The ion is square planar

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra

Invariance, Ch Character tables at work: vibrations, selection rules and splitting

Problem

The ion

[\mathrm{PtCl_4}]^{2-}

is square planar, with the platinum at the origin and the chlorines at

\pm x

and

\pm y

, so its point group is

D_{4h}

with the axes of the chapter's

D_{4h}

table. Let

r_1

r_2

r_3

and

r_4

be the changes in the Pt-Cl bond lengths to the chlorines at

+x

+y

-x

and

-y

. ((a)) Find the characters of the representation carried by the four stretches on the ten classes of

D_{4h}

, and decompose it. ((b)) Apply the projection operator to

r_1

to build the combination belonging to each species you found, and find the second combination of the two-dimensional species by applying it to

r_2

. ((c)) Say which of these combinations can absorb infrared light and which can scatter light in the Raman effect.

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