Tải bản đầy đủ - 0 (trang)
3 The Si2++H and Si3++He Collision Systems

3 The Si2++H and Si3++He Collision Systems

Tải bản đầy đủ - 0trang

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



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].



Tài liệu bạn tìm kiếm đã sẵn sàng tải về

3 The Si2++H and Si3++He Collision Systems

Tải bản đầy đủ ngay(0 tr)

×