Ab Initio Study of the Chlorine Nitrate Protonation Reaction - American

the two major stratospheric reservoirs of C1," are involved in ... the initial hypothesis of Wofsy et al. that dissociation of C 1 0 N a ... 97, No. 2...
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J. Phys. Chem. 1993,97, 66376644

Ab Initio Study of the Chlorine Nitrate Protonation Reaction: Implications for Loss of CION02 in the Stratosphere Timothy J. Lee' NASA Ames Research Center, Moffett Field, California 94035-1 OOO

Julia E. Rice IBM Research Division, Almaden Research Center, Sun Jose, California 95120 Received: February 17, 1993

The energetics of the protonation reaction of chlorine nitrate, ClONO?, have been investigated using stateof-the art ab initio quantum mechanical methods. Specifically, equilibrium structures, vibrational spectra, and thermochemical data have been obtained using second-order Msller-Plesset perturbation theory (MP2), singles and doubles coupled-cluster theory (CCSD), and the CCSD(T) method, which includes a preturbational estimate of the effects of connected triple excitations. It is shown that the lowest energy form of protonated ClONO2 corresponds to a complex between HOCl and NOz+-similar to the situation for HONOz and CH3ON02. The proton affinity of ClONO2 is determined to be 176.8 3 kcal/mol (0 K)while the second most stable isomer of protonated ClONO2 is 20 kcal/mol higher in energy. The HOCl-N02+ complex is bound by 12.9 f 2 kcal/mol, The heat of formation of ClONO2 is computed to be 7.4 kcal/mol a t 298 K,in good agreement with the experimental value of 6.3 kcal/mol. The present study supports a recent hypothesis that the reaction of ClON02 on the surface of polar stratosphericclouds(PSCs) is protoncatalyzed, although the specific mechanism is different. The results are also consistent with other recent findings concerning the reactions of ClONOz and HOCl with HCl on the surface of PSCs.

*

Introduction There has been considerable interest in the mechanisms of the chemical reactions that take place in the chemically perturbed region of the Antarctic ozone hole. The importance of chemical reactions taking place on the surface of polar stratosphericclouds (PSCs) has been firmly established (for example, see refs 1-13). It has been determined that chlorine nitrate (ClONOz) and HCl, the two major stratospheric reservoirs of C1," are involved in chemical reactions on the PSCs, and that these reactions lead to the release of C1 in the more reactive forms of Clz and HOCl. Some details of the heterogeneous reactions involving ClONOz have been extensively studied in the last yearIIO-IZand it is now generally accepted that at least when low concentrations of HONOl are present, ClONOz reacts with the water-ice surface to form HOC1, which subsequently reacts with HC1 to form Clz. Earlier Wofsy et ~ 1 . postulated ~ 3 that the dissociation of ClONOz on the surface of PSCs is proton catalyzed. Specifically, Wofsy et al. proposed the following mechanism: ClONO,

+ H+

-

HON02-C1+

(1) which leads to a C1+ leaving group. Nelson and Okumura,15 however, have recently concluded via molecular beamexperiments that a major product from protonation of ClON02 in the gas phase is HOCl. This conclusion is consistent with the currently accepted view of ClON02 reactions on PSCs, and it does support the initial hypothesis of Wofsy et al. that dissociation of C 1 0 N a on the surface of PSCs is proton catalyzed, although not the specific mechanism. It is also important to point out that Nelson and Okumura's observations are consistent with the established products from protonation of both HONOz and CH3ONOz.l6l9 For both of these nitrates, the most stable form of the protonated species is a complex involving N a + ; that is for HONOz the complex is H20--NOz+, while for CH3ON02+ the complex is CH3OH--NOz+. Thus one might expect that the most stable isomer of protonated ClONOz would be the HOCl--NOz+ complex, and Nelson and Okumura's observations are consistent with this 0022-3654/93/2097-6637$04.00/0

expectation [they actually observe (HzO),NOz+-the reason for this is discussed later]. However, their experimentsdo not firmly establish several reaction enthalpies that are of interest. For example, the proton affinity of ClONOz, the energy difference between HOCl-*NOz+ and the second most stable isomer of protonated ClONOZ, and the binding energy of the HOCl*-NOz+ complex relative to HOCl NOz+ are all of interest in order to obtain a better understanding of the chemical reactions taking place on the PSCs. It is the purpose of the present study to provide accurate ab initio predictions of these quantities together with accurate predictions of the molecular structures and vibrational spectra of the relevant species. It must be borne in mind that the present calculations are for gas-phase species and that the enthalpies of the various reactions studied herein will be affected by neighbor interactions in a condensed phase. However, gas-phase enthalpies can be used to deduce qualitatively the possible reaction mechanisms occurring on the PSCs, and they also provide raw input data for possible future simulations of the more complicated heterogeneous environment. As such, a discussion concerning the possible loss of ClONOz in the chemically perturbed region of the Antarctic stratosphere, based on the gas-phase enthalpies determined in this study, is also presented. The theoretical methods employed in the present study are described in the next section, followed by the presentation and discussion of the results. Conclusions are presented in the final section.

+

Theoretical Approach As in our previous studies of the protonation of HONOz and CH3ONOz,l7J9 geometry optimizations have been performed using second-order M~rller-Plesset(MP2) perturbation theory, singles and doubles coupledcluster (CCSD) theory, and the CCSD(T) methodm which includes a perturbational estimate of the effects of connected triple excitations. These methods, especially CCSD(T), have been shown to yield very accurate molecular geometries, vibrational spectra,and relative energetics Q 1993 American Chemical Society

Lee and Rice

6638 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993

TABLE L Total Energies ( E d , Equilibrium Bod Lengths (A), Bond Angles (degrees), Dipole Moments (D), and Rotational ConsUnts ( M H 2 ) for CION02 (I) Obbiaed at Various Lev& ef Theory (See Finve 1 for Labeling of Atoms) MP2 CCSD(T) MP2 MP2 CCSD CCSD(T) TWP TZ2P TZ2PP expt’ DZP DZP DZP Eb HIf

TI* P

rao, “0,

“4 “0,

LClOlN LO~NOZ LOzN01 A B C

0.323 882 0 0.83 1.712 1.551 1.209 1.213 111.4 134.9 117.2 11558 2612 2170

0.221 501 0 0.021 1.53 1.719 1.463 1.208 1.209 113.0 132.3 118.5 12028 2723 2221

0.259 243 0 0.022 1.25 1.729 1 SO0 1.214 1.216 112.4 133.1 118.3 11733 2676 2179

0.552 188 0 0.74 1.691 1.572 1.187 1.191 110.8 135.8 116.4 11786 2714 2206

0.464 060

0.693 282

0.021 1.08 1.707 1.511 1.195 1.197 111.9 133.6 117.8 11981 2723 2218

0.74 1.673 1.546 1.186 1.190 110.9 135.5 116.4 11950 2771 2249

0.77

12106 2771 2258

a Dipole moment from ref 46; vibrationally averaged rotational constants from ref 47. The total energy is reported as -(E + 739). Hessian index (i.e., the number of negative eigenvalues obtained from diagonalization of the force constant matrix). I, The T Idiagnostic; see text for details.

For the A N 0 basis sets, only the spherical harmonic components (see for example, refs 21-24). Three basis sets have been used of the d- andf-type functions were included. in the geometry optimizations. The smallest is denoted DZP and consistsof the Huzinaga-DunningU.26[4s2p/2s] contracted sets All electrons and orbitals were allowed to be active in the MP2 on (0,N) and H, respectively, augmented with one set of geometry optimizations. In the coupled-cluster geometry optipolarization functions ( a d = 0.85 and 0.80 for 0 and N; ap= 1.0 mizations the (0,N) 1s-like molecular orbitals and the C1 Is, 2s, for H). The H s functions were scaled by 1.2 as recommended and 2plike molecular orbitalswere required to be doubly occupied by Dunning. The C1 DZP basis set is composed of McLean and in all configurations. In addition, for the DZP basis set the six Chandler’s27 [6s4p] contracted set, augmented with one polarhighest-lyingmolecular orbitals were deleted from the correlation ization function (ad = 0.619). The second basis set is denoted procedure whereas for the TZ2f basis set only the five highestTZ2P and consists of the H u z i n a g a - D ~ n n i n g ~[5s3p/3s] ~~~~ lying molecular orbitals were deleted. As an example, there are contracted Gaussian functions for (0,N) and H, respectively. 681,590and 801,345 singleanddoubleexcitations (Cssymmetry) These sp sets are supplemented with two sets of polarization in the CCSD/TZ2P wave functions for ClONOz and functions ( a d = 2.314, 0.645 for 0 1.654, 0.469 for N; ap = HOCl*-N02+, respectively. For all single-point energies com1.407, 0.388 for H). The C1 TZ2P basis set is composed of puted with the A N 0 basis sets [including MP2, CCSD, and McLean and Chandler’s2’ [6s5p] contracted functions suppleCCSD(T)] the(0,N) lsandtheC1 Is-,2s-,and 2plikemolecular mented with twosetsof polarization functions (ad= 1.072,0.357). orbitals were required to be doubly occupied in the correlation A previous study29 has shown that little is gained by further procedure. uncontraction of thesp basis set. The final basis is denoted TZ2Pf For all levels of theory, the dipole moment p has been evaluated and is obtained by adding anf function to the 0, N, and C1 atoms as an energy derivative, and for charged species p has been ( a=~1.428,1.093, and 0.743 for 0,N and Cl) and a d function determined with respect to the center of mass. AI1 SCF and to H ( a d = 1.057). The polarization function orbital exponents MP2 calcul’ations were performed with the Cambridge Analytic for the TZ2P and TZ2Pf basis sets have been taken from Derivatives Package (CADPAC).42 All coupled-cluster calcuDunning30 for 0,N, and H and from Ahlrichs and Taylor” and lations were performed with the TITAN43 set of electronic Alml6f and Taylors2for C1. In the geometry optimizations, all structure programs. For the single-point energy calculations, six and ten Cartesian components of the d and f functions, the TITAN coupled-cluster programs have been interfaced to respectively, have been included in the basis sets. Analytical the SWEDEN44 program system, and they utilized the gradient method@-36 have been used in all of the geometry SEWARW5 integral program. optimizations. Harmonic vibrational frequencies (and infrared intensities) were determined from analytical second-derivative Results and Discussion methods for the MP2 level of theory37338 and from finite difference of analytical gradients for the other methods. ChlorineNitrate. Equilibrium geometriesand dipole moments of ClONO2 obtained at the various levels of theory are presented As in our earlier studies, large atomic natural orbital (ANO) in Table I, together with the experimental dipole momenta basis s e t ~ 3have ~ been used in conjunction with the CCSD(T) (vibrationally averaged) and the experimental vibrationally correlation method in order to obtain a better estimate of the averaged rotational c0nstants.~7 We are not aware of an relative energies of the various isomers of protonated ClONOZ. experimental determination of the molecular geometry. ComThe A N 0 basis sets are those of Almldf and Tayl0r.3~ For C1 parison of the CCSD/DZP and the CCSD(T)/DZP geometries the density matrices of the neutral atom and the negative ion were averaged. The primitive basis sets are van Duijneveldt’s” and dipole moments shows that connected triple excitations have (13s8p/8s) sets augmented with an even tempered sequence of significant effects on these properties, particularly the dipole (6d4f/6p4d) polarization functions for (0,N) and H, respectively. moment, and the N-01 bond distance (seeFigure 1for the labeling The polarization function orbital exponents are obtained from a of the atoms). Thus the CCSD method has not been used for the = 0.13 and 0.39 for the 0 d and = 2 . 9 ~ ~ n0 ;= 0, ..., k with TZ2P basis set. The MP2 and CCSD(T) results exhibit large differences also, particularly for the dipole moment, the N-01 f functions, respectively;a0 * 0.10 and 0.30 for N; a0 5 0.10 and 0.26 for H. The C1 primitive basis set is Partridge’s41 ( 1 9 ~ 1 4 ~ ) bond distances and the 0 3 N 0 2bond angle. Except for the dipole moment, these differences are larger for the TZ2P basis than for set augmented with a (6d4j) set of polarization functions with the DZP basis set. On the basis of experience, it is expected that a0 = 0.06 and 0.19 for the C1 d and f functions. The basis set the CCSD(T)/TZ2Pf method would provide the most reliable denoted AN01 consists of 5s4p2d, 4s3p2d, and 4s2p ANOs on equilibriumgGomotry of ClON02. However, a CCSD(T)/TZZPf C1, (N,O), and H, respectively. The AN02 basis set is composed geometry optimization would be very expensive, and therefore a of 5s4p2dlJ 4s3p2dlJ and 4s2pldANOs on C1, (N,O), and H.

The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6639

The Chlorine Nitrate Protonation Reaction

A

Figure 1. Graphical representation of chlorine nitrate and its various protonated forms.

good approximationis simplyto add the CCSD(T)/TZ2P-MP2/ TZ2P differencesto the MP2/TZ2Pf equilibriumstructure. This procedure does not always work very well (indicating the nonadditive nature of basis set and correlation effects-when starting with the TZ2P basis set this type of procedure usually overcorrects),but a similar procedure performed well in our earlier studies17*19of HON02 and CH30N02. Following this procedure gives 1.485 A and 133.3O for the N-01 bond distance and the 03N02 bond angle, respectively, which are the geometrical parameters most affected. Comparison of the theoretical equilibriumrotational constants with the experimental vibrationally averaged quantities shows that both the CCSD(T)/TZ2P and MP2/TZ2Pf values are in good agreement with experiment, suggestingthat these structures are at least semiquantitative in accuracy. The CCSD(T)/TZ2P dipole moment would appear to be too large compared to experiment, while the MP2 value is probably somewhat low as vibrational averaging of the theoretical values is likely to reduce themagnitudeof thedipole. Themaindeficiency with the CCSD(T)/TZ2P dipole moment is probably due to basis set inadequacies. Predicted harmonic vibrational frequencies and IR intensities of ClONO2 are presented in Table 11, together with the experimentalfundamental vibrational frequencies.4”50 It should be noted that the mode descriptions given in Table 11, which are based on potential energy distribution analyses, are only approximate. In particular, there is a lot of mixing among the internal coordinate contributions for modes W3-W6. In fact the MP2 method actually reverses the order of w3 and w4. This last observationis apparent from both the potential energy distribution analyses and also from the relative IR intensities. Acomparison of the MP2/DZP and CCSD(T)/DZP harmonic frequencies exhibits features similar to those observed earlier17J9 for HONO2 and CH30NOz-that is, the MP2 01 (N-02, N-03 antisymmetricstretch) value is considerablyoverestimatedrelative

to the CCSD(T) quantity, while 0 3 , ws, and W6 are somewhat underestimated at the MP2 level. From knowledge of the ab initio harmonic frequencies of ClONO2 presented here, and those presented in earlier work on HONO2 and CHsON02, it is evident that the MP2 level of theory consistently overestimatesthe N-O antisymmetric stretch of nitrate compounds, but that it performs reasonably well in describingthe symmetriccombinationof N-O stretches (w2 for ClON02). In some cased9 it has been shown that the differences between MP2 and CCSD(T) harmonic frequencies are fairly independent of the basis set and hence are additive. If theCCSD(T)/DzP-MP2/DZP differencesare added to the MP2/TZ2P harmonic frequencies, values of 1795,1285, 813, 783, 569, 413, 254, 707, and 115 cm-l are obtained for ~ 1 - 0 9 , respectively. These are in good agreement with the observed fundamental frequencies, especially considering that we have not determined the anharmonic corrections. Based on the ab initio calculationsof CION02 discussedabove, it is clear that the levels of theory used here provide reliable results for the geometry and harmonicfrequencies. The reliability ofthe CCSD(T) method issupported by the?, diagnosticvalues51 reported in Table I. (The TI diagnostic has been shown51 to be a reliable indicator of the importance of nondynamical correlation effects.) In this case ?I = 0.022, indicating that the CCSD(T) method shouldperform reasonablywell in describingthe electronic structure of chlorine nitrate. Thus we may expect that the structures and harmonic frequencies of the protonated species, for which no experimental data are available, should also be reliable. Protonated Chlorine Nitrate. On the basis of our previous work on the protonation reactions of HONOz and CH30N02, it was expected that there would be two main isomers of protonated C10N02. In other words, it was expected that the lowest energy form of protonated ClONOz would be a complex between HOC1 and NO2+ (11 in Figure l), and that the second lowest energy form would correspond to protonation of one of the other oxygen atoms (III in Figure 1). It was also expected that there would be several other isomers of protonated ClONOz that are similar in energy to the second most stable form of CIONOzH+ (IV, V, and VI in Figure 1). Isomers 111 through VI only differ in the position of the proton relative to the chlorine a t o m s e e Figure 1. Our previous studies have shown that although the energy difference between the various isomers such as 111-VI is small, this energy difference is very consistent and rather independent of level of theory (onceelectron correlation is included). Therefore an initial examination of isomers III-VI was carried out at the MP2/DZP and MP2/TZ2P levels of theory. Isomer III was found to be the lowest energy form and thus the higher levels of theory were applied only to III. The ab initio equilibrium structures of II and III are presented in Tables I11 and IV, respectively, while Table V contains the MP2 structures of IV-VI. Comparison of the MP2 and CCSD(T) structures for 11and III shows that there is generally good agreement between the two levels of theory. In fact, the largest deviation in any bond distance is 0.012 A (“qand “0,) for II and 0.023 A (mol)for III. The fact that the largest deviation is larger for III than for 11 is consistent with the different ?I diagnostic values (7‘1s=. 0,018 for 11and -0.022 for III). Both ?1 diagnostics indicate that the CCSD(T) level of theory should perform well in describing 11 and III, and the rather small differences between the MP2 and CCSD(T) structures support this assertion. Sincethe differencesbetween the MP2 and CCSD(T) predicted equilibrium structures for 11and III appear to be fairly consistent with the DZP and TZ2P basis sets, our best prediction for the true equilibriumstructures can be obtained by adding the CCSD(T)/TZ2P-MP2/TZ2Pdifference to the MP2/TZ2Pf structure. Comparison of the MP2/TZ2P and MP2/TZ2Pf structures indicates that there should not be any major basis set deficiencies

6640 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993

Lee and Rice

TABLE II: Harmonic Vibrational Frequencies (cm-l) and Infrared Intensities (km/mol) for Chlorine Nitrate Obtained at Various Levels of Theory (See Figure 1 for Labeling of Atoms). approx description N-O a str N-O s str

4a3 w(a? w3(a? o4(a3 w5(a?

O N 0 bend C1-O str N-01 str O3NOl bend NOCl ip bend NO2 op wag C10lN02 torsion

W6(4

MP2 DZP

CCSD DZP

CCSD(T) DZP

MP2 TZ2P

exptb

1955(177) 1306(237) 754(180) 788(23) 524(92) 387(105) 244( 1.1) 678(7.8) 125(0.8)

1798(407) 1367(277) 846(221) 822(4.3) 640(22) 464( 1 .O) 267(0.02) 726( 13) 117(0.3)

1765(311) 13 16(255) 799( 178) 776( 18) 573(40) 432(6.5) 252(0.1) 688(10) 113(0.4)

1905(225) 1295(224) 769( 126) 795(59) 520(77) 369( 129) 246( 1.4) 697 (7.2) 127(0.6)

1735 1292 809 780 560 434 270 71 1 121

w7(a? da’3 wg(a’3 IR intensities are in parentheses. ip = in-plane;op = out-of-plane. Gas-phasefundamental frequencies from ref 48, vg is estimated; from far-IR spectra (ref 49) this is determined to be 120 cm-’. Liquid-phase Raman spectra are given in ref 50.

TABLE III: Total Energies (&), Equilibrium Bond Lengths (A), Bond An es (degrees), and Dipole Moments (D) for HOCI-..NOz+$ Obtained I) at Various Levels of Theory (See Figure 1 for Labeling of Atoms) MP2 DZP

E’

HI*

P I C

P

rclo, ~

0

,

“4 mo3 RN..Q, LO2NO1 LClOlN LHOlCl fO2NO3

CCSD(T) DZP

0.626 921 0.550 372 0 0 0.019 5.57 1.729 1.741 0.974 0.973 1.160 1.148 1.161 1.149 2.479 2.475 89.1 89.6 112.2 113.5 103.7 103.4 177.6 177.2

MP2 TZ2P

CCSD(T) TZ2P

0.854 828 0.757 586 0 0.018 5.61 1.717 1.727 0.968 0.966 1.138 1.126 1.138 1.127 2.492 2.496 89.2 89.7 111.8 113.2 103.2 103.3 177.2 176.9

* The total energy is reported as -(E T Idiagnostic; see text for details.

+ 739).

MP2 TZ2Pf 0.994 226

1.699 0.970 1.134 1.134 2.475 88.8 111.9 103.7 177.9

Hessian index. e The

TABLE IV Total Energies (&), uilibrium Bond Lengths (A), Bond Angles (degrees), and Dipo e Moments (D) for CIONO2H+ (III) Obtained at Various Levels of Theory (See Figure 1 for Labelinn of Atoms)

Ep

MP2 DZP

CCSD(T) DZP

0.578 990 0.525 172 0 0 0.023 3.54 1.733 1.746 0.988 0.986 1.336 1.358 1.204 1.190 1.322 1.336 105.9 105.9 126.7 126.8 127.2 127.3 112.4 112.2

MP2 TZ2P

0.805530 0.727 889 0 0.022 3.44 1.714 1.725 0.984 0.982 1.35 1 1.328 1.169 1.180 1.330 1.314 105.6 105.7 126.8 126.8 127.1 127.2 111.9 111.8

The total energy is reported as -(E

T Idiagnostic; see text for details.

CCSD(T) TZ2P

+ 739).

MP2 TZ2Pf 0.946 061

1.698 0.986 1.322 1.178 1.307 106.1 126.8 126.9 112.0

Hessian index. The

remaining. Thus we expect that our best prediction for the equilibrium structures of II and III,obtained as described above, should be quite close to the true values. Both II and I11 are shown to have large dipole moments, although the dipole moment of I1 (5.61 D, at the CCSD(T)/ TZ2P level) is considerably larger than that for III (3.44 D, at the CCSD(T)/TZ2P level). Thus it should be possible to distinguish between IIand 111from microwave spectroscopy. Not surprisingly, the equilibrium structures of IV,V, and VI exhibit similar basis set effects to those found for III,and therefore these structures will not be discussed in detail. It is also pertinent to point out that for protonated HON02, CH30N02, and now ClONO2 the second most stable form corresponds to the “W-

shaped” isomer. It would appear that of the structures III-VI the most stable form usually corresponds to this “W-shaped” isomer. Harmonic vibrational frequencies and IR intensities for II and 111are given in Tables VI and VII, respectively, while MP2/DZP harmonic frequencies for IV,V, and VI are presented in Table VIII. A comparison of the MP2/DZP and CCSD(T)/DZP harmonic frequencies for 11shows that except for 0 2 and w3 there is very good agreement between the two approaches. The fact that 0 2 and w3 exhibit some differences between the MP2 and CCSD(T) levels of theory is not surprising since protonated HON02 showed the same effect.” Our best estimates for the harmonic frequencies of II may be obtained by adding the CCSD(T)/DZP-MP2/DZP difference to the MP2/TZ2P frequencies. For those modes which are expected to have a relatively small anharmonic correction (such as bending and torsional motions), the best estimates for the harmonic frequencies should also be very close to the observable fundamental frequencies. The agreement between the MP2/DZP and CCSD(T)/DZP levels of theory for the harmonic frequerrcies of 111is not quite as good as found for II. Nonetheless, the agreement is still reasonably good and the frequencies displaying the largest deviations are again the N - O stretching normal modes (02 and wq). The best estimates for the harmonic frequencies may again beobtained by adding the CCSD(T)/DZP-MP2/DZP difference to the MP2/TZ2P harmonic frequencies. An important point to note is that the vibrational frequencies of II and III exhibit noticeable differences, indicating that vibrational spectroscopy can be used to distinguish between these different forms of protonated ClON02. The IR intensities included in Tables VI and VI1 shows, qualitatively, which vibrational modes should be most easily observed. The MP2/DZP harmonic vibrational frequencies for IV-VI show that all three structures correspond to minima on the ClON02H+ potential energy surface. Thus it is quite possible that these isomers of III will also form in the protonation of ClON02. The MP2/DZP harmonic frequencies of III-VI exhibit small differences that may allow the differentforms to be identified via IR spectroscopy,but it seemslikely that, due to the structural differences between the various forms (see Figure l), microwave spectroscopywill be a better means of distinguishing theseisomers. We have not investigated the transition states connecting these various isomers, but the barrier heights will also be. important considerations when trying experimentally to characterize the different isomers. An investigation of the transition state structures is outside the scope of the present study. HOCl and NOz+. As well as determining the relative energies of I-VI, we have also examined the binding energy of the HOCl.-N02+ complex, II. Thus the equilibrium geometries, dipole moments, harmonic vibrational frequencies and IR intensities of HOCl and N02+ have been determined using identical levels of theory to those used for II. These results are presented in Table IX together with the available experimental

The Journal of Physical Chemistry, Vol. 97,No. 25, 1993 6641

The Chlorine Nitrate Protonation Reaction

TABLE V: Total Energies (&), Equilibrium Bond Lengths (A), Bond Angles (degrees), and Dipole Moments (D) for Higher-Lying Forms of Protonated Chlorine Nitrate Obtained at the MP2 Level of Theory (See Figure 1 for Labeling of Atoms) IV V VI DZP TZ2P DZP TZ2P DZP TZ2P E‘

HIb rclo, -03

“0, “q

“&

0.576 424 0 1.732 0.988 1.357 1.193 1.318 108.3 123.0 126.8 112.9

fHO3N LO3NO2 LOzNOl LNOlCl The total energy is reported as -(E

0.803 589 1.712 0.983 1.352 1.169 1.311 107.9 123.2 126.6 112.3

+ 739).

0.572 840 0 1.739 0.990 1.332 1.204 1.323 105.6 126.0 119.3 117.1

0.799 201 1.720 0.985 1.325 1.181 1.314 105.3 125.9 119.3 117.0

0.563 876 0 1.733 0.992 1.378 1.192 1.312 108.9 122.6 117.0 115.8

0.794 466 1.713 0.992 1.378 1.168 1.299 107.4 123.6 117.1 115.1

Hessian index.

TABLE VT: Harmonic Vibrational Frequencies (cm-l) and Infrared Intensities (km/mol) for the Complex between HOCl and NO2+ (I€), Obtained at Various Levels of Theory (See Figure 1 for Labeling of Atoms)’ MP2 CCSD(T) MP2 approx DZP DZP TZ2P description 3812( 157) 3831( 139) 3773( 156) wl(a’) 0-Hstr 2350(231) 2459(94) 2571(68) o2(a9 N-0 a str 1295(0.5) 1357(0.8) 1295(0.4) w3(a’j N-Osstr 1273(40) 1270(37) 1265(36) w,(a? HOCl bend 747(13) 711(9.8) 743(16) w&’) C1-0str 502(17) 529(26) 476(19) os(a’) ONObend 209(12) 209(13) 193(12) w7(03 0.* .N str 140(3.7) 145(4.0) 138(3.9) ws(a’) ON. .Obend 94(9.4) 92(8.9) 94(10) w~(a’) H0.e .N bend 523(2.1) 556(1.2) 574(4.7) W~O(CI’? NO2 op wag 221(187) 230(183) 177(147) w11(a’’) HOCl op wag 32(1.1) 30(0.9) 28(0.9) wlz(a”) HONO torsion 0 IR intensities are in parentheses; ip = in-plane and op = out-ofplane.

TABLE VIIk Harmonic Vibrational Frequencies (cm-l) and Infrared Intensities (km/mol) for the Higher Lying Forms of Protonated ClON02 (IV-VI) Obtained at the MP2/DZP Level of Theory (See Figure 1 for Labeling of Atoms)’ approx description IV V VI 3633(330) 3612(358) ol(a’) 0-Hstr 3516(253) 1709( 169) 1663(288) 168 1 (232) wz(a3 N-02str 1392(450) 1455(47) 1387(417) HONbend 1 191(205) 1 174(517) 1 140( 123) w&z’) N-03 str 931(118) 978(63) 861(149) q(a’) N-01 str 816(21) 804(4.1) 795(19) wg(09 01NO3 bend + C1-0 str 658(10) 614(19) 617(9.3) 47’) O2NO3 bend 444(2.3) 468(1.3) 469(3.2) ws(a3 01NO3 bend + C1-0 str 253(5.4) 276(0.8) 278(9.0) w9(a ’) ClON bend 701(0.1) 687(12) 690(0.01) wlo(a‘? &NO2 op bend 490(180) 575(168) 498(143) wI1(a”) HONO torsion 156(4.4) 133(3.6) 118(1.4) w1z(a’’) ClONO torsion IR intensities are in parentheses; ip = in-plane and op out-ofplane. 5

TABLE W: Harmonic Vibrational Frequencies (cm-l) and Infrared Intensities (km/mol) for the Second Lowest Form of Protonated ClONO2,III, Obtained at Various Levels of Theory (See Figure 1 for Labeling of Atoms)‘ MP2 MP2 CCSD(T) approx DZP TZ2P description DZP 0-H str 3629(397) 3663(350) 3576(396) wl(a’) 1679( 195) 1733( 196) 1654(203) wz(a’) N-02str 1479(16) 1473(35) 1479(4.6) w3(a3 HONbend N-03 str 1194(594) 1145(403) 1163(550) w&? 969(105) 990(88) 884(84) w&f,l N-01 str 826(35) 817(25) 786(27) w&’) OlNO3 bend + C1-0 str 665(1.5) 646(3.6) 624(2.0) w7(4 02NO3 bend 428(7.9) 460(9.6) 451(9.4) 01NO3 bend + wg(a’) C1-0 str 271( 1.0) 263(1.0) 256(0.7) ~ ( a ’ ) ClONbend 671(11) 728(10) 701(9.9) w~o(a’’) &NO2 opbend 528(169) 485(166) 520(147) w ~ ~ ( a ” )HONO torsion 144(1.8) 162(1.6) 158(2.2) w~z(a’’) ClONO torsion 0 IR intensities are in parentheses; ip = in-plane and op = out-ofplane. information.52-55 Note that the DZP basis set results for N02+ are taken from our earlier study” on the protonation of HONOz and that the TZ2P basis set used in ref 17 is different from that used in the present study. It is also worthwhile to mention that highly accurate ab initio calculations of the equilibrium geometry and the fundamental vibrational frequencies of N02+ are presented in 56-a recent experimental study55has confirmed the accuracy of these predictions. Comparison of the MP2/TZ2P and CCSD(T)/TZ2P geometries, dipole moments, and harmonic frequencies shows that there is very good agreement between these electron correlationmethods for HOC1. Only roc1 and 03, the C1-0 stretch, exhibit small

deviations between the two levels of theory. In addition, except for the dipole moment, the CCSD(T)-MP2 differences are smaller for the TZ2P basis set than for the DZP basis set, suggesting some coupling between the 1- and n-electron basis sets. The situation for NOz+ is different. That is, the agreement between the MP2/TZ2P and CCSD(T)/TZ2P levelsof theory is not nearly as good, although it is still reasonable. The inadequacies of the MP2 method in describing the electronic structure of N02+ have been discussed earlier.” It is also interesting, although not surprising, to note that the differences between the MP2 and CCSD(T) levels of theory for HOCl and NOz+ are entirely consistent with those noted previously for 11. The agreement between experiment and theory for HOCl is reasonably good especially considering that the ab initio data do not account for vibrational averaging of the geometrical parameters nor anharmonic corrections to the vibrational frequencies. For NOz+, the agreement between the CCSD(T)/TZZP predictions and the experimental data is reasonable, again taking into consideration that the ab initio data do not account for vibrational effects. As noted previously, however, the CCSD(T) method used with larger basis sets gives more accurate ab initio results as presented in ref 56. The ab initio data for NOz+ given in Table IX are presented merely to give an indication of the type. of accuracy to be expected for the calculations on HOCl.-NOz+, 11. Energetics. MP2, CCSD, and CCSD(T) energies of 11-VI relative to CION02 are given in Table X. For example, A E I I is the amount of energy, in kcal/mol, that II is below I, while A E I i I , AE,“, A E v , and AEm, are the corresponding values for III-VI. The values in Table X do not include zero-point energies-these will be discussed below. As mentioned earlier, III was found to

6642 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993

Lee and Rice

TABLE Ix: Total Energies (&), Equilibrium B a d L e q h (A)and Bond Angles (degrees), Dipole Momeats (D), Harmonic Frequencies (cm-I), and IR Intensities (km/mol) for HOCl and NOa+ Obtained at Various Levels of Theory' MP2 DZP

CCSD DZP

CCSD(T) DZP

MP2 TZ2P

CCSD(T) TZ2P

MP2 TZ2Pf

0.375 985

0.333 481 0.011 1.56 0.964 1.723 101.7 3802(63) 1274(41) 704(4.2)

0.442 154

0.401 936 0.022 1.128 1356 544( 14) 2287(281)

0.465 864

exptb

HOCl 0.244 907 0.010 1.74 0.970 1.728 102.7 3866(55) 1275(44) 727(2.9)

0.253 486 0.010 1.73 0.971 1.740 102.2 3839(51) 1257(44) 694( 1.8)

0.242 134 0.022 1.138 1434 606( 16) 24 12(399)

0.272 102 0.023 1.150 1351 571(11) 2336(255)

0.282 828 1.75 0.972 1.724 102.4 3837(61) 1262(49) 747(6.8)

1.58 0.965 1.710 101.8 3802(75) 1273(45) 746(9.9)

1.59 0.967 1.692 102.4 3801(80) 1274(45) 771( 11)

0.960 1.689 102.5 3609 1240 725

N02+ 0.318 930 1.163 1283 552(2) 2561(63)

0.455 970 1.139 1285 518(3) 2446(96)

1.138 1298 495(3) 2457(99)

1.125 1397 639 2362

0 IR intensities are in parentheses. The DZP results for NOz+ are taken from ref 17. HOCl: vibrationally averaged geometry from ref 52; fundamental frequencies from refs 53 and 54. NOz+: vibrationally averaged geometry and fundamental frequencies from ref 55. The energy is reported as -(E 535) for HOCl and as -(E + 204) for N02+.

+

TABLE X

Energetics (kcal/mol) of the Various Isomers of

Protonated CION02 Relative to CION02 (I)'

method MP2/DZF MP2/TZ2PC MP2/ANOld MPZ/ANOle MP2/AN02d MP2/AN02e CCSD/ANOld CCSD/ANOle CCSD/AN02d CCSD/ANOZe CCSD(T)/DZPC CCSD(T)/TZ2PC CCSD(T)/ANOld CCSD(T)/ANOle CCSD(T)/ANOZd CCSD(T)/AN02e

EI 0.323 882 0.552 188 0.454 262 0.454 499 0.573 413 0.574 075 0.440 639 0.439 705 0.563 565 0.562 997 0.259 243 0.464 060 0.496 223 0.495 392 0.626 620 0.625 800

~

I

190.2 189.9 190.2 190.3 188.5 188.5 185.5 185.4 183.9 183.7 182.7 184.2 184.9 185.0 182.9 183.2

u rI r r ~ I uV v UVIA h b 160.1 158.5 156.2 150.6 15.8 159.0 157.8 155.0 152.0 14.4 157.9 14.7 158.1 14.7 158.0 14.9 158.5 14.9 167.6 14.3 168.0 14.5 167.5 14.5 168.2 14.8 166.9 15.6 165.6 13.9 164.7 14.3 164.5 14.5 164.3 14.5 14.7 164.6

Zero-point vibrational energies not included. See text for energy differences that include zero-point effects. El is the total energy of ClONOz in hartrees, reported as -(E 739), while the other columns report relative energies in kcal/mol. See text for details. bEnergy difference between I1 and the separated HOCl N02+ monomers. Geometriesoptimizedat the samelevelof theory. Geometriesoptimized at the CCSD(T)/TZ2P level of theory. e Geometries optimized at the MP2/TZ2Pf level of theory.

+

+

f

be lower in energy than IV-VI a t the MP2/DZP and MP2/ TZ2P levels of theory, and therefore the higher levels of theory were not applied to IV-VI. Examination of the AEffvalues shows that as found previously

for the protonation of HON02 and CH3ON02, the MP2 level of theory dramatically overestimates the stability of II relative to ClON02. Comparison of the CCSD and CCSD(T) values shows that connected triple excitations do not contribute much to MI!. This is somewhat different to that observed for protonation of HONO2 and C H 3 0 N 0 2 and no doubt results from a better cancellation of the contribution from connected triple excitations to the total energies of I and 11. Although the amount of data on which to draw a conclusion is small, it appears that geometrical and one-particle basis set effects also have only a small effect on AEII. Thus our best estimate for AEIf is taken as 183.1 kcal/mol, the average of the two CCSD(T)/ANO2 values. The major remaining error in this computed value is probably due to inadequacies in the one-particle basis set. On the basis of our earlier studies, we assign a conservation uncertainty of f3.0 kcal/mol. Including the effect of zero-point energies

decreases A E I I by 6.3 kcal/mol, yielding our final estimate of 176.8 f 3.0 kcal/mol at 0 K. Examining the A E f f f values in Table X shows that the MP2 level of theory substantially underestimates the stability of III. Contrary to that found for AEff,connected triple excitations are found to have a noticeable effect on A E f r f , reducing it by about 3 kcal/mol. On the other hand, one-particle basis set effects are than found for A E f f . Comparison of the A E f f f smaller for values for the MP2/TZ2Pf and CCSD(T)/TZ2P geometries shows that geometrical effects are small for A E f f f . Thus our best estimate for AEfffis 164.5 kcal/mol, obtained by averaging the two CCSD(T)/ANO2 values. Because the one-particle basis set effects are small, we also assign an uncertainty of f3.0 kcal/mol by 8.2 to this value. Zero-point vibrational energies reduce kcal/mol, yielding a final value of 156.3 f 3.0 kcal/mol (0 K). Thus similar to the protonation of HONOl and CH3ON02, the lowest energy form of protonated CION02 is a complex between HOCl and NOz+. The proton affinity (PA) of CION02 is therefore 176.8 f 3.0 kcal/mol (0K). As indicated earlier, it is also important to determine the binding energy of the HOCI-.N02+ complex, and this quantity is referred to as AEMin Table X. Examination of the various AEM values shows that this quantity is not very sensitive with regard to the level of theory employed (including electron correlation, oneparticle basis set, and geometry). Our best estimate is taken as 14.6 kcal/mol, the average of the two CCSD(T)/ANO2 values. It is necessary to correct A E M for the basis set superposition energy (BSSE). Computing the BSSE correction using the c0unterpoise5~ method and the A N 0 2 basis set, we obtain corrections of -0.9, -0.9, and 4 . 9 kcal/mol a t the MP2, CCSD, and CCSD(T) levels of theory, yielding a AEM value of 13.7 kcal/mol. Given the lack of sensitivity of A& with regards to the level of theory, a conservative uncertainty of f 2 . 0 kcal/mol is assigned to this value. Including the effects of zero-point energies reduces AEMby 0.8 kcal/mol, giving a final estimate of 12.9 f 2.0 kcal/mol (0 K). One test of the ab initio methods that may be easily performed is to compute the heat of formation of C l O N q using the following isodesmic reaction: ClONO,

+ H,O

-

HOCl + HONO,

and then comparing to the experimental value.58 In other words, the heat of reaction 2, AHz, will be computed, and then the heat of formation of CION02 will be determined by combining this computed reaction energy with the experimental AH1 valuess9

The Chlorine Nitrate Protonation Reaction

The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6643

HONO2 than with ClON02, and therefore PSCs that contain a for H20, HOC1, and HONO2. The enthalpy of reaction 2 (not large fraction of HON02 will not be as effective in removing including zero-point energy effects) has been computed at the CION02 from the stratosphere. It should be borne in mind that MP2/DZP, CCSD/DZP, CCSD(T)/DZP, and C!CSD(T)/ these qualitative conclusions are for systems with no other TZ2P levels of theory (the relevant data for H2O and HONO2 reactants, including HCl, and that the inclusion of such other can be found in refs 17 and 29; the CCSD(T)/TZ2P results for reactants will likely have an effect. HON02 used here are unpublished) and is determined to be 2.3, It is also important to point out that the binding energy of the -2.6, -0.4, and 0.2 kcal/mol, respectively. The range of values HOCl-.N02+ complex is not as large as the binding energy of is somewhat larger than would normally be expected for an the H30-N02+ complex (17.3 f 2 kcal/mol, from ref 17). This isodesmic reaction, and therefore we have also determined this explains why Nelson and Okumura observed hydrated NO2+ reaction enthalpy using the AN02 basis set. With the AN02 clusters, but did not observe the HOCI-N02+ complex. This basis set, the ME!, CCSD, and CCSD(T) reaction enthalpies also explains why some of the HOCl that derives from CION02 are 2.4, -2.9, and -0.3 kcal/mol, respectively. Thus it would is released into the stratosphere and the remainder is available appear that these values are insensitive to improvemehts in the to react with HC1 on the surface of PSCs. one particle basis set, but A H 2 exhibits some dependency an the choice of electron correlation method. We take -0.3 kcal/mol Conclusions as our best computed L w 2 value, and correct it for the effects of zero-point energiesto give 1.2 kcal/mol(O K). Finally, correoting The equilibrium geometries, dipole moments, and harmonic this value for temperature effects (thermal population of vibravibrational frequencies of ClON02, HOC1, N02+, and four tional levels) to 298 K yields 0.5 kcal/mol for L w 2 . Using the isomer8 of protonated ClONO2 have been determined via ab initio experimental MJ (at 298 K) valuess9 for HOCI, H20, and quantum mechanical methods, including coupled-clustertheory. HONO2 together with our computed A H 2 value gives 7.4 kcal/ For the equilibrium structures and harmonic frequencies of mol for the heat of formation'of CION02 (298 K). This value ClON02, HOCl, and N02+, the highest-level theoretical preis in very good agreement with the eqerimental estimates8of 6.3 dictions have been shown to be in good agreement with the f 0.2 kcal/mol. This good agreement gives confidence as to the available experimental information. It is therefore expected that reliability of the computed MII,MIII,and M Mvalues. the ab initio structures and frequencies of the protonated forms of ClONO2 will aid in the experimental characterization of these Implications for the Antarctic Stratosphe~. It is certainly species. true that knowledge of gas-phase reaction enthalpies will not be Protonation of CION02 has been shown to lead to formation sufficient to quantify the thermodynamics of condensed-phase of a complex between HOCl and N02+, in agreement with recent reactions. However, it is conceivable that knowledge of gasexperiments by Nelson and Okumura,ls and also consistent with phase reaction enthalpies will help to explain in a qualitative the protonation reactionsof HONO2 and CHpON02. The proton manner the reactions, mechanisms and processes taking place in affinity of ClONO2 has been computed to be 176.8 f 3 kcal/mol the condensed phase. The results of this investigation clearly (0 K), while the binding energy of the HOCI.-N02+ complex has show that the most stable form of protonated ClONO2is a complex between HOCl and N02+, as deduced by Nelson and O k u m ~ r a , ~ ~ been determined to be 12.9 f 2 kcal/mol (0 K). The second most stable isomer of protonated ClONO2 is determined to be bound and as expected based on analogy with HONO2 and CHpON02. by 156.3 f 3 kcal/mol (0 K)relative to ClON02 H+-nearly Moreover, the results of this investigation support the hypothesis 20 kcal/mol less stable than the HOCI.-N02+ complex. Thus of Wofsy et a l l 3 that the reaction of ClONO2 on the surface of the present study supportsthe recent hypothesid3that the reaction PSCs is proton catalyzed. The actual mechanism suggested by of ClONOz on PSCs is proton catalyzed, although the specific Wofsy et al., that C1+ is the leaving group, is not supported. The mechanism is different. Specifically, the results of the present formation of the HOCl.-N02+ complex upon protonation of study suggest that the reaction of CION02 on water/ice surfaces CION02 is also consistent with the increased concentrations of of PSCs is proton catalyzed but that HOCl should be a major HOCl observed in the chemicallyperturbed region of the Antarctic product, in agreement with recent laboratory observations.lG12 stratosphere (for example, see ref lo), and also with the recent The results of the present study, together with our earlier laboratory findings that HOCl and HCI readily react on PSCinvestigations,17J9are also consistent with other recent findings8v9 type materials to form C12, a more reactive form of C1.11J2 Indeed, concerningthereactionof ClONO2on nitricacid saturated water/ several groups10-12 have recently argued that the reaction of ice surfaces. ClONOZ and HCl on the surface of PSCs to form Cl2 is probably a two-step process-passing through the HOCl intermediateand Acknowledgment. We thank Professor Mitchio Okumura for the results of this study are in complete agreement with this several helpful discussions. assertion. In other words, results of the present study strongly suggest that the reaction of ClONO2 on the water-ice surfaces References and Notes of PSCs is proton catalyzed and that a major reaction product is HOC1, in agreement with laboratory observations. It should (1) Tolbcrt, M. A.; Rossi, M. J.; Malhotra, R.; Golden, D. M. Science 1987, 238, 1258. be noted that in some of these studies,11J2it is thought that a (2) Molina, M. J.; Tso, T.-L.;Molina, L. T.; Wang, F. C.-Y. Science direct mechanism, rather than a two-step mechanism, takes place 1987,238, 1253. on nitric acid trihydrate (NAT) surfaces. It would seem that (3) Rossi, M. J.; Malhotra,R.; Golden,D. M. Geophys. Res. Lett. 1987, 14, 127. more investigation of this particular point is warranted, especially (4) Tolbcrt, M. A,; Rossi, M. J.; Golden, D. M. Geophys. Res. Lett. . . considering the results of the present investigation. 1988, 15, 847. ( 5 ) Leu, M.-T. Geophys. Res. Lett. 1988, 15, 851. The second most stable form of protonated ClONOz is a full (6) Quinlan, M. A.;Reihs, C. M.;Golden,D. M.;Tolbert,M. A. J . phys. 20 kcal/mol higher in energy and is therefore probably not of Chem..I&, 94, 3255. importance in the chemistry occurring on the polar stratospheric (7) Hofmann, D. J.; Oltmans, S.J. Geophys. Res. Lett. 1992,19,2211. (8) Hanson,D. R.; Ravishankara,A. R. J . Geophys.Res. 1991,96,5081. clouds (PSCs). It is interesting that the PA of CION02 is about (9) Leu, M.-T.; Moore, S.B.; Keyser, L. E. J . Phys. Chem. 1991, 95, 6 kcal/mol less than that of HONO2 (182.5 f 4.0 kcal/mol from 7163. refs 17 and 19). This Occurrence suggests that surfaces saturated (10) Rather, M. J. Nuture 1992, 355, 534. (1 1) Hanson. D. R.; Ravishankara, A. R. J . Phys. Chem. 1992,96,2682. with nitric acid would not readily react with ClON02, which is (12) Abbatt, J. P. D.; Molina, M. J. J. Phys. Chem. 1992, 96, 7674. consistent with the results of laboratory s t u d i e ~of ~ .the ~ reaction (13) Wofsy, S. C.; Molina, M. J.; Salawitch, R. J.; Fox, L. E.; McElroy, of CION02 on water/ice and nitric acid/water/ice surfaces. In M. B. J. Geophys. Res. 1988, 93, 2442. (14) Rowland, F. S. Annu. Rev. Phys. Chem. 1991.42, 731. other words, the available protons will react more readily with

+

6644 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 (15) Nelson, C. M.;Ohunura, M.J. Phys. Chem. 1992,96,6112.

(16) Cacace, F.; Attina, M.;de Petris, G.; Speranza, M.J. Am. Chem. Sm. 1990,112,1014. (17) Lee, T. J.; Rice, J. E. J. Phys. Chem. 1992,915,650. (18) Attina, M.;Cacace, F.; Yanez, M.J. Am. Chem. Soc. 1987,109, 5092. (19) Lee, T. J.; Rice, J. E. J. Am. Chem. Soc. 1992,114,8247. (20) Raghavachari, K.;Truck, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989,157,479. (21) Rendell, A. P.; Lee, T. J.; Taylor, P. R. J. Chem. Phys. 1990,92, 7050. (22) Lee, T. J.; Rendell, A. P.; Taylor, P. R. J. Chem. Phys. 1990,93, 6636. (23) Lce, T. J.; Scuacria, G. E. J. Chem. Phys. 1990,93,489. (24) Lec, T. J.; Rice, J. E. 1. Chem. Phys. 1991,94, 1215. (25) H u z ~ M S. ~ ,J. Chem. Phys. 1966.42, 1293. (26) Dunning, T. H.1. Chem. Phys. 1970,53,2823. 72, 5639. (27) McLcan, A. D.; Chandler, 0. J. Chem. PhyJ. 1W, (28) Dunning, T. H. J. Chem. Phys. 1971,55,716. (29) Lee,T. J.; Rohlfing,C. M.;Rice, J. E.J. Chem.Phys. 199597,6593. (30) Dunning, T. H. J. Chem. Phys. 1989.90, 1007. (31) Ahlricb, R.; Taylor, P. R. J. Chim. Phys. 1981,78,315. (32) Almlbf, J.; Taylor, P. R. Adv. Quantum Chem. 1992,22, 301. (33) Pulay, P. Mol. Phys. 1969,17, 197. (34) Handy, N.C.; Amoh R. D.; Gaw, J. F.; Rice, J. E.; Simandiras,E. D. Chem. Phys. Lett. 1985,120, 151. (35) Rendell, A.P.; Lee,T. J. J. Chem. Phys. 1991,94,6219. (36) Lee, T. J.; Rendell, A. P. J. Chem. Phys. 1991,94,6229. (37) Handy, N. C.; Am-, R.D.; Gaw, J. F.; Rice, J. E.; Simandim, E. D.;Lee, T. J.; Harrison. R. J.; Laidig, W.D.; Fitzgerald, G.; Bartlett, R. J. In Geometrical Derivatives of Energy Swfaes and Molecular Properties; Jorgerwn, P., Simons, J., Edr.; Reidel: Dordrccht, 1986. (38) Simandiras,E. D.; Am-, R. D.; Handy, N. C. Chem. Phys. Lett. 1987,114,9.

Lee and Rice (39) AImlM, J.; Taylor, P. R.J. Chem. Phys. 1987,86,4070. (40)van Duijnwddt, F. B. IEM Res. Dept. RJ 1971.945. (41) Partridge, H. J. Chem. Phys. 1987,87,6643. (42) Amor, R.D.; Rice,J. E., CADPAC CambridgeAnalytic Derivatives Package, h u e 4.0;Cambridge University, Cambridge, England, 1987. (43) TITAN ia a act ofdcctronicctructure program, written by T. J. Lee, A. P. Rendell, and J. E. Rice. (44)SWEDEN is an electronic ctructure program system written by J. Almlbf, C. W. Baurchlicher, M. R. A. Blombcrg, D. P. Chong. A. Heibcrg, S.R. Langhoff,P.-A. Malmqvht,A. P. Rendell, B. 0.Roos,P. E. M.Siegbahn, and P. R. Taylor. (45) Lindh, R.; Ryu, U.; Liu, B. J. Chem. Phys. 1991,95,5889. (46) Suenram, R. D.; Johnron, D. R. J. Mol.Spectrosc. 1977,65,239. (47) Suenram, R. D.; Lover, F. J. J. Mol. Spcctmc. 1984,105,351. (48) Miller,R.H.; Bernitt, D. L.; Hmtaunc, I. C . Spctmchim. Acta A 1967,23, 223. (49) Chance, K.V.; Tmub, W. A. J. Mol. Spec:rosc. 1982,95,306. (50) Chdste, K.0.;Schack,C. J.; Wilson, R. D. Inorg. Chem. 1974,13, 2811. (51) Lee,T. J.;Taylor,P. R. Int. J. QuuntumChem.Symp.1989,23,199. (52) Mirri, A. M.;Scappini, F.; Cauoli, 0. J. Mol.Spectrosc. 1971,38, 218. (53) Ashby, R. A. J. Mol. Spectrosc. 1971, 40,639. (54) Welb, J. S.;Sam, R. L.; Lafferty, W. J. J. Mol.Spectrosc. 1979, 77, 349. (55) Bryant,G.;Jmng, Y.;Grant, E. Chem. Phys. Lett. 1992,200,495. (56) Lee, T. J. Chem. Phys. Lett. 1992,188, 154. (57) BOB. S.F.: &mad. F. Mol. Phvs. 1970.19. 553. i58j Alqimi, R.;Knauth; H.-D.; Rodlack, D.'Ber. Bunsen-Ges. Phys. Chem. 1978,82,217. (59) Chuc,M. W.;Davies,C.A.;Do~ey,J.R.;Frurip,D. J.;McDonald, R. A.; Syverud, A. N. J. Phys. Chem. Re$ Data 1985,14, Supplement 1.