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The collinear F + H2 reaction evaluated by S-matrix propagation along delves' radial coordinate
CHEMICAL
Volume 87. number 3
THE COLLINEAR EVALUATED Joxhtm
PHYSICS LCITERS
F + H, REACTION
BY S-MATRIX
PROPAGATION
ALONG
DELVES
RADIAL
COORDINATE
RehlELT
Received 31 December 1981;in linti form 23 January 1982
The method of S-maIn\ propagsuon along Delves’ rrdlal coordmstc r IS used to evaluate ewct qu~ntum-mechmwd reacuon probablbrxs for the cohncar r+Hz rcacl~on.Thc mass asymmetry inducts Important crossmgr and rroulsd crossm&s of the wbratlonal encrg~esalong *-The rcsuhs arc m good agreement wth the standard rcfcrcnccs.
2. Consequences of the mass asymmetry
1. Introduction In previous papers [l-3] (or hypersphertcal
for the quantum-mechanical collinear method tions
Delves’ coordmates
coordtnates)
evaluation
[l-3,5].
of asymmetric
[
r, which are numencally
do not occur for symmetrtc The first apphcation collinear
reactions.
.md
(1)
as well as theoretically quantum-mechanical
studied experimentally
calculsttons
F + Hz system have been reported and Connor et al. [
[7]).
Exact
on the collmear previously
Schatz et al. [8], Adams et al. [9],
-10
Light and Walker
i
I1 1. Their results unll be For all calcula-
t~ons the hluckerman
energy surface
LEPS potenttal
____
.I
by
used as tests for the present method. No. V [
.-_---
(cf. the recent review by Ander-
son [6] and by Polanyt and Schreiber
along Delves’ angular coordtnate p
r.75:
IS to the
+ H .
This process has been extenstvely
[IO]
Tl~e most drastic change occurs tn the one-dtmension31 equation
reactton
F + Hz(v) -c FH(u’)
t J-4
IS e.y-
processes.
of the new technique
dsym-
merry, whiclt doffer from the trc~tntcn~ of synunctrtc
reacttons. This
challengmg
the consequences of rhe nws
rcx-
extension IS not trivtal. smce the massasymmetry inducts crossmgs of the vlbrational energies along Delves’ coordmate
r leas been gtven tn refs
I,? j . TIIUS for the purpose of this paper tt IS sutfi-
ctent to elaborate
of the
to sample symmetric
In the present work this method
tended to calculattons
of tl~c S-tndtrtY prop.@ton
along Delves’ radial coordmatc
of trtatomtc
reactions. So far, the applicatton has been restncted
A general dertvatton
[4]
have been adopted
“,I.,
----_
-_~--------~-------
.m.
__
..,
__.-
----
..I
----
..I
-.
c..,.,
,.
Ty. I The potcnual protile V(‘(rd)along the an&r vwuble 9 31 a constant VLIIUC air = 75 A for the system IIIH (gmA, = 0 8106 nd). The loucst lcrcls of the Jiscrcte energy spectrum
121has been used.
c, for the rextants
r + Hz(u) and products FH(u’)
+ H arc also
indicltcd.
0 009-2613/82/0000-0000/S
02.75 0 1982 North-Holland
259
~‘olun~ 87. number 3 (ci. cq (S) m rei
es [representing
[?I).
[-N/2d)a~/aJ
f vtrm9) - E,(T)]+,(T.
where V(r,gj now has an asymmerrtc prolile
(ci. fig. I)
TINS asymmetry
9) = 0. (2)
double-mmlmum induces several
processes tt IS sufiicwnt
to solve
only for the range 0 < 9 G qm.J7
sylttntetrp
wavefunction or reactant
But m the case oiasymmetrtc
properties.
an unphystcal
modes between
however,
pxtlcu1.x lxgc
m the asymptotic
potentrdl
barrier between
uct valley (cf. fig. numcncal
region ofr
where the
the reactant
and prod-
I) ma>- lead to msrablhtxs
solution
of eq. (2) (ct.. appendix
of the A m ref.
long-range exchange of vtbrais obalso ap-
A (cf. fig. 2). There,
of e4(r) and es(r) has to be
as a ktnd oi avoided crossing. Both solu-
‘Pj(r, IJI)and a5(r, g) are now located tn the
ttons
in
lo-
respectively.
energies e4(r) and E&)
the behavior
constdered same regon
however.
completely valley,
reactants and products
proach each other at r = 34
reactions the cmue range 0 < 9 < qma, has to be This ts drl-ficult,
de-
tamed
consldrred
esphcltly.
1982
it IS necessary to calcu-
late the corresponding
Both vtbrattonal
IS the skew angle oi the system). The solution (%U for the range ym.J2
= O)] are acctdentally
cahzed in the product tional
(a) For symmetric
F + Hl(u
generate *. For this situatton
Othenvlse
consequenccseq (2) e\plicttly
16 hlxch
CHEMICAL PHYSICS LETTERS
(reactant
and product
minima are not yet
separated) and therefore a direct crosstng tj forbtdden - m contrast to the situatton at r = S-9 A. Presently, we are investigating
the dynamical
consequence
of
such avotded crossings.
[?I). To overcome this problem we found IL necessary to implement
the renormaltzed
Numerov
method
of 3. Discussion of the results
ref. [ 131. (b) Asymptottcaliy
(for r + 00) the thfferent
vtbraEsact quantum
tional energies E,(T) can be assIgned to reactants or products
by localizmg
tant or product
valley,
and Ej dre tdenttlied EmI ,FoI,
the wavefuncuon respectively.
Jsymptotically
For example.
e4
as E(t-H,V’=3) and
the vlbrattonal
along tlte rxktl
coordatstc
transttion
probabthties
linear reactIon (I) have been calculated range where one Hz vIbrational or five product
vtbrattonal
state (u = 0) and four
[9], Ltght and Walker [IO]
energies e,(r) may cross
tn th? F + Hz s> stein at r - S-9x the two levels e4 (represenrmg
in fig. 3 and com-
pared with those of Schatz et al. [S]. Adams et al.
double-mmimum
r. Thus situation
for the coltn an energy
FH states (u’ = 0, I,?,3.4)
are open. The results are presented
respectively.
(c) Because oi the asymmetrIc potential
tn the reac-
IS vertlicd
(cf. fig. 2) Here
The correspondmg
and Connor et al.
potential
parameters
[I 11.
are gtven m
table 1.
FH(u’ = 3) + H) and
AU results are tn good overall agreement. ferences are presumably and conversion
constants to hfferent ehamplr,
factors which m turn lead
values of the vtbrational
thresholds.
For
tn the present work flzH = 1.008 amu,
whereas Connor et al. [ 1 I Therefore product
Some dif-
due to the use of different
] used It+., = 1.0 amu.
their vibratIonal molecule
levels of the reactant
are shifted
towards
and
higher energtes
.L‘-
pE=----
.LI.
I
1
by the dotted
the Connor
et al. thresholds
would lead to neatly perfect
.LE-
1
(as Indicated
b
‘01
*
TIT. 2. Dcpa~dcncr of the cncrpcs CJ and ES on the ndlal COordmate r ior the system THH. Note rhc avolded crossmg at r = 3-t 4 and the cmssmg at r = B-9 A.
arrows in fig. 3). Scaling to the present ones agreement of the corre-
* From 3 mathemarkd point of view the sauation corresponds to an avoIded crossmg urkss both regrons (reactant and ptoduct valley; cf. fig. I) are separated by an mtirute watl. But the actual separation between both states is smtier than 1Om8 cV and therefore
II seam
crossing 3t this potnt.
to be jumlied
10 comder
a red
CHCMCAL
Volume 87, number 3
26 hbrch 1982
PtlYSlCS LCTTERS
Table I Potcntul p3ramclcrs 3nd con~I3nrs NH21 (W Lw,) (x-1) Ro(H2) (A)
4.748 I 942
S3to p3r3mclcr (112)
0 106
D(W) (cv) P(rH) (A-‘) Ro(W (4 .%I0 psnmetcr (l-11)
6.1’7 2 219 0917 0 167
0.7-12
,,r~ (amuj
19.0
“IH (smu) roa) (i)
1 008 ‘0 1.OO’ 70
Ob) ‘m3xcj (A)
Jj ru IS the smlimg r4uc 0fr (cc rci. [‘]I ‘~1TJ plca1 propq3rron factor r,,, = r,@. cj \I.wmum \3Iuc oir. (The propag311on IO llus IJgc I vdur 1sneccs~~y IO do the asymptonc analysts of the !‘$, 3s described in rci.
[ 21 Work Is III progress to
inlpkrwn~
J
pro;ccuon slmdar 10 that used by Kuppurnmnn CI ~1. [3j. ahich uqll rcducc rhc raluc air,,, by a consldcrablc amount.)
.IS well as Ihe few points
[IO]
al. [9] arc in almost
pcrfcct
die range ofErr3ns
pubhshed
be due to the fimrc
et
with ours III
eV.
Ems
= 0.0-0.35
0 1 eV some difiercnces
by Addms
agreement
hmc
Around
=
to be noticed. rhcy nay
basis set .md 111c hmltcd
numbsr
of SecIors used in ref. [ 101. In table 1 we demonstrate respect
to the number
distmct
energres.
energy show
channels
are suflklent
even furlher
spondmg
4. Conclusion
rhe results
reactron probabilities.
Some minor
of Schatz et al. [S] haw
already
shifts
in
Iorically
closed),
1O-3
wrtlr 41 two
energy
= 0. I-18 2V corrange. The rcsulrs
energy
range only
IO
(-l/S open and G/S asyrnptoticJly to achieve
to 7 channels
convergence hater
of channels
IS dccreacd
(q/S open and 3/Z JSYIIIP-
the transItion
by only rt: 10% irom from
while Em,
1%. When the nulnber
Fg. 3 Enc~py dependence oithr reacl~on probabihr~csP$.+, ior F + H3(” = 0) -l-H(;) + H x Schstz et d [8], adzptcd iromi$.2olrci lll],nAd3mseIzIl 19].*LyhIandWalltcr, 3d3pred from lip. 5 oi ref. [ 101; o Connor et al.. adapted from fw. 2 of ref. Ill], contmuous hne: present resulrs
ch.mncls
= 0 0 I3 2V rcprcscn 1s .in
that even In rhe resonance
closed) than
E,,,,
IO a non.resonanr
propagated
prob.rbllwcs
of propagated
nedr 3 resonance
responds
the el[raordulanly
ofthe reaction
rapId convergence
their exact
probabrlrtres wlues
which
deviate range
to I.
been dls-
cussed in ref. [ 111. The results of Light and Waker
The extensionof our new techalque [I ,2I, S-matnx 261
Vohm~c 87. number 3
CHMICAL
PHYSICS LETTERS
26 March 1982
Table 1 Con~ergnce bebwlour
of ICXIIOII prob3bdittes
wth respect to the number of propagated
chmnels T p3-o
,I 3)
‘topen b,
T PI-0
T &lJ
16 l-1 12 10 9 a 7
4 4 4 1 4 4 .I
0.005 I 0.005 1 00051 0.005Z 0 0052 0.0053 0 0054
0 285 0.185 0 285 0.284 0181 0.174 0161
-
I6 I? 10 9 a 7
5 5
0.0013 0 0013 0.00 IJ 0 001-l 0.0015 0.0018
0 061 0.062 0 062 0 063 0 065 0 069
0.551 0551 0.551 0551 0549 0557
PO-o
-________ E~r~“S=0013cV
El,,,,
= 0 l-IS CV
; 5 5
0.710 0.710 0.710 0.712 0.714 0.721 0.73, 0.385 0 385 0.385 0.384 0.383 0 383
d) n IS the number of prop3:atcd chxmcls b) ,lopcn 1s the number oiopc’n chxmcls.
pr~pagauon
dong
rrc colhnear
rexuons
The resultmg F + H,(u)
-
Delves’ coordmae
reaction FH(u’)
references. Therefore
r. to asymmet-
has been tested successfully. probabllirxs
for the collinear
+ H process agree well with the we cortstder
the present work
3s the b3sIs ior 3 series of further applications
to
3syinmctrlc redctions. In particular for cdses (I.?. 112avy and hght heavy atom processes) where the conventional
rechnlques arc chftkull
The author
to apply.
thanks Dr. J. Manz ior many helpful
dicussrons and Professors S.D. Peyerirnhoff Buenker
for their contmuing
support.
and R J.
The calcula-
tlons were carried out at the Computation the Umverslry of Bonn.
Center of
References [ 11 G. HxtLc,J. bf3nz xtd J. Ram&. (1980) SOJO.
262
_I Chcm. Phys. 73
I?-] J. Ramelt,Chem Phys Lelters 74 (1980) 263 [3] A.Kuppcrmann,J A.Knyextd PJ.Dnyer.Chcm. Ph}s Letters 74 (1980) ‘57 [?I LAI. Delvcs,Nucl. Phys 9 (1959) 391; 20 (1960) 175. [S] J. Mm12 nnd J. Ramclt.Chcm. Phys. Letters 76 (1980) 337;77 (1981) 171; J.A. K~ye and A. Kuppermxtn,Chem. Phbs. Letters 77 (1981) 573; 78 (1981) 546: I. Llanz and J. Ram&, Chem. Phys. Letters 81 (1981) 179. [6] J B. Anderson. Adwn Chem. Phys 41 (1980) 1’9 171 J C. Polanyt xtd J.L. Schrciber, Fx3dq Dtscuss~ons Chem. Sot 61(1977) 267. [El G C. Schatz. J.M. Bowman and A. Kuppcrmsnn, J. Chem. Phys. 58 (1973) 4023; 63 (1975) 67% [9] J T. Adams. R L. Seth xtd E.F Hn~es. J. Chem Phj s 61(1974) 2193. [ 101 J.C. I_Ight snd R.B. Wticr, J. Chem. Phys 65 (1976) 1271. 1111 J N.L. Connor. W. Jtiubstz wd J Manz, hfol. Phys. 35 (1978) 1301;39 (1980) 799. 1l?] J.T. hluckermztn. m:Theorcr~;ll chemtstry, advances and perspecttves, Vol. 6A, ed D. Henderson (Acadetmc Press,Ncw York. 1981) pp. l-77, J. Chem. Phys. 56 (1972) ,997. J.C. Polany~and J.L. Schrelber, Chrm. Phys. Letters 29 (1974) 319. [ 131 B.R. Johnson, J. Chem. Phys 67 (1977) 3086.
Volume 87. number 3
THE COLLINEAR EVALUATED Joxhtm
PHYSICS LCITERS
F + H, REACTION
BY S-MATRIX
PROPAGATION
ALONG
DELVES
RADIAL
COORDINATE
RehlELT
Received 31 December 1981;in linti form 23 January 1982
The method of S-maIn\ propagsuon along Delves’ rrdlal coordmstc r IS used to evaluate ewct qu~ntum-mechmwd reacuon probablbrxs for the cohncar r+Hz rcacl~on.Thc mass asymmetry inducts Important crossmgr and rroulsd crossm&s of the wbratlonal encrg~esalong *-The rcsuhs arc m good agreement wth the standard rcfcrcnccs.
2. Consequences of the mass asymmetry
1. Introduction In previous papers [l-3] (or hypersphertcal
for the quantum-mechanical collinear method tions
Delves’ coordmates
coordtnates)
evaluation
[l-3,5].
of asymmetric
[
r, which are numencally
do not occur for symmetrtc The first apphcation collinear
reactions.
.md
(1)
as well as theoretically quantum-mechanical
studied experimentally
calculsttons
F + Hz system have been reported and Connor et al. [
[7]).
Exact
on the collmear previously
Schatz et al. [8], Adams et al. [9],
-10
Light and Walker
i
I1 1. Their results unll be For all calcula-
t~ons the hluckerman
energy surface
LEPS potenttal
____
.I
by
used as tests for the present method. No. V [
.-_---
(cf. the recent review by Ander-
son [6] and by Polanyt and Schreiber
along Delves’ angular coordtnate p
r.75:
IS to the
+ H .
This process has been extenstvely
[IO]
Tl~e most drastic change occurs tn the one-dtmension31 equation
reactton
F + Hz(v) -c FH(u’)
t J-4
IS e.y-
processes.
of the new technique
dsym-
merry, whiclt doffer from the trc~tntcn~ of synunctrtc
reacttons. This
challengmg
the consequences of rhe nws
rcx-
extension IS not trivtal. smce the massasymmetry inducts crossmgs of the vlbrational energies along Delves’ coordmate
r leas been gtven tn refs
I,? j . TIIUS for the purpose of this paper tt IS sutfi-
ctent to elaborate
of the
to sample symmetric
In the present work this method
tended to calculattons
of tl~c S-tndtrtY prop.@ton
along Delves’ radial coordmatc
of trtatomtc
reactions. So far, the applicatton has been restncted
A general dertvatton
[4]
have been adopted
“,I.,
----_
-_~--------~-------
.m.
__
..,
__.-
----
..I
----
..I
-.
c..,.,
,.
Ty. I The potcnual protile V(‘(rd)along the an&r vwuble 9 31 a constant VLIIUC air = 75 A for the system IIIH (gmA, = 0 8106 nd). The loucst lcrcls of the Jiscrcte energy spectrum
121has been used.
c, for the rextants
r + Hz(u) and products FH(u’)
+ H arc also
indicltcd.
0 009-2613/82/0000-0000/S
02.75 0 1982 North-Holland
259
~‘olun~ 87. number 3 (ci. cq (S) m rei
es [representing
[?I).
[-N/2d)a~/aJ
f vtrm9) - E,(T)]+,(T.
where V(r,gj now has an asymmerrtc prolile
(ci. fig. I)
TINS asymmetry
9) = 0. (2)
double-mmlmum induces several
processes tt IS sufiicwnt
to solve
only for the range 0 < 9 G qm.J7
sylttntetrp
wavefunction or reactant
But m the case oiasymmetrtc
properties.
an unphystcal
modes between
however,
pxtlcu1.x lxgc
m the asymptotic
potentrdl
barrier between
uct valley (cf. fig. numcncal
region ofr
where the
the reactant
and prod-
I) ma>- lead to msrablhtxs
solution
of eq. (2) (ct.. appendix
of the A m ref.
long-range exchange of vtbrais obalso ap-
A (cf. fig. 2). There,
of e4(r) and es(r) has to be
as a ktnd oi avoided crossing. Both solu-
‘Pj(r, IJI)and a5(r, g) are now located tn the
ttons
in
lo-
respectively.
energies e4(r) and E&)
the behavior
constdered same regon
however.
completely valley,
reactants and products
proach each other at r = 34
reactions the cmue range 0 < 9 < qma, has to be This ts drl-ficult,
de-
tamed
consldrred
esphcltly.
1982
it IS necessary to calcu-
late the corresponding
Both vtbrattonal
IS the skew angle oi the system). The solution (%U for the range ym.J2
= O)] are acctdentally
cahzed in the product tional
(a) For symmetric
F + Hl(u
generate *. For this situatton
Othenvlse
consequenccseq (2) e\plicttly
16 hlxch
CHEMICAL PHYSICS LETTERS
(reactant
and product
minima are not yet
separated) and therefore a direct crosstng tj forbtdden - m contrast to the situatton at r = S-9 A. Presently, we are investigating
the dynamical
consequence
of
such avotded crossings.
[?I). To overcome this problem we found IL necessary to implement
the renormaltzed
Numerov
method
of 3. Discussion of the results
ref. [ 131. (b) Asymptottcaliy
(for r + 00) the thfferent
vtbraEsact quantum
tional energies E,(T) can be assIgned to reactants or products
by localizmg
tant or product
valley,
and Ej dre tdenttlied EmI ,FoI,
the wavefuncuon respectively.
Jsymptotically
For example.
e4
as E(t-H,V’=3) and
the vlbrattonal
along tlte rxktl
coordatstc
transttion
probabthties
linear reactIon (I) have been calculated range where one Hz vIbrational or five product
vtbrattonal
state (u = 0) and four
[9], Ltght and Walker [IO]
energies e,(r) may cross
tn th? F + Hz s> stein at r - S-9x the two levels e4 (represenrmg
in fig. 3 and com-
pared with those of Schatz et al. [S]. Adams et al.
double-mmimum
r. Thus situation
for the coltn an energy
FH states (u’ = 0, I,?,3.4)
are open. The results are presented
respectively.
(c) Because oi the asymmetrIc potential
tn the reac-
IS vertlicd
(cf. fig. 2) Here
The correspondmg
and Connor et al.
potential
parameters
[I 11.
are gtven m
table 1.
FH(u’ = 3) + H) and
AU results are tn good overall agreement. ferences are presumably and conversion
constants to hfferent ehamplr,
factors which m turn lead
values of the vtbrational
thresholds.
For
tn the present work flzH = 1.008 amu,
whereas Connor et al. [ 1 I Therefore product
Some dif-
due to the use of different
] used It+., = 1.0 amu.
their vibratIonal molecule
levels of the reactant
are shifted
towards
and
higher energtes
.L‘-
pE=----
.LI.
I
1
by the dotted
the Connor
et al. thresholds
would lead to neatly perfect
.LE-
1
(as Indicated
b
‘01
*
TIT. 2. Dcpa~dcncr of the cncrpcs CJ and ES on the ndlal COordmate r ior the system THH. Note rhc avolded crossmg at r = 3-t 4 and the cmssmg at r = B-9 A.
arrows in fig. 3). Scaling to the present ones agreement of the corre-
* From 3 mathemarkd point of view the sauation corresponds to an avoIded crossmg urkss both regrons (reactant and ptoduct valley; cf. fig. I) are separated by an mtirute watl. But the actual separation between both states is smtier than 1Om8 cV and therefore
II seam
crossing 3t this potnt.
to be jumlied
10 comder
a red
CHCMCAL
Volume 87, number 3
26 hbrch 1982
PtlYSlCS LCTTERS
Table I Potcntul p3ramclcrs 3nd con~I3nrs NH21 (W Lw,) (x-1) Ro(H2) (A)
4.748 I 942
S3to p3r3mclcr (112)
0 106
D(W) (cv) P(rH) (A-‘) Ro(W (4 .%I0 psnmetcr (l-11)
6.1’7 2 219 0917 0 167
0.7-12
,,r~ (amuj
19.0
“IH (smu) roa) (i)
1 008 ‘0 1.OO’ 70
Ob) ‘m3xcj (A)
Jj ru IS the smlimg r4uc 0fr (cc rci. [‘]I ‘~1TJ plca1 propq3rron factor r,,, = r,@. cj \I.wmum \3Iuc oir. (The propag311on IO llus IJgc I vdur 1sneccs~~y IO do the asymptonc analysts of the !‘$, 3s described in rci.
[ 21 Work Is III progress to
inlpkrwn~
J
pro;ccuon slmdar 10 that used by Kuppurnmnn CI ~1. [3j. ahich uqll rcducc rhc raluc air,,, by a consldcrablc amount.)
.IS well as Ihe few points
[IO]
al. [9] arc in almost
pcrfcct
die range ofErr3ns
pubhshed
be due to the fimrc
et
with ours III
eV.
Ems
= 0.0-0.35
0 1 eV some difiercnces
by Addms
agreement
hmc
Around
=
to be noticed. rhcy nay
basis set .md 111c hmltcd
numbsr
of SecIors used in ref. [ 101. In table 1 we demonstrate respect
to the number
distmct
energres.
energy show
channels
are suflklent
even furlher
spondmg
4. Conclusion
rhe results
reactron probabilities.
Some minor
of Schatz et al. [S] haw
already
shifts
in
Iorically
closed),
1O-3
wrtlr 41 two
energy
= 0. I-18 2V corrange. The rcsulrs
energy
range only
IO
(-l/S open and G/S asyrnptoticJly to achieve
to 7 channels
convergence hater
of channels
IS dccreacd
(q/S open and 3/Z JSYIIIP-
the transItion
by only rt: 10% irom from
while Em,
1%. When the nulnber
Fg. 3 Enc~py dependence oithr reacl~on probabihr~csP$.+, ior F + H3(” = 0) -l-H(;) + H x Schstz et d [8], adzptcd iromi$.2olrci lll],nAd3mseIzIl 19].*LyhIandWalltcr, 3d3pred from lip. 5 oi ref. [ 101; o Connor et al.. adapted from fw. 2 of ref. Ill], contmuous hne: present resulrs
ch.mncls
= 0 0 I3 2V rcprcscn 1s .in
that even In rhe resonance
closed) than
E,,,,
IO a non.resonanr
propagated
prob.rbllwcs
of propagated
nedr 3 resonance
responds
the el[raordulanly
ofthe reaction
rapId convergence
their exact
probabrlrtres wlues
which
deviate range
to I.
been dls-
cussed in ref. [ 111. The results of Light and Waker
The extensionof our new techalque [I ,2I, S-matnx 261
Vohm~c 87. number 3
CHMICAL
PHYSICS LETTERS
26 March 1982
Table 1 Con~ergnce bebwlour
of ICXIIOII prob3bdittes
wth respect to the number of propagated
chmnels T p3-o
,I 3)
‘topen b,
T PI-0
T &lJ
16 l-1 12 10 9 a 7
4 4 4 1 4 4 .I
0.005 I 0.005 1 00051 0.005Z 0 0052 0.0053 0 0054
0 285 0.185 0 285 0.284 0181 0.174 0161
-
I6 I? 10 9 a 7
5 5
0.0013 0 0013 0.00 IJ 0 001-l 0.0015 0.0018
0 061 0.062 0 062 0 063 0 065 0 069
0.551 0551 0.551 0551 0549 0557
PO-o
-________ E~r~“S=0013cV
El,,,,
= 0 l-IS CV
; 5 5
0.710 0.710 0.710 0.712 0.714 0.721 0.73, 0.385 0 385 0.385 0.384 0.383 0 383
d) n IS the number of prop3:atcd chxmcls b) ,lopcn 1s the number oiopc’n chxmcls.
pr~pagauon
dong
rrc colhnear
rexuons
The resultmg F + H,(u)
-
Delves’ coordmae
reaction FH(u’)
references. Therefore
r. to asymmet-
has been tested successfully. probabllirxs
for the collinear
+ H process agree well with the we cortstder
the present work
3s the b3sIs ior 3 series of further applications
to
3syinmctrlc redctions. In particular for cdses (I.?. 112avy and hght heavy atom processes) where the conventional
rechnlques arc chftkull
The author
to apply.
thanks Dr. J. Manz ior many helpful
dicussrons and Professors S.D. Peyerirnhoff Buenker
for their contmuing
support.
and R J.
The calcula-
tlons were carried out at the Computation the Umverslry of Bonn.
Center of
References [ 11 G. HxtLc,J. bf3nz xtd J. Ram&. (1980) SOJO.
262
_I Chcm. Phys. 73
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