Ci Cs nc2 Cn? σ h? nσ v? Cn Cnh Cnv σ h? 2σ d? Dn D2d Dnh