Info

"See text for a discussion of C10(cap°), C20(off-belt), and C10(belt). The same building blocks listed in this table are found in C50, C70, C^, etc.

fcThe irreducible representations for each x*'1' in this table are given in Table 4.18.

"See text for a discussion of C10(cap°), C20(off-belt), and C10(belt). The same building blocks listed in this table are found in C50, C70, C^, etc.

fcThe irreducible representations for each x*'1' in this table are given in Table 4.18.

Table 4.18

Irreducible representations of atomic sites s for Dih of relevance to the C70 molecule" [4.15],

Table 4.18

Irreducible representations of atomic sites s for Dih of relevance to the C70 molecule" [4.15],

X"\D5h)

Irreducible representations

C10(cap°)

A\ + A'i + E[+ E" + E'2 + E'i

Qoioff-belt)

A\ + A'2 + A'i + A'[ + 2E[ + 2 E'{ + 2 E'2 + 2 E'{

Cio(belt)

A\ + A'2 + 2 E[ + 2 E'2

"The characters for the equivalence transformation for these sets of carbon atoms are given in Table 4.17.

"The characters for the equivalence transformation for these sets of carbon atoms are given in Table 4.17.

for C70 are found by summing the contributions from the various layers appropriately:

;T-(C70) = 2*as[C10(cap0)] + 2*as[C20(off-belt)] + *as[C10(belt)]. (4.4)

From Table 4.18 and Eq. (4.4), we then obtain the irreducible representations of D5h contained in the equivalence transformation for C70 as a whole:

*as(C70) = 5 A\ + 3 A'2 + 2 A" + 4 A'; + 8E[ + 8 E'2 + 6 E'[ + 6 (4.5)

If instead of C70 we were to consider an isomer of C90 with D5h symmetry, the same procedure as in Eqs. (4.4) and (4.5) would be used, except that an additional j-"-8-(off-belt) would be added to Eq. (4.4). The same building block approach could be used to describe C80 or C100 isomers with DSd symmetry using Tables 4.19 and 4.20.

The symmetries of the molecular vibrations (see Table 4.21) are then found using the relation

*m'v'(C7o) = Xas (C70) <g> *vec,or - *transia,ions - A'rotat,ons (4.6)

Table 4.19

Characters of atomic sites *as for Dsd of relevance to the DSd isomer of the C80

Table 4.19

Characters of atomic sites *as for Dsd of relevance to the DSd isomer of the C80

Xas(D¡d)

Was this article helpful?

0 0

Post a comment