J . Phys. Chem. 1993,97, 2085-2091
Prediction of Activation Energies for the Exchange Reaction H Molecular Orbital Metbodst
+ H‘X
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2085
H’ + HX by ab Initio
Kerwin D. Dobbs’ and David A. Dixon’ Du Pont Central Research and Development, Experimental Station E328. Wilmington, Delaware 19880-0328 Received: September 18, 1992; In Final Form: December 2, I992
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Ab initio molecular orbital theory has been used to calculate the exchange barriers for the reaction H XH. The calculations employed large basis sets, and a variety of methods were used to calculate the correlation energy up through PMP4 and QCISD(T) (or CCSD(T)). The barriers to exchange at the QCISD(T) level, uncorrected for zero point effects, are 42.7,20.2, 13.8, and 6.4 kcal/mol for X = F, C1, Br, and I, respectively. The effect of basis set superposition was studied and found to be 0.4-2.2 kcal/mol depending on X and the basis set. These barriers are consistent with previous calculations which show large barriers instead of the low barriers expected from a number of experimental results. Rate constants and effective activation energies were calculated from transition-state theory and compared to experiment. The results suggest that the experiments need to be reinterpreted in terms of large activation energies instead of the small values used in many of the previous studies.
Introduction The reactions of hydrogen atoms are of interest in a wide range of processes, especially for abstraction of a halogen to form a hydrogen halide acid. The simplest such system is the thermoneutral process as shown in reaction 1 with, for example, H’ =
H + XH’+ [HXH’]* .-+H X + H’
(1)
D. This reaction has been studied experimentally for many years because of the competition represented between the exchange process shown by reaction 1 as compared to the abstraction process represented by reaction 2. For X = F, reaction 2 is substantially H+H’X-[HH’X]*-HH’+X
(2)
endothermic, for X = C1, slightly exothermic,and for X = Brand I, substantially exothermic. Thus, for X = C1, Br, and I, it is expected that abstraction would dominate over exchange. The experimental studies of these reactions began with the work of Bodenstein’just before 1900, and a range of kinetic experiments have been performed.2-a Much of this work focused on the ratio of rateconstants for reactions 1 and 2, k2/kl, with widelydiffering values. In the late 1960sand into the 19709with the development of crossed molecular beam ‘s~permachines”,~ it became possibly to study the reactions of H atoms with a variety of molecules.I0 Usually these studies focused on understanding the detailed dynamics of fundamental processes that were well-understood from traditional kinetic experiments. In 1975, McDonald and Herschbach” published a pioneering crossed beam study of reaction 1 for X = C1, Br, and I. In their analysis, they noted that there was good agreement between the beam experiments and classical trajectory studies performed on semiempirical potential energy surfaces with low-energy barriers. They also noted that many of the calculations and observations were consistent with k2/kl 1. They estimated that reaction cross sections were of the order of 1-10 A2 and that the activation energies were low. Subsequently, Toennies and co-workersI2 carried out crossed beam experiments on the same reaction for the same halogens and found cross sections on the order of 2 A2. They also were able to estimate activation energies from their data and obtained values consistent with the results of Endo and Glass.2 These activation energies were much higher than those
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’ Contribution No.6345. 0022-3654 193/ 2097-2085 $04.00/0
used in the analysis of the earlier crossed beam experiments. However, these authors later suggested that their initial measurements were not correct, as the source of their H signal in the mass spectrometer was from fragmentationof unscattered HCl. *b Interest in the abstraction and exchangereactions has generated a number of theoretical studies of these two processes ranging from classical and quantum trajectory calculations on semiempirical energy surfaces13to high-level ab initio molecular orbital calculations of the structure of the transition state.lP18 These reactions are of interest in terms of the dynamics, as they are a good example of the L HL’- LH L’ case for reaction 1 with essentially no skewing of the coordinates, and of the L L’H LL’ H case for reaction 2 with significant skewing of the coordinates. The L corresponds to light and the H corresponds to heavy. Based on the experimental results, the semiempirical potential energy surfaces (PES’S) all had low barriers to exchange. There are distinct differences between the ab initio results and most of the experimental results (and consequently the semiempirical PES’S) for these processes. The ab initio calculations suggest that reaction 1 should have significantactivationenergies. The results of the various experiments and previous calculations are summarized in Table I. In the one case where the same computational method was used to calculate the abstraction and exchange activation energies, the values for the abstraction reaction are much lower than for the exchange process.16 Miller and Gordon4have obtained the rate constant for reaction 2 with X = C1 and H’ = H and find Ea = 3.52 kcal/mol in the range of T = 200-500 K. For comparison, Dunning’s calculated value for the barrier for this process is 7.3 kcal/mol, whereas Dunning calculates 23.5 for the barrier for reaction 1.16 Our interest is in understanding the formadon of HX in a variety of systemswhere hydrogen atoms are present, so we decided to test a variety of computational methods for the treatment of reaction 1. As we are interested in large numbers of complex systemswith a significant number of valenceelectrons, we decided to study these reactions based on single configuration wave functions. The wave functions for the transition-state structures were obtained at the unrestricted HartreeFock (UHF) level. We then examined the correlation corrections at a variety of levels based either on perturbation expansions through MP4(SDTQ)I9 or CCSD(T)20 and QCISD(T).*’ CCSD is based on an exponential ansatz, and the (T) is a perturbative correction to account for the effect of triples. QCISD is an approximation toCCSD whereselected terms have beendropped from the CCSD
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0 1993 American Chemical Society
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Dobbs and Dixon
2086 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993
TABLE I: Electronic Energy Barrier Heights and Activation Energies (kcrl/mol) source
HFH
HClH
ref I6 ref I7 ref 15 ref 18 PMP4(FC)" QCISD(T)" expt
48.8 44.9 43.5 47.7 42.1 42.7 8.24 1 .36 2.43 8.02
HBrH
HIH
16.2 17.2
9.6
12.8(12.8)b 13.8(13.8)b 5.22
6.2(5.6)b 7.4(6.4)b
Results
This work. * Values in parentheses are nonlinear structures. Value given in ref 2 as consistent with known experimental data. Calculated from k J k l given in refs 6 and 3 and using the value for E, (reaction 1) from ref 3. (1
TABLE 11: Basis Sets ~
~
~~
atom
~~
~
ref -
basis set
H F
(5S2P)/[3S2Pl (10s6p4dl f)/[ 5s3p2dl fl
CI
(1 3sl Op4dl f)/[7s5p2dl fl
Br
(15s12p7dlf)/[ 1 Is9p4dlfl
I
( 16s12p8d 1 f)/ [ 1 1s9p6d 1 f)
H"
(6s2pld)/ [4s2pld] (1 3~7p3d2f)/[6sSp3dZfl (14sl1 p3dlf)/ [ 1 ls9p3dl fl
F"
c14
projection is taken from the PMP3 calculations. The basis sets are summarized in Table 112629and are at least of triple-fquality in the valence space plus double polarization plus f functions on the heavy atoms.
polarization exponents
pt = 1.4, 0.35 2-term S T O / d r s = 2.2,0.7; 8 = 1.08 27 2-term S T O l d r s = 1.9,0.7; fi= 1.0 28 d r s = 0.4504,O. 154; fi = 0.4668 29 dt's = 0.326,O.I 14; 8 = 0.3 192 36 36 s = 0.0976, p = 0.0700 33 26 26
" Large basis sets for BSSE calculations. equations. We hope that these studies will lead to further development of other high-level treatments for describing the correlation problem for open-shell molecules. Methods The calculations described below were done with the program system Gaussian 90/92220na Cray YMPcomputer. Geometries of the various species were optimized at the M P P level with all electrons correlated, MP2(FU). The frequencies were also calculated at this level. Subsequent higher level correlation calculations were carried out with only the valence electrons correlated (MP2(FC)). Thesecorrelation calculationsweredone at the MP2, PMP2, ROMP2,24 MP3, PMP3, MP4(SDTQ), PMP4(SDTQ), CCSD(T), and QCISD(T) levels. The spinprojection method of Schlegel was used to correct for spin contamination of the MPn energies.2s For PMP2 and PMP3 wave functions, the spin projections have been calculated from the appropriate wave function, whereas for PMP4, the spin
Geometries. The total energies are given in Table 111, and the geometry and frequency information are in Table IV. The geometry for the diatomics is in good agreement with the experimental results,30 especially as we have not included relativistic corrections. The harmonic frequencies are also in good agreement with the experimental values.30 The calculated diatomic frequencies are too high by 0.4%,2.2%, 23% and 3.3% for X = F, C1, Br, and I, respectively. First we discuss the geometries of the linear HXH structures which could serve as transition states. These structures are not all transition states, as they may not have the requisite numbers of real degrees of freedom. A transition state is defined as having one negative direction of curvature which corresponds to an imaginary frequency. The r(X-H) bond in the transition state increases by 2 1%, 15%, 13%,and 10%as compared to the diatomic distance for X = F, C1, Br, and I, respectively. This results in an r(H-X) bond length in the transition state that is about 0.2 A longer than the bond in the free diatomic. The frequency analysis for the HFH transition state showed that at the MP2 level, a nonlinear structure is preferred. The energy difference is small, with the bent structure being 0.50 kcal/mol lower in energy at the MP2(FU) level. We then carried out calculations every 10' where the value of r(F-H) was reoptimized. At the MP2(FU) level, the energy decreases from 180 to 114' as shown in Table V and Figure 1. Calculations at the MP2(FC) level show the same behavior. However, if the spin is projected out, PMP2(FC) level, a different result is found with the linear structure lower in energy by 1.49 kcal/mol. At the MP4(FC) level, the same analysis shows that there is a bent structure with a bond angle of about 155' that is 0.07 kcal/mol lower in energy as compared to the linear structure and 0.26 kcal/mol lower in energy than a structure with a bond angle of 114'. At the PMP4(FC) level, the bent structure of angle 114O is 1.3 1kcal/mol higher in energy as compared to the lowest energy linear structure. At the QCISD(T) level, a bent structure of 170' is only slightly lower in energy than the linear structure and the bent structure with 8 = 114' is only 1.02 kcal/mol higher in energy. We reoptimized the HFH transition state at the QCISD level and found the linear structure to be lower in energy with essentially no change in geometry. Clearly the potential energy surface is very flat with regions of the PES accessible to a wide range of impact parameters at low collision energies above E,. Our calculated geometry for the linear structure is similar to that found by Bender et al.I4 and Botschwina and Meyer," who
TABLE In: Total Energies (au) and Zero Point Energies (ZPE) (kcal/mol)
molecule H' HF HCI HBr HI WF-Hl'(e = IUO) [H-F-HI'o 114 I ) [H-CI-HI'(r- ino) [H-Br-Hl'(r = 180) [H-Br-H]'(r = 1 7 2 2 ) [H-Br-HI'o = 77 4 ) [H-I-Hl'(r ino) [H-I-H]'(r = 1 6 0 6 ) [H-I-H]'(r = 7s 3)
-
-
ZPE 5.94 4.37 3.90 3.41 3.45 (3i) 4.01 ( l i ) 3.57 (li) 2.66 (3i) 2.94 (li) 4.50 ( l i ) 2.46 (3i) 3.15 ( l i ) 4.22(1i)
MP2(FU)/ TZ+2p+f/l MP2( FU)/ TZ+2p+f -0.499 809 -100.317 854 -460.353 270 -2573.587 366 -6918.673922 -100.746 212 -100.747 014 460.814 393 -2574.058 436 -2574.058 450 -2574.024 854 -6919.156 388 -6919.157 090 -6919.140 156
MP2( FC) / TZ+2p+f// MP2( FU)/ TZ+2p+f
ROMPZ(FC)/ TZ+Zp+f// MP2( FU)/ TZ+2p+f
-100.298 056 -460.293 839 -2573.144 971 -6918.113449 -100.726 218 -100.726 819 -460.754 692 -2573.616 151 -2573.616 172 -2573.583 104 -6918.595 044 -6918.596 109 -6918.580058
-100.298 056 -460.293 839 -2573.144 971 -6918.113449 -100.728 681 -100.727 276 -460.159 874 -2573.621 837 -2573.621 702 -2573.585 895 -6918.600 604 -6918.600 357 -6918.582 126
PMP2(FC)/ TZ+2p+f// MP2( FU)/ TZ+2p+f
MP3( FC)/ TZ+2p+f// MP2(FU)/ TZ+2p+f
-100.730 637 -100.278 265 -460.761 649 -2573.623 199 -2573.623 716 -2573.588 213 -6918.603 068 -6918.603 360 -6918.584 827
-100.296 915 -460.3 13 93 1 -2573.163 461 -6918.132 296 -100.725 961 -100.725 638 -460.776 323 -2573.636 538 -2573.636 616 -2573.605 431 -6918.616 019 -6918.617 572 -6918.603 134
The Journal of Physical Chemistry, Vol. 97, NO.10, 1993 2087
Exchange Reaction Activation Energy Prediction calculate r(H-F) = 1.14 A at the CI and PNO-CEPA levels, respectively, with our calculated value being 0.025 A shorter than their values. Dunning, on the other hand, based on GVB wave functions obtained values ranging from 1.22 to 1.18 A.16 Wadt and Winter15 also studied this surface with GVB and GVB CI wave functions and obtained a value of r(H-F) = 1.18 A for the linear structure. However, they obtained a lower energy bent structure with r(H-F) = 1.06 A and B(HFH) = 105O. The bent structure is 0.5 kcal/mol lower in energy than the linear structure, consistent with our MP2 structure. These resultsi5 were obtained with a DZ+P basis set augmented by diffuses and p functions on F. Without diffusefunctions, only a linear structure was found. Our lowest energy structure for the reaction H ClH is linear even at the MP2 level. Botschwina and Meyeri7report a bond distance of 1.50 A, somewhat longer than our value of 1.465 A, and Dunningi6reports a range of values from 1.54 to 1.50 A. The transition state for the H BrH reaction is bent slightly away from from linearity by 8O at the MP2(FU) level. It is essentially the same energy as the linear structure but has all real frequencies. There is a second transition state for exchange that is much higher in energy, 21.1 kcal/mol above the near linear structure. This transition state has a bond angle of 77.4O and slightly shorter bond distances as compared to the near linear structure. Botschwina and Meyeri7only examined the colinear structure and found a bond distance of 1.60 A, in good agreement with our value. Again Dunning's values based on GVB calculations are 0.04-0.08 A longer.16 The transition state for H + IH is clearly bent by almost 20° and is 0.44 kcal/mol lower in energy than the linear structure. There is a second transition state with a very acute bond angle of 75.3O for the exchange reaction. This strongly bent structure is 10.6 kcal/mol higher in energy than the bent structure with a bond angle of 161O . As expected from the above discussion, Dunningi6calculates bond distances that are 0.03-0.07 A longer than our values. Frequencies. The frequency analysis was very important even for such a potentially simple system of only three atoms. For linear HFH, the only mode that is real is the symmetric stretch of 2411 cm-I, which is 58% of that in the diatomic. The bent structure has an a i symmetric stretch of similar magnitude. The asymmetric stretch corresponding to the reaction path motion is of significantly higher frequency in the linear structure as compared to the bent structure. For the linear structure, this stretch is 86% of that in the diatomic, whereas for the bent structure it is only 62%of the diatomicvalue. Because the highest level calculations suggest that [HFH] * is linear and we require the transition-state frequencies,we reoptimized the geometry of [HFH]* at theQCISD(FC) level and recalculatedthe frequencies. The H-F bond lengthens to 1.139 A, the symmetric stretch is
+
+
+
2130 cm-I, the bend is 60 (r)cm-I, and the asymmetric stretch is 31 16i cm-I. For the H + ClH transition state, the real symmetric and imaginary asymmetric stretches are of comparable magnitude with the symmetric mode being 65% and the asymmetric being 63% of the diatomic mode. For near linear HBrH, the symmetric stretch is of significantly greater magnitude as compared to the asymmetric imaginary mode. The symmetric mode is 68% of the diatomic stretch, and the asymmetric is 57% of the diatomic value. For the strongly bent structure, the symmetric stretch is essentially unchanged from that of the linear structure, but the bending vibration has increased by more than a factor of 6 to >1250 cm-1. The asymmetricmode is now extremely high, 7853icm-', but analysis of the motion shows that it still corresponds to an exchange transition state. The splitting between the magnitudes of the symmetric and asymmetric modes in near linear HIH has increased even more, with the symmetric stretch being 74% of the diatomic value and the asymmetric 36% of this value. The bend is significantly nonzero. The strongly bent structure has a symmetric stretch frequency that is little changed from that in the near linear structure, but the imaginary asymmetric stretch has increased by a factor of about 2.7. Energetics. The energetics of the transition states relative to the reactants are shown in Table VI. As shown in Table VI, the MP2 energies are usually higher than the MP3 and MP4 energies. This is most pronounced for I. Including spin projection leads to decreases in the energies relative to the MPn energies. The largest effect is found for the MP2 values. Apparently, the higher order MP levels correct for the fact that Szfor the UHF wave function is not exactly 0.75.31 We also calculated the energies at the restricted open-shell level, ROMP2.32 The ROMP2 values are below the MP2 values and are 1-1.2 kcal/mol above the PMPZ values for F, C1, and Br. For I, the ROMP2 values are above the PMP2 values by 1.5-2.0 kcal/mol. It should be noted that the ROMP2 level favors a linear transition state. The QCISD(T) numbers are the lowest energies if no spin projection is employed. The QCISD(T) values are very similar to the PMPZ values and are 0-1 kcal/mol higher in energy than are the PMP4 values. Calculations were also done at the CCSD(T) level based on the UHF wave function,and these values are virtually identical to the QCISD(T) results. The results in Table VI show that the inclusion of the triples correction lowers the energy barrier by about 1 kcal/mol at both the QCISD(T) and CCSD(T) levels. We compare our two best calculations, PMP4 and QCISD(T) (or CCSD(T)), with the other values in Table I. Our calculated values are about 2.5 kcal/mol lower in energy as compared to the lowest energy for the HFH transition state. For the HClH transition state, we are also lower in energy than the previously
TABLE 111 (Continued) PM3( FC)/ TZ+Zp+f// MP2(FU)/ TZ+2p+f
-100.728 -100.726 -460.780 -2573.641 -2573.641 -2573.608 -6918.621 -6918.622 -6918.606
602 474 504 249 260 71 1 077 111 159
M P4( FC) / TZ+2p+f// MPZ(FU)/ TZ+2p+f -100.307 708 -460.319 897 -2573.169 790 -6918.138 786 -100.739 71 1 -100.739 426 -460.784 945 -2573.645 348 -2573.645 425 -2573.614 11 1 -69 18.624 734 -6918.626 269 -6918.611 593
PMP4( FC)/ TZ+2p+f// MP2(FU)/ TZ+2p+f
QCISD(FC)/ TZ+Zp+f// MP2(FU)/ TZ+2p+f
QCISD-T(FC)/ TZ+ZQ+f// MP2(FU)/ TZ+2p+f
CCSD(FC)/ TZ+2p+f// MP2(FU)/ TZ+2p+f
CCSD-T(FC)/ TZ+2Q+f// MP2(FU)/ TZ+2p+f
-100.742 352 -100.740 261 -460.789 126 -2573.650 060 -2573.650 068 -2573.617 391 -6918.629 791 -691 8.630 808 -6918.614 618
-100.301 322 -460.313 866 -2573.163 690 -6918.133 431 -100.733 513 -100.731 640 -460.780 059 -2573.640 859 -2573.640 919 -2573.609 197 -6918.621 298 -6918.622 733 -6918.607 473
-100.306 358 -460.320 298 -2573.170 246 -6918.139 471 -100.740 326 -100.738 700 -460.788 030 -2573.648 789 -2573.648 853 -2573.617 221 -6918.628 571 -69 18.629 960 -6918.614 560
-100.300 452 -460.3 13 796 -2573.163 620 -6918.133 344 -100.732 474 -100.730 604 -460.779 797 -2573.640 595 -2573.640 657 -2573.609 013 -6918.621 039 -6918.622 484 -69 18.607 304
-100.306 027 460.320 272 -2573.170 214 -6918.139 428 -100.739 864 -100.738 263 -460.781 902 -2573.648 651 -2573.648 714 -2573.617 114 -69 18.628 429 -6918.629 816 -6918.614 466
Dobbs and Dixon
2088 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993
TABLE I V Calculated Geometries' and Frequencies (cm-I) (MPZ/TZ+2P+f) molec HF HCI HBr
HI molec H FH H FH HClH HBrH HBrH HBrH HIH HIH HIH
r(calc)
r(expt)b Diatomics 0.917 1.275 1.414 1.609
0.923 1.274 1.414 1.619
e
r 1.115 1.074 1.465 1.604 1.603 1.586 1.786 1.782 1.754
w,(calc)
w,(expt)h
1.60
3-
4156 3058 2725 2387
WI
Transition States 180 241 1 114.1 2392 180 1984 180 1861 172.2 1868 77.4 1868 180 1718 160.6 1757 75.3 1828
4138.3 2990.9 2649.4 2309.0 w2
w3?
1
4- MPZ(FU)
_I
1.40 1.20
-3 MP2(FC)
1.00
-A-
PMP2(FC)
+ MP4(FC)
0.80 0.60 0.40 0.20
4- PMP4(FC)
+ QCISD(T)
0.00 -0.20
2493 41 1 257 134i 190 1279 3503 449 1126
35633 25853 19283 15653 15533 78533 10223 8693 23171'
Bond distances in angstromsand bond angles in degrees. Reference 30. L' Imaginary mode correspondingto transition-statemotion along the reaction path.
reported values by about 2-3 kcal/mol. In order to compare with the result of Botschwina and MeyerI7for H + ClH, we redid the calculationswith their basis set taken from the workof Werner and Rosmus on HCl.33 (See Table I1 for a summary of the CI basis set and Table VI1 for the energies.) This basis set led to a lowering of the values for HClH relative to H HCl of 0.38 kcal/mol at the PMP4 level and a lowering of 0.34 at the QCISD(T) level, giving electronic energy differencesof 18.8 and 19.8 kcal/mol, respectively. Thus, our basis set for CI is reasonably adequate, and the differences between our work and theirsi7is in the correlation energy treatment. Based on these differences, the error estimates given by Botschwina and MeyerI7 seem somewhat large. For HBrH, our values are again lower in energy as compared to previous workers by about 3-4 kcal/mol. This is probably due to a combination of basis set completeness (saturation of the 1-particle space) and the correlation treatment (treatment of the n-particle space). For HIH, a comparable lowering of the energy is observed as compared to the work of Dunning.I6 Dunning used a primitive basis set similar to ours but contractedit toasplit-valencelevelso that it wasonlydouble-{ in the valence. Only a single set of polarization functions was added to each atom. Thus, it is not surprising that his energies are higher than our values, as our treatment of the 1-particle space is more complete and we are able to include higher order excitations in our correlation energy treatment. A possible source of error to consider in the calculations is that of basis set superposition error (BSSE). BSSE arises because the halogen in the transition state may use orbitals from the additional H to improve its energy. One way to estimate the effect of this is to perform a calculation on HX with a set of "ghost"orbita1s on the oppositeside from the other H at the H-X distance in the linear transiton state.34 This should provide an upper limit to the BSSE for these systems. Although such an effect may be small at the SCF level for the size of the basis sets under consideration,thecorrection may be larger at thecorrelated
+
-0.40 -0.60
i i o iio
130
iio
150
i i o iio i i o
HFH Bending Angle
Figure 1. HFH bendingangleasa functionoflwelofcorrelation treatment with the TZ+2P+f basis set. See Table V for values.
We performed BSSE calculations as described above for the various X, and the results are shown in Table VIII. As noted previou~ly,~~ the MP2 level provides a very good estimate of the BSSE for these systems. The BSSE is largest for F, 2.2 kcal/ mol, and decreases by almost 1 kcal/mol to C1 and to about 0.5 kcal/mol for Br and I. Although it is gratifying that BSSE is small for the larger halogens, the error for F is larger than one would like. In order to examine this more carefully, we decided to look at larger basis sets which are supposed to recover more of the correlation energy. The two choices are the correlation consistent (CC)36and atomic natural orbital (ANO) basis sets.37 Both basis sets involvegeneral contractions, but the CC basis sets are generally contracted in only a few orbitals. Because Gaussian 92 employs segmented contractions, we used the CC basis sets. For F, we used the (12s6p3d2f) primitive set contracted to [6s4p3d2fl and augmented it with a diffuse s and p obtained by geometric extrapolation based on the A N 0 basis sets. For H, we used the (6s2pld) primitiveset contracted to [4s2pld]. Thetotalenergiesareshown in Table VII. The electronic energy barrier for H + FH at the QCISD(T) level with the large basis set is 42.6 kcal/mol, which is 1.3 kcal/mol above the result with the smallet,basis seta3*The BSSE is now reduced to 0.43 kcal/mol. Most of the 1.3 kcal/ mol difference in the barrier heights can be attributed to the larger BSSE with the smaller basis set. We also evaluated the BSSE for the H + ClH reaction with the large basis set on C1 and here the BSSE is reduced to 0.43 kcal/mol at the QCISD(T) level. These values are now more in line with the BSSE found for Br and I. We recalculated the energies of H F (r(F-H) = 0.921 A) and HFH at the QCISD(FC) geometries because of the change in r(F-H) in the linear transition state as compared to the UMP2(FU) result. The total energies are given in Table VIII. The barrier height at the QCSID(T) level is 42.3 kcal/mol with a BSSE of 0.39 kcal/mol. At the PMP4 level, the corresponding values are 41.7 and 0.41 kcal/mol. In Table IX, we report our best values for the electronic contribution to the barrier height. For these values, we take the results from the largest basis sets and correct them by adding in the BSSE values.
TABLE V: HFH Transition-State Energies as a Function of Bendiig Angle
e( H FH) 180 170 160 150 140 130 120 114
r(H-F) 1.115 1.114 1 . 1 10 1.104 1.096 I .087 1.078 1.074
MP2(FU) 0.00 -0.04 -0.13 -0.21 -0.27 -0.36 -0.47 -0.50
MP2(FC) 0.00 -0.04 -0.13 -0.20 -0.24 -0.30 -0.37 -0.38
Energies in kcal/mol relative to energy at e(HFH) = 1 8 0 O .
PMP2( FC) 0.00 0.01 0.14 0.39 0.73 1.07 1.34 1.49
MP4(FC) 0.00 -0.03 -0.08 -0.08 -0.01
0.07 0.12 0.18
PMP4( FC) 0.00 0.01 0.10 0.29 0.59 0.90 1.17 1.31
QCISD(T) 0.00 -0.01
0.02 0.15 0.39 1.02
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2089
Exchange Reaction Activation Energy Prediction
TABLE VI: Electronic Eneraies AEo*(elec) (kcal/mol) of tbe Transition State Relative to Reactants' MP2(FU) MP2(FC) ROMP2( FC) PMP2( FC) MP3( FC) PMP3(FC) MP4(FC) PMP4( FC) QCISD QCISD(T) CCSD CCSD(T) a
F(L)
F(B)
CUL)
Br(L)
Br(BI)
Br(B2)
44.8 45.0 43.4 42.2 44.4 42.7 42.5 40.9 42.4 41.3 42.5 41.4
44.3 44.6 44.3 43.7 44.6 44.1 42.7 42.2 43.6 42.3 43.7 42.4
24.3 24.4 21.2 20.1 23.5 20.9 21.8 19.2 21.1 20.1 21.2 20.2
18.0 18.0 14.4 13.2 16.8 13.8 15.2 12.3 14.2 13.3 14.4 13.4
18.0 18.0 14.5 13.2 16.7 13.8 15.2 12.3 14.2 13.3 14.3 13.4
39.1 38.7 36.9 35.5 36.3 34.2 34.8 32.8 34.1 33.2 34.2 33.2
L = Linear. B = bent. BI = near linear bending. B2 = acute bending (O(HXH)
TABLE VII. Large Basis Set Total Energies (au) for H XH HX + H for X = F and CI
+
+
molec
X
HX
HX
+ Ghost
I(L) 10.9 11.4 7.9 6.4 10.1 6.9 8.7 5.5 7.5 6.7 7.6 6.8
UBI) 10.4 10.8 8.1 6.2 9.1 6.3 7.7 4.9 6.6 5.8 6.7 5.9
< 90O).
TABLE IX: Activation Energies and Preexponential FactoWb
[HXHI'
F
CI
Br ~~
PMPZ PMP4 QCISD(T) QC ISD(T) PMP4 PMPZ PMP4 QCISD(T)
F" F" F' Fa.h Fa.b CI' CI' CI"
-100.358 -100.368 -100.367 -100.367 -100.368 -460.309 -460.336 -460.337
710 665 142 152 670 332 789 158
-100.359 41 1 -100.369 347 -100.367 805 -100.367 781 -100.369 319 -460.309 960 -460.337 466 -460.337 836
-100.789 496 -100.801 512 -100.799 222 -100.799 734 -100.802 129 -460.777 69 1 -460.806 626 -460.805 424
*
a Energy(H) = 0.499 946 au. See Table 11, footnote a. Evaluated at optimum QCISD(FC)/TZ+ZP+f geometry for H F and HFH. Energy for H from Table 111. Evaluated at the optimum MP2(FU) geometry with this basis set. For HCI, r(H-CI) = 1.276 A; for HCIH, r(H-CI) = 1.470 A. See Table 11, footnote a.
fie1cdPMP4) A&C(QCISD(T)) Azpe Ea(PMP4)(0 K) E,(QCISD(T))(O K) E,(PMP4) A(PMP4) Ea(PMP4)(Wig) A(PMP4)(Wig) Ea(QCISD(T)) A(QCISD(T)) E,(QCISD(T))(Wig) A(QCISD(T))(Wig)
TABLE MII: BSSE Effects to Barrier Height (kcal/mol) atom
MP2
QCISD(T)
CCSD(T)
Fa Fh Fhs Cld CP Br
2.14 0.44 0.42 1.21 0.33 0.49 0.66
2.22 0.42 0.39 1.37 0.43 0.53 0.69
2.22
I
1.37 0.53 0.69
Smaller F basis set, Table 11. Larger F and H basis set, Table 11, footnote a. I' Calculated using QCISD(FC) optimized geometry parameters. Smaller CI basis set, Table 11. Large CI basis set, Table 11, footnote a.
Discussion Although we would like to report that theory and experiment are in good agreement for these barriers, we cannot do so at the present, as the experimental picture is somewhat muddled. In order to compare to experiment, we have used transition-state theory39 (TST) to calculate the rate constants from our barrier height and the properties of the transition state. We have calculatedthese quantitieswith the PMP4 and QCISD(T) barriers and have used the Wigner correctiona in order to estimate tunneling corrections. The TST calculations were done in the rigid rotor, harmonic oscillator approximation,and the symmetry number factor s is 0.5. From these rate constants, we can then back-calculatean activation energy. The rate constantsat selected temperatures are given in Table X,and the activation energy parameters derived from them are given in Table IX. For HFH, the only real experimental data come from that of Polanyi andco-workers.5 It isuseful tonote that the H-abstraction channel which is dominant for the other halogens is endothermic by 32 kcal/mol and thus plays a different role in this reaction. Bartoszek et al.5 used the technique of chemiluminescence depletion with mass spectrometry. With this method, they show that the exchange process can be observed for the reaction HF(vr5) + D DF + H but not for Y = 4. This places an upper limit to the barrier of 52 kcal/mol. The amount of vibrational
-
I(W 21.1 20.8 19.5 17.8 18.2 16.3 16.9 15.0 16.2 15.5 16.2 15.5
E,( PMP4) A(PMP4) Ea(PMP4)(Wig) A( PMP4) (W ig) Ea(QCISD(T)) A(QCISD(T)) E,(QCISD(T))(Wig) A(QCISD(T))(Wig)
42.1 19.2 42.7 20.2 2.7 0.8 39.4 18.4 40.0 19.4 High T (Max = 3000) 42.3 19.6 6.OE-9 1.6E-IO 40.6 18.7 4.2E-9 1.4E-10 42.9 20.6 1.6E-10 6.OE-9 41.2 19.7 4.2E-9 1.4E-I0 Low T (Max = IOOO) 41.1 19.0 2.OE-9 5.5E-11 39.4 18.0 1.6E-9 4.7E-I 1 41.7 20.0 5.5E-11 2.OE-9 40.0 19.0 1.6E-8 4.7E-11
12.8 13.8
I ~
~~
11.8 13.8
5.6 6.4 0.3 5.3 6.1
12.9 8.OE-11 12.1 7 .DE- 10 13.9 8.OE-11 13.1 7.OE-1 I
6.1 9.OE-11 5.7 8.OE-11 6.9 9.OE-11 6.5 8.OE-11
12.4 3.8E-11 11.6! 3.OE-1 I 13.4 3.8E-11 12.6 3.OE-11
5.7 4.6E-11 5.3 3.8E-11 6.5 4.6E-11 6.1 3.8E-11
1.o
a E, in kcal/mol, A in cmJ molecule-I s-l. Wig = Wigner correction. All corrected for s = 0.5. Values given as E-n are X 1 t n .
*
energy for the Y = 4 state is 43 kcal/mol. However, for the Y = 4 reaction to proceed, all of the vibrational energy would have to be used in overcoming the barrier, and dynamical constraints may prevent this, as the calculated barrier for 0 K molecules is about 40 kcal/mol for the linear structure. It is unlikely that all of the vibrational energy can be used to overcome the barrier, so it is not surprising that no DF was produced from HF(vr4). For the other halogens, the dominant process is H abstraction to form Hz and the halogen. As the abstraction reactions are exothermic and become more so with increasing halogen atomic number, they occur with very low barriers and are easily the dominant channel. For C1, Endo and Glass2 were able to measure a rate constant for D HCl DCI + H and obtained a value of (1.6 f 0.9) X 10-13 cm3 molecule-' s-I. Our highest value (PMP4) at 1000 K is 0.07 X lef3 cm3 molecule-l s-I when tunneling is included. This is smaller than the Endo and Glass2 value which may actually be too high.4 However, it is unlikely that E, will be lower than 15-16 kcal/mol. For H BrH, Endo and Glass2 report a similar experiment but only report avalue of k at 295 K. This is 4 orders of magnitude greater than our value, but we note that in the H + CIH reaction, a similar difference is found at room temperature. For H + IH, there are no data on the exchange process. Are the calculated values consistent with the molecular beam results? This is difficult to assess. In the McDonald and Herschbach" crossed beam experiment, a thermal beam of D
+
+
-
2090 The Journal of Physical Chemistry, Vol. 97, No. IO, 1993
Dobbs and Dixon
TABLE X: Rate Constants k (cm3 molecule-' s-')~
(I
P
Wigb
k
E*'
k
0. I6E-30 0.42E-26 0.40E-23 0.56E-2 1 0.238-19 0.46E-17 0.66E-14 0.29E-12 0.45E-11 0.1 6E- 10
sWigk HFH PMP4 0.498-30 0.90E-26 0.658-23 0.75E-21 0.27E-I 9 0.428-17 0.468-14 0.17E-12 0.26E-11 0.90E-11
400 500 600 700 800 1000 1500 2000 2600 3000
6.2 4.4 3.3 2.7 2.3 1.8 1.4 1.2 1.1 1.1
200 300 400 500 600 1000 1500 2000 2600 3000
39.1 39.2 39.4 39.6 39.9 40.6 42.7 44.8 47.2 48.7
8.7 4.4 2.9 2.2 1.9 1.3 1.1 1.1 1 .o 1 .o
0.24E-30 0.148-23 0.39E-20 0.48E-18 0.1 2E-16 0.1 1E- 1 3 0.41E-12 0.29E-I 1 0.1 3E- 10 0.26E-10
HClH PMP4 0.1OE-29 0.3 2E-23 0.55E-20 0.55E-18 0.12E- 16 0.70E-14 0.23E-12 0.16E-11 0.65E-11 0.13E-I 0
200 300 400 500 600 1000 1500 2000 2600 3000
5.9 3.2 2.2 1.8 1.5 1.2 1.1 1 .o 1 .o 1 .o
0.238-23 0.61E-19 0.1 1E-16 0.25E-15 0.22E-14 0.19E-12 0.21E-11 0.76E-11 0.20E-10 0.32E-10
200 300 400 500 600 1000 1500 2000 2600 3000
2.5 1.7 1.4 1.2 1.2 1.1 1 .o 1 .o 1 .o
0.6 1E-I 6 0.6OE-14 0.62E-13 0.27E-12 0.73E-12 0.63E-11 0.22E-10 0.46E-10 0.8 1E-1 0 0.1 1E 4 9
1 .o
0.74E-3 1 0.23E-26 0.248-23 0.368-2 1 0.16E-19 0.39E-17 0.54E-14 0.25E-12 0.40E-11 0.15E-10
sWigk HFH QCISD(T) 0.23E-30 0.5OE-26 0.408-23 0.50E-21 0.18E-19 0.32E-17 0.378-14 0.1 5E-12 0.22E-11 0.80E-11
39.7 39.8 40.0 40.2 40.5 41.2 43.3 45.4 47.8 49.3
17.8 17.8 18.0 18.2 18.5 20.0 22.0 23.8 25.9 27.2
0.19E-3 1 0.27E-24 0.1 1E-20 0.17E-18 0.54E-17 0.65E-14 0.298-12 0.23E-11 0.1OE-10 0.22E-10
HClH QCISD(T) 0.858-31 0.60E-24 0.16E-20 0.2OE-I 8 0.50E-17 0.42E-14 0. I8E-I 2 0.12E-11 0.55E-1 I 0.1 1E-10
18.8 18.8 19.0 19.2 19.5 21.0 23.0 24.8 26.9 28.2
HBrH PMP4 0.70E-23 0.10E-18 0.12E-16 0.22E-15 0.16E-14 0.llE-12 0.1 1 E-1 1 0.4OE-I 1 0.10E-10 0.16E-10
11.4 11.4 11.6 11.8 12.0 13.2 14.6 15.8 17.2 18.1
0.19E-24 0.1 1E-19 0.3 1 E- 17 0.938-16 0.93E-15 0.1 1 E-1 2 0.15E-11 0.59E-1 I 0.17E-10 0.27E-10
HBrH Bent QCISD(T) 0.55E-24 0.18E-19 0.34E-I 7 0.85E-16 0.70E-15 0.65E-13 0.8OE-12 0.3lE-11 0.85E-11 0.14E-10
12.4 12.4 12.6 12.8 13.0 14.2 15.6 16.8 18.2 19.1
HIH PMP4 0.80E-16 0.50E-14 0.438-13 0.16E-12 0.43E-I2 0.34E-11 0.12E-10 0.23E-10 0.42E-10 0.55E-10
4.9 5.0 5.2 5.5 5.7 6.8 8.0 9.1 10.4 11.2
0.82E-I7 0.16E-14 0.23E-13 0.12E-12 0.3 7E- 12 0.42E-11 0.17E-10 0.37E-10 0.69E-10 0.94E-10
HIH QCISD(T) 0.1OE-16 0.13E-I 4 0.16E-13 0.75E-13 0.22E-12 0.22E-11 0.85E-11 0.19E-I 0 0.35E- 10 0.47E-10
5.7 5.8 6.0 6.3 6.5 7.6 8.8 9.9 11.2 12.0
EaC
Temperature in K. Wigner correction. Activation energy in kcal/'mol. Values given as E-n are X IO-".
atoms produced at 2800 K by thermal dissociation of D2 in a tungsten oven was crossed with a thermal HX beam generated a t 250 K. Although the average center-of-mass (CM) energies4I are on the order of 9 kcal/mol, there are a considerable number of fast D atoms in the Maxwellian velocity distribution. For the D + IH reaction, there is sufficient average kinetic energy to overcome the barrier and there is no discrepancy between our results and the experimental ones based on the observation of scattered DI. For the D BrH and D ClH reactions, there is not enough energy unless one considers much higher velocities. For a Maxwellian velocity distribution, the fraction of molecules with velocities 50%greater than the average velocity is 0.64, and those with a factor of 2 is 20%. Because the velocity in the centerof-mass coordinate system required for evaluating the energy is dominated by the velocity of the D atom beam,ll there is considerable spread in the available energy due to the thermal D atom beam. A factor of 1.5 in the velocity increases the translational energy by a factor of 2.25, and that of 2.0 increases it by a factor of 4, clearly providing enough energy to overcome the calculated barriers. Thus, the predicted activation energies are not inconsistent with the observation of the products under the conditions of the crossed molecular beam experiment. There is a potential constraint on the activation energies from the experiment in terms of the lab angular distributions. In the original kinematic analysis, barriers of 3.0, 1 .O, and 0.0 kcal/mol
+
+
were used for X = C1, Br, and 1. It would be useful to redo the kinematic analysis with the barriers calculated in this study. The presence of a possible second transition state is of real interest for the H + BrH and H + I H reactions. In order to verify that theseare indeed possible transition states, we performed calculationsat a bond angle of 110' and with appropriately scaled bond distances. For Br, the energy of this structure is 23.4 kcal/ mol above the structure with e(HBrH) = 77.4O, and for I, the structureat 1 loo is 25.4 kcal/mol abovethestructurewithB(H1H) = 75.3O a t the PMP4 level. Thus, there are secondary transition states on the potential energy surface. As discussed by others,I5J6 it is appropriate to compare these reactions to those of H H2. For the H H2 reaction,42 the barrier is about 10 kcal/mol and the reaction in the simplest model involvesthe following molecular orbitals
+
+
0 0 0
0 . 0
0 0 0
Exchange Reaction Activation Energy Prediction Note that each H atom has one electron, so all of the electrons in the system can be considered as active in this reaction. If we now replace the central H atom with a halogen atom, we have the same number of active orbitals, but now the central atom involves a p orbital, as the ns orbital is a doubly occupied lone pair. This s-like lone pair will clearly have a repulsive interaction with the three active electrons, which in the case of F leads to a much higher barrier. For CI,the barrier is still almost a factor of 2 higher than that for H + H2, and for Br, the barrier is comparable to that for H + H2. Of course, we have not considered the two other lone pairs on the halogen, which in this simple model can be considered as being orthogonal to the active orbitals as shown below in A. If the H atom now approaches at a bond
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2091 ( I I ) McDonald, J. D.; Herschbach, D. R. J. Chem. Phys. 1975,62,4740. (12) Bauer, W.; Rusin, L. Y.; Toennies, J. P. J . Chem. Phys. 1978, 68, 4490. Beck, W. H.; GBtting, R.; Toennies, J. P.; Winkelmann, K. J . Chem. Phys. 1980, 72. 2896. ( I 3) Thompson, D. L.; Suzukawa, H. H., Jr.; Raff, L. M. J. Chem. Phys. 1975,62,4727. Raff,L. M.;Suzawaka, H. H., Jr.;Thompson,D. L.J. Chem. Phys. 1975,62,3743. Wilkins,R. L.J. Chem.Phys. 1975,63,534. Valencich, T.; Hsieh, J.; Kwan, J.;Stewart, T.; Lenhardt, T. Ber. Bunsenges. Phys. Chem. 1977,81. 13 I . Clary, D. C. Chem. Phys. Lett. 1981,80, 27 I . Clary, D. C. Chem. Phys. 1982, 71, 117. Clary, D. C.; Drolshagen, G. J . Chem. Phys. 1982, 76, 5027. (14) Bender, C. F.; Garrison, B. G.; Schaefer, H. F., Ill. J . Chem. Phys. 1975, 62, 1188. (15) Wadt, W. R.; Winter, N. W. J . Chem. Phys. 1977, 67, 3068. (16) Dunning, T. H., Jr. J . Phys. Chem. 1984,88,2469. Dunning, T . H., Jr. J. Chem. Phys. 1977.66. 2752. (17) Botschwina, P.;Meyer, W.J. Chem. Phys. 1977,67,390. Botschwina, P.; Meyer, W. Chem. Phys. 1977, 20, 43. (18) Voter, A. F.; Goddard, W. A., 111. J. Chem. Phys. 1981, 75, 3638. (19) Krishnan, R.; Pople, J. A. I n f . J . Quantum Chem. 1978, 14, 91. Krishnan, R.; Frisch, M. J.; Pople, J. A. J. Chem. Phys. 1980, 72, 4244. (20) Bartlett, R. J. J . Phys. Chem. 1989, 93, 1697. Kucharski, S. A.; Bartlett, R. J . Ado. Quantum Chem. 1986, 18, 281. (21) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J . Chem. Phys. 1987,87,5968. Raghavachari, K.;Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (22) Gaussian 90; Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.;
Foresman, J.; Schlegel, H. B.; Raghavachari, K.; Rabb, M. A,; Binkley, J.
S.;Gonzalez, C.; DeFrees, D. J.; Fox, D. A.; Whiteside, RA. A.; Seeger, R.;
Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.;Stewart, J. J. P.;Topiol,
A
B
angle of 90° (B) rather than interacting with the s-like lone pair first, it will interact with the doubly occupied p lone pair. Because this orbital is more directed in space, the barrier should be significantly higher in energy, as is found. The presence of the second transition state in such a simple system is a novel feature which could have dynamical consequences for the I system, as it is energetically accessible in the experiments under consideration. There are two ways to reach the products that are separated by a large barrier, and these should have different dynamical consequences, as the impact parameters leading to the various reactions are quite different. The results will probably only show up experimentally under beam conditions when velocity analysis is used to observe the products.
Acknowledgment. We thank Dr. Andrew Komornicki for helpful discussions. We also thank Dr.A. F.Wagner for providing the program for calculating the transition-state properties and rate constants. References and Notes ( I ) Bodenstein, M. Z. J. Phys. Chem. A (Leipzig) 1899, 29, 295. (2) (a) Endo, H.; Glass, G. P. Chem. Phys. Lett. 1976, 44, 180. (b) Endo. H.; Glass, G. P. J. Phys. Chem. 1976, 80, 1519. (3) Klein, F. S.; Veltman, 1. J. Chem. SOC.,Faraday Trans. 2 1978.74, 17. de Vries, A. E.; Klein, F. S . J. Chem. Phys. 1964, 4 1 , 3428. (4) Miller, J. C.; Gordon, R. J. J . Chem. Phys. 1981,75,5305; 1982,76, 5167; 1983, 78, 3713. (5) Bartoszek, F. E.; Manos, D. M.; Polanyi, J. C. J. Chem. Phys. 1978, 69, 933. (6) Wood, G. 0. J. Chem. Phys. 1972, 56, 1723. (7) Heidner, R. F., Ill; Bott, J. F. J. Chem. Phys. 1976,64, 2267. Bott, J. F.; Heidner, R. F., 111 J. Chem. Phys. 1976, 64, 1544. (8) Leighton, P. A.; Cross, P. C. J . Chem. Phys. 1938,6, 345. Steiner, H.; Rideal, E. K. Proc. R . SOC.London, Ser. A 1939, 173,503. Steiner, H. Proc. R . SOC.London, Ser. A 1939, 173, 531. Persky, A,; Kuppermann, J. Chem. Phys. 1974,61,5035. Wolfrum, J. Ber. Bunsenges. Phys. Chem. 1977, 81. 114. (9) Lee. Y. T.; McDonald, J. D.; LeBreton, P. R.; Herschbach, D. R. Rev. Sci. Instrum. 1969, 40, 1402.
(IO) McDonald, J. D.; LeBreton, P. R.; Lee, Y. T.; Herschbach, D. R. J . Chem. Phys. 1972, 56.769.
S.; Pople, J. A.; Gaussian Inc., Pittsburgh, PA, 1990. G90. (23) (a) Moller, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. (b) Pople, J. A.; Binkley, J. S.; Seeger, R. I n t . J . Quantum Chem. Symp. 1976, IO, I . Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. In?. J . Quantum Chem. Symp. 1979, 13, 325. Handy, N. C.; Schaefer, H. F., Ill. J . Chem. Phys. 1984, 81, 5031. (24) (a) Andrews, J. S.; Jayatilaka, D.; Bone, R. G. A.; Handy, N. C.; Amos, R. D. Chem. Phys. Lett. 1991, 183,423. (b) For another approach see: Lauderdale, W. J.; Stanton, J. F.; Gauss, J.; Watts, J. D.; Bartlett, R. J. Chem. Phys. Lett. 1991, 187, 21. (25) Schlegel, H. 8. J. Chem. Phys. 1986,84, 4530. (26) Dunning, T. H. J . Chem. Phys. 1971, 55, 716. (27) McLean, A. D.; Chandler, G.S. J . Chem. Phys. 1980, 72, 5639. (28) Dunning, T. H. J . Chem. Phys. 1977,66,1382. Eades, R. A., Dixon, D. A. J . Chem. Phys. 1980, 72, 3309. (29) Dunning, T. H. Private communication. (30) Huber, K. P.; Herzberg, G. Constants ofDiatomic Molecules; Van Nostrand Reinhold: New York, 1979. (31) Values of at the MP2(FU)/TZ+2P+f optimized geometries with this basis set are [HFH]' linear, 0.787; [HFH]' bent, 0.761; [HCIH]' linear, 0.813; [HBrH]' linear, 0.826; [HBrH]' opt, 0.824; [HBrH]' bent, 0.803; [HIH]' linear, 0.836; [HIHI' opt, 0.827; and [HIHI' bent, 0.801.
(s2)
Values with the CC basis set are similar. (32) ROMP2 as formulated in ref 24a does not satisfy the property of invariance with respect to unitary transformations among the virtual and occupied orbitals. An approach that does satisfy this unitary invariance has been described in ref 24b. Furthermore, ROMP2 is not a spin eigenfunction and satisfies the projected condition (m@21aOMp) = S(S + 1) as compared to q(R0HF) which is an eigenfunction of 3 . (33) Werner, H.-J.; Rosmus,P. J . Chem. Phys. 1980, 73, 2319. (34) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (35) Komornicki, A.; Dixon, D. A. J . Chem. Phys. 1992, 97, 1087. (36) Dunning, T. H. J . Chem. Phys. 1989, 90, 1007. (37) AlmlBf, J.;Taylor, P. R. J. Chem. Phys. 1987,86,407& Adu. Quantum Chem. 1991, 22, 301. (38) We recalculated the energy difference between the 0 = 180° and 114' structures for HFH using the CC basis set augmented by an additional set of diffuse s and p functioni with exponents s[ =-0.0361 and p [ = 0.0226 at theQCISD(T) level. Theoptimized MP2(FU)/TZ+2P+fgeometrieswere used. Thelinear structure is0.54 kcal/mol lower in energy. E([HFH] ',linear) = -100.799 710 au. (39) Kreevoy, M. M.; Truhlar, D. G. In Inuestigations of Rates and Mechanisms of Reactions, 4th ed.; Bernasconi, C. F., Ed.; Wiley: New York, 1986; Part I , Chapter 1, p 13. Steinfeld, J. 1.; Francisco, J. S.;Hase, W. L. ChemicalKineticsand Dynamics; Prentice-Hall: Englewocd Cliffs, NJ, 1989. Johnston, H. S.Gas Phase Reaction Rate Theory; Ronald Press: New York, 1966. (40) Wigner, E. P. Z . Phys. Chem. 1932, B19, 203. (41) Levine, R. D.; Bernstein, R. 8. Molecular Reaction Dynamics and Chemical Reactivity; Oxford University Press: New York, 1987. (42) Siegbahn, P.; Liu, B. J. Chcm. Phys. 1978, 68, 2457. Liu, B. J . Chem. Phys. 1984,80,581. Liu, B.J. Chem. Phys. 1973,58,9125. Truhlar, D. G.; Horowitz, J. C. J. Chem. Phys. 1978, 68, 2466.
