MIT OpenCourseWarehttp://ocw.mit.edu 5.04 Principles of Inorganic Chemistry II �� Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. C C C HH H 5.04, Principles of Inorganic Chemistry II Prof. Daniel G. Nocera Lecture 5: Molecular Point Groups 2 The D point groups are distiguished from C point groups by the presence of rotation axes that are perpindicular to the principal axis of rotation. Dn : Cn and n⊥C2 (h = 2n) Example: Co(en)33+ is in the D3 point group, Reorient the moleculealong the (1,1,1) axis, i.e the C3 axis In identifying molecules belonging to this point group, if a Cn is present and one ⊥C2 axis is identified, then there must necessarily be (n–1)⊥C2s generated by rotation about Cn. Dnd : Cn, n⊥C2, nσd (dihedral mirror planes bisect the ⊥C2s) Example: allene is in the D2d point group, d d C2 HC2 C2 HH d Reorient the moleculealong the Cn Hd axisTwo C2s bisect σds. The example on the bottom on pg 3 of the Lecture 4 notes was a harbinger of this point group. As indicated there, it is often easier to see these perpendicular C2s by reorienting the molecule along the principal axis of rotation. H 5.04, Principles of Inorganic Chemistry II Lecture 5 Prof. Daniel G. Nocera Page 1 of 4 Note: Dnd point groups will contain i, when n is odd S102 S104 S106 S108 ≡≡≡≡E C5 C52 C53 C54 5σd (generated with C5 axis) 5⊥C2 (generated with C5 axis) S10, S103, S105, S107, S109 ≡i Dnh : Cn, n⊥C2, nσv, σh (h = 4n) C5 C2, d S102 S104 S106 S108 Ru Ru ≡≡≡≡ E, C5, C52, C53, C54 5σv 5⊥C2 S5, S53,S55, S57, S59 σh ′ when n is even, n σv and n σv22 C∞v : C∞ and ∞σv (h = ∞) linear molecules without an inversion center a σv is easily identified as the plane of the paper, by virtue of the C∞, ∞σvs are generated D∞h : C∞, ∞⊥C2, ∞σv, σh, i (h = ∞) linear molecules with an inversion center ≡the C∞, generates ∞σv and ∞C2 when working with this point group, it is often convenient to drop to D2h and then correlate up to D∞h 5.04, Principles of Inorganic Chemistry II Lecture 5 Prof. Daniel G. Nocera Page 2 of 4 Td : E, 8C3, 3C2, 6S4, 6σd (h = 24) through each face σd’s through each edge through each corner a cubic point group; the cubic nature of the point group is easiest to visualize by inscribing the tetrahedron within a cube Oh : E, 8C3, 6C2, 6C4, 3C2 (=C42), i, 6S4, 8S6, 3σh, 6σd (h = 48) through each face σh bisect faces of cube σd contains edges of cube C2 bisect edges of cube through each corner O : E, 8C3, 6C2, 6C4, 3C2 (=C42) A pure rotational subgroup of Oh, contains only the Cn’s of Oh point group T : E, 8C3, 3C2 A pure rotational subgroup of Td, contains only the Cn’s of Td point group a cubic point group; an octahedron inscribed within a cube O and T are rare point groups; whereas few molecules possess this symmetry, they are mathematically useful for molecules of Oh and Td, respectively Ih : generators are C3, C5, i (h = 120) the icosahedral point group Kh : generators are Cφ, Cφ’, i (h = ∞) the spherical point group 5.04, Principles of Inorganic Chemistry II Lecture 5 Prof. Daniel G. Nocera Page 3 of 4 Flow chaart for assiigning moleecular poinnt groups: 5.04, Principles of Inorganic Chemistry II Lecture 5Prof. Daniel G. Nocera Page 4 of 4