3 The Si2++H and Si3++He Collision Systems
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372
M.C. Bacchus-Montabonel and D. Talbi
b
E (a.u.)
radial coupling (a.u.)
−2.7
−2.8
−2.9
−3
E (a.u.)
a
0
−2.75
−0.5
−1
−1.5
−3
−3.25
−2
−2.5
2
4
6
8
10
12 14
R (a.u.)
−3.5
g12
−3.75
−3.1
−3.2
−4
−3.3
−4.25
−3.4
−4.5
−3.5
2
4
6
8
10
12
14
R (a.u.)
−4.75
5
4
3
2
1
2
4
6
8
10 12 14 16 18 20
R (a.u.)
Fig. 21.1 (a) Adiabatic potential energy curves for the 2 Σ+ (full lines) and 2 Π (dashed
lines) states of the collision system Si2+ + H. (1) 2 Σ+ ,2 Π{Si+ (3s2 3p)2 P + H+ }. (2) 2 Σ+
{Si2+ (3s2 )1 S + H(1s)}, entry channel. (b) Adiabatic potential energy curves for the
2 Σ+ (full lines) and 2 Π (dashed lines) states of the collision system Si3+ + He. (1) 2 Σ+ {Si2+
(3s2 )1 S + He+ (1s). (2) 2 Σ+ {Si3+ (3s) 2 S + He}, ground entry channel. (3) 2 Σ+ ,2 Π
{Si2+ (3s3p)3 P + He+ }. (4) 2 Σ+ ,2 Π{Si2+ (3s3p)1 P + He+ }. (5) 2 Σ+ ,2 Π{Si3+ (3p)2 P + He},
metastable entry channel
is a relatively simple collision system where only three molecular states are
involved, the 2 Σ+ entry channel and the 2 Σ+ and 2 Π states correlated to the oneelectron capture channel {Si+ (3s2 3p)2 P + H+ }. Such potentials are displayed in
Fig. 21.1a and present a sharp avoided crossing around R = 10.5 a.u. corresponding
to a peaked radial coupling matrix element, 2.47 a.u. high.
The Si3+ (3s)2 S + He collision system is also a simple molecular system
Si3+ (3s)2 S + He(1s2 )1 S → Si2+ (3s2 )1 S + He+ (1s)2 S,
but, for a complete treatment of the process, we have to take into account
simultaneously the charge transfer from the metastable Si3+ (3p) ion as molecular
states are close in energy and can interact. We have thus to consider also the reaction
Si3+ (3p)2 P + He(1s2 )1 S → Si2+ (3s3p)1,3 P + He+ (1s)2 S
which involves 2 Σ+ and 2 Π levels. The potential energy curves are presented
in Fig. 21.1b. The ground state Si3+ (3s)2 S + He entry channel leads to a simple
electron capture process. The potential energy curves present a pronounced
avoided crossing around R = 6.0 a.u. with the {Si2+ (3s2 )1 S + He+ (1s)2 S} exit
channel. A very sharp avoided crossing may also be observed around R = 7.0
a.u. between the metastable entry channels 2 Σ+ ,2 Π {Si3+ (3p)2 P + He(1s2 )1 S} and
the {Si2+ (3s3p)1 P + He+ (1s)2 S} in 2 Σ+ and 2 Π symmetries and a smoother
one, around R = 5.0 a.u., between the {Si2+ (3s3p)1 P + He+ (1s)2 S} and
21 Recombination by Electron Capture in the Interstellar Medium
b
10
rate coefficient(10−9 cm3s−1)
rate coefficient(10−9 cm3s−1)
a
1
10−1
10−2
10−3
103
104
105
T(K)
373
10
1
10−1
10−2
10−3
103
104
105
T(K)
Fig. 21.2 (a) Rate coefficients (10−9 cm3 s−1 ) for the charge transfer recombination processes
Si2+ + H. From Si2+ (3s2 ), (blue) this work; (red) [30]; (magenta) [31]; (green) [32]. From
Si2+ (3s3p), (light blue) [30]. (b) Rate coefficients (10−9 cm3 s−1 ) for the charge transfer recombination processes Si3+ + He. From Si3+ (3s), (blue) this work; (red) [35]; (green) [34]; (magenta)
[33]. From Si3+ (3p), (yellow) this work; (light blue) [35]
{Si2+ (3s3p)3 P + He+ (1s)2 S}2 Σ+ and 2 Π exit channels. At shorter internuclear
distance, around R = 3.2 a.u., an important avoided crossing between the
2 Σ+ {Si2+ (3s3p)3 P + He+ (1s)2 S} level and the ground state entry channel may also
be pointed out.
The collision dynamics has been performed for both systems. The rate coefficients for the Si2+ (3s2 )1 S + H system are presented in Fig. 21.2a and compared to
the SCVB ab-initio calculation of Clarke et al. [30] with radial coupling only, as well
as with the close-coupling approach of Gargaud et al. [31] using model potentials,
and the Landau-Zener analysis of Bates and Moiseiwitsch [32]. The different results
are in globally good agreement. As already noticed by Clarke et al. [30], their
quantal close-coupling approach differs slightly from the results of Gargaud et al.
[31] and Bates and Moiseiwitsch [32]. On the contrary, they are in good agreement
at high temperatures with the present ones using a semi-classical method, exhibiting,
of course, some discrepancies at lower temperatures related to trajectory effects
which are not considered in our theoretical approach. The Fig. 21.2a displays also
the results for the electron capture from the Si2+ (3s3p)3 P◦ metastable ion
Si2+ (3s3p)3 P◦ + H(1s)2 S → Si+ (3s3p2 )2 D + H+
→ Si+ (3s2 3p)2 P◦ + H+
determined by Clarke et al. [30] to be two orders of magnitude lower than the capture
by the ground state ion. Such process appears non determinant and so has not been
taken into account in our calculation.
374
Table 21.1 Rate coefficients
for charge transfer and
ionization processes in
the Si3+ + He collision
(in 10−9 cm3 s−1 )
M.C. Bacchus-Montabonel and D. Talbi
T(K)
500
1,000
2,000
3,000
5,000
10,000
20,000
30,000
40,000
50,000
100,000
kCT
0.08
0.10
0.15
0.21
0.33
0.62
1.14
1.58
1.97
2.31
3.60
kCT [34]
0.17
0.39
0.96
2.00
kion
0.00002
0.0065
0.05
0.15
0.29
1.28
kion [34]
0.00003
0.07
1.21
For the Si3+ + He system, the coupling equations were solved simultaneously
for all the levels involved in the charge transfer process from both the ground state
and the excited entry channels. The rate coefficients are displayed in Fig. 21.2b and
compared to the ion-trap experiment of Fang and Kwong [33]. For the capture
process from the ground state Si3+ (3s), a global agreement is observed between
the Landau-Zener calculations [34], the present ab-initio treatment and the ab-initio
calculations of Stancil et al. [35] with almost the same variation of rate constants
with temperature. Nevertheless, all theoretical results provide rate coefficients lower
than the experimental point of Fang and Kwong [33]. On the contrary, the rate
coefficients calculated for the capture from the metastable Si3+ (3p) ion are of the
same order of magnitude than the experimental point. Some uncertainty on the
temperature of the trap have to be considered, however, we could suggest certainly
the presence of excited Si3+ (3p) in the experiment.
At typical astrophysical temperatures, only the ground state Si3+ (3s) is significantly populated and the charge transfer process leads to the ground Si2+ (3s2 ) level.
The rate constant for the reverse ionization process kion may be determined easily
by means of the microreversibility relation from the corresponding charge transfer
rate constant kCT :
kion = g exp −
ΔE
kT
kCT ,
where g is the ratio of the statistical weights of initial and final states (g = 1), and
ΔE is the energy gain of the charge transfer reaction. The ionization rate coefficients
are presented in Table 21.1. They reach significant values for temperatures above
3 × 104 K, they are rapidly negligible for lower temperatures with regard to the
exponential factor. They are in good agreement with the previous calculation of
Butler and Dalgarno [34].
21 Recombination by Electron Capture in the Interstellar Medium
375
21.4 The C+ +S Collision System
The C+ + S charge transfer is a determinant reaction for both carbon and sulphur chemistry. The rate constant generally considered for this process is 1.5 ×
10−9 cm3 s−1 [36] between 10 and 41,000 K, but it remains uncertain for such
a large temperature domain and detailed calculations have to be performed. At
low temperatures where the process takes place, the different species may be in
their ground state. With regard to the correlation diagram, only two molecular
states {C+ (2s2 2p)2 P + S(3s2 3p4 )3 P} and {C(2s2 2p2 )3 P + S+ (3s2 3p3 )4 S} would
thus have to be considered in the charge transfer reaction.
Correlation diagram
Configuration
C(2s2 2p2 )1 S + S+ (3s2 3p3 )4 S
C+ (2s2 2p)2 P + S(3s2 3p4 )1 D
C(2s2 2p2 )3 P + S+ (3s2 3p3 )2 D
C(2s2 2p2 )1 D + S+ (3s2 3p3 )4 S
C+ (2s2 2p)2 P + S(3s2 3p4 )3 P
C(2s2 2p2 )3 P + S+ (3s2 3p3 )4 S
Molecular states
4Σ
2 Σ,2 Π,2 Δ,2 F
2,4 Σ,2,4 Π,2,4 Δ,2,4 F
4 Σ,4 Π,4 Δ
2,4 Σ,2,4 Π,2,4 Δ
2,4,6 Σ,2,4,6 Π
Asymptotic energy (eV) [37]
2.68
2.04
1.86
1.26
0.92
0.0
Such two-channel process is presented in Fig. 21.3a for the doublet states.
However, a strong interaction with the higher {C(2s2 2p2 )1 D + S+ (3s2 3p3 )4 S} is
pointed out for the quartet manifold as shown on Fig. 21.3b and three levels have to
be taken into account for this spin multiplicity.
b −46.8
E (a.u.)
E (a.u.)
a −46.8
−46.9
−47
−47.1
−46.9
−47
−47.1
−47.2
−47.2
−47.3
2
−47.4
−47.3
1
−47.5
−47.5
−47.6
−47.6
−47.7
−47.7
−47.8
3
2
1
−47.4
2
3
4
5
6
7
8
R (a.u.)
−47.8
2
3
4
5
6
7
8
R (a.u.)
Fig. 21.3 (a) Adiabatic potential energy curves for the Σ (full lines) and Π (dashed lines)
states of the doublet manifold of the CS+ molecular system. (1) {C(2s2 2p2 )3 P + S+ (3s2 3p3 )4 S}.
(2) {C+ (2s2 2p)2 P + S(3s2 3p4 )3 P} entry channel. (b) Adiabatic potential energy curves for the Σ
(full lines) and Π (dashed lines) states of the quartet manifold of the CS+ molecular system. (1)
and (2), same labels as in Fig. 21.3a. (3) {C(2s2 2p2 )1 D + S+ (3s2 3p3 )4 S}
376
b
8
radial coupling (a.u.)
radial coupling (a.u.)
a
M.C. Bacchus-Montabonel and D. Talbi
7
6
radp12
5
4
3
radp12
30
25
20
15
10
5
2
rad12
0
rad12
1
−5
−10
0
−1
35
1
2
3
4
5
6
7
8
R (a.u.)
−15
radp23
1
2
3
4
5
6
7
8
R (a.u.)
Fig. 21.4 (a) Radial coupling matrix elements between Σ (rad12, red line) and Π (radp12,
blue line) states of the doublet manifold of the CS+ molecular system. (1) {C(2s2 2p2 )3 P +
S+ (3s2 3p3 )4 S}. (2) {C+ (2s2 2p)2 P + S(3s2 3p4 )3 P} entry channel. (b) Radial coupling matrix
elements between Σ (rad12, red line) and Π (radp12, radp23, blue lines) states of the quartet manifold of the CS+ molecular system. (1) and (2), same labels as in Fig. 21.4a. (3) {C(2s2 2p2 )1 D +
S+ (3s2 3p3 )4 S}
The 2 Σ and 2 Π potentials present a smooth avoided crossing around R = 5 a.u.,
in agreement with the previous calculations of Larsson [38] and Honjou [39]. The
corresponding radial coupling matrix elements are drawn in Fig. 21.4a. They show
smooth peaks around R = 5 a.u., respectively, 0.823 a.u. and 0.459 a.u. high for
2 Σ and 2 Π states as well as a sharp radial coupling, 6.475 a.u. high, at R = 1.8
a.u. in the repulsive part of the potential energy curves between the 2 Π states.
For the quartet 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(2s2 2p2 )1 D + S+ (3s2 3p3 )4 S} level is exhibited around R = 4
a.u. and three 4 Π states have to be considered in the calculation. Such interaction
is not observed between the 4 Σ levels and only the two lowest 4 Σ levels have
been taken into account. The corresponding radial coupling matrix elements are
presented in Fig. 21.4b. A smooth peak, 0.915 a.u. high is observed for the radial
coupling between the 4 Σ states, relatively similar to the interaction between 2 Σ
levels. However, the radial coupling between the 4 Π entry channel and the upper
4 Π{C(2s2 2p2 )1 D + S+ (3s2 3p3 )4 S} level reaches up to 10.093 a.u. in absolute value
and may be determinant in the collision treatment. An extremely sharp radial
coupling matrix element between the two lowest 4 Π levels is also exhibited at short
range. It could certainly be considered as quasi-diabatic in the collision dynamics.
The Δ states correlated by means of rotational coupling have not been considered in
the calculation and the sextuplet states cannot be involved in the process, since there
are no states of equivalent spin correlating to any higher asymptotic limits.
21 Recombination by Electron Capture in the Interstellar Medium
cross section (10−16 cm2)
Fig. 21.5 Partial and total
cross sections for the CS+
molecular system: doublet
manifold (red, dashed line);
quartet manifold (red, dotted
line); total cross section (blue,
solid line)
377
10
s4
1
stot
10−1
10−2
10−3
10−4
s2
1
10
102
103
104
ECM(eV)
The collision dynamics has been performed for the direct reaction C+ (2s2 2p)2 P+
S(3s2 3p4 )3 P → C(2s2 2p2 )3 P + S+ (3s2 3p3 )4 S for a wide range of collision velocities, in particular at low velocities where trajectory effects should be considered
and results have to be considered as qualitative. As expected, the sharp peaks
presented by the radial coupling matrix elements radp12 at short range appear as
quasi-diabatic in the dynamical treatment. This is the case, of course for the 4 Π
states, where radp12 is extremely sharp, but also for the corresponding coupling
between 2 Π states. As spin-orbit effects may be neglected in the collision energy
range of interest, calculations have been performed separately for doublet and
quartet manifolds. With consideration of statistical weights between Σ and Π states,
the cross sections for doublet and quartet manifolds is expressed from the cross
sections σΣ and σΠ for Σ and Π states respectively:
2,4
σ = 1/3σΣ + 2/3σΠ .
The total cross section is then:
σtot = 1/32 σ + 2/34 σ
with regard to the statistical weights between doublet and quartet manifolds. They
are presented in Fig. 21.5. The quartet states provide the main contribution to the
total cross section at low collision energies and the consideration of the upper
4 Π{C(2s2 2p2 )1 D + S+ (3s2 3p3 )4 S} level is necessary for an accurate description
of the system.
The rate constants for the direct reaction C+ (2s2 2p)2 P + S(3s2 3p4 )3 P →
C(2s2 2p2 )3 P + S+ (3s2 3p3 )4 S are presented in Table 21.2 together with the rate
coefficients for the reverse process deduced, as in previous paragraph, from
the symmetry properties of the S-matrix. In that case, the degeneracy is g = 3
378
M.C. Bacchus-Montabonel and D. Talbi
Table 21.2 Rate coefficients for the C+ + S and reverse reaction (in 10−9 cm3 s−1 )
T(K)
C+ (2 P) + S(3 P) → C(3 P) + S+ (4 S)
C(3 P) + S+ (4 S) → C+ (2 P) + S(3 P)
500
0.018
–
1,000
0.038
0.0000026
5,000
0.072
0.026
10,000
0.073
0.075
50,000
0.13
0.31
100,000
0.20
0.55
with regard to the multiplicity of initial and final states and the energy gain is
ΔE = 0.92 eV.
The rate constants for the direct reaction are small, about 7.2 × 10−11 cm3 s−1
at 5,000 K. Such a value is significantly lower than the suggested one 1.5 ×
10−9 cm3 s−1 given in the UMIST data base [36] for the 10–41,000 K temperature
range. However, the variation of the calculated rate coefficients is relatively weak
in a wide temperature domain and a value of about 1 × 10−10 cm3 s−1 may be
assumed in the 5,000–50,000 K temperature range with a reasonable accuracy. This
result is in global accordance with the constant value considered in astrophysical
models; the usual value seems anyway to be overestimated by about a power of
10. The total rate constant for the reverse process C(3 P) + S+ (4 S) reaches the
value 2.6 × 10−11 cm3 s−1 at 5,000 K but, as previously noticed, it becomes rapidly
negligible for lower temperatures with the exponential factor.
21.5 Conclusion
This study provides reasonably accurate rate constants for charge transfer processes
important to model the interstellar medium. The Si2+ + H and Si3+ + He reactions
are rather efficient charge transfer processes with rate constants of the order of
10−9 cm3 s−1 . On the contrary, the C+ + S → C + S+ charge transfer and its reverse
reaction appear to be less efficient, with a rate constant an order of magnitude lower
than the one used in the astrochemical model. It might be wise to test the effect of
a lower rate coefficient in the chemistry of carbon and sulphur in the interstellar
medium. It is important to outline the importance of the 4 Π{C(2s2 2p2 )1 D +
S+ (3s2 3p3 )4 S} level in the mechanism. This state is determinant for the efficiency
of the reaction and has to be considered in order to have an accurate description of
the collision system.
Acknowledgements This work was granted access to the HPC resources of [CCRT/CINES/IDRIS]
under the allocation i2010081566 made by GENCI [Grand Equipement National de Calcul
Intensif]. The support of the COST Action CM0702 CUSPFEL is gratefully acknowledged.
21 Recombination by Electron Capture in the Interstellar Medium
379
References
1. M.A. Hayes, H. Nussbaumer, Astrophys. J. 161, 287 (1986).
2. G.D. Sandlin, J.D.F. Bartoe, G.F. Baureckner, R. Tousey, M.E. Van Hoosier, Astrophys. J.
Suppl. 61, 801 (1986).
3. H. Nussbaumer, Astron. Astrophys. 155, 205 (1986).
4. P. Honvault, M.C. Bacchus-Montabonel, R. McCarroll, J. Phys. B.. 27, 3115 (1994).
5. P. Honvault, M. Gargaud, M.C. Bacchus-Montabonel, R. McCarroll, Astron. Astrophys. 302,
931 (1995).
6. M. Gargaud, M.C. Bacchus-Montabonel, R. McCarroll, J. Chem. Phys. 99, 4495 (1993).
7. M.C. Bacchus-Montabonel, P. Ceyzeriat, Phys. Rev. A58, 1162 (1998).
8. N. Vaeck, M.C. Bacchus-Montabonel, E. Baloătcha, M. Desouter-Lecomte, Phys. Rev. A 63,
042704 (2001).
9. S.L. Baliunas and S.E. Butler, Astrophys. J. 235, L45 (1980).
10. M.C. Bacchus-Montabonel, Theor. Chem. Acc. 104, 296 (2000); Chem. Phys. 237, 245 (1998).
11. P. Honvault, M.C. Bacchus-Montabonel, M. Gargaud, R. McCarroll, Chem. Phys. 238, 401
(1998).
12. M.C. Bacchus-Montabonel and D. Talbi, Chem. Phys. Lett. 467, 28 (2008).
13. J. Le Bourlot, G. Pineau des Forˆets, E. Roueff, D.R. Flower, Astron. Astrophys. 267, 233
(1993).
14. D. Teyssier, D. Fosse, M. Gerin, J. Pety, A. Abergel, E. Roueff, Astron. Astrophys. 417, 135
(2004).
15. B. Huron, J.P. Malrieu, P. Rancurel, J. Chem. Phys. 58, 5745 (1973).
16. M. P´elissier, N. Komiha, J.P. Daudey, J. Comput. Chem. 9, 298 (1988).
17. A.D. McLean, G.S. Chandler, J. Chem. Phys. 72, 5639 (1980).
18. M.C. Bacchus-Montabonel, Phys. Rev. A46, 217 (1992).
19. M.C. Bacchus-Montabonel and F. Fraija, Phys. Rev. A49, 5108 (1994).
20. D.E. Woon, T.H. Dunning Jr. J. Chem. Phys. 98, 1358 (1993).
21. H.J. Werner, P.J. Knowles, MOLPRO (version 2009.1) package of ab-initio programs.
22. A. Nicklass, M. Dolg, H. Stoll, H. Preuss, J. Chem. Phys. 102, 8942 (1995).
23. M.C. Bacchus-Montabonel, N. Vaeck, M. Desouter-Lecomte, Chem. Phys. Lett. 374, 307
(2003).
24. M.C. Bacchus-Montabonel, Y.S. Tergiman, Phys. Rev. A 74, 054702 (2006).
25. M.C. Bacchus-Montabonel, C. Courbin, R. McCarroll, J. Phys. B 24, 4409 (1991).
26. F. Fraija, A.R. Allouche, M.C. Bacchus-Montabonel, Phys. Rev. A 49, 272 (1994).
27. L.F. Errea, L. Mendez, A. Riera, J. Phys. B.. 15, 101 (1982).
28. R.J. Allan, C. Courbin, P. Salas, P. Wahnon, J. Phys. B23, L461 (1990).
29. M. Gargaud, R. McCarroll, P. Valiron, J. Phys. B 20, 1555 (1987).
30. N.J. Clarke, P.C. Stancil, B. Zygelman, D.L. Cooper, J. Phys. B31, 533 (1998).
31. M. Gargaud, R. McCarroll, P. Valiron, Astron. Astrophys. 106, 197 (1982).
32. D.R. Bates, B.L. Moiseiwitsch, Proc. Phys. Soc. A67, 805 (1954).
33. Z. Fang, V.H.S. Kwong, Astrophys. J. 483, 527 (1997).
34. S.E. Butler, A. Dalgarno, Astrophys. J. 241, 838 (1980).
35. P.C. Stancil, N.J. Clarke, B. Zygelman, D.L. Cooper, J. Phys. B32, 1523 (1999).
36. The UMIST database for Astrochemistry. http://www.udfa.net.
37. NIST Atomic Spectra Database Levels. http://www.nist.gov/pml/data/asd.cfm
38. M. Larsson, Chem. Phys. Lett. 117, 331 (1985).
39. N. Honjou, Chem. Phys. 344, 128 (2008).
Chapter 22
Systematic Exploration of Chemical Structures
and Reaction Pathways on the Quantum
Chemical Potential Energy Surface by Means
of the Anharmonic Downward Distortion
Following Method
Koichi Ohno and Yuto Osada†
Abstract Anharmonic downward distortion (ADD) of potential energy surfaces
has been used for automated global reaction route mapping of a given chemical
formula of BCNOS. It is demonstrated that the ADD following method gives not
only the larger numbers (122) of equilibrium structures (EQ) than those (103) of the
earlier method by a stochastic approach but also the entire reaction pathways via 430
transition structures (TS) connecting the discovered EQ as well as 155 dissociation
channels, 60 via TS and 95 without TS. Interesting propensities were found for
chemical preference of isomeric structures and their dissociated fragments as well
as characteristic reaction pathways, such as a fragment rotation mechanism.
22.1 Introduction
It has been a primitive but difficult problem to elucidate entire reaction channels for
a given chemical composition of a chemical formula This problem includes several
fundamental questions, what kinds of chemical species (isomers) are producible
from a given chemical formula, how the isomers can be converted one another, and
how they are decomposed into smaller species or conversely how they are made
of smaller species. These questions are of great significance to discover unknown
reaction channels and chemical species.
K. Ohno ( )
Toyota Physical and Chemical Research Institute, Nagakute, Aichi 480-1192, Japan
e-mail: ohnok@m.tohoku.ac.jp
†
Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
P.E. Hoggan et al. (eds.), Advances in the Theory of Quantum Systems in Chemistry
and Physics, Progress in Theoretical Chemistry and Physics 22,
DOI 10.1007/978-94-007-2076-3 22, © Springer Science+Business Media B.V. 2012
381
382
K. Ohno and Y. Osada
The above fundamental questions can be solved in principle theoretically from
mathematical properties of the potential energy surface (PES) [1, 2].
1. An individual equilibrium structure (EQ) on PES corresponds to a chemical
species.
2. A first-order saddle point on PES, a maximum along only one direction and a
minimum for all other perpendicular directions, is called a transition structure
(TS), which connects the reactant with the product via minimum energy paths or
intrinsic reaction coordinates (IRC) [3].
3. A valley leading to fragment species is denoted as a dissociation channel (DC).
The above questions for diatomic systems are trivial. In the case of three-atom
systems, there are several isomers in general, but all isomers as well as all reaction
channels can be studied easily. However, for four-atom systems such as H2 CO
a full theoretical search of possible chemical species and reaction channels had
long been eluded. In 1996 Bondensg˚ard and Jensen first reported a global map of
all isomers and reaction channels for H2 CO based on quantum chemical PES at
the level of HF/STO-3G [4]. The global reaction route map for H2 CO was also
reported by Quapp and coworkers in 1998 [5]. Because of considerably heavy
computational demands for the global reaction route mapping (GRRM), a full search
of all transition structures of systems with more than four atoms was seemed to be
impossible [1].
The major obstacle for performing GRRM was the time-consuming quantum
chemical sampling processes of PES, which requires 3 × 1010 years of computation
time even for a five-atom system (N = 5) with very rough samplings of 100 grid
points in each directions of 3N-6 = 9 variables, if the samplings are taken at
conventional regular grids [6]. Similarly Mote Carlo samplings cannot avoid the
difficulties. Such sampling methods inevitably include huge numbers of useless
points far from EQ and TS on the PES.
The most efficient way of quantum chemical samplings on PES can be made,
if samplings are confined around reaction pathways. The numbers of EQ and TS
are finite, and their connections are also in the limited area along the reaction
coordinates with essentially one dimensional nature which can be described by
small numbers of sampling points. Downhill walks from TS toward EQ or DC along
reaction pathways on PES can easily be made by conventional methods, such as the
steepest decent method [1]. On the other hand for uphill walks from EQ toward TS
or DC along reaction pathways on PES without any intuition, no algorithm has been
reported before the anharmonic downward distortion (ADD) following [7].
The common feature of reaction channels from an EQ point can be summarized
as ADD, as indicated by arrows in Fig. 22.1. On going toward DC, the potential
energy curve becomes flattened over the long distance. The presence of another EQ
leads to TS. Such propensities due to the existence of another EQ or DC affect
the local properties of potentials around an EQ, which necessarily appear as ADD.
It follows that ADD around an EQ point can be considered as a “compass” of the
chemical reaction [7–9].