Rotation Axis(Cn) Center of Symmetry In general present if you can draw a straight line from any n fold rotation axis s rotation by(360/n) point, through the center, to an equal distance the other side, and arrive at an identical point Can rotate by120° about the o·Cl bond and the molecule looks identical This is called a rotation ax tation axis, as rotate by 120(= 888 3603)to reach an identical o。。0 Center of No center of I symmetry ats symmetry Symmetry Operation n Axis - Symmetry Inversion Axis of rotary Inversion Rotoinversion Axis(Sn or n):nfold rotation combined with an inversion side of a center of symmetry has a similar point at an equal distance the er of 1=i 2 3=3-fold rotation Mac Symmetry Elements Point groups Electrical resistance Thermal expansion Magnetic susceptibility= Macroscopic symmetry 8 =3-fold rotation Macroscopically measured Translation symmetry mirror plane Combination of mirror, center of symmetry rotational symmetry, center of inversion point groups8 Can rotate by 120° about the C-Cl bond and the molecule looks identical Þ the H atoms are indistinguishable. This is called a rotation axis Þ in particular, a three fold rotation axis, as rotate by 120° (= 360°/3) to reach an identical configuration Rotation Axis (Cn) In general: n-fold rotation axis = rotation by (360°/n) “present if you can draw a straight line from any point, through the center, to an equal distance the other side, and arrive at an identical point”. Center of symmetry at S No center of symmetry (x,y,z) (-x,-y,-z) Center of Symmetry (Inversion symmetry) i Symmetry Operation Inversion every point on one side of a center of symmetry has a similar point at an equal distance on the opposite side of the center of symmetry. Rotoinversion Axis ¾¾ Symmetry Axis of Rotary Inversion Rotoinversion Axis (Sn or ) : n-fold rotation combined with an inversion. n 1 = i 2 = m 3 = 3-fold rotation + inversion 4 6 =3-fold rotation with perpendicular mirror plane Macroscopic Symmetry Elements: Point Groups Electrical resistance Thermal expansion Magnetic susceptibility Elastic constants Macroscopically measured properties Þ Macroscopic symmetry XÛ Translation symmetry Combination of mirror, center of symmetry, rotational symmetry, center of inversion Þ point groups