Character table for dirhenium decacarbonyl of full non-rigid molecule group
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| 3. Results and Discussions It is now time to consider in detail the nonrigid molecule, dirhenium decacarbonyl. We first note that we consider the speed of the rotations of the molecule to be sufficiently high that makes the meantime dynamical symmetry of the molecule makes sense. Next, we note that each dynamic symmetry operation of this molecule consists of physical symmetry of Dirhenium Decacarbonyl which consist of 2 Re and 10 carbon atoms which are denoted by ab in Figure 2 . Since a and b do not have any affect on the permutation (a,b), it will be omitted and, therefore, the group will be generated by (1,2,3,4)(6,7,8,9),(1,6)(2,7)(3,8)(4,9)(5,10) and since the rotation on each CO gives the identity, the group will be given as G = 〈(1,2,3,4)(6,7,8,9),(1,6)(2,7)(3,8) (4,9)(5,10)〉 and when we use the package GAP, we have the following results: gap> G := Group((1,2,3,4)(6,7,8,9),(1,6)(2,7)(3,8) (4,9)(5,10)); Group([ (1,2,3,4)(6,7,8,9), (1,6)(2,7)(3,8)(4,9)(5,10) ]) gap> Elements(G); [ (), (1,2,3,4)(6,7,8,9), (1,3)(2,4)(6,8)(7,9), (1,4,3,2) (6,9,8,7), (1,6)(2,7)(3,8)(4,9)(5,10), (1,7,3,9)(2,8,4,6) (5,10), (1,8)(2,9)(3,6)(4,7)(5,10), (1,9,3,7)(2,6,4,8) (5,10) ] gap> Order(G); 8 Equivalently G = Z 2 ×Z 4 . We now apply GAP to get the character table of the molecule. gap> CT := Character table(G); Character table Group (1,2,3,4)(6,7,8,9), (gap > Display(CT); Download 0.64 Mb. Share with your friends:
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