5. (a) Work out the symmetry pint group of the following species. (1) S₂032 (ii) H3BO3 (iii) allene (C3H4) (b) Show figuratively using an appropriate example of C3v point group. C3¹'0vC3² = 0 (c) Show that the n-orbital, p₁+P2-P3-P40f cis-butadiene belongs to A₂ irreducible representation (IR).
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- Determine the point groups of the following molecules. a Fe(CO)5, which has a trigonal bipyramidal structure, b CO32, which has three resonance structures that contribute to its overall shape, c The perfectly staggered conformation of ethane, d The perfectly eclipsed conformer of ethane.Neopentane, C(CH3)4, has Tď symmetry, with character table provided below. Suppose the characters of a reducible representation of this point group are x(E) = 17, x(C3) = 2, x(C₂) = 5, x(S4) = -3, and x(od) = -5 (this is shown explicitly in the last row of the character table). (a) Use the T₁ irreducible representation to determine the order of the point group using the Little Orthogonality Theorem (Vallance Eq. 1.15.13, see Problem 3). (b) Determine how many times each irreducible representation in Ta is contained in this reducible representation. Td A₁ A₂ E Τ1 T₂ r E 1 1 2 3 3 17 8C3 1 1 -1 1 0 0 2 3C₂ 1 1 2 -1 6S4 1 -1 1 101 1.5 7 0 1 713 7. 1.5 -1 -1 60d -3 -1 -1 -5Give the ground state electron configurations of(a) Li2 (b) Be2 (c) C2 .Use the symmetry-specific nomenclature appropriate for homonuclear diatomics. Example, Sg would stand for σg. Enclose each MO in parenthesis followed by the number of electrons in that MO, e.g., the entry (1Sg)2 would represent 1σg2. Letter P then is used to represent a pair of π MO's.
- List the symmetry elements of the following molecules and name the point groups to which they belong: (a) staggered CH3CH3, (b) chair and boat cyclohexane, (c) B2H6, (d) [Co(en)3]3+, where en is 1,2-diaminoethane (ignore its detailed structure), (e) crown-shaped S8. Which of these molecules can be (i) polar, (ii) chiral?PCl3 belong to C3V point group ? (b) Write down the totally symmetric representation of the point group of PCl3. (c) What is a symmetry-adapted linear combination of atomic orbitals? (d) Construct a linear-combination of 3s(Cl) atomic orbitals, ?1, such that ?1 belongs to the totally symmetric representation of the point group of PCl3. (e) Construct a linear-combination of 3p(Cl) atomic orbitals, ?2, such that ?2 belongs to the totally symmetric representation of the point group of PCl3.Consider the ClO4 – anion. Use symmetry analysis to determine the orbitals used in bonding by the central atom. (a) As a consequence of the multiple Cn axes with n > 2, the pi bonding cannot be separated into perpendicular and parallel components as was done with SO3. Rather these orbitals must be operated on together, an inseparable pair.
- a )Find the representation of the C2v point group to which a px orbital belongs. b)The four symmetry-adapted linear combinations (SALCs) built from the Cl 3s orbitals in the square planar (D4h) [PtCl4]2– anion have symmetry A1g, B1g, and Eu. List all expected Pt – SALC orbital combinations. and What information does the extended 1D2 term symbol provide about a given atom?(b) Identify the symmetry elements of CO₂. Then consider CO₂ as being constructed from a carbon atom and an O2. Show whether your fragment orbitals are symmetric or anti-symmetric with respect to each of these. (c) Using the symmetry from part (b) identify which fragments can interact together and construct the corresponding molecular orbitals. To simplify this process, you can ignore the 20 orbital from O₂.Take the four hydrogen 1s orbitals of CH4 and determine how they transform under Td. b) Confirm that it is possible to reduce this representation to A1 + T2. c) With which atomic orbitals on C would it be possible to form MOs with H1s SALCs of symmetry A1 + T2?
- (a) Given the operator = -0 C₁¹ show that [‚Â] = 0 =0 (b) Decompose the representation below into the irreducible representations of C3v. C3v T E 17/0 2C3 1 30₂ 1 ] ] (c) With the use of diagrams, find the representation of the C₂ point group to which a day orbital belongs. ]Consider the three following molecules and answer the questions below.HC≡CHH2C=CH2H3C-CH3 (3 conformers with different symmetry)(a) For each molecule, including all conformers as indicated, draw the molecule, assign it toits point group, and draw on the diagram the symmetry elements that were used to makethe assignment. State in each case whether or not the species is dipolar and/or chiral.(b) If one hydrogen atom in each molecule is substituted by a chlorine atom, sketch the newmolecules and assign them to their point group. For this set of mono-chloro compounds: state the most common point group state how many are chiral state how many are dipolar state which molecule/conformer has the highest symmetry point group state which molecule/conformer has the lowest symmetry point group identify which of these molecules/conformers have three different H atomenvironments(c) For the dichlorinated versions of the molecules/conformers considered in part (a): state the most common point…(a) Identify the symmetry elements in ethene and in allene, and assign each molecule to a point group. (b) Consider the biphenyl molecule, Ph–Ph, in which different conformations are possible according to the value of the dihedral angle between the planes of the two benzene rings: if this angle is 0°, the molecule is planar, if it is 90°, the two rings are perpendicular to one another. For each of the following dihedral angles, identify the symmetry elements present and hence assign the point group: (i) 0°, (ii) 90°, (iii) 45°, (iv) 60°.