- Email: [email protected]
Distribution of reaction products (theory). Investigation of an ab initio energy-surface for F + H2 ⇀ HF + H
Volume 29, nur&cr
3
CHEMICAL
DISTRIBUTIQNOFREA~IONPRODUCTS MVESTIGATIQN
1 December
PHYSICS LETTERS
OF AN AB INITIO,ENERGY-SUWACE
1974
~THEoW. FOR F + E, + ISI? +R
J.C. pDLANYLand Department of Gemistry,
Universiv
3.L SCHREIBER of Toronto, Toronto M5S
iA1. ConffdQ
Received 28 August 1974
Pearson and Schaefer (BOPS) have computed extensive configuration interaction. We have fitted ison with semi-empirical surfaces fcr FHH shows that the generrl ab iniiio fintings Evidence is presented which indicates that’the ‘energy along the favoured route intu the exit valley. Bender,
O’Noil,
ofFHH,using
The reaction F ‘Hz + HF t H is becoming a testing ground for theories of reaction,dynamics. Considersble,experimertal data exist [l-S]. Classical 16-131 and quantum [Id, 151 calculations have been perforrned on semi-empirical potential-energy surfaces. Bender, O’Neil, Pearson and Schaefer (BOPS) [16] have computed 232 ab initio energies, corresponding to collinear FHH configurations, using an extended basis set and 338 configuration wavefunction. The results are most promising. The exothermicity Me = 05 - 07 = 34.4 kcal mole-’ (De is the bond-dissociation energy measured from the bottom of the well; subscripts 1 and 2 refer to the atomic pairs AB and BC in A + BC). The correct ADe lies in the range 3132 kc-al mole-l. The ha&r-height was found to be E, = 1.66 kcal mole -l. This can be compared with the experimental activation energy Ea = 1.6 kcal mole-l [171. We have attempted to make a first assessment cf ,ehe accuracy of the surface on the basis of the fti grid of232 collinear energies. Our comments are ten. tative in the light of the fact that (a) they are based on a classical trajectory study, and (b) we must es& mate the effect of rel&ing the 1D constr+t imposed by the BOPS computations. We b&eve that neither (a) nor (II) are likely to vitiate our findings, which are in the main qualitative. In regard to (a), it should be nbted that we have re-
ab initio energies for 232 coUinev configurations these points using an LEPSWe function. Camp=form
of these suchces
is in goti
accord
~4th the
BOPS ab initio surface exhibits too peat a drop in
stricted burselves to the comparison of average product vibrational excitations, (V’>. Average attributes can be expected to agree satisfactorily zs between classical and quantum calculations [IsI. In connection with (b), it has been found 16,192 - especially for. LEPS surfaces and FYrcdmass combinations - that the collinear cut through the hypersurface gives a qualitative guide to the behatiour on the 3D surface. Hence we can draw qualitative conclusions even prior to correcting for change in dimensional&f . Following an unsuccessful attempt to fit the ab initio points using a hyperbolic map function [21,22], v&switched to using 2.n extended LEPS (London, Eyring, Polanyi, Sato) f&ion [I9] incorporating the Pederson-Porter four-parameter triplet reprezntation [23]. For FHH there were two triplet functions, and hence 8 tripIet paranleters
to be adjusted
by a
non-linear least squares procedure. The rms deviation fro& the 232 ab titio points wa+ < I kcd mole;1 per poir,t. There was a s-mall (spurious) well, 0.35 kca! mole” deep, in the entrance vtiey of the fitted sur-
* here l~s been
of crotig beand t&e non-reactive F’(ZP,,2) t Hz surface. Iitis is believed to be s improbable event [ 13,201. Such c&sings as do oicur MI1 t&e place well out in the entry v&z-y,.arih should have little effect on the mea& product v~brstionzl exdtrction. Bscusdon
of the posaitity
twe=n the F(2P3,z) + I-f2ener&-tirface
319 :
.
Volume 29, number 3.
:
CHEMICAL PHYSICS LETTERS
,’
1 December 1974
I I, Constants for BOPS-FIT a)
:
,fect ?n W’> (as tie have.found G a further trajectory study O~I F + Hz [ 121). The constants for DOPS-FIT are given in table 1. .The collinear ‘energy-surface; BOPS-FIT, is shown
..HF De
> D3
in fig; 1. For comparison we record potentialenergy .contours taken from *be collinear cut through an extended !LEPS [I93 hyper-surface, SE-l, that we have
R*
adjusted on the basis of a full 3D trajectory study to
0
give a satisfactory representation oft!!e experimental product energy_distribution.[12] t. The -mean percentage. conversions of energy into product vibration
Cb) ~b)
P3
(kcalmple-r) (A-‘j:
”
.,
-,:
.‘.Hz. 129.3
94.8
2.316
2047
(A-‘)
; 0.931 St.83 2.229
34.56 1.522
w (A-‘).
1.217 3.090
(A) (kcd mole-‘)
(kcal
mole-! A-‘)
1174.9 1.315
(A)
a) The consents
:
0.753
0.443
1.929 388.8 0.762
arc defined in ref. [23].
b) Values chosen to make the triplet curves smooth at R*.
f The constants for SE-1 were@ = 140.5kcalmole-‘, Dg = 109.5 kczl mole-‘, er= 2.2.2 A-‘, .e2= 1.94 A-l, ry = 0.917 &.r;=0.742A. a=O.lSO,b =O.OEO(o isthe Satoparam-’ eter between F and H,‘b is the corresponding parameter for HH). Surface SE-1 has a classical barrier .heigh t E, = 2.16 kcd mole-l.
:..
,i ‘,
.‘.Table 3
,face, BOPS-FIT. This f&i& will have some’effe.ct on. ,~t.hresh~id behaviotir; but will have tie s-ign~ficanni ef--
and rotation where = 66.5% and = 9.5% (the experimental v&es are 66% and 8% respectively). The ab initio surface shares’with the semi-empirical
,
..
/ 1.00
/ I.25
':A' I.50 @&-3
/ 2.00 !.
,Fig. 1. T!le solid contoursgive the scaled and’skewed collinear potenti&nergy-surface for “BOPSFIT”; a least-squares fit to tbe ab initio computation of ref. 1161 for tbhe resction F + I-IL+ HF + H. Reagents.start at lower right, products are formed at upper, relative to the reagents as zero. Tbe broken contours (energies in parentheses) are taken ,I& Contour energies are in +linoie-‘, frqm YSE_l”,a collineazcut throughihebest semi-empiricalpotential~nergy hypcrsurface obtained in a 3D trajectory study [ 121. The ,-X .indiutes the location of the barrier-crest on BOP%FIT,. and (X) shows the corresponding point on SEL The heavy contours inditite the “shoulder” region from which a typical trajectory is deflected into the exit valley, r2, on BOPSFLT and on SE-L The approximate range of values, rzx, at which trajectories first cross the minimum or the wit valley is.indicated to either side of & .. ,Jtte median value of tV>; l?re approximate range of rzx and.value of& is comtnon to BC!PSFIT:and @-L.
: .-.3g:
,. :
... ‘:1-y 1 : ,’ _,,.,
‘.
.-; .,
.,--
., ..
.: : :.
_..
.’
Volume 29. number 3
CHEMLCAL PHYSICS LETTERS
surfaces reported for this reaction in the literature [6-151 the property of being highly repulsive. The energy-profile along the minimum path qualitatively re‘sembles that obtained in the BEBO (bond energy bond order) approximation, which is, therefore, also indicative of strongly repulsive energy release [24]. We have computed the curvatures of tire minimum paths on SE-l and BOPS-FIT at intervals along their lengths. The region of large curvature comes at approximately the same energy on both surfaces, and is of similar magnitude. We have done the same for Muckerman’s best empirical surface MS [25] ?, with the same result. Truhlar [26] has compared the curvature of the BEBO minimum path for F fH2 with the BOPS ab initio prediction, and has found good agreement. The difference between SE-l and BOPS-FIT (fig. 1) is that the down-hill portion of the surface comes ear-. lier on the BOPS-FIT (ab initio) surface. Examination of over 200 trajectories in 1D and 3D on SE-l, showed that the majority exhibited mixedenergy release [19]; i.e., they “cut the comer” of the surface. Muckerman has reported the same behaviour for F fH2 on. a series of LEPS surfaces (see MT in table II of his 1972 paper; ref. [ci]). Following “comercutting” a trajectory first crosses the exit valley at a configuration we designate rzX (the value of ‘2 at which rl is for the first time reduced to r$). The range of initial vibrational phases in the Hz bond gives rise to a range, of r s; this range is indicated approximately in fig., 1, for HZ (v = 0) and a collision energy near threshold. The mean ‘2X on BOPS-FIT is shown in fig. 1 as &. The corresponding trajectory is deflected off the = 5 kcal contour (the zero point energy of H2 is 6.1 kcal mole-l) in the region indicated by the heavy curve, and enters the exit valley laterally. It is found that, in general, the greater qx the greater Y’. ‘The range of ‘2X it similar on SE-1 and BOPS-FIT, and so is Fh. The difffereence is that a particu!ar r2x gives rise to = 7 kcal mole-l greater V’ on BOPS-FIT than on SE-I, due to the greater acceleration of the representative mass in falling from = 5 kcal down to ~2~(f& is at approx. -32 kcal mole-l on the ab initio surface, and at approx. -22 kcai mole-l on SE-I). i T$e constants for MS were those @ven in Muckerman’s 1972 paper, ref. [e], surface 2, v$th the Sat0 pUaTlekiS set to v&es intermediate between surfaces 2 and 3; A(HF) =o = 0.167, a(HH) =b = 0.106.
1 December
1974
The minimum energy path on Muckermart’s best empirical surface, M5, is intermediate between SE-1 and BOPS-FIT. However, MS clcsely resembles SE-1 in the location of the 5 kcal ‘X-roulder” (the heavy broken contour in fig. 1) thzt marks the onset of mixed energy release, and in the positions of the successive contours along ‘he steepest descent from this point into the exit valley. Both MS and SE-l, tberefore, differ in the same way from BOPS-NT in this important region of configuration space. For SE-lwe have made a systematic study [12I of the effect of lifting the collinear restraints. With the reagents in the range of room temperature, a batch of 1D trajectories on SE-1 yielded C&,1= 74%; in 3D the value was C_&>= 66.5%. For BOPS-FIT, the corresponding batch of 1D trajectories yielded (f’v) = 90%. If one applies the same correction for ID + 3D the fraction of energy entering vibration becomes C&J = 80%. This is significantly in excess of the experimental value of 66%. Increase in dimensionality from lD to 2D or 3D introduces angular momentum. It is noteworthy that on SE-I the decrease in (V’) as 10 --F3D was exactIy matched by increase in a’>. It may be general that AiT/“) z 6(R’) (8 is for lD+2D or 3D). The value of CR’)on SE-l rose from zero, when lD + 3D, to R’) = 3.2 kcal mole-1 -close to the experimental value. If the 1D + 3D transformation of BQPS were to bring (V’) and (li’> from theory into agreement with experiment it would be necessary that -6(V’> = 8 kcal mole-l, much in excess of &CR’). The decrease in (V’J as lD+ 3D is discussed from a general standpoint in two recent papers [27,28]. The Bernstein-Levine theory, predicts the correct sign and order of magnitude for -S(V’). It is noteworthy that their formulation predicts a similar decrease in (Y’) for both SE-I and BOPS-FIT (somewhat Iarger for SE-I). The ab initio findings of Bender, O’NeiI, Pearson and Schaefer are most encouraging for the semi-empirical theorist, since they lend substance to the claims that the energy-surface for F f X2 is highly re-. pulsive, and that it has a curvature along the minimum ene& path of the type associated with the LEPS function. :
More refined collinear ab initio computations should concentrate on the comer region in whkh the energy release occurs. The potentialenergy drop from 321
CHEMICAL FHYSICs LE-ITIIRS
the “shoulder” (characte,&ed by the +5 $cal mole-’ contour) direct& into the exit v&jr appears to be : -too large by:roughly 7 kcal mole-lon.the BOPS ab initio surFace. This results in too great a vibrational enqy release, by-a comparable amount. A significant fraction of this discrepancy can be understood in .terms of ‘the correlation between increased vjbrational excitation’and increased heat of reaction on otherwise comparable energy+urfaces.[24]: the ab initio surface is more exothermic by 3.5 kcal m.ole-* than is SE-L
Acknowledgement’ We are indebted to Drs. C.F. Bender and &. Schaefer III for supplying the ab initiq energies, and to Drs. R.B. Bernstein, T.F. George, A. Kuppennann, K. Morokuma, J.T. Muckemian and D.G. Truhlar for helpful discussions. J.L.S. thanksthe National Research Council of Car&da for a Scholarship during the tenure of which this work ~2s done. J.C.P. thanks the Canada Council for a Xi&k Memorial Scholarship. The work’was supported by grants from the National Research Council of Canada and the Defence Research Board of Canada (Grant No. ?530-104 U.G.). .’
1 Deccmkr
[6] J.T. Muckermq J. Chem. Phyi (1972) 2997: 57 (1972) 3388.
54 (1971)
1974
11.55; 56
[7] R.L. Jnffe-aid J.B. Anderson, J. Chem. Phys 54 (1971) .22:4. ,;.: [8] R.L. Wilkins, J. Chcm. Phys. 57 (1972) 912;58,(1973) 3038. [9] D.G. Truhlar, J. Chem. Phys. 56 (1972) 3189. [lo] J.T. Muckermsn and M.D. Newton, J. Chem. Phys. 56 (1972) 3191. [ll] N.C.‘Blais and D.G. Truh1ar.J. (Shem. Phys Sg(1973) 1090. [ 121 J.L. Schreiber, Ph.D. Thesis, University of Torontc .(J973). [13] 3-C Tuiy, J. Chem. Phys. 60 (1974) 3042. (141 SF. Wu, B.R. Johnson and R.D. Levine, Mol. Phys. 25 (1973) 839. [15] G.C. Schatz, J.M. Bowman and A.,Kuppermann, J. Chem. Phys 58 (1973) 4023. [16] C.F.‘Bender,S.V. O’Neil,P.K. Pearsonand H.F. Schaefer III, Science 176 (1972) 1412. 1171 K.H. van Homann, W.C. Sol.oman, J. Warnatz, H. Gg. Wagner and C. Zetzsch, Z. Elektrochem. 6 (1970) 565. [li3] W.E. Miher, J. Chem. Phys 54 (1971) 5386; R.G..Gordon, Faraday Discussions Chem. Sot. 55 -/1973) 22. [19] P.J. Kuntz, E.M. Nemeth, J.C. Polanyi, S.D. Rosner and CE. Young, J. Chem. Phys. 44 (1966) 1168. [20] T-F. George and K. Morokuma, privite communication. [21 j D.L. Bunker and N.C. Blais, J. Chem. Phys. 41 (1964) 2377. [22] D.L. Bunker and CA Parr, J. Chem. Phys. 52 (1970)
.5700.
References [l] [2] [3] [4] [5]
J.H. Parker and G.C. Pimentel. J. Chem. Phys 51 (1969) 91. J.C. Polanyi ai@ D.C. Tardy, J. ‘Chem. Phys 51 (1969) 5717. N. Jonathan, C.M. Melliar-Smith and D.H. Slater, Mol. Phys 20 (1971) 93. J,C. Polanyi and K.B. Woodall,J. Chem. Phys. 57 (1972) 1574. M-J. Berry, J. Chem. Pbys i9 (1973) 6229..
[23] L. Pederson and R.N. Porter, J. Chem. Phys 47 (1967) 4751; LM. Raff. L. Stivers, R.N. Porter, D.L. Thompson and L.B.. Sims, J. Chem. Phys. 52 (1970) 3449. [24] M.H. Mok and J.C. Polanyi, J. Chem, Phys. 51 (1969) 1451. .[2.5] J.T. Muckem& private communication. [26] D.G. Truhlar, J. Am. Chem. Sot. 94 (1972) 7584. [27] R.B. Walker and RX. Wyatt, Mol. Phys. 28 (1974) 101. [28] R-B. Bernstein and R.D. Levine, Chem. Phys Letters 29 (1974) 314.
.
322: .:
‘-..
.,
.,,
‘,
:. -.
.,.
3
CHEMICAL
DISTRIBUTIQNOFREA~IONPRODUCTS MVESTIGATIQN
1 December
PHYSICS LETTERS
OF AN AB INITIO,ENERGY-SUWACE
1974
~THEoW. FOR F + E, + ISI? +R
J.C. pDLANYLand Department of Gemistry,
Universiv
3.L SCHREIBER of Toronto, Toronto M5S
iA1. ConffdQ
Received 28 August 1974
Pearson and Schaefer (BOPS) have computed extensive configuration interaction. We have fitted ison with semi-empirical surfaces fcr FHH shows that the generrl ab iniiio fintings Evidence is presented which indicates that’the ‘energy along the favoured route intu the exit valley. Bender,
O’Noil,
ofFHH,using
The reaction F ‘Hz + HF t H is becoming a testing ground for theories of reaction,dynamics. Considersble,experimertal data exist [l-S]. Classical 16-131 and quantum [Id, 151 calculations have been perforrned on semi-empirical potential-energy surfaces. Bender, O’Neil, Pearson and Schaefer (BOPS) [16] have computed 232 ab initio energies, corresponding to collinear FHH configurations, using an extended basis set and 338 configuration wavefunction. The results are most promising. The exothermicity Me = 05 - 07 = 34.4 kcal mole-’ (De is the bond-dissociation energy measured from the bottom of the well; subscripts 1 and 2 refer to the atomic pairs AB and BC in A + BC). The correct ADe lies in the range 3132 kc-al mole-l. The ha&r-height was found to be E, = 1.66 kcal mole -l. This can be compared with the experimental activation energy Ea = 1.6 kcal mole-l [171. We have attempted to make a first assessment cf ,ehe accuracy of the surface on the basis of the fti grid of232 collinear energies. Our comments are ten. tative in the light of the fact that (a) they are based on a classical trajectory study, and (b) we must es& mate the effect of rel&ing the 1D constr+t imposed by the BOPS computations. We b&eve that neither (a) nor (II) are likely to vitiate our findings, which are in the main qualitative. In regard to (a), it should be nbted that we have re-
ab initio energies for 232 coUinev configurations these points using an LEPSWe function. Camp=form
of these suchces
is in goti
accord
~4th the
BOPS ab initio surface exhibits too peat a drop in
stricted burselves to the comparison of average product vibrational excitations, (V’>. Average attributes can be expected to agree satisfactorily zs between classical and quantum calculations [IsI. In connection with (b), it has been found 16,192 - especially for. LEPS surfaces and FYrcdmass combinations - that the collinear cut through the hypersurface gives a qualitative guide to the behatiour on the 3D surface. Hence we can draw qualitative conclusions even prior to correcting for change in dimensional&f . Following an unsuccessful attempt to fit the ab initio points using a hyperbolic map function [21,22], v&switched to using 2.n extended LEPS (London, Eyring, Polanyi, Sato) f&ion [I9] incorporating the Pederson-Porter four-parameter triplet reprezntation [23]. For FHH there were two triplet functions, and hence 8 tripIet paranleters
to be adjusted
by a
non-linear least squares procedure. The rms deviation fro& the 232 ab titio points wa+ < I kcd mole;1 per poir,t. There was a s-mall (spurious) well, 0.35 kca! mole” deep, in the entrance vtiey of the fitted sur-
* here l~s been
of crotig beand t&e non-reactive F’(ZP,,2) t Hz surface. Iitis is believed to be s improbable event [ 13,201. Such c&sings as do oicur MI1 t&e place well out in the entry v&z-y,.arih should have little effect on the mea& product v~brstionzl exdtrction. Bscusdon
of the posaitity
twe=n the F(2P3,z) + I-f2ener&-tirface
319 :
.
Volume 29, number 3.
:
CHEMICAL PHYSICS LETTERS
,’
1 December 1974
I I, Constants for BOPS-FIT a)
:
,fect ?n W’> (as tie have.found G a further trajectory study O~I F + Hz [ 121). The constants for DOPS-FIT are given in table 1. .The collinear ‘energy-surface; BOPS-FIT, is shown
..HF De
> D3
in fig; 1. For comparison we record potentialenergy .contours taken from *be collinear cut through an extended !LEPS [I93 hyper-surface, SE-l, that we have
R*
adjusted on the basis of a full 3D trajectory study to
0
give a satisfactory representation oft!!e experimental product energy_distribution.[12] t. The -mean percentage. conversions of energy into product vibration
Cb) ~b)
P3
(kcalmple-r) (A-‘j:
”
.,
-,:
.‘.Hz. 129.3
94.8
2.316
2047
(A-‘)
; 0.931 St.83 2.229
34.56 1.522
w (A-‘).
1.217 3.090
(A) (kcd mole-‘)
(kcal
mole-! A-‘)
1174.9 1.315
(A)
a) The consents
:
0.753
0.443
1.929 388.8 0.762
arc defined in ref. [23].
b) Values chosen to make the triplet curves smooth at R*.
f The constants for SE-1 were@ = 140.5kcalmole-‘, Dg = 109.5 kczl mole-‘, er= 2.2.2 A-‘, .e2= 1.94 A-l, ry = 0.917 &.r;=0.742A. a=O.lSO,b =O.OEO(o isthe Satoparam-’ eter between F and H,‘b is the corresponding parameter for HH). Surface SE-1 has a classical barrier .heigh t E, = 2.16 kcd mole-l.
:..
,i ‘,
.‘.Table 3
,face, BOPS-FIT. This f&i& will have some’effe.ct on. ,~t.hresh~id behaviotir; but will have tie s-ign~ficanni ef--
and rotation where
,
..
/ 1.00
/ I.25
':A' I.50 @&-3
/ 2.00 !.
,Fig. 1. T!le solid contoursgive the scaled and’skewed collinear potenti&nergy-surface for “BOPSFIT”; a least-squares fit to tbe ab initio computation of ref. 1161 for tbhe resction F + I-IL+ HF + H. Reagents.start at lower right, products are formed at upper, relative to the reagents as zero. Tbe broken contours (energies in parentheses) are taken ,I& Contour energies are in +linoie-‘, frqm YSE_l”,a collineazcut throughihebest semi-empiricalpotential~nergy hypcrsurface obtained in a 3D trajectory study [ 121. The ,-X .indiutes the location of the barrier-crest on BOP%FIT,. and (X) shows the corresponding point on SEL The heavy contours inditite the “shoulder” region from which a typical trajectory is deflected into the exit valley, r2, on BOPSFLT and on SE-L The approximate range of values, rzx, at which trajectories first cross the minimum or the wit valley is.indicated to either side of & .. ,Jtte median value of tV>; l?re approximate range of rzx and.value of& is comtnon to BC!PSFIT:and @-L.
: .-.3g:
,. :
... ‘:1-y 1 : ,’ _,,.,
‘.
.-; .,
.,--
., ..
.: : :.
_..
.’
Volume 29. number 3
CHEMLCAL PHYSICS LETTERS
surfaces reported for this reaction in the literature [6-151 the property of being highly repulsive. The energy-profile along the minimum path qualitatively re‘sembles that obtained in the BEBO (bond energy bond order) approximation, which is, therefore, also indicative of strongly repulsive energy release [24]. We have computed the curvatures of tire minimum paths on SE-l and BOPS-FIT at intervals along their lengths. The region of large curvature comes at approximately the same energy on both surfaces, and is of similar magnitude. We have done the same for Muckerman’s best empirical surface MS [25] ?, with the same result. Truhlar [26] has compared the curvature of the BEBO minimum path for F fH2 with the BOPS ab initio prediction, and has found good agreement. The difference between SE-l and BOPS-FIT (fig. 1) is that the down-hill portion of the surface comes ear-. lier on the BOPS-FIT (ab initio) surface. Examination of over 200 trajectories in 1D and 3D on SE-l, showed that the majority exhibited mixedenergy release [19]; i.e., they “cut the comer” of the surface. Muckerman has reported the same behaviour for F fH2 on. a series of LEPS surfaces (see MT in table II of his 1972 paper; ref. [ci]). Following “comercutting” a trajectory first crosses the exit valley at a configuration we designate rzX (the value of ‘2 at which rl is for the first time reduced to r$). The range of initial vibrational phases in the Hz bond gives rise to a range, of r s; this range is indicated approximately in fig., 1, for HZ (v = 0) and a collision energy near threshold. The mean ‘2X on BOPS-FIT is shown in fig. 1 as &. The corresponding trajectory is deflected off the = 5 kcal contour (the zero point energy of H2 is 6.1 kcal mole-l) in the region indicated by the heavy curve, and enters the exit valley laterally. It is found that, in general, the greater qx the greater Y’. ‘The range of ‘2X it similar on SE-1 and BOPS-FIT, and so is Fh. The difffereence is that a particu!ar r2x gives rise to = 7 kcal mole-l greater V’ on BOPS-FIT than on SE-I, due to the greater acceleration of the representative mass in falling from = 5 kcal down to ~2~(f& is at approx. -32 kcal mole-l on the ab initio surface, and at approx. -22 kcai mole-l on SE-I). i T$e constants for MS were those @ven in Muckerman’s 1972 paper, ref. [e], surface 2, v$th the Sat0 pUaTlekiS set to v&es intermediate between surfaces 2 and 3; A(HF) =o = 0.167, a(HH) =b = 0.106.
1 December
1974
The minimum energy path on Muckermart’s best empirical surface, M5, is intermediate between SE-1 and BOPS-FIT. However, MS clcsely resembles SE-1 in the location of the 5 kcal ‘X-roulder” (the heavy broken contour in fig. 1) thzt marks the onset of mixed energy release, and in the positions of the successive contours along ‘he steepest descent from this point into the exit valley. Both MS and SE-l, tberefore, differ in the same way from BOPS-NT in this important region of configuration space. For SE-lwe have made a systematic study [12I of the effect of lifting the collinear restraints. With the reagents in the range of room temperature, a batch of 1D trajectories on SE-1 yielded C&,1= 74%; in 3D the value was C_&>= 66.5%. For BOPS-FIT, the corresponding batch of 1D trajectories yielded (f’v) = 90%. If one applies the same correction for ID + 3D the fraction of energy entering vibration becomes C&J = 80%. This is significantly in excess of the experimental value of 66%. Increase in dimensionality from lD to 2D or 3D introduces angular momentum. It is noteworthy that on SE-I the decrease in (V’) as 10 --F3D was exactIy matched by increase in a’>. It may be general that AiT/“) z 6(R’) (8 is for lD+2D or 3D). The value of CR’)on SE-l rose from zero, when lD + 3D, to R’) = 3.2 kcal mole-1 -close to the experimental value. If the 1D + 3D transformation of BQPS were to bring (V’) and (li’> from theory into agreement with experiment it would be necessary that -6(V’> = 8 kcal mole-l, much in excess of &CR’). The decrease in (V’J as lD+ 3D is discussed from a general standpoint in two recent papers [27,28]. The Bernstein-Levine theory, predicts the correct sign and order of magnitude for -S(V’). It is noteworthy that their formulation predicts a similar decrease in (Y’) for both SE-I and BOPS-FIT (somewhat Iarger for SE-I). The ab initio findings of Bender, O’NeiI, Pearson and Schaefer are most encouraging for the semi-empirical theorist, since they lend substance to the claims that the energy-surface for F f X2 is highly re-. pulsive, and that it has a curvature along the minimum ene& path of the type associated with the LEPS function. :
More refined collinear ab initio computations should concentrate on the comer region in whkh the energy release occurs. The potentialenergy drop from 321
CHEMICAL FHYSICs LE-ITIIRS
the “shoulder” (characte,&ed by the +5 $cal mole-’ contour) direct& into the exit v&jr appears to be : -too large by:roughly 7 kcal mole-lon.the BOPS ab initio surFace. This results in too great a vibrational enqy release, by-a comparable amount. A significant fraction of this discrepancy can be understood in .terms of ‘the correlation between increased vjbrational excitation’and increased heat of reaction on otherwise comparable energy+urfaces.[24]: the ab initio surface is more exothermic by 3.5 kcal m.ole-* than is SE-L
Acknowledgement’ We are indebted to Drs. C.F. Bender and &. Schaefer III for supplying the ab initiq energies, and to Drs. R.B. Bernstein, T.F. George, A. Kuppennann, K. Morokuma, J.T. Muckemian and D.G. Truhlar for helpful discussions. J.L.S. thanksthe National Research Council of Car&da for a Scholarship during the tenure of which this work ~2s done. J.C.P. thanks the Canada Council for a Xi&k Memorial Scholarship. The work’was supported by grants from the National Research Council of Canada and the Defence Research Board of Canada (Grant No. ?530-104 U.G.). .’
1 Deccmkr
[6] J.T. Muckermq J. Chem. Phyi (1972) 2997: 57 (1972) 3388.
54 (1971)
1974
11.55; 56
[7] R.L. Jnffe-aid J.B. Anderson, J. Chem. Phys 54 (1971) .22:4. ,;.: [8] R.L. Wilkins, J. Chcm. Phys. 57 (1972) 912;58,(1973) 3038. [9] D.G. Truhlar, J. Chem. Phys. 56 (1972) 3189. [lo] J.T. Muckermsn and M.D. Newton, J. Chem. Phys. 56 (1972) 3191. [ll] N.C.‘Blais and D.G. Truh1ar.J. (Shem. Phys Sg(1973) 1090. [ 121 J.L. Schreiber, Ph.D. Thesis, University of Torontc .(J973). [13] 3-C Tuiy, J. Chem. Phys. 60 (1974) 3042. (141 SF. Wu, B.R. Johnson and R.D. Levine, Mol. Phys. 25 (1973) 839. [15] G.C. Schatz, J.M. Bowman and A.,Kuppermann, J. Chem. Phys 58 (1973) 4023. [16] C.F.‘Bender,S.V. O’Neil,P.K. Pearsonand H.F. Schaefer III, Science 176 (1972) 1412. 1171 K.H. van Homann, W.C. Sol.oman, J. Warnatz, H. Gg. Wagner and C. Zetzsch, Z. Elektrochem. 6 (1970) 565. [li3] W.E. Miher, J. Chem. Phys 54 (1971) 5386; R.G..Gordon, Faraday Discussions Chem. Sot. 55 -/1973) 22. [19] P.J. Kuntz, E.M. Nemeth, J.C. Polanyi, S.D. Rosner and CE. Young, J. Chem. Phys. 44 (1966) 1168. [20] T-F. George and K. Morokuma, privite communication. [21 j D.L. Bunker and N.C. Blais, J. Chem. Phys. 41 (1964) 2377. [22] D.L. Bunker and CA Parr, J. Chem. Phys. 52 (1970)
.5700.
References [l] [2] [3] [4] [5]
J.H. Parker and G.C. Pimentel. J. Chem. Phys 51 (1969) 91. J.C. Polanyi ai@ D.C. Tardy, J. ‘Chem. Phys 51 (1969) 5717. N. Jonathan, C.M. Melliar-Smith and D.H. Slater, Mol. Phys 20 (1971) 93. J,C. Polanyi and K.B. Woodall,J. Chem. Phys. 57 (1972) 1574. M-J. Berry, J. Chem. Pbys i9 (1973) 6229..
[23] L. Pederson and R.N. Porter, J. Chem. Phys 47 (1967) 4751; LM. Raff. L. Stivers, R.N. Porter, D.L. Thompson and L.B.. Sims, J. Chem. Phys. 52 (1970) 3449. [24] M.H. Mok and J.C. Polanyi, J. Chem, Phys. 51 (1969) 1451. .[2.5] J.T. Muckem& private communication. [26] D.G. Truhlar, J. Am. Chem. Sot. 94 (1972) 7584. [27] R.B. Walker and RX. Wyatt, Mol. Phys. 28 (1974) 101. [28] R-B. Bernstein and R.D. Levine, Chem. Phys Letters 29 (1974) 314.
.
322: .:
‘-..
.,
.,,
‘,
:. -.
.,.