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By D. Wales, R.A. Christie, G.E. Ewing, B. Jeziorski, K.D. Jordan, K. Patkowski, K. Szalewicz, S.S. Xantheas

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Extra resources for Structure and Bonding, Volume 2

Sample text

Tx -- ~ y > . [*T,- ~ y > tiT, { z > , ['T, ~ z > , [*T,- ~ z > , ]'Tx -- ~- z > in which x, y, and z represent real components of the representation T,. Alternatively, the three components of TI may be written in complex form; thus for M = ] we would have I'TI g 1 > , I'Tx ~ 0 > . I'T1 ~- - 1 > in which 1, 0 and --1 designate the complex components of TI. The notation both for the real and complex components of T1 is designed to be reminiscent of atomic p-functions to which the T1 representation in the cubic group is closely related.

We shall then get relationships of the type shown in Eqs. (74). However, for later calculations it is useful to list the basis functions in 0 which ultimately become associated with a particular representation in D~. For example, in Eqs. (64) leA1 89 al > wlfich is a basis function in O, is associated with 16A1 U' X > , a basis function in O*. The latter, according to Table 8, goes over t o - ]6A1 E ' ~' > in D~. Hence ]6A1 ~ al > m a y be associated with 18A1 E' ~' > . Alternatively, it is seen t h a t when leA1 E ' a' > (in D~) is expanded in terms of basis functions in O, the expansion contains ]6A1 ~ al > (multiplied by a numerical coefficient).

They are E (x) --~ 4- ~ H x [ ( B 1 + C1) 2 - A ~ ] E (y) ~ -4- ~ H y [ ( A t - C1) 2 - BI~] (89) Therefore the principal components of the g-tensor are gx = 2[(B1 -{- CI)2-- AI~I gy = 2[(A I -- CI) 2 -- BI2[ gz = 2 ] ( A 1 - - B1)~-- C~[ (90) where absolute values are used to ensure that gx, gy and gz are positive quantities. Inserting the observed g-values into Eqs. 097 (92) It is assumed, and borne out by subsequent calculation, that the observed g-values are associated with the splitting of the lowest Kramers doublet.

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