124
M.C. Bacchus-Montabonel
Fig. 6.2 Internal Jacobi
coordinates
manifold, a similar smooth avoided crossing is observed for the 4 Σ potential energy curves. But a strong interaction between the 4 Π entry channel and the upper
4 Π{C(2s 2 2p 2 ) 1 D + S + (3s 2 3p 3 ) 4 S} level is exhibited around R = 4 a.u. It corresponds to a strong radial coupling, about 10 a.u. high which might be determinant
in the description of the charge transfer process (Fig. 6.1c). A very peaked radial
coupling appears also between states 1 4 Π and 2 4 Π in the repulsive part of the potential energy curves.
We have performed the same theoretical treatment for the C 2+ + CO and C 2+ +
N 2 isoelectronic collision systems. The geometry has been described using the internal Jacobi coordinates {R, r, α} with the origin at the centre of mass of the target
molecule (see Fig. 6.2). The equilibrium geometries of the CO and N 2 diatomics
have been optimized, respectively r CO = 2.140535 a.u. and r N 2 = 2.0749 a.u., and
provide accurate ionization potentials [7, 12]. The orientation of the projectile toward the molecular target may be studied for different values of the angle α, from
linear to perpendicular geometry (α = 90 ◦ ). The angle α = 180 ◦ corresponds to the
collision in the linear approach toward the oxygen atom for the C 2+ + CO charge
transfer.
Considering the symmetry of the entrance channels, respectively C 2+ (1s 2 2s 2 ) 1 S+
CO( 1 Σ + ) and C 2+ (1s 2 2s 2 ) 1 S + N 2 ( 1 Σ +
g ), only 1 Σ + levels could be involved in
the process by means of radial coupling, and 1 Π levels by means of rotational coupling. Seven levels have thus been taken into account in the calculation for each
system:
C 2+ (1s 2 2s 2 ) 1 S + CO(1Σ + )/N 2 ( 1 Σ +
g )
4 1 Σ +
C + (1s 2 2s 2 2p) 2 P + CO
+ (B 2 Σ + )/N
+
2 ( 2 Σ +
u )
3 1 Σ + , 3 1 Π
C + (1s 2 2s 2 2p) 2 P + CO
+ (A 2 Π)/N
+
2 ( 2 Π u )
2 1 Σ + , 2 1 Π
C + (1s 2 2s 2 2p) 2 P + CO
+ (A 2 Σ + )/N
+
2 ( 2 Σ +
g )
1 1 Σ + , 1 1 Π
The potential energy curves of these isoelectronic systems are presented respectively in Figs. 6.3a, c. They show very similar features, with a relatively smooth
avoided crossing around 6–7 a.u. between the entrance channel and the 3 1 Σ + level,
as well as between respectively the 2–3 1 Σ + and 1–2 1 Σ + states. A sharper avoided
crossing may be observed at shorter range between the entrance channel and the
highest 3 1 Σ + exit channel as exhibited in Fig. 6.3b for the C 2+ + CO system.
M.C. Bacchus-Montabonel
Fig. 6.2 Internal Jacobi
coordinates
manifold, a similar smooth avoided crossing is observed for the 4 Σ potential energy curves. But a strong interaction between the 4 Π entry channel and the upper
4 Π{C(2s 2 2p 2 ) 1 D + S + (3s 2 3p 3 ) 4 S} level is exhibited around R = 4 a.u. It corresponds to a strong radial coupling, about 10 a.u. high which might be determinant
in the description of the charge transfer process (Fig. 6.1c). A very peaked radial
coupling appears also between states 1 4 Π and 2 4 Π in the repulsive part of the potential energy curves.
We have performed the same theoretical treatment for the C 2+ + CO and C 2+ +
N 2 isoelectronic collision systems. The geometry has been described using the internal Jacobi coordinates {R, r, α} with the origin at the centre of mass of the target
molecule (see Fig. 6.2). The equilibrium geometries of the CO and N 2 diatomics
have been optimized, respectively r CO = 2.140535 a.u. and r N 2 = 2.0749 a.u., and
provide accurate ionization potentials [7, 12]. The orientation of the projectile toward the molecular target may be studied for different values of the angle α, from
linear to perpendicular geometry (α = 90 ◦ ). The angle α = 180 ◦ corresponds to the
collision in the linear approach toward the oxygen atom for the C 2+ + CO charge
transfer.
Considering the symmetry of the entrance channels, respectively C 2+ (1s 2 2s 2 ) 1 S+
CO( 1 Σ + ) and C 2+ (1s 2 2s 2 ) 1 S + N 2 ( 1 Σ +
g ), only 1 Σ + levels could be involved in
the process by means of radial coupling, and 1 Π levels by means of rotational coupling. Seven levels have thus been taken into account in the calculation for each
system:
C 2+ (1s 2 2s 2 ) 1 S + CO(1Σ + )/N 2 ( 1 Σ +
g )
4 1 Σ +
C + (1s 2 2s 2 2p) 2 P + CO
+ (B 2 Σ + )/N
+
2 ( 2 Σ +
u )
3 1 Σ + , 3 1 Π
C + (1s 2 2s 2 2p) 2 P + CO
+ (A 2 Π)/N
+
2 ( 2 Π u )
2 1 Σ + , 2 1 Π
C + (1s 2 2s 2 2p) 2 P + CO
+ (A 2 Σ + )/N
+
2 ( 2 Σ +
g )
1 1 Σ + , 1 1 Π
The potential energy curves of these isoelectronic systems are presented respectively in Figs. 6.3a, c. They show very similar features, with a relatively smooth
avoided crossing around 6–7 a.u. between the entrance channel and the 3 1 Σ + level,
as well as between respectively the 2–3 1 Σ + and 1–2 1 Σ + states. A sharper avoided
crossing may be observed at shorter range between the entrance channel and the
highest 3 1 Σ + exit channel as exhibited in Fig. 6.3b for the C 2+ + CO system.