5 Application of the Uniformly Charged Sphere Stabilization
109
Table 5.1 Average parameters and its linear deviations (×10 5 ) of the lowest 1 S resonance for
V 0 = 1 a.u. All data are given in a.u.
Basis
Root
E res
ΔE res
Γ
Δ Γ
R res
(19,2)
7
0.35209
1
0.00286
3
16.8
8
0.35146
4
0.00211
11
19.8
9
0.35123
15
0.00182
19
23.1
10
0.35115
24
0.00173
25
26.6
11
0.35116
44
0.00151
16
30.8
12
0.35113
62
0.00135
17
35.9
(23,2)
7
0.35210
0
0.00285
0
16.8
8
0.35149
1
0.00208
2
19.7
9
0.35129
3
0.00186
5
22.6
10
0.35122
7
0.00174
9
25.6
11
0.35123
7
0.00174
28
28.8
12
0.35121
14
0.00169
50
32.1
(27,2)
7
0.35210
0
0.00285
0
16.8
8
0.35150
0
0.00208
0
19.7
9
0.35131
0
0.00185
1
22.6
10
0.35126
1
0.00178
2
25.4
11
0.35123
2
0.00176
6
28.3
12
0.35120
6
0.00174
17
31.5
(31,2)
7
0.35210
0
0.00286
0
16.8
8
0.35150
0
0.00208
0
19.6
9
0.35131
0
0.00185
0
22.5
10
0.35126
1
0.00177
1
25.4
11
0.35123
1
0.00175
1
28.3
12
0.35121
3
0.00172
5
31.1
ones were obtained for the stabilization curves with R res ≈ 70 a.u. (Table 5.4). Nevertheless, the good agreement between our estimations and reference results has not
been found for the all used AO sets but the tendency to improve our estimations is
observed.
The presented method should be considered as a modification of the uniformly
charged sphere stabilization including the new routine of the phase shift calculation.
This routine has two significant features. First one is in the using the parameters
of the external potential and energy of discrete level only. Second one is in the
stationarity of the tan δ l (E) with respect to the small variations of the energy of
quasidiscrete level. It should be noted that the requirement δE| E=E = 0 is not a
unique way to introduce the variational method. Another way is to define the optimal
V 0 value for the fixed energy from the variational equations.
109
Table 5.1 Average parameters and its linear deviations (×10 5 ) of the lowest 1 S resonance for
V 0 = 1 a.u. All data are given in a.u.
Basis
Root
E res
ΔE res
Γ
Δ Γ
R res
(19,2)
7
0.35209
1
0.00286
3
16.8
8
0.35146
4
0.00211
11
19.8
9
0.35123
15
0.00182
19
23.1
10
0.35115
24
0.00173
25
26.6
11
0.35116
44
0.00151
16
30.8
12
0.35113
62
0.00135
17
35.9
(23,2)
7
0.35210
0
0.00285
0
16.8
8
0.35149
1
0.00208
2
19.7
9
0.35129
3
0.00186
5
22.6
10
0.35122
7
0.00174
9
25.6
11
0.35123
7
0.00174
28
28.8
12
0.35121
14
0.00169
50
32.1
(27,2)
7
0.35210
0
0.00285
0
16.8
8
0.35150
0
0.00208
0
19.7
9
0.35131
0
0.00185
1
22.6
10
0.35126
1
0.00178
2
25.4
11
0.35123
2
0.00176
6
28.3
12
0.35120
6
0.00174
17
31.5
(31,2)
7
0.35210
0
0.00286
0
16.8
8
0.35150
0
0.00208
0
19.6
9
0.35131
0
0.00185
0
22.5
10
0.35126
1
0.00177
1
25.4
11
0.35123
1
0.00175
1
28.3
12
0.35121
3
0.00172
5
31.1
ones were obtained for the stabilization curves with R res ≈ 70 a.u. (Table 5.4). Nevertheless, the good agreement between our estimations and reference results has not
been found for the all used AO sets but the tendency to improve our estimations is
observed.
The presented method should be considered as a modification of the uniformly
charged sphere stabilization including the new routine of the phase shift calculation.
This routine has two significant features. First one is in the using the parameters
of the external potential and energy of discrete level only. Second one is in the
stationarity of the tan δ l (E) with respect to the small variations of the energy of
quasidiscrete level. It should be noted that the requirement δE| E=E = 0 is not a
unique way to introduce the variational method. Another way is to define the optimal
V 0 value for the fixed energy from the variational equations.