Theory of MX Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 118

Fig. 8.7 (a) One-electron
excited state and (b) two-
electron excited state

a b

μσ μσ

νσ '

j σ '

i σ i σ

Similarly, the states like C ms C is C ns 0 C js 0 jF 0 i

also correspond to particle-hole
excitations, but in this case two electrons are excited from the valence band to the
conduction band, as shown in Fig. 8.7b . In the following calculations, we only treat
the former states and diagonalize the hamiltonian within the subspace of one-
electron excitations. This type of calculation is the simplest form of so-called
configurational interaction (CI) calculations and is often called single CI. In this
framework, the singlet excited state and the triplet excited state of S z ¼ 0 compo-
nent are expressed as

p

X

mi ðC m" C i" þ C m# C i# ÞjF 0 i

S

f S

jC

r i¼ð

1 = Þ (8.16)

mi

and

X

p 2

mi ðC m" C i" C m# C i# ÞjF 0 i;

T
r i¼ð

f T jC 1 = Þ (8.17)

mi

respectively. Here, the new functions, f S

mi and f T mi , are to be obtained by the following

eigenvalue equation:

M ðS;TÞ

mi;nj f ðS;TÞ

ðnjÞ¼E r f ðS;TÞ ðmiÞ ; (8.18)

r r

where

X

M S

mi;nj d mi;nj ðe m e i Þþ

Vf m ðlÞf n ðlÞf i ðlþ 1 Þf j ðlþ 1 Þ½l$ðlþ 1 Þ

l

þ 2 Vf m ðlÞf n ðlþ 1 Þf i ðlÞf j ðlþ 1 Þþ½l$ðlþ 1 Þ

þUf m ðlÞf n ðlÞf i ðlÞf j ðlÞ ;

(8.19)