12.3 A Look at the CI Method
191
(b) Use RSPT (as in Exercise 4.2b) for the exact ground-state energy E 0 and
analyze the M-dependence in the second- and fourth-order contributions.
12.4 Local ionization in the 2E-2O array:
(a) Use an analogous CI approach to determine the energy of the ionic state
resulting upon removing one electron from subsystem 1. The corresponding
one-hole (1h) configuration (spin symmetry S z =
1
2
) reads | 1g
= c 1gβ |
M
0
.
In addition, there are M −1 3h-2 p configurations, c 1gβ ˆ
C i |
M
0
, i = 2, . . . , M,
which differ from the 1h state by a double excitation on site i.
(b) Consider the ionization energy E 1g = E
−
1g − E 0 and compare the Mdependent CI result with the exact ionization energy (see Exercise 3.2). Examine the cases M = 1 and M 1.
(c) Adapt the ADC(2) scheme (Eq. 10.33) to the 2E-2O array and verify the
explicit size-consistency of the ionization energies.
References
1. Mertins F, Schirmer J (1996) Phys Rev A 53:2140
2. Schirmer J, Mertins F (1996a) Int J Quantum Chem 58:329
3. Meunier A, Levy B (1979) Int J Quantum Chem 16:955
191
(b) Use RSPT (as in Exercise 4.2b) for the exact ground-state energy E 0 and
analyze the M-dependence in the second- and fourth-order contributions.
12.4 Local ionization in the 2E-2O array:
(a) Use an analogous CI approach to determine the energy of the ionic state
resulting upon removing one electron from subsystem 1. The corresponding
one-hole (1h) configuration (spin symmetry S z =
1
2
) reads | 1g
= c 1gβ |
M
0
.
In addition, there are M −1 3h-2 p configurations, c 1gβ ˆ
C i |
M
0
, i = 2, . . . , M,
which differ from the 1h state by a double excitation on site i.
(b) Consider the ionization energy E 1g = E
−
1g − E 0 and compare the Mdependent CI result with the exact ionization energy (see Exercise 3.2). Examine the cases M = 1 and M 1.
(c) Adapt the ADC(2) scheme (Eq. 10.33) to the 2E-2O array and verify the
explicit size-consistency of the ionization energies.
References
1. Mertins F, Schirmer J (1996) Phys Rev A 53:2140
2. Schirmer J, Mertins F (1996a) Int J Quantum Chem 58:329
3. Meunier A, Levy B (1979) Int J Quantum Chem 16:955