PNO-CEPA calculation of collinear potential energy barriers for thermoneutral exchange reactions

Chemical Physics 20 (1977) 43-52 0 North-HoUand Publishing Company

PNO-CEPA

CALCULATION

FOR THERMONEUTRAL

OF COLLINEAR EXCHANGE

POTENTIAL

ENERGY

BARRIERS

REACTIONS

Peter BOTSCHWINA and Wilfried MEYER Inrtitut fG Physikalische Chetnie tier Universit% Mainr. Gerntatty Received 7 July 1976

The barrier crests for the colIinear thermoneutral exchange reactions H’+ XH - H’X + H (X = H. F. Cl and CHs) have been c.aIcuIattxi from PNOCEPA wavefunctions, which acaun? for a large fraction of the valence correlation energy (80 per cent or more). At the barrier crests. the HX bond lengths are somewhat elongated with respect to the equilibrium bond lengths of the HX molecules (in A): 0.17. 0.23, 0.23 and 0.27 for X = H, F, Cl and CHs, respectively. The RHF-SCF barrier heights are lowered by 13.7 kcal/mol for H + Ha and by about 20 kcal/mol for tbe other reactions upon inclusion of correlation effects, with the CEPA barrier heights amounting to (ii the same order as above, in kcal/mol): 10.7,44.9.22-L and 41.6. These values are estimated to be too large by the following amounts (in kcallmol): 0.9 to 1.3 for H-H-H, 5 to 7 for H-F-H, 7 to 12 for H-Cl-H and 5 to 10 for H-CHs-H. Except for H + B t, the barrier heights obtained with the bond energy -bond order method of Parr and Johnston deviate dnstically from the present results.

I. Introduction The knowledge of activation energies for thermoneutral exchange reactions, especially in halogen-hydrogen systems, is of considerable interest. Such reactions, like Cl’ + HCl + Cl’?! + Cl,

(RI)

Or

H’ + CIH -f H’CI + H,

(=9

may be partly responsible for the rapid relaxation of vibrationally excited molecules and may thus provide a limiting factor in chemical Laser systems. The direct measurement of the activation energies seems to be difficult and rather different values are discussed for (Rl) and (R2) [l-3] . For the reactions H’+FH+H’F+H,

(=Q

and F’+HF-+F’H+F,

for a successful construction of semi-empirical potential energy surfaces, which are widely used in dynamical mostly quasiclassical trajectory calculations. Calculation of the interesting parts of potential energy surfaces from ab initio wavefunctions has become popular in the last few years [4--61. For thermoneutral reactions, where at least one of the reactants is an open-shell atom or molecule, it is crucial to take properly account of electron correlation effects, as may be recognized from the simplest example, the H f H2 reaction. In this case, the RHF (restricted Hartree-Fock) method overestimates the barrier height by roughly 15 kcal/mol or about 150 per cent. The PNOCEPA method (Coupled Electron Pair Approximation based on a configuration interaction method with pseudonatural orbitals) provides an efficient tool for treating electron correlation [7,8] _This method will be applied to the calculation of the barrier heights for the collinear exchange reactions. H’+H2-fH’H+H,

(R4)

even no experimental activation energies have been reported so far. A fairly good knowledge of activation energies, however, is the minimal information required

H’ i- CH, + H’CH,

(R5) + H,

(R6)

and the reactions (R2) and (R3). With the exception of (R5), previous ab initio calculations of these reactions

are rather scarce. RHF-SCF and UHFSCF calculations with different basis sets have been reported for (R6) by Ehrenson and Newton [9], while Morokuma and Davis [IO] have calculated some points of the potential energy surface (PES) for the same reaction by the convential configuration interaction (CI) method and obtained about 25 per cent of the valence correlation energy when using a double zeta (DZ) basis set of Slater type orbitals (STOs). Linear symmetric HFH has been calculated by Bender, Garrison and Schaefer [l 1] by CI calculations including all interacting singly and doubly excited contigurations with respect to the RHF detemrinant. These calculations recovered probably about 70 per cent of the valence correlation energy. To the authors’ knowledge, no ab initio calculations have been reported for (R2) so far. 2. Method and details of calculations For a detailed description of the PNO-CEPA method we refer to (81. Here we discuss only briefly the points which are of particular importance for its application to the calculation of potential energy surfaces. In its present form, the PNO-CEPA wavefunction is constructed from a one-determinantal reference wavefunction @,, (usually the RHFSCF determinant). Pseudonatural orbitals (PNOs) are calculated for each spin-irreducible electron pair by perturbation theory. The actual number of PNOs per pair is determined by an energy criterion. “Diagonal” doubly and singly substituted configurations with respect to at, are constructed from these PNOs. Since the importance of particular configurations changes drastically in the course of a reaction, these configurations should be treated on equal footing with @,,_ This can be done in an approximate manner by the Coupled Electron Pair Approxi-mation (CEPA), in which parts of the correlation explicitly calculated for a0 are transferred to the other configurations. In practise this is achieved by a simple modification of the PNO-CI eigenvalue equation. Throughout this work we will use version 2 of the CEPA method (called CEPA-2, eq. (14) of ref. IS] )_ This CEPA concept can be successfully applied as long as a0 really dominates the CEPA wavefunction. It breaks down when the reference configuration becomes nearly degenerate with other configurations as is normally the case for the dissociation of a molecule http the corresponding atoms. Although this fact pre-

vents the calculation of complete potential energy surfaces, it is well possible to calculate particular regions of a PES. For the collinear barrier crests of the exchange reactions studied in this work, the coefficients of a0 in the normalized CEPA wavefunction are always greater than 0.94. As a further example, the minimum energy paths for the important reactions X+HZ-+XH+H

(X=F,Cl,CH,

andNH;)

present no serious problems for a treatment with the present CEPA method 1121 . In this work, we will apply the PNO-CEPA method to the calculation of some part of the PES for the reactions (R2), (R3), (R5) and (R6). We will restrict ourselves to collinear arrangement of the reactants in the case of (IG?), (R3) and (RS) and to D3h symmetry in the case of (R6). For (RS) and (R6) it seems to be certain [6,10,13] , that the saddle points have D_, and DJh symmetry, respectively. For HFH (R3) and HClH (R2) we have performed some additional calculations with bent geometries, which are in favour of the linear arrangement. The basis sets of gaussian type orbitals are given in table I. Essentially, they are standard atomic basis sets with modifications to give a greater flexibility in the valence shells. For the three-atomic systems, we use orbitals which are partially localized by the Boys procedure (only for the valence shells and maintaining o - rr separation); for CH5 canonical orbit& are employed. Unless otherwise stated, the energy threshold for the selection of the PNOs is chosen to be I O4 hartrees. Although the larger basis sets account for 80 per cent or more of the valence correlation energy of the reactants for all systems under investigation, theremain@ errors are not negligible_ The most important errors arise from the use of an incomplete basis set (called basis truncation error) and from the incomplete exhaustion of the given basis set due to the selection of the PNOs by a finite energy criterion (called configuration truncation error). The latter error may be estimated from the perturbational calculation of the PNOs’ energy contributions. In the present calculations with the larger basis sets, the exhaustion of the configuration space (limited to “diagonal” single and double substitutions with respect to au) is poorer for the barrier crests than for the reactants by 1 to 2 per cent. Estimates for the relative configuration truncation er-

P. Botschwina, IV_Meyer/Collinear potential em-r&ybarriers

45

Table 1 Basis sets of gaussian type orbitah (GTOs) ‘) System

Designation

Atom and type

Exponents and contmctionsb)

H-H-H

6.2

H. s H.P

(68.16. 1.2.0.3

H-F-H

lO%5.2/5,2

F, s F. P F, d H. s H.P

(9994.8.1506.0.350.3). 104.1,34.84, (44.36. 10.08), 2.996,0.9383,0.2733 2.8,0.7 (33.64,5.058), 1.147.0.3211,0.1013 1.2, 0.3

12,8,3.1/6.2

I=, s F, P F. d I;. f H.s H-P

(37736.5867.1, 1332.5,369.4). 116.8,40.35. 14.97,5,876, 0.2333,0.08 (102.3.23.94,7.521). 2.773, 1.100.0.4468,0.1719,0.07 4.2, l-4,0.47 1.4 same as for H-H-H 1.2.0.3

11.7.2l5.2

CI. s CL P Cl. d H. s H. P

(28656.4299.0,976.3.274.4), 89.01, 31.24,7.110,3.3, (150.4.34.71), 10.41.3.5,1.0.0.28,0.09 1.0,0.25 sane as for H-F-H. smaller basis 1.0,0.25

13,10,3,1/6,2

Cl, s Cl. P Cl, d Cl, f H. s H.P

(105812, 15872.3619.7, 1030.8,339.9), 124.5.49.51,20.81, 0.5378,0.1935,0.08 (589.8,139.8.44.79, 16.61), 6.600,2.714,0.9528,0.3586, 1.54,0.48,0.15 0.6 same as for H-H-H 1.0,0.25

C. s C. P C, d H, s H, P

(4240.3,637-S. 146.7),42.53.14.18,5.176.2.1,0.778,0.288.0.107 (18.10.3.977), 1.145,0.3619,0.1146 0.7 same as for H-F-H and H-Cl-H, smaller basis sets 0.65

H-Cl-H

H-CH3-H

lOl5,ll5,l

10.25,2.347),

Our basis sets are based on standard atomic basis sets 134-361

b, Parenthesesdenote

0.6733.0.2247,0.0822 12.22,4.5,

1.5.0.5.0.167

1.653,0.6108.

1.0, 0.3, 0.1

6.465, 2.525, 0.125,0.05

with some modifications in order to obtain greater flexibility in

contractions.

rots are 0.2,2.0,2-S and 3.2 kcal/mol for H-H-H, H-CH,-H, H-F-H and H-Cl-H, respectively. The error arising from the perturbational calculation of the PNOs amounts to about one per cent for all the systems that could be investigated so far. Further errors of usually minor importance are due to the neglect of nondiagonal substitutions and from the approximate treatment of multiple substitutions. The first one could be surmounted by including the few most important nondiagonal substitutions belonging to the configurations with large coefficients. The second would require

an explicit treatment of multiple substitutions, which presents a rather formidable problem. Previous experience with the CEPA method for potential curves [8,14--191 indicates, however, that this error should be small. CEPA potential curves for diatomic molecules parallel the experimental curves almost completely over a rather large range of the nuclear separation. As will be shown in the following sections, the crests of the barriers for our collinear exchange reactions occur for only slightly elongated bond lengths (with respect to the equilibrium bond lengths

of the reactants), for which the CEPA concept works well. _ Since it seems to be hardly possible to give reliable ab initio estimates for all the different errors, we will apply semiempirical procedures for estimating the correlation defect. Two of such procedures have been recent!? described in some detail by Mehler and Meyer [20] _ Our reference systems will be the positive ions HX& (X = H, F, Cl and CH3) at the geometries of the barrier crests. For the barrier height we have thus the expression: % H = @.HXH - EHXH +) + (QXH-

- EaX)

-

J+

=-VVIP-PA-EH. The first term (VIP) may be viewed as the “vertical ionization potential” of HFH, the second (PA) as the ‘proton affinity” of the molecule HX with elongated HX bond length and EH is the energy of a hydrogen atom. We now make ihe assumption that PA is accurately (say, within about one kcaljmol) obtained from the CEPA calculations. This assumption is based on (a) the observation that near-equilibrium CEPA potential curves are very accurate, so that the energy difference between elongated HX and HX in i!s equilibrium geometry should be correctly reproduced (note that the bulk of this energy difference comes from low-energy configurations, especially from the HX antibonding configurations), and (b) the well-known fact that the eIectronic structure of a molecule changes only slightly upon protonation so that good values for proton affiiities are calculated even in the RHF-SCF approximation. Thus our problem reduces to an estimation of VIP. Vertical ionization potentials may well show errors of about 5 kcal/mol even when they are calculated from high-quality CEPA wavefunctions, which account for more than 85 per cent of the valence correlation energy [IP]. We will make use of the two extrapolation techniques described in [ZO] in order to get estimates for VIP from the CEPA calculations with the larger basis sets: (a) scaling of the all-external correlation contributions (which had previously been applied to rhe ionization energies of HZ0 [7], CH4 [8] and OH [14]), and (b) linear extrapolation involving the contributions from all configurations of two related systems (ii our case these are HXH and HXH+).

The valence correlation energy of our reference tem HXti may be written as E’(HXH+)

= fi(HX)

sys-

+ PA’,

where &(HX) is the valence correlation energy of HX and PA’ is the correlation contribution to PA, which is assumed to be correctly calculated. We will use the following values for _&(HX), in hartrees: -0.0408 (HZ), -0.319 (HF), -0.26 (HCl) and -0.241 (CHJ. The value for HZ is exact 12 I] , the other values have been estimated from previous large-scale CEPA calculations [8,16] _A very accurate knowledge of these valence correlation energies is not necessary for the application of our extrapolation techniques, however, since the error in VIP resuhing from an error in Ec(HX) is normally smaller than the latter by a factor of three or techniques assume more. Since both extrapolation equal convergence for both systems, we have to add the configuration truncation errors to the scaled and Iinearly extrapolated values, respectively. .In order to get some idea of the energy profile along the minimum energy path (MEP) for the reactions involving three atoms, we make the following ansatz for the MEP: II

d-J'

1 +,g

CZi(X-J’)*’=C.

Here x = RI - R,andy = R2 -R,, where RI and R2 are the actual HX distances andR, is the equilibrium HX bond length. The constant c is fiied by the condition that the barrier crest lies on the MEP, while the coefficients ai are determined from further points (x , y ) of the MEP, which are calculated from suit.p abPe Imear cuts through the energy surface. The asymptotic behaviour of our ansatz is not correct, sincey decreases only with some inverse power of x for large x. But since deviations of 0.02 bohr result in energy differences of less Lhan 0.1 kcal/mol for our systems, this defect of our approximate MEPs is not serious. We have checked the quaIity of our ansatz for the H3 surface by comparison with the ab initio MEP of Liu 1223 _Using only one term of the series (a1 # 0), a rather good approximate MEP is obtained: the approximatey values.differ from Liu’s by less than 0.01 bohr foryp ranging between 0.05 bohr and 0.30 bohr (the maxlmaly value is 0.356, the miniial0). For the coefficient nl which is obtained from the optimaI point (xp ,JJ,), the maximal deviation of they values even

decreases to 0.005 bohr.

P. Botschwina,

IV. Meyer/Collinear

Table 2 Coefficients of the leading RHF-SCF configuration and relative energies for some points of the mlliiear Hs potential energy surface =) --____ R1

(bohd

RZ

(bohr)

CO

E,,l (kcallmol) This work

Liu b)

3.571

1.407

0.9904

1.52

1.30

3.371 3.171

1.410 l-414

0.9901 0.9897

2.10 2.85

1.82 2.49

2.971

1.421

0.9892

3.78

3.32

2.771

1.431

0.9884

4.87

4.32

2.572

IA48

0.9872

6.17

5-48

2.374

1.475

0.9855

758

6.75

2.179 1.992 1.757 =)

1.518 1.590 1.757c)

0.9834 0.9814 0.9820

9.02 10.3 10.7

8.02 9.09 9.80

1.10

1.10

0.9899

102.4

101.1

1.50 1.70 2.50

1.50 1.70 2.50

0.9858 0.9830 0.9611

19.6 11.1 39.8

18.5 10.2 38.5

4.00

4.00

0.8360

98.7

95.9

a) The asymmetric geometries correspond to Liu’s minimum energy path. The total energies (ii hartrees) for the reactants are -1.63321 (RHF-SCF) and -1.67111 (CEPA). The RHF-SCF saddle point occurs at 0.913 A with a barrier

height of 24.4 kcal/mol. b, Ref. [22]. =) Saddle point.

3.H’+HZ---H’H+H(RS) For a discussion of previous ab initio calculations of the PES for this reaction we refer to [6] _ The most elaborate calculations published to-date are those of L.iu [22] for the collinear arrangement of the H atoms. These calculations have probably errors of less than 0.5 kcal/mol for relative energies smaller than 10 kcal/ mol (with respect to H + H, at infinite separation) and represent the most accurate collinear PES available at present-we will refer to the results of that work for the discussion of the accuracy of our calculations. Our attempt was not to get a particularly good PES for the H3 system. Instead, we wanted to examine the limitations of our method and the accuracy of calculations which can be also performed for systems with

potential enerz!~ barriers

47

a considerably larger number of electrons. Thus, our basis set for the H, system (table 1) is of the sime quality as those hydrogen basis sets used for the HFH and HClH systems. We have calculated some points on Liu’s minimum energy path and several points with DBh symmetry. The results of these calculations are summarized in table 2. Deviations from Liu’s values amount to less than 1.5 kcal/mol for the points on the MEP. The condition for a successful application of the present CEPA concept is well satisfied along the MEP: the coefficient of Q. in the normalized CEPA wavefunction is always greater than 0.98 while the excitation energies of all doubly substituted configurations are greater than 1 hartree with respect to the RHF-SCF energy. For linear symmetric H,, agreement becomes worse for larger HH distances. But even for R, = R2 = 4.0 bohr, where the coefficient of the RHF-SCF determinant is only 0.836, the deviation from Liu’s value amounts to only 3% or 2.8 kcal/mol. 4_H’+FH+H’F+H(FG) Very little is experimentally known about this reaction. Heidner and Bott [23] have recently studied the deactivation of HF(u = 1) and DF(IJ = 1) by H and D atoms by means of laser-induced IR fluorescence and isothermal calorimetry. Since these experiments were carried out at only one temperature (295 K), no frequency factors or activation energies could be determined. Comparison of the experimental r-ate constants with the results of quasiclassical trajectory calculations on a LEPS surface with a barrier height of 1.4 kcat [24] showed bad agreement. For D + HF(u = 0) --f 1-I+ DF(u = 0), Heidner and Bott [23] give an upper limit for the rate constant of 2.5 X lo8 cm3/mol s, while Wilkins’ trajectory calculations yielded 3.7 X lOI cm3/mol s. The upper limit for the rate constant reported by Heidner and Bott only means that no effect from reactive collisions could be measured within the accuracy of the experiments. Assuming a reasonable value for the freqency factor, Heidner and Bott [23] estimate a lower bound to the activation energy of 7 kcal/mol. Bender et al. [ 1 l] have carried out RHF-SCF and CI calculations for linear symmetric H-F-H yielding barrier heights of 67.8 and 49.0 kcal/mol, respectively. The results of our calculations are summarized in table

p. Eotschwinn. IV. Meyer/Cokrmw potential energy barriers

48 Table 3 Results for HF + Ha) hlethod

Ref.

Basis sat

EO

ES

BH

R=

(au)

(au)

(kcallmol)

(Al

63.0 45.1 64.1 44.9 (38-40) 67.8 49.0

1.098 1.143 1.143 bl 1.143b)

RWF-SCF PNGCEPA RUF-SCF PNGCEPAd)

* * * *

10,5,2/5.2 lO,S.2&2 12,8,3,1/6,2 12,S,3.1/6,2

-100.55452 -100.80155 -100.56820 -100.84646

-1OOA541 -1OB.1296 -100.4660 -100.7750

RHF-SCF CI

11 11

9,5,2/5,1 %.5,2&l

nd. e, nd.

n.d. nd.

e) 1.12 1.14

a) Resulll of this work are marked with an asterisk. The following symbols axe used in the tables;E’ - total energy of reactants, ES - total energy at the barrier crests, BH - barrier height, RS - XH distance at the barrier crests (X = H. F.Cl and C). b, Geometry not optimized, but PNG-CEPA geometry of smaller basis set is used. ‘1 Estimated from linear extrapolation and scaling, respectively. including an estimate for the relative configuration truncation error of 2.8 kcallmol. d, Threshold for PNO selection is 5 X lo* hartrees for lairs involving o-orbit& otherwise lo* hartrees. At the saddle point, the CEPA wavefunction is buiit up from 291 configumti&~ e, n.d. stands for not documented. 3. Our basis sets account for 77 and 87 per cent of the valence correIation energy for the reactants. Our CEPA barrier heights are 4 kcaI/mol lower than the CI value of Bender et aI. [ 1 I J . Scaling (see table 6) and linear extrapolation (including the reIative configuration truncation error) reduce the barrier height by 5 and 7 kcal/ mol, respectively, so that our estimated barrier height amounts to 3840 kcal/moI. . The correIation contribution to the HF distance at the barrier crest, RS, is calculated to be 0.045 A from the CEPA method (smaher basis), while the PNO-CI method yieIds 0.032 & Thus; double and single substitutions with respect to the BHF-SCF determinant make up 71 per cent of the CEPA contribution to R’. X similar ratio of 74 per cent was obtained for the correlation contribution to re for hydrogen fluoride by Meyer and Rosmus 1161. Bender et al. [l l] obtained from their Cl calculations a correlation contribution of only 0.02 A to RS, but their fmal RS value is practically identical with our CEPA value due to the rather large discrepancy of 0.02 A at the BHF-SCF level. From previous experience with potential curves, we estimate our RS value to be correct to about 0.005 A. An approximate MEP has been constructed using one asymmetric point (1.2804,1.0423, in A) and the barrier crest (1.143, 1.143, in A)). The corresponding energy profde is displayed in frg. I.

1 *FEEL

h

Fig. 1. Relative energies (in kcallmol) for H-F-H and H-CL-H along the approximate MEPs &nali basis sets). R = RI - Rz Ci bohr). The parameters of the approximate MEPs (see set tion 2) are: a) H-F-E a, = 0.604; b) H-CL-H: LIP= -0.488.

a2 = 2.489.

49

Table 4 Results for

HCl + H Method

RHF-SCF PNO-CEPA RHF-SCF PNO-CEPAb)

Ref.

* * * l

Basis set

EO WI

ES (au)

BH

460.49594 460.68093 -46Q.6Q871 -460.81039

-460.4272 460.6429 460.5338 460.7752

43 ’ 23.9 42.0

1.472 1.502 1.502a)

22.1 (lo-15)C)

1.502=)

11.7,2/5.2 11,7,2/5,2 13.10,3.1/6,2 13.10,3,1/6,2

(kcdlmol)

a) Geometry not optimized, but PNOCEPA seometry of smaller basis set used. b, Threshold forPN0 selection is 5 X l@ hartrees for pairs involving o-orbit&. otherwise ltf‘t ’ nartreer At the saddle point, the CEPA wavefunction is built up from 252 mnf~rations. ') Estimated from linear extracolation and sczdiie. rescectivclv. lnduded is an estimate for the reIative configuration truncation error of 3.2 kcrd/moI. _ “,

-

5.H’+ClH-tH’CI+H Available experimental information about the exchange reactions D + HCl% DC1 + H and H + DCl% HCI + D is rather contradictory. For a detailed discussion we refer to the recent paper of Thompson et al. yield [2] _Briefly, photochemical experiments [25,26] low frequency factors (- lOlo cm3/mol s) and activation energies (- 1 kcal/mol), whereas trajectory calculations on a semiempirical PES of the type proposed by Raff et al. [27,2] and a crossed molecular beam study [28] indicate the frequency factors to be larger by four orders of magnitude. Very recently, Heidner and Bott [3] obtained an upper limit for k, at 295 K of (7 f 3) X 10” cm3/mol s. Adcpting a large frequency factor of lOI cm3/mol s, the Arrhenius activation energy E, must thus be equal to or greater than 3 kcal/ mol. Our results for the collinear barrier height are given in table 4. The CEPA calculations account for 71 (smaller basis) and 81 per cent (larger basis) of the valence correlation energy of the reactants. The CEPA barrier heights amount to 23.9 and 22.1 kcal/mol, which means a reduction of the RHF-SCF barrier heights by 19.2 and 19.9 kcal/mol, respectively. Estimates for the “true” collinear barrier heights from scaling of the all-external correlation energy (see table 6) and linear extrapolation of the energy contribution of all configurations amount to 15 and 10 kcal/mol, respectively (including an estimated configuration truncation error of 3.2 kcal/mol).

Fig. 1 presents the energy profile along the approximate minimum energy path, the parameters of which are given in the subscript of this figure. The energy profile along our MEP differs considerably from that of Thompson et al. (see fig. I of ref. [2]). The PES of these authors shows relative minima for linear symmetric HClH and linear asymmetric HCIH both lying deeper in energy than the reactants. We can hardly believe that the “true” collinear barrier height is significantly smaller than 10 kcal/mol.

6. H’ + CH4 -, H’CH3 + H The hot atom reaction T + C&I4 + CH,T t H has been investigated by Chou and Row!and [29], who extrapolated a threshold energy of about 35 kcal/mol. The results of our and previous calculations are summarized in table 5. Our RHF-SCF energy for the reactants lies about 0.01 bartrees above the RHF limit_ The corresponding CEPA valence correlation energy makes up 80.4 per cent of the estimated value (see section 2). Our RHF-SCF value for the barrier height of 61.9 kcal/ mol is only slightly smaller than those of previous investigations [9,10] and thus confirms that it is only slightly basis dependent (see table 5). Inclusion of correlation effects by means of the CEPA method reduces the barrier height by 20.3 kcal/mol. Estimating the relative configuration truncation error to 2.0 kcal/mol, scaliig of the all-external correlation contributions

50 Table 5 Results for Cb

+ H =I Ref.

Method

RHF-SCP

Basis set

10,5.1/5.1

*

ES (au)

BH

(au) -40.70835

40.6097

61.9

EO

(kial/m01)

RS (A) 1.339 1.079

PNO-CEPA

.

*

lO,S.1/5,1

40.90202

-40.8357

41.6 (32-36)

1.361 b,

1.090

RHF-SCF

10

SYO-D-L

-40.68345

-40.5819

63.7

1.349

CI

10

STO-DZ

40.745s5

-40.6791

41.7

1.349 C) 1.086 c)

1.086

RHF-SCF

9

4-3 1G

40.6390

40.5350

65.3

1.342

UHF-SW

9

4-31G

40.6390

-40.5520

54.6

1.452

RHF-SCF

9

4-31G,

-40.6609

-40.5597

63.5

1.320c)

UHF-SCF

9

431G.

40.6609

40.5734

54.9

1.079 1.074 +PH’dC

1.077

=J

1.320 =)

+pH+dC

1.077 =)

a) Dsh geometry assumed. Upper and lower values in column Rs correspond to CH k&al) and CH kquatorial), respectively. b) Estimated from linear extrapolation and scaling, respectively, including a relative wnfmration truncation error of 2.0 kcal/mol. c, Geometrical parameters not optimized.

Table 6 Components of the vertical ionization energies for HXH ‘1 (large basis sets, in hartrees) Type b)

X=H

X=CHs

ESCF

0.37715

0.26071

Exx

0.01395

0.02121

0.01877 0.00304

0.02198 0.01149

-0.02695 0.38595

-0.040530 0.27486 1.244

EP 531 D&b TOti SGding facfor=' Scaled ionization energy d)

1.078

0.38704

0.28004

X=F 0.2745 1 0.02536 0.01292

X=CI 0.33908 0.02638 0.02376

0.00875

0.01404

-0.01973 0.30181 1.146 0.30551

-0.04510 0.35816 1.240 0.36449

‘) At the calculated geometries for the barrier crests (see tables 2-5). b, We use the notation of ref. [S] for the different contributions to thevertical ionization energy. In thegiven order these are: SCF contribution, change in all-external correlation, change in polarization-type and semi-internal correlation and change in extem nal correiation due to the deformation of the orbitals upon ionization. ‘) For the scaling factor we use the fommlaf= EC ,p(HX)/Ec!&JHX), where E&pWX) and EC&,+X) denote the experimental (or estimated) and calculated valence correlation energies of HX. respectively. d) Scaling refers to the change in &-external correlation only.

51

P. Botschvina, IV.Meyer/Collinear potential energy barriers Table 7 Comparison of CEPA results with results of calculations using the bond energy-bond order (BEBO) method system

H--H--H

R:

R:

0;

05

Pa

0.741

0.741

109.5

109.5

1.942

H-F--H

0.917

0.741

141.1

109.5

1.942

H-Cl-H

1.275

0.741

106.4

109.5

1.942

H-CHs-H

1.090

0.741

RS-R,

fkcal/tnolJhJ

BEBO panmetersel

106.9

109.5

1.942

II

1

9.9

11.8

6.6 -5.6

6.6 -5.9

8-l

7.8

(A)

CEPA ‘1

BEBO

CEPA dl

10.7

0.18

0.19

(9.81 44.9 (38-40)

0.18

0.23

22.1

0.18

0.23

(10-15) 41.6

0.18

0.27

(32-361 ‘J The noble gas parameters used to calculate the bond indices are taken from [31]. bJ I is the usual BEBO method with the madiied Sato triplet function: 11 employs the triplet function suggested by Arthur et al. 1331. ‘) Larger basis sets. Values in parentheses are estimnted barrier heights. For Hs Lie’s value [22] is given in parentheses. d, Smaller basis sets.

(see table 6) yields an estimate for the barrier height of 36 kcaI/mol, while Iinear extrapolation resuIts in a value of 32 kcallmol. Since the experimental threshold energy and the classical activation energy of the PES may well differ by a few kilocalories, agreement between experimental and our estimated values is quite satisfactory. The optimized geometrical parameters for CH5 (Dsh svmmetrv)-_ are -&en in table S-While the CH bond distances for equatorial CH bonds are practically unchanged with respect to the equilibrium bond lengths in CH4, the axial bond lengths are calculated to be longer by 0.27 A or 25 percent (PNO-CEPA).

In table 7 our results are compared with results obtained from the bond energy-bond order (BEBO) method of Johnston and Parr [30,3 l] . Except for H3, our estimated barrier heights are in bad agreement with the BEBO values. Furthermore, Pauliig’s bond order-bond length relationship 1321 is not well satisfied for the _ thermoneutral exchange reactions. BEBO predicts RS -R, to be constant for our reactions, the numerical value amounting to 0.26 In 2 = 0.18 (in A)_ Table 7 shows that RS - R, takes on values between 0.19 and 0.27 a. Only for H3, the BEBO value agrees we]1 with the exact value of 0.189 A [22]_

Acknowledgement 7. Conclusions An investigation of barrier heights for some thermoneutral collinear exchange reactions of type H’ f XH + H’X -CH (X = H, F. Cl and CH,) has been performed by means of highly-correlated PNO-CEPA wavefunctions. The remaining correlation defects have been estimated from two semiempirical extrapolation techniques. The estimated barrier heights agree well with an accurate theoretical value for H, and an experimental threshold energy for CHs _For HFH and HClH, where no reliable experimental data are oveilable, we estimate the collinear barrier heights to 3840 and to lo-15 kcal/mol, respectively.

This work was partly supported by a grant from the Studienstiftung des Deutschen Volkes (to P-B.), which is gratefully acknowledged.

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