Honors Chemistry

Honors Chemistry

Honors Chemistry

Honors Chemistry

Why Inorganic Chemistry? 2008 Dodge Nitro 2005 Dodge Neon 2008 Chevrolet Cobalt 2007 Saturn Ion Honors Chemistry

Lecture 6 Periodic properties of atoms Ionization energy Electron affinity Atom size Electronegativity Electronic structure of molecules VSEPR Molecular symmetry Group theory September 9, 2010 Honors Chemistry

Structures of Monocentric Molecules Molecules of a given ABnEm type are isostructural. Terminal atoms are arranged around the central atom such that Coulomb repulsion between electron pairs on central atom are minimized. Lone pairs tend to occupy more space around the central atom than bonding pairs. Multiple bonds occupy more space around the central atom than single bonds. Model applies to: main group elements transition metals with d0, d5, and d10 configuration Honors Chemistry X = Cl, Br, I; R = alkyl, aryl.

“Nature-made” Symmetry Honors Chemistry

“Nature-made” Symmetry Honors Chemistry

“Nature-made” Symmetry Honors Chemistry

“Man-made” Symmetry Honors Chemistry

“Man-made” Symmetry Honors Chemistry

“Chemist-made” Symmetry Honors Chemistry

From Molecular Formula to Properties Molecule Structure Point Group Orbital Symmetry Bonding Description Properties Honors Chemistry

Symmetry Elements and Operations Symmetry operation: reorientation of a body such that the initial and final orientations are indistinguishable. Symmetry element: geometrical entity (line, point, or plane) with respect to which a symmetry operation is performed. Honors Chemistry

Symmetry Elements and Operations INVERSION REFLECTION ROTATION IMPROPER ROTATION Honors Chemistry

Case Study: IF5(AB5E) 4 1 2 3 5 C41, C43, C2 5 2 1 4 3 5 4 3 sV2 sd2 Honors Chemistry

Case Study: IF5(AB5E) (cont.) C41, C43, C2 z C41, C43, C2 5 4 3 sV2 sV2 sd1 sd1 1 x 2 sd2 sd2 sV1 y sV1 E C41,C43 C2 sv1, sv2 sd1, sd2 The collection of all symmetry elements of a molecule form a Point Group. C4v E 2C4 C2 2sv 2sd1 Honors Chemistry

Character Table of Point Groups (See also Table 4-7 of textbook) h, Order of group = # symmetry operations 1+2+1+2+2 = 8 Classes of operations C4v 1E 2C4 1C2 2sv 2sd A1 1 1 1 1 1 A2 1 1 1 -1 -1 B1 1 -1 1 1 -1 B2 1 -1 1 -1 1 E 2 0 -2 0 0 c, Dimension of irreducible representations Honors Chemistry

Character Tables of Point Groups C2v E C2 svxz svyz A1 1 1 1 1 z, x2,y2, z2 A2 1 1 -1 -1 Rz, xy B1 1 -1 1 -1 x, Ry, xz B2 1 -1 -1 1 y, Rx, yz x, y, z axes or p orbitals at the central atom of a molecule; z axis coincides with highest order axis of the molecule xy, xz, yz planes defined by the x and y, x and z, or y and z axes, respectively Rx, Ry, Rz rotation around the x, y, and z axes, respectively Honors Chemistry

Point Group Assignment Does the molecule belong to a special group? linear molecules D∞h (CO2) or C∞v (HCl, CO) molecules with multiple high order axes: Oh octahedral (SF6) or Td tetrahedral (CH4) Molecule doesn’t have proper or improper rotation axes C1, no symmetry element except identity, CHClBrF Cs, molecule has only a symmetry plane, H2CCBrCl Ci, molecule has only an inversion center Molecule has only Sn axes, Sn Decision tree for C and D groups Identify Cn (highest order) No C2 Cn nC2 Cn There is sh no sh There is sh no sh There is sv no sv There is sd no sd Cnh Cnv Cn Dnh Dnd Dn Honors Chemistry

Irreducible and Reducible Representations C2v E C2 svxz svyz G 9 -1 3 1 A1 1 1 1 1 z, x2,y2, z2 A2 1 1 -1 -1 Rz, xy B1 1 -1 1 -1 x, Ry, xz B2 1 -1 -1 1 y, Rx, yz Honors Chemistry

You should be able to: Identify and show the symmetry operations of a molecule Determine the point group of a molecule Apply symmetry operations to atoms, orbitals or (x,y,z) axes centered at an atom in the molecule Determine the irreducible representation(s) corresponding to the p orbitals of the central atom of a molecule or of axes centered at the central atom of the molecule Determine if a group of 1 or more atoms, orbitals, or axes centered at atoms in a molecule are or are not a representation of the point group of a molecule Calculate the total degrees of freedom for a given molecule Determine the irreducible representations corresponding to translations and rotations of molecules Calculate the number of vibrations of a linear or non-linear molecule Decompose a reducible representation in irreducible representations Determine the symmetry of vibrations Determine which vibrations are IR and/or Raman active Determine if a molecule can have a dipole moment based on its symmetry/point group Honors Chemistry

Irreducible and Reducible Representations C2v E C2 svxz svyz G 9 -1 3 1 A1 1 1 1 1 z, x2,y2, z2 A2 1 1 -1 -1 Rz, xy B1 1 -1 1 -1 x, Ry, xz B2 1 -1 -1 1 y, Rx, yz # of classes of operations = # irreducible representations h = sum(cE(j))2, j represents irreducible representations Formula for reducing reducible representations: # of operations in class R character of reducible representation for class R character of irreducible representation for class R Honors Chemistry

Molecular Vibrations for H2O C2v E C2 svxz svyz G 9 -1 3 1 A1 1 1 1 1 z, x2,y2, z2 A2 1 1 -1 -1 Rz, xy B1 1 -1 1 -1 x, Ry, xz B2 1 -1 -1 1 y, Rx, yz Translations along x, y, and z: A1,B1,B2 Rotations around x, y, and z: A2,B1,B2 Vibrations: 2A1+B1 # (A1) = (1x9-1x1+3x1+1x1)/4 = 3 # (A2) = (1x9-1x1-3x1-1x1)/4 = 1 # (B1) = (1x9+1x1+3x1-1x1)/4 = 3 # (B2) = (1x9+1x1-3x1+1x1)/4 = 2 G = 3A1 + 1A2 + 3B1 + 2B2 A molecular vibration is infrared active if it changes the molecule dipole moment. In group theory, this rule translates in the fact that a vibration is IR active if it corresponds to an irreducible representation with the same symmetry as the cartesian coordinates x, y, and/or z. Polarizability is the relative tendency of a molecule’s charge to be distorted from its normal shape by an external electric field, such as an externally applied field or that caused by another molecule. A molecular vibration is Raman active if it changes the polarizability of the molecule . In group theory, this rule translates in the fact that a vibration is Raman active if it corresponds to an irreducible representation with the same symmetry as a product of cartesian coordinates , ie x2, y2, z2, xy, xz, yz. Honors Chemistry

Molecular Vibrations for H2O Table 4-11, p. 106 H H A1 Symmetric stretch IR active 3652 cm-1 B1 Antisymmetric 3756 cm-1 bend 1545 cm-1 Honors Chemistry

IR and Raman Spectroscopy IR Spectroscopy IR light source IR light detector Incident Light Transmitted Light Sample cell IR light detector Scattered Light Sample cell Incident Light IR light source Raman Spectroscopy Honors Chemistry

Q charge on each of two atoms separated by distance r Dipole Moment = Qr is the dipole moment Q charge on each of two atoms separated by distance r H - Br +0.123 -0.123 r = 1.415 Å e- charge = 0.123 x (1.602 x 10-19 C) x (1.415 x 10-10 m) = 2.779 x 10-30 Cm = 0.833 D D = Debye = 3.335 x 10-30 Cm H - Br Honors Chemistry

Dipole Moment Molecule types that may have dipole moment (Section 3-3): molecules with no inversion center molecules with coincident Cn axes molecules with one mirror plane and no Cn axis molecules with mirror planes that contain the coincident Cn axes molecules with no symmetry Only molecules of symmetry Cn, Cnv, and Cs, may have a dipole moment. Honors Chemistry