- Email: [email protected]
An ab initio study of the potential surface for the reaction H2CO+H → HCO+ + H2
Yolume
:
40, riu&er
CHEMICAL
3
PHYSICS
LETTERS
15 June 1976
AN AR JNITIO STUDY OF THE POTENTIAL SURFACE FOR THE RRACTION H2CO+H --f HCO+ + Hz
Department
of Chemistry.
University of Oslo. Oslo 3, Norwa_v
Received 4 March 1976
The potential surface for the reaction HzCO+H 4 HCO+ + Ha has been studied by rib initio SCF calculations, using gaussian-type basis Su&tions. A saddle point on the surface has been found, and a reaction path is proposed to explain the observed release of kinetic energy. The energy of activation and AE for the reaction have been estimated.
1. Introduction
CH,=O+H + Hc=O’ -I-H2 ,
Unimolecular decompositions of positive ions have been previously studied by means of mass spectrometry 111, and the concept of orbital symmetry conservation 123 has been used to explain the observed release of kinetic energy. All the reactions studied in ref. [I ] involve 1,2-elimination of molecular hydrogen. For the reaction CH,-CH;
+ CH,=CH;
+ H,
(1)
full Czv symmetry can be conserved, and an orbital correlation diagram can be constructed in which the ground state configuraiicn of the reactant is correlated with an excited state configuration of the products and vice versa (fig. la). For the reaction
A
,x.: energy
S
A
A
SJ
reactant
products a
Fig..i. Orbital correlation .tb) for reaction (2).
..
..
reacta-nt products b
diagrams (a) for reaction
(1) and
(2)
where the symmetry-constraints of (1) are absent, the correlation diagram takes the form illustrated in fig. 1b. The distance d in fig. 1b will increase as the deviation from symmetry increases. For both types of reactions, however, a “symmetry-imposed” barrier is expected, i.e. a relatively high energy of activation_ This is also in accordance with experimental findings [ 11. For reaction (?) the experimental estimate of the energy of activation is 80 kcal/mol and for M 27 kcal/mol. This gives an energy of activation of 53 kcal/mol for the reverse reaction, whiIe the observed release of kinetic energy is 33 kcal/mol
VIIn addition
the correlation diagram (fig. la) indicates that the transition state cannot be satisfactorily described by a single-configuration wavefunction. To a certain extent this is also the case for reaction (2). This implies that calculations based on a single configuration model will overestimate the energies of activation for “symmetry-forbidden” reaction [like (1) and (2% In this work, ab initio SCF calculations on the potential surface for the reaction (2) have been performed. The aim has primarily been to find a reaction path and to investigate the transition state region. Furthermore it has been our hope to find a reaction mechanism explaining the observed release of kinetic energy_
Volume40.number
.CHEMlCAL
3
PHYSICSLETFEKS
lSJunel976
2. Method of calcuIation The calcul?tions were carried out using the computer program MOLECULE [3] which solves the Roothaan-Hall equations for a basis set of contracted gaussian functions. Two types of basis set were applied. The majority of the calculations were performed using a (7~3~14~1p) basis contracted to (4s2p/2slp). The orbital exponents and contraction coefficients applied for carbon and oxygen were those of Roos and Siegbahn [4 1. For the hydrogen s-functions Huzinaga’s basis [S] scaled by a factor 1.2 [6] was used, while for the hydrogen pfunctions an exponent value of 0.90 was applied 171. For a few selected conformations, calculations were carried out using a (9s5pl d) basis contracted to (4~2~1 d) for carbon and oxygen, leaving the hydrogen basis unchanged. The orbital exponents and contraction coefficients were those of Huzinaga [5], except for the d-orbitals where orbital exponents of 0.95 were applied for both atoms [7].
3. Results The results below refer to calculations with the (7~3~14~1p) basis if nothing else is specified. For the reactant ion (fig. 2) a planar structure was assumed. Furthermore the two CH bond lengths were assumed equal, and the H-C-H angle was fixed at 120°. Under these assumptions the remaining molecular parameters were optimized. For the product species (fig. 3) full geometry optimization was performed. The results from these calculations are given in table 1 _ The number of independent geometry parameters was considered toolarge to make feasible a full calcu-
Fig. 2. The geometry and labelling of the atoms for ?he reactant.
A
Hc--~---_
%I---
0+
Hb
Fig. 3. The geometry and labelling product species.
of the atoms for the
lation of the reaction surface. As an approximation to the reaction path, a reaction coordinate R was defined as the distance between the centers of the CO and the HH bond. The C-H, and 0-Hb distances were assumed equal. From table 1 it is seen that the CH bond length is practically unaffected by the reaction, so in alI following calculations the C-H, bond length was fixed at 1.080 a The reaction was first simulated by a number of calculations where the reaction coordinate R was varied. For each value of R the remaining molecular parameters, ~HH, I-,-O and the angle A (fig. 3) were optimized. The results from these calculations are given in table 2 as calculations no. l-6 and 13-22.
Table 1 Resuits from the calcuIations on the reactant and the products Rotonated W--H
formaldehyde a) = 1.080 A b)
= 1.260 A &!=o = 0.959 A rO-H LH-C=O= 116.8” c) LH-O=C = 120.8” Etot = - 114.0137S au a) k planar structure was assumed.
Formylium(+) rC-H
ion
= 1.079 A
= 1.102 A rc-_=o LH-C&O = 180.C” au Etot = -112.79392
b) The two C-H bonds
were assumed equal.
Hydrogen molecule ~HH = 0.737 A Etot = -1.13122
au
c) The C-H bond cis to the O-H bond.
463
-, t’ol~me’&j,-.&&f
j.:
_ :
_-
CHEMIC.$L ~Ii~~I~S
LJZITERS
.
15 June 197Q
.,:-
.-
-I’ Tabi&. ;- 1 ,. : Results fronY&su&tions otiihe rea&ion H&O*H --* HCO++ Hz .;
.-
c&l no .-.
7 a’
3.83328 -113.80144 --113.;940s -113.79280
-II
.
-113.79408
,.-
-113.78762 -113.76622
9
-113.74883 -113.76764
‘co
= 0:86 1.cloo 1.450 1.500 1.517 1s20
.2.343 2.090 2.080 2.080 2.080 2.080
1.260 1.270 1.261 1.261 1.261 1.261
t82.24 ~86.29
1.517 1.117
2.080 1.800
+99.72
1.517
1.500
i110.63 -+98.83
1.517 1s17
1.200 1.000
1.261 1.261 1.261 1.186 1.139
131.7 149.3 163.5
+g2.17
I.517
0.723
1.119
172.9
1.119 1.119 1.119 1.102 1.102 1.102 1.102 1.102 1.102 1.102
172.9 172.9 172.9 178.5 180.0 180.0 180.0 180.0 180.0 180.0
10 11 13
.-113.79419
13
-113.78781
i-86.17
1.soo
0.723
14 15 16 17 18
-113.79419 -113.79528 -113.89912 -113.92311 -113.92626 -113.92573 -113.92541 -113.92529 ,113.92514
t-82.17 +81.49 s16.33 + 1.27 -_ 0.70 - 0.37 - 0.17 - 0.09 0.0
1.517
0.723 0.723 0.725 0.734 0.737 0.737 0.737 0.737 0.737
:: 21 22 d)
-
a) Relative to the energy of the products, c) The reactant (table 1, fig. 2):
-113.92514
1.520 2.ooe 2.500 3.000 4.000 5.000 6.000
au.
For R-values near 1.5 A, intersections of the potential surface
along R have two minima,
one for a short
HH distance (= 0.727 a) which corresponds
to the
bond iength in the hydrogen molecule, and one for a considerably longer one (a 2.080 A) which is near the co!responcJing distance in the reactant ion. In fig. 4 a plot of the total enerB as a function of R is given. It is seen that this plot consists of two distinct curves intersecting at R = 1.5 17 A. This implies that a single vafiable R is insufficient- to adequately describe the r&action pa&, and at least one additional degree of frtiedom, r&, has tb be taken@0 consideration. The !olid curvti in fig. 4 passes thrdugh a tinimum at R R 3.0 a. This predicts a weak Complex between the product species with a bond energy of ~0.7 kcal/mol... Fe ca!ctilations made so far gs.ve +I estimate of .‘AE for the re&tiqn of 56 kcallmol. The &+erimentd data indicate. .!hat this -glue is too large. in order to Y-,_._
-.,.. ._.
,._
I-.
(deg) b)
rHH (Aj
-55.60 -44.41 i63.92 +17.62 +82.24 -+83.04
-113.99591
A
R.(A)
(kcal/moI)
.- :-114.01375
‘,-.1c) 2. :3 4 5 B
A.!?+
Got (au) _.
(A)
116.8 119.0 124.9 124.9 124.9 124.9 124.9
126.2
b) The angle A is defined in fig. 3. d) The separatedproduct species (table 1, fig. 3).
test whether a larger basis set would influence upon this result, 2 few calculations were performed with the (9s5pl d/4slp) basis. The results.are given in table 3. With the exception of the value of AE for the reaciion, which decreased to 46 kcal/mol, the calculations with the larger basis set seem to reproduce the main features of the potential surface calculated with the (7s3p/4slp) basis. From the results so far, it would seem probable that the contraction of ‘HH will occur within a rather narrow range of R around I -517 A. A number of calculations were then performed in which R was kept constant at 1.517 A and ‘HH .varied. rco and LA were optimized for each value of rHH. The results are given in table 2 as caltiulation_no. 7-12. These results indicate that it is necessary to cross an energy barrier of-= 50 kczi/mol in order to come from the dashed to the &lid -ctirve &I fig. 4; Maxi&urn ener& is reached
_-_,.: _-.
Volume 40, number 3
CHEMICAL PHYSlCs LETTERS
15 June 1976
Table 3 Comparison between cakvlations Sgstem c,
with (9s5pld/4sl.p) (9sSpldj4slp)
basis and (7~3p/$lp) --
basis
ac” d
Etot (au)
_--l-l (7s3~/4sl P) basis
basis
#.?b)
E&t (au)
(kcal/mol)
(kcal/mol) reac@nt HCO* R = 3.0
-114.01375 -112.79392 -113.92626
-46.33
-114.17536 -112.97029 -114JO269
-
0.74
-55.60 - 0.70
intersection point of the two curves in fig. 4: (9.5.1/4.E) basis : R = 1.494 A, AEa) = 82.5 (7.3i4.1) AE h) = 82.2 basis : R = 1.517 A* -___ a) Relative to the energy of the products, -114.10151 au. c) For both basis sets the geometry Found with the (7.3/4-l)
t
--
b) Relative to the energy of the products, -113.92514 basis is used (tables 1 and 2).
Table 4 Fnergy results for determination of the saddle point. The energies are given in au X lO* relative to -113.75000 au
AE(kcal/mol)
R (A)
‘HH (A)
1.397
70 1.020 1.040 1.060
50 -
1.080 l-100 1.120 1.140
JO-
lo-
1.160 1.0;
-lO-
au.
2.0
3.0
L.0
50
"Cl
1.417
1.437
1.457
1.477
1.497
-292
-275 -551
-195
-229 -205
-449 -227 -672
-
-251
-244
-852
-381
-263 -159
-112 486
R(A)
Fig. 4. Variationbf the energy (AE in kcsl/mol relative to the energy of the products) with the reaction coordinake R (R bx A). The dashed cu_we’corresponds to ‘HH * 0.73 A, while the solid curve corresponds to ~HH = 2.08 A.
for ‘HH * 1.2 A, but further information is required to decide whether t&is point can be regarded & art approximation to the transition state for the reaction. Therefore R and ~HH were varied systematically in small steps starting from the point R = 1.5 17 A, rHH = 1.200 A. Assuming the couplings betjveen the geometry parameters to be ,small, rco and LA were faed at the optimal values for the starting point;. 1 .186 A, 149.3’. A saddle point was localized, and in table 4 the energies used for the final determination of this are given. According to this data, the point
.CHEMICAL PHYSICS LEMERS
Volume 40, number 3
15 June 1476
4. Discussion The-calculation of the potential surface is not complete, but if the calculations are systematized, the main features appear. The surface is characterized by two roughly parallel “valleys”, the higher parts of which are separated by the saddle-point region. From here they go down in opposite directions, ending in the reactant and the products, respectively. A probable reaction path will then be the following approximative three-step reaction: In the first step R increases with near constant ‘HH, i.e. the dashed part of fig. 4 is followed. The second step involves a contraction of THH passing the saddle point, and accompanied by a small increase of R. This step brings the reacting sys-
102 lOGI-
106-
108 ’
110-
112
-
Il.5 -
tem from a point on the dashed to a point on the
1 r”,A
116
Fig. 5. Semiquantitative contour diagram of tile sadd!e-point are;i. The diagram is based on the results from table 4 (marked with points). The isoenergetic contours correspond to I?= - 113.75200 au and E = -113.75230 au and the saddle point is localized at R = 1.450 A, ?HH = 1.070 A, E= -113.75115 au_
must be close to R = 1.45 # and rHH = 1.07 A. The saddle structure of the surface is easily seen from fig. 5, lsrhere regions of energy higher and Iower than the saddle point are shown. Finally the energy of the saddle point was minimized with respect to rco and LA. The results, 1.191 Aand !51.1° are close to the previously assumed ones, and the energy gain is also small (0.00009 au). ‘&is shows that the couplings between the geometry parameters are small, as assumed. The cdculated results for the saddle point are summarized in table 5. Table 5 CMculatPd results for the saddie point of the potential surface for.the reaction Hz&H - HCO’ + Ha = 1.450 A = 1.070 ii = 1.191 A : LA =-151x
Got = - 1 i 3.75224 au AE a) = 164.1 kcal/mol tib) = 108.~ licd/mol
R. f& y-J
’
a) Relz&a to the energy. of the react&t’, -114.01375 au. b) Rehtive‘to the energy of the products, -113.925 14 au.
466
solid curve in fig. 4. At this stage the situation can be physically described as a hydrogen molecule and a formylium (+) ion very close together, and the third step involves a mutual repulsion of these two molecular species. Again R is increasing with near constant ‘HH, and the solid part of fig. 4 is followed. The main part of the liberated energy is released in the third step, and in this step essentially all the released energy is used to increase the reaction.coordinate R, not to excite the stretching vibration of the Hz molecule. The proposed reaction mechanism therefore might explain the observed release of kinetic energy in this reaction. The calculated energy of activation is 164.1 kcal/mol, while the corresponding experimental value is only 80 kcal/mol [l]. This discrepancy is expected, however, as due to near degeneration correlation effects. Concerning the estimate of AE for the reaction, this is compared with experimental estimates of the enthalpy change for the reaction. AH for the reaction is found as the difference botween the AH! values for the reactant and the products. However, AHfO values for ions are not easily determined, and the reported values vary from 220-197 kcal/mol [S-l 21 and 173-170 kcal/mol [13,14] for HCOf and HZCO+H respectively. This gives a AH of 24-50 kcal/mol. It is generally accepted that the lowest experimental ionicheat of formation is the best approximation to the true value [9], and the difference between the lowest repoited A@ values for the reactant and the products gives AH = 27 kcal/mol. The calculated estimate for AE is 46 kcal/mo!. In this reaction two o bonds are
Volume 40, number 3
CHEMICAL PHYSICS LEZTERS
Table 6 Results from the population analysis, (7s3p/Sslp) basis Reactant
Transition state
Products
5.401 8.372
5.354
15 June 1976
found for this state are in fair accordance with the results obtained in this work.
Acknowledgement
gross atomic Populations C
5.479
0
8.352
% Ha %
0.755 0.778
0.637
overlap populations C 4.363 0 7.716 c-o 0.723 Hc 0.410 CHc 0.780 Ha 0.442 Hb 0.337 C-Ha 0.778 O-Hb Ha-Hb
0.657 -0.006
0.667 1.134 0.427
8.063 0.584 1.000 1.000
4.359 8.147 0.750 0.345 0.696 0.907 0.193
4.310 7.355 1.418 0.251 0.669 0.583 0.583
0.536 0.058 0.310
0.834
broken and one new o bond and one ‘ITbond are formed. Since a bonds are generalIy better described than fl bonds within the HF approximation, the calculated AE is expected to be too bigb. This error can be estimated to be of the order 5-10 kcal/mol. Some results from a Mulliken population analysis of the wavefunctions IIS] are given in table 6. We observe that, in going from the reactant to the transition state, the C-H, and the O-Hb bonds are polarized in opposite directions. Similar charge transports are found in the calculations by Smyth and Shannon [ 161. They proposed a semi-ion-pair-model of the transition state, and both the geometrical and electronic structure
The author is indebted to Dr. G. Hvistendahl for stimulating discussions on the experimentaf background, and to Drs. I. Almlijf and H. Jensen for helpful discussions and comments on the manuscript.
References 111D.H. Williams and G. Hvistendahl, J. Am. Chem. Sot. 96 (I 974) 6753.
PI R.B. Woodward and R. Hoffmann, Angew. Chem. intern. Ed. 8 (1969) 797. 131 J. Almliif, WSIP Rep. 74-29, University of Stockholm (1974).
[41 B. Roos and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 209. 151 5. Huzinaga, J. Chem. Phys. 42 (196% 1293. [61 T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823. 171 H. Jensen and 6. Aamodt, unpublished results. 181 C.S. Matteus and P. Warneck, J. Chem. Phys. 51 (1969) 854.
PI H. Pritchard and A.G. Harrison, J. Chem. Phys. 48 (1968) 2827. F.H. Dorman, J. Chem. Phys. 50 (1969) 1042. ‘,::; A.G. H&rison, J. Chem. Phys. 50 (1969) 1043. [=I J-P. Majer, C.P. Patrick and J.C. Robb, Trans. Faraday Sot. 57 (1961) 14. 1131 K.M.A. Refaey and W.A. Chupka, J. Chem. Phys. 48 (1968) 5205. El41 M.T. Bowers, W.J. Chesnavich and W.T. Huntress, Intern. J. Mass Spectrom. Ion Phys. 12 (1973) 357. 115 ] R.S. Multiken, J. Chem. Phys. 23 (195.5) 1833. [ 161 K.C. Smyth and T.W. Shannon, J. Chem. Phys. 51
(1969) 4633.
467
:
40, riu&er
CHEMICAL
3
PHYSICS
LETTERS
15 June 1976
AN AR JNITIO STUDY OF THE POTENTIAL SURFACE FOR THE RRACTION H2CO+H --f HCO+ + Hz
Department
of Chemistry.
University of Oslo. Oslo 3, Norwa_v
Received 4 March 1976
The potential surface for the reaction HzCO+H 4 HCO+ + Ha has been studied by rib initio SCF calculations, using gaussian-type basis Su&tions. A saddle point on the surface has been found, and a reaction path is proposed to explain the observed release of kinetic energy. The energy of activation and AE for the reaction have been estimated.
1. Introduction
CH,=O+H + Hc=O’ -I-H2 ,
Unimolecular decompositions of positive ions have been previously studied by means of mass spectrometry 111, and the concept of orbital symmetry conservation 123 has been used to explain the observed release of kinetic energy. All the reactions studied in ref. [I ] involve 1,2-elimination of molecular hydrogen. For the reaction CH,-CH;
+ CH,=CH;
+ H,
(1)
full Czv symmetry can be conserved, and an orbital correlation diagram can be constructed in which the ground state configuraiicn of the reactant is correlated with an excited state configuration of the products and vice versa (fig. la). For the reaction
A
,x.: energy
S
A
A
SJ
reactant
products a
Fig..i. Orbital correlation .tb) for reaction (2).
..
..
reacta-nt products b
diagrams (a) for reaction
(1) and
(2)
where the symmetry-constraints of (1) are absent, the correlation diagram takes the form illustrated in fig. 1b. The distance d in fig. 1b will increase as the deviation from symmetry increases. For both types of reactions, however, a “symmetry-imposed” barrier is expected, i.e. a relatively high energy of activation_ This is also in accordance with experimental findings [ 11. For reaction (?) the experimental estimate of the energy of activation is 80 kcal/mol and for M 27 kcal/mol. This gives an energy of activation of 53 kcal/mol for the reverse reaction, whiIe the observed release of kinetic energy is 33 kcal/mol
VIIn addition
the correlation diagram (fig. la) indicates that the transition state cannot be satisfactorily described by a single-configuration wavefunction. To a certain extent this is also the case for reaction (2). This implies that calculations based on a single configuration model will overestimate the energies of activation for “symmetry-forbidden” reaction [like (1) and (2% In this work, ab initio SCF calculations on the potential surface for the reaction (2) have been performed. The aim has primarily been to find a reaction path and to investigate the transition state region. Furthermore it has been our hope to find a reaction mechanism explaining the observed release of kinetic energy_
Volume40.number
.CHEMlCAL
3
PHYSICSLETFEKS
lSJunel976
2. Method of calcuIation The calcul?tions were carried out using the computer program MOLECULE [3] which solves the Roothaan-Hall equations for a basis set of contracted gaussian functions. Two types of basis set were applied. The majority of the calculations were performed using a (7~3~14~1p) basis contracted to (4s2p/2slp). The orbital exponents and contraction coefficients applied for carbon and oxygen were those of Roos and Siegbahn [4 1. For the hydrogen s-functions Huzinaga’s basis [S] scaled by a factor 1.2 [6] was used, while for the hydrogen pfunctions an exponent value of 0.90 was applied 171. For a few selected conformations, calculations were carried out using a (9s5pl d) basis contracted to (4~2~1 d) for carbon and oxygen, leaving the hydrogen basis unchanged. The orbital exponents and contraction coefficients were those of Huzinaga [5], except for the d-orbitals where orbital exponents of 0.95 were applied for both atoms [7].
3. Results The results below refer to calculations with the (7~3~14~1p) basis if nothing else is specified. For the reactant ion (fig. 2) a planar structure was assumed. Furthermore the two CH bond lengths were assumed equal, and the H-C-H angle was fixed at 120°. Under these assumptions the remaining molecular parameters were optimized. For the product species (fig. 3) full geometry optimization was performed. The results from these calculations are given in table 1 _ The number of independent geometry parameters was considered toolarge to make feasible a full calcu-
Fig. 2. The geometry and labelling of the atoms for ?he reactant.
A
Hc--~---_
%I---
0+
Hb
Fig. 3. The geometry and labelling product species.
of the atoms for the
lation of the reaction surface. As an approximation to the reaction path, a reaction coordinate R was defined as the distance between the centers of the CO and the HH bond. The C-H, and 0-Hb distances were assumed equal. From table 1 it is seen that the CH bond length is practically unaffected by the reaction, so in alI following calculations the C-H, bond length was fixed at 1.080 a The reaction was first simulated by a number of calculations where the reaction coordinate R was varied. For each value of R the remaining molecular parameters, ~HH, I-,-O and the angle A (fig. 3) were optimized. The results from these calculations are given in table 2 as calculations no. l-6 and 13-22.
Table 1 Resuits from the calcuIations on the reactant and the products Rotonated W--H
formaldehyde a) = 1.080 A b)
= 1.260 A &!=o = 0.959 A rO-H LH-C=O= 116.8” c) LH-O=C = 120.8” Etot = - 114.0137S au a) k planar structure was assumed.
Formylium(+) rC-H
ion
= 1.079 A
= 1.102 A rc-_=o LH-C&O = 180.C” au Etot = -112.79392
b) The two C-H bonds
were assumed equal.
Hydrogen molecule ~HH = 0.737 A Etot = -1.13122
au
c) The C-H bond cis to the O-H bond.
463
-, t’ol~me’&j,-.&&f
j.:
_ :
_-
CHEMIC.$L ~Ii~~I~S
LJZITERS
.
15 June 197Q
.,:-
.-
-I’ Tabi&. ;- 1 ,. : Results fronY&su&tions otiihe rea&ion H&O*H --* HCO++ Hz .;
.-
c&l no .-.
7 a’
3.83328 -113.80144 --113.;940s -113.79280
-II
.
-113.79408
,.-
-113.78762 -113.76622
9
-113.74883 -113.76764
‘co
= 0:86 1.cloo 1.450 1.500 1.517 1s20
.2.343 2.090 2.080 2.080 2.080 2.080
1.260 1.270 1.261 1.261 1.261 1.261
t82.24 ~86.29
1.517 1.117
2.080 1.800
+99.72
1.517
1.500
i110.63 -+98.83
1.517 1s17
1.200 1.000
1.261 1.261 1.261 1.186 1.139
131.7 149.3 163.5
+g2.17
I.517
0.723
1.119
172.9
1.119 1.119 1.119 1.102 1.102 1.102 1.102 1.102 1.102 1.102
172.9 172.9 172.9 178.5 180.0 180.0 180.0 180.0 180.0 180.0
10 11 13
.-113.79419
13
-113.78781
i-86.17
1.soo
0.723
14 15 16 17 18
-113.79419 -113.79528 -113.89912 -113.92311 -113.92626 -113.92573 -113.92541 -113.92529 ,113.92514
t-82.17 +81.49 s16.33 + 1.27 -_ 0.70 - 0.37 - 0.17 - 0.09 0.0
1.517
0.723 0.723 0.725 0.734 0.737 0.737 0.737 0.737 0.737
:: 21 22 d)
-
a) Relative to the energy of the products, c) The reactant (table 1, fig. 2):
-113.92514
1.520 2.ooe 2.500 3.000 4.000 5.000 6.000
au.
For R-values near 1.5 A, intersections of the potential surface
along R have two minima,
one for a short
HH distance (= 0.727 a) which corresponds
to the
bond iength in the hydrogen molecule, and one for a considerably longer one (a 2.080 A) which is near the co!responcJing distance in the reactant ion. In fig. 4 a plot of the total enerB as a function of R is given. It is seen that this plot consists of two distinct curves intersecting at R = 1.5 17 A. This implies that a single vafiable R is insufficient- to adequately describe the r&action pa&, and at least one additional degree of frtiedom, r&, has tb be taken@0 consideration. The !olid curvti in fig. 4 passes thrdugh a tinimum at R R 3.0 a. This predicts a weak Complex between the product species with a bond energy of ~0.7 kcal/mol... Fe ca!ctilations made so far gs.ve +I estimate of .‘AE for the re&tiqn of 56 kcallmol. The &+erimentd data indicate. .!hat this -glue is too large. in order to Y-,_._
-.,.. ._.
,._
I-.
(deg) b)
rHH (Aj
-55.60 -44.41 i63.92 +17.62 +82.24 -+83.04
-113.99591
A
R.(A)
(kcal/moI)
.- :-114.01375
‘,-.1c) 2. :3 4 5 B
A.!?+
Got (au) _.
(A)
116.8 119.0 124.9 124.9 124.9 124.9 124.9
126.2
b) The angle A is defined in fig. 3. d) The separatedproduct species (table 1, fig. 3).
test whether a larger basis set would influence upon this result, 2 few calculations were performed with the (9s5pl d/4slp) basis. The results.are given in table 3. With the exception of the value of AE for the reaciion, which decreased to 46 kcal/mol, the calculations with the larger basis set seem to reproduce the main features of the potential surface calculated with the (7s3p/4slp) basis. From the results so far, it would seem probable that the contraction of ‘HH will occur within a rather narrow range of R around I -517 A. A number of calculations were then performed in which R was kept constant at 1.517 A and ‘HH .varied. rco and LA were optimized for each value of rHH. The results are given in table 2 as caltiulation_no. 7-12. These results indicate that it is necessary to cross an energy barrier of-= 50 kczi/mol in order to come from the dashed to the &lid -ctirve &I fig. 4; Maxi&urn ener& is reached
_-_,.: _-.
Volume 40, number 3
CHEMICAL PHYSlCs LETTERS
15 June 1976
Table 3 Comparison between cakvlations Sgstem c,
with (9s5pld/4sl.p) (9sSpldj4slp)
basis and (7~3p/$lp) --
basis
ac” d
Etot (au)
_--l-l (7s3~/4sl P) basis
basis
#.?b)
E&t (au)
(kcal/mol)
(kcal/mol) reac@nt HCO* R = 3.0
-114.01375 -112.79392 -113.92626
-46.33
-114.17536 -112.97029 -114JO269
-
0.74
-55.60 - 0.70
intersection point of the two curves in fig. 4: (9.5.1/4.E) basis : R = 1.494 A, AEa) = 82.5 (7.3i4.1) AE h) = 82.2 basis : R = 1.517 A* -___ a) Relative to the energy of the products, -114.10151 au. c) For both basis sets the geometry Found with the (7.3/4-l)
t
--
b) Relative to the energy of the products, -113.92514 basis is used (tables 1 and 2).
Table 4 Fnergy results for determination of the saddle point. The energies are given in au X lO* relative to -113.75000 au
AE(kcal/mol)
R (A)
‘HH (A)
1.397
70 1.020 1.040 1.060
50 -
1.080 l-100 1.120 1.140
JO-
lo-
1.160 1.0;
-lO-
au.
2.0
3.0
L.0
50
"Cl
1.417
1.437
1.457
1.477
1.497
-292
-275 -551
-195
-229 -205
-449 -227 -672
-
-251
-244
-852
-381
-263 -159
-112 486
R(A)
Fig. 4. Variationbf the energy (AE in kcsl/mol relative to the energy of the products) with the reaction coordinake R (R bx A). The dashed cu_we’corresponds to ‘HH * 0.73 A, while the solid curve corresponds to ~HH = 2.08 A.
for ‘HH * 1.2 A, but further information is required to decide whether t&is point can be regarded & art approximation to the transition state for the reaction. Therefore R and ~HH were varied systematically in small steps starting from the point R = 1.5 17 A, rHH = 1.200 A. Assuming the couplings betjveen the geometry parameters to be ,small, rco and LA were faed at the optimal values for the starting point;. 1 .186 A, 149.3’. A saddle point was localized, and in table 4 the energies used for the final determination of this are given. According to this data, the point
.CHEMICAL PHYSICS LEMERS
Volume 40, number 3
15 June 1476
4. Discussion The-calculation of the potential surface is not complete, but if the calculations are systematized, the main features appear. The surface is characterized by two roughly parallel “valleys”, the higher parts of which are separated by the saddle-point region. From here they go down in opposite directions, ending in the reactant and the products, respectively. A probable reaction path will then be the following approximative three-step reaction: In the first step R increases with near constant ‘HH, i.e. the dashed part of fig. 4 is followed. The second step involves a contraction of THH passing the saddle point, and accompanied by a small increase of R. This step brings the reacting sys-
102 lOGI-
106-
108 ’
110-
112
-
Il.5 -
tem from a point on the dashed to a point on the
1 r”,A
116
Fig. 5. Semiquantitative contour diagram of tile sadd!e-point are;i. The diagram is based on the results from table 4 (marked with points). The isoenergetic contours correspond to I?= - 113.75200 au and E = -113.75230 au and the saddle point is localized at R = 1.450 A, ?HH = 1.070 A, E= -113.75115 au_
must be close to R = 1.45 # and rHH = 1.07 A. The saddle structure of the surface is easily seen from fig. 5, lsrhere regions of energy higher and Iower than the saddle point are shown. Finally the energy of the saddle point was minimized with respect to rco and LA. The results, 1.191 Aand !51.1° are close to the previously assumed ones, and the energy gain is also small (0.00009 au). ‘&is shows that the couplings between the geometry parameters are small, as assumed. The cdculated results for the saddle point are summarized in table 5. Table 5 CMculatPd results for the saddie point of the potential surface for.the reaction Hz&H - HCO’ + Ha = 1.450 A = 1.070 ii = 1.191 A : LA =-151x
Got = - 1 i 3.75224 au AE a) = 164.1 kcal/mol tib) = 108.~ licd/mol
R. f& y-J
’
a) Relz&a to the energy. of the react&t’, -114.01375 au. b) Rehtive‘to the energy of the products, -113.925 14 au.
466
solid curve in fig. 4. At this stage the situation can be physically described as a hydrogen molecule and a formylium (+) ion very close together, and the third step involves a mutual repulsion of these two molecular species. Again R is increasing with near constant ‘HH, and the solid part of fig. 4 is followed. The main part of the liberated energy is released in the third step, and in this step essentially all the released energy is used to increase the reaction.coordinate R, not to excite the stretching vibration of the Hz molecule. The proposed reaction mechanism therefore might explain the observed release of kinetic energy in this reaction. The calculated energy of activation is 164.1 kcal/mol, while the corresponding experimental value is only 80 kcal/mol [l]. This discrepancy is expected, however, as due to near degeneration correlation effects. Concerning the estimate of AE for the reaction, this is compared with experimental estimates of the enthalpy change for the reaction. AH for the reaction is found as the difference botween the AH! values for the reactant and the products. However, AHfO values for ions are not easily determined, and the reported values vary from 220-197 kcal/mol [S-l 21 and 173-170 kcal/mol [13,14] for HCOf and HZCO+H respectively. This gives a AH of 24-50 kcal/mol. It is generally accepted that the lowest experimental ionicheat of formation is the best approximation to the true value [9], and the difference between the lowest repoited A@ values for the reactant and the products gives AH = 27 kcal/mol. The calculated estimate for AE is 46 kcal/mo!. In this reaction two o bonds are
Volume 40, number 3
CHEMICAL PHYSICS LEZTERS
Table 6 Results from the population analysis, (7s3p/Sslp) basis Reactant
Transition state
Products
5.401 8.372
5.354
15 June 1976
found for this state are in fair accordance with the results obtained in this work.
Acknowledgement
gross atomic Populations C
5.479
0
8.352
% Ha %
0.755 0.778
0.637
overlap populations C 4.363 0 7.716 c-o 0.723 Hc 0.410 CHc 0.780 Ha 0.442 Hb 0.337 C-Ha 0.778 O-Hb Ha-Hb
0.657 -0.006
0.667 1.134 0.427
8.063 0.584 1.000 1.000
4.359 8.147 0.750 0.345 0.696 0.907 0.193
4.310 7.355 1.418 0.251 0.669 0.583 0.583
0.536 0.058 0.310
0.834
broken and one new o bond and one ‘ITbond are formed. Since a bonds are generalIy better described than fl bonds within the HF approximation, the calculated AE is expected to be too bigb. This error can be estimated to be of the order 5-10 kcal/mol. Some results from a Mulliken population analysis of the wavefunctions IIS] are given in table 6. We observe that, in going from the reactant to the transition state, the C-H, and the O-Hb bonds are polarized in opposite directions. Similar charge transports are found in the calculations by Smyth and Shannon [ 161. They proposed a semi-ion-pair-model of the transition state, and both the geometrical and electronic structure
The author is indebted to Dr. G. Hvistendahl for stimulating discussions on the experimentaf background, and to Drs. I. Almlijf and H. Jensen for helpful discussions and comments on the manuscript.
References 111D.H. Williams and G. Hvistendahl, J. Am. Chem. Sot. 96 (I 974) 6753.
PI R.B. Woodward and R. Hoffmann, Angew. Chem. intern. Ed. 8 (1969) 797. 131 J. Almliif, WSIP Rep. 74-29, University of Stockholm (1974).
[41 B. Roos and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 209. 151 5. Huzinaga, J. Chem. Phys. 42 (196% 1293. [61 T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823. 171 H. Jensen and 6. Aamodt, unpublished results. 181 C.S. Matteus and P. Warneck, J. Chem. Phys. 51 (1969) 854.
PI H. Pritchard and A.G. Harrison, J. Chem. Phys. 48 (1968) 2827. F.H. Dorman, J. Chem. Phys. 50 (1969) 1042. ‘,::; A.G. H&rison, J. Chem. Phys. 50 (1969) 1043. [=I J-P. Majer, C.P. Patrick and J.C. Robb, Trans. Faraday Sot. 57 (1961) 14. 1131 K.M.A. Refaey and W.A. Chupka, J. Chem. Phys. 48 (1968) 5205. El41 M.T. Bowers, W.J. Chesnavich and W.T. Huntress, Intern. J. Mass Spectrom. Ion Phys. 12 (1973) 357. 115 ] R.S. Multiken, J. Chem. Phys. 23 (195.5) 1833. [ 161 K.C. Smyth and T.W. Shannon, J. Chem. Phys. 51
(1969) 4633.
467