I. INTRODUCTION JOURNAL OF CHEMICAL PHYSICS VOLUME 109, NUMBER NOVEMBER 1998

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1 JOURNAL OF CHEMICAL PHYSICS VOLUME 109, NUMBER NOVEMBER 1998 Accurate ab initio near-equilibrium potential energy and dipole moment functions of the X 2 B 1 and first excited 2 A 2 electronic states of OClO and OBrO Kirk A. Peterson Department of Chemistry, Washington State University, 2710 University Drive, Richland, Washington and the Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington Received 7 May 1998; accepted 18 August 1998 Using highly correlated multireference configuration interaction wave functions with large correlation consistent basis sets, three-dimensional near-equilibrium potential energy functions PEFs have been calculated for the X 2 B 1 and first excited 2 A 2 electronic states of the atmospherically important OClO and OBrO radicals. The analytical PEFs have been used in perturbational and variational calculations of the anharmonic spectroscopic constants and vibrational spectra of both species. Excellent agreement with the available experimental data are observed for both species and electronic states, e.g., the vibrational fundamental frequencies in the ground electronic states are reproduced to within about 5 cm 1. For the A 2 A 2 state of OClO, it is demonstrated that the anomolously strong intensity of the 3 mode in the UV absorption spectrum is due to strong anharmonic coupling between the stretching vibrations and not to a double minimum in the potential. Three-dimensional electric dipole moment functions have also been calculated for the ground electronic states of both species. These were used to calculate accurate absolute infrared absorption intensities for the fundamentals and low-lying overtones and combination bands of both species American Institute of Physics. S I. INTRODUCTION Over the last several years, there has been strong interest, both experimental and theoretical, in halogen oxide species due to their probable deleterious role in polar stratospheric ozone chemistry see, e.g., Refs The symmetric chlorine dioxide radical, OClO, is an important nighttime reservoir for inorganic chlorine in the upper atmosphere 4 and is believed to be formed from the reaction between chlorine and bromine monoxide radicals. 5 There is much less known about the source chemistry of OBrO in the atmosphere, but recent work has proposed that it is formed through heterogeneous chemistry. 6 There has been very strong interest in the photochemistry and spectroscopy of OClO over the last several years, stemming in part from an earlier proposal that it may contribute to ozone loss via a photoisomerization mechanism. 7 The negative influence of OClO on ozone has since been shown to be negligible in the gas phase, 8 but it may very well be important in condensed phase reactions Refs. 9, 10, and references therein. Spectroscopically, both the electronic ground state and excited A 2 A 2 state have been relatively well characterized. For the ground state, recent microwave and infrared spectroscopy experiments have yielded an accurate equilibrium structure, vibrational frequencies, and even a quartic force field. Spectroscopic characterization of the A 2 A 2 state of OClO was initiated by the early work of Coon 17 and was studied most recently in this regard by Vaida and co-workers 18,19 using jet-cooled Fourier transform ultraviolet spectroscopy. Of course, there has also been numerous investigations of the excited state dynamics of OClO, which exhibits a strong competition between a direct photodissociation mechanism to yield the dominate products ClO O and an indirect spin orbit mediated mechanism leading, in part, to Cl O 2 see, e.g., Refs. 9, 8, and 20. In contrast to OClO, the bromine dioxide radical has only recently been the subject of spectroscopic study. Vibrational data from studies in rare gas matrices 21,22 have recently been augmented by high resolution microwave spectroscopy and the detection of its C 2 A 2 X 2 B 1 visible absorption spectrum. 6 These studies have resulted in an estimated equilibrium structure and the fundamental vibrational frequencies for the electronic ground state, as well as a characterization of the symmetric vibrational modes in the excited state. The most extensive theoretical work carried out for OClO was our previous multireference configuration interaction MRCI calculations 20,26 on its ground and low-lying excited electronic states. Accurate equilibrium geometries and harmonic frequencies were computed for the first four electronic states, as well as an anharmonic force field for the ClOO isomer. The main emphasis of that work, however, was to deduce the photochemistry and photodissociation mechanisms of OClO, while the present study is concerned with a more accurate calculation of its spectroscopic properties. Other studies of OClO that have included the effects of electron correlation include the MP2 and QCISD T calculations of Radom and co-workers 27 and the MP2 work of Pacios and Gomez. 28 These calculations, which used basis sets of double- and triple-zeta quality, only considered the elec /98/109(20)/8864/12/$ American Institute of Physics

2 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson 8865 tronic ground state and yielded equilibrium geometries and harmonic frequencies. In the case of OBrO, only two ab initio studies have recently been reported, MP2 and CCSD T calculations by Pacios and Gomez 28 and CCSD T calculations by Miller et al. 6 In each case a basis set of triple-zeta quality was employed and similar CCSD T geometries between the two studies were obtained. Pacios and Gomez also characterized the dissociation asymptotes and the peroxy isomer BrOO, while Miller et al. obtained accurate harmonic frequencies of the ground state and equilibrium geometries of the first three excited electronic states. To our knowledge, ab initio anharmonic force fields have not been previously reported for either OClO or OBrO. The present work extends our previous studies on halogen oxide species by reporting accurate anharmonic potential energy and dipole moment functions for the ground state and first excited 2 A 2 states of OClO and OBrO using highly correlated multireference CI wave functions and large correlation consistent basis sets. The specific details of the calculations are given in Sec. II. The calculated spectroscopic constants and infrared intensities for the ground electronic states are presented and discussed in Sec. III A, while the results for the excited 2 A 2 states appear in Sec. III B. The results are summarized in Sec. IV. II. DETAILS OF THE CALCULATIONS A. Basis sets and correlation treatment The one-particle basis sets used in the present work were derived from the cc-pvqz correlation consistent basis sets of Dunning and co-workers These sets consisted of the following contracted functions: 5s,4p,3d,2 f,1g for oxygen, 6s,5p,3d,2 f,1g for chlorine, and 7s,6p,4d,2 f,1g for bromine. For bromine, however, a 28-electron quasirelativistic effective core potential ECP was used, 32 which replaced the innermost 3s,2p,1d functions (Ar 3d core and resulted in a contracted 4s,4p,3d,2 f,1g basis set for bromine. To ensure smooth matching of the ECP to the bromine Gaussian basis set, new contraction coefficients for the Hartree Fock HF 4s and 4p functions were generated in the presence of the ECP in HF calculations on the atom. For all atoms, the quadruple zeta basis sets were then augmented by a set of diffuse s and p functions, which were taken from the standard aug-cc-pvqz basis sets. 30,31,33 Lastly, as in our previous work for HOCl, 34,35 a single tight d function with exponent a 2 0 was added to the chlorine basis set. The importance of additional high exponent polarization functions for the second row atoms has recently been shown to greatly improve calculated equilibrium bond distances and bond energies The final basis sets for OClO and OBrO totaled 186 and 176 contracted Gaussian-type functions, respectively. As in our previous work on OClO, 20,26 MRCI calculations were based on complete active space self-consistent field CASSCF orbitals. The active space in the CASSCF consisted of the nine orbitals arising from the 2p, 3p, and 4p atomic orbitals of oxygen, chlorine, and bromine, respectively 13 electrons in 9 orbitals. All other low-lying orbitals were fully optimized, but constrained to be doubly occupied. All calculations were carried out in C s symmetry, which resulted in a total of 936 configuration state functions CSFs. In each case, two 2 A states were averaged in the CASSCF calculations to yield a common set of orbitals. In the subsequent MRCI calculations, the reference function was the same as the CASSCF active space 936 CSFs and all valence electrons were correlated the frozen core approximation was employed. All single and double excitations with respect to this reference function were included in the MRCI and the doubly-external configurations were internally contracted 39,40 icmrci to keep the calculations manageable. Even so, the total number of variational parameters in the present calculations totalled about million. The multireference analog 41,42 of the Davidson correction 43 has also been used throughout the present work and is denoted as icmrci Q. For each species the two electronic states were computed in a contracted basis specific to each state, 44 which significantly decreased the computational effort of the excited state calculations. All of the electronic structure calculations in the present work were carried out on a Hewlett Packard K260 workstation with the MOLPRO suite of ab initio programs. 45 B. Potential energy functions Using the basis sets and correlation treatment described above, 3D potential energy functions PEFs for the X 2 B 1 and first excited 2 A 2 electronic states (1 2 A and 2 2 A states in C s symmetry, respectively of OClO and OBrO were calculated at 49 symmetry unique points in C s symmetry. The calculated PEFs approximately covered the range 0.4 a 0 (r r e ) 0.7 a 0 and 30 ( e ) 30. The energy points were fit to polynomials of the form V r 1,r 2, ijk C ijk Q 1 i Q 2 j Q 3 k, 1 where the stretching coordinates, Q 1 and Q 2, were Morsetype coordinates 46 defined by Q 1 e (r r e )/r e /. In each case the Morse parameter was roughly optimized. The bend, Q 3, was expressed in terms of the Carter Handy coordinate, 47 which consists of a cubic expansion in e as Q 3 A 0 A 1 2 A 2 3. The value of A 0 for each surface was optimized and the A 1 and A 2 coefficients were obtained from the normalization and boundary conditions. A total of 30 symmetry unique terms were used in the polynomial of Eq. 1, which included some sextic terms. The resulting fits, the coefficients of which are shown in Table I, yielded root-mean-square rms errors of about 1 cm 1. For OBrO, however, this required deleting two points those at r r e 0.7 a 0 from the fit. Spectroscopic constants for each species and electronic state were calculated from the analytical PEFs by first transforming the set of polynomial coefficients of Eq. 1 into coefficients of dimensionless normal coordinates by L-tensor algebra. 48 The resulting normal coordinate force constants were then used in the usual second-order perturbation theory expressions. 49 The fitting of the surfaces and the perturbation calculations were carried out with the SURFIT program. 50 Vibrational band origins have also been calculated variationally

3 8866 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson TABLE I. The expansion coefficients C ijk ( C jik ) a of the icmrci Q potential energy functions for OClO and OBrO in a.u. and radians. i j k X 2 B 1 OClO b X 2 B 1 OBrO c A 2 A 2 OClO d C 2 A 2 OBrO e a See Eq. 1 for the definition of the PEF terms. b The potential was expanded about r 1 r a 0, and The Morse parameter was , while the coefficients of the bending coordinate expansion see the text were A , A rad 1, and A rad 2. c The potential was expanded about r 1 r a 0, and The Morse parameter was , while the coefficients of the bending coordinate expansion see the text were A , A rad 1, and A rad 2. d The potential was expanded about r 1 r a 0, and The Morse parameter was , while the coefficients of the bending coordinate expansion see the text were A , A rad 1, and A rad 2. e The potential was expanded about r 1 r a 0, and The Morse parameter was , while the coefficients of the bending coordinate expansion see the text were A , A rad 1, and A rad 2. using the full three-dimensional PEFs and the program suites of Tennyson and co-workers. 51,52 These calculations employed scattering coordinates defined by the OO distance (r 1 ), the distance of the halogen atom X from the center of mass of the OO diatom (r 2 ), and the angle between r 1 and r 2. Equivalent calculations were also carried out which used the X O distance as r 1 and the distance of the other oxygen atom from the center of mass of the X O diatom as r 2.In the first case, the asymmetric stretch is carried by the angular basis functions, while the second corresponds nearly to bond length, bond angle coordinates. Comparison of the results from the two approaches, which yielded identical vibrational frequencies, greatly simplified the assignment of high lying vibrational levels. In either case, the vibrational basis functions were constructed from products of Morse functions for the radial coordinates, and the angular coordinate was treated using a discrete variable representation DVR see, i.e., Ref. 53 based on associated Legendre polynomials. A total of 17 Morse functions were used for each radial coordinate, while for the angular coordinate, 80 DVR points were chosen over a range of angles from 0 to 180. After solving the effective 2D radial Hamiltonian at each DVR point, the lowest eigenvalues below cm cm 1 for the excited states were selected to construct the full 3D Hamiltonian matrix, which was then diagonalized to obtain the final eigenvalues and eigenvectors. C. Electric dipole moment functions The electric dipole moments of the ground states of OClO and OBrO were also calculated at each geometry as an expectation value of the icmrci wave function. After rotating the dipole moments into an Eckart frame 54 defined by the icmrci Q equilibrium geometries, the resulting x and y

4 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson 8867 components were fit to quartic polynomials in simple internal displacement coordinates. Rotationless (J 0) dipole moment matrix elements were then calculated with the program DIPOLE Ref. 55 using the vibrational wave functions obtained in the variational calculations and the threedimensional analytical functions of the x and y components of the electric dipole moment. Infrared intensities are expressed in terms of the band strength S, S(km/mol) R 2, where is the anharmonic wave number of the band origin and the total dipole moment matrix element R is in atomic units. (ea 0 ). III. RESULTS AND DISCUSSION A. The X 2 B 1 ground states of OClO and OBrO 1. Potential energy functions and spectroscopic constants Calculated spectroscopic constants for the electronic ground states of OClO and OBrO are shown in Table II, where they are also compared to the available experimental results. The calculated equilibrium structures yield very similar errors with respect to experiment; the bond lengths are too long by just 2 3 må, and the bond angles are only about too large. This is consistent with the expected core-valence correlation effect based on previous results for HOCl, 56 where the Cl O bond length was contracted by Å. For OClO, where the experimental data set is much more complete, excellent agreement is observed for the vibration-rotation interaction constants, centrifugal distortion constants, and the harmonic and anharmonic vibrational constants. In fact for the case of the vibrational anharmonicity constants, only two of the six values differ from those derived experimentally by more than 0.2 cm 1 (x 22 and x 23, and these two correspond to those obtained in an earlier, lower resolution study. 57 Recent values of x 22 and x 23 also shown in Table II derived from an accurate empirical force field 13 are in excellent agreement with our ab initio results. The vibrational fundamental frequencies of OClO are predicted to within about 5 cm 1 of experiment by the icmrci Q PEF. Very little difference is observed between the band origins calculated variationally and those obtained from the second-order perturbation theory expressions. For OBrO, the harmonic force field would appear to be of similar accuracy as OClO, based on the similarly good agreement for the centrifugal distortion constants, as well as the harmonic frequencies determined from Ar matrix 22 and microwave spectroscopy 23,24 experiments. Our calculated fundamental frequencies for OBrO can be compared to the experimental values obtained from an analysis of the hot bands in the C X visible absorption spectrum. 6 Again, very similar accuracy as noted for OClO is observed with errors on the order of 5 cm 1. The previous CCSD T work of Miller et al. 6 yielded harmonic frequencies with errors rangingfrom3to20cm 1 when compared to the experimentally derived harmonic frequencies shown in Table II. The MP2 calculations of Pacios and Gomez 28 yielded harmonic frequencies with much larger errors, especially for the asymmetric stretch. Quartic internal coordinate force fields defined in terms of simple displacement coordinates are shown in Table III for OClO and OBrO, where they are also compared to those recently derived from experiment by Müller et al. 13,25 Very good agreement between theory and experiment is observed for the quadratic coefficients in both cases, particularly for OBrO. The icmrci Q PEF for OClO, however, yields a smaller value for f r 0.007, compared to the value derived by Müller et al. of For the cubic force constants, very good agreement for OClO is observed. Two exceptions are the f rr and f rrr terms, where the ab initio values are of equal magnitude but opposite in sign to the experimentally derived quantities. This is seemingly at odds with the excellent agreement with experiment for the ab initio vibrationrotation interaction constants shown in Table II. Considering the strong sensitivity of the quartic force constants to any inversion of experimental data to obtain empirical force fields, very good agreement is observed between the ab initio and empirical values. Using the full 3D PEFs given in Table I, low-lying vibrational band origins have been computed variationally and are shown in Table IV for the ground states of both OClO and OBrO. As noted above, the fundamentals of both species are well reproduced by the ab initio potentials. For OClO the differences from experiment are 5.2 cm 1 ( 1 ), 2.2 cm 1 ( 2 ), and 4.6 cm 1 ( 3 ). In the case of OBrO, the observed errors are similar for 1 and 2, with a slightly larger error, 7.8 cm 1, for 3. At this level of theory, it is expected that most of the errors in the present calculations are in the harmonic part of the potential, hence the low-lying combination bands and especially the overtones should have errors directly proportional to those observed for the fundamentals. In the case of OClO this expectation is borne out by comparison with experiment for several overtone bands, where the ab initio values differ by 10.4(2 1 ), 3 1(2 2 ), 8 2(2 3 ), and 11 2(3 3 )cm 1 ranges are due to estimated experimental uncertainties. The combination bands shown in Table IV appear to exhibit similar trends. 2. Dipole moment functions and infrared and microwave transition probabilities The calculated icmrci electric dipole moment functions EDMFs for OClO and OBrO are shown in Table V. The equilibrium values at the icmrci Q equilibrium geometries were calculated to be and D 1 a.u D for OClO and OBrO, respectively negative end of the dipole toward the oxygens. Using the vibrational wave functions obtained in the variational calculations together with the 3D EDMFs of Table V, rotationless dipole moment matrix elements have been computed for both OClO and OBrO. In the vibrational ground state, the permanent dipole moments are calculated to be smaller in magnitude than their equilibrium values by and D for OClO and OBrO, respectively, i.e., 000 (OClO) D and 000 (OBrO) D. These are in good agreement with the experimental values of D Ref. 58 and D Ref. 25, respectively. In order to ascertain the source of the residual error in the ab initio

5 8868 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson TABLE II. Spectroscopic constants of the X 2 B 1 ground states of OClO and OBrO calculated from the icmrci Q PEFs compared to experimental values. a O 35 ClO O 79 BrO Constant icmrci Q Expt icmrci Q Expt r e Å b,c j e deg b,c j A e (cm 1 ) b B e (cm 1 ) b C e (cm 1 ) b A 1 MHz b 64.0 A 2 MHz b j A 3 MHz b B 1 MHz b 41.9 B 2 MHz b j B 3 MHz b 37.8 C 1 MHz b 32.4 C 2 MHz b j C 3 MHz b 24.8 A 0 (cm 1 ) c j B 0 (cm 1 ) c j C 0 (cm 1 ) c j D N (MHz) c j D NK (MHz) c j D K (MHz) c j d 1 (MHz) c j d 2 (MHz) c j 1 (cm 1 ) d k 2 (cm 1 ) d k 3 (cm 1 ) d l x 11 (cm 1 ) e x 22 (cm 1 ) , d 0.39 g x 33 (cm 1 ) f x 12 (cm 1 ) e x 13 (cm 1 ) e x 23 (cm 1 ) , d 5.56 g cm G 000 (cm 1 ) (cm 1 ) h m 2 (cm 1 ) i m 3 (cm 1 ) i m a Values in parentheses were derived from the variationally calculated vibrational energy levels using the full icmrci Q PEFs, e.g., x ( 1 ) /2 and x 12 ( 1 2 ) 1 2. The centrifugal distortion constants correspond to the S-reduced form of the Hamiltonian. b Reference 12. c Reference 13. d Reference 57. e Reference 16. f Reference 61. g Values obtained from the accurate, empirical force field of Müller et al. Ref. 13. h Reference 14. i Reference 15. j Equilibrium structure of Ref. 25 estimated from their r z geometry. The 2 values are effective, i.e., 2 (eff) 2 12 /2 23 /2. k Argon matrix results, Ref. 22. l References 23, 24. m Reference 6. dipole moments, calculations were also carried out whereby the dipole moments were computed as energy derivatives. At the icmrci Q equilibrium geometries, icmrci dipole moments calculated as energy derivatives, D and D, for OClO and OBrO, respectively, were slightly larger than their expectation value counterparts. At the icmrci Q level the dipole moments calculated as first derivatives of energy, D and D for OClO and OBrO, respectively, are in somewhat better agreement with experiment for both species in comparison to the icmrci expectation values. It would appear that a much larger MRCI treatment would be required to obtain more accurate equilibrium dipole moments for these two species. For the estimation of infrared intensities, it is convenient

6 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson 8869 TABLE III. Quartic internal coordinate force fields for the X 2 B 1 ground states of OClO and OBrO in aj Å n rad m. Term a OClO OBrO icmrci Q Expt b icmrci Q Expt d f rr f f rr f r f rrr f f rrr f rr f rr f r f rrrr f f rrrr c f rrrr f rrr c f rrr f rr c f rr f r a The force constants are defined such that V(q r,q R,q ) V e (1/2!) ij f ij q i q j (1/3!) ijk f ijk q i q j q k (1/4!) ijkl f ijkl q i q j q k q l, where q r r 1 r 1e, q R r 2 r 2e, and q e. The force fields in terms of dimensionless normal coordinates are available on request from the author. b Force field c in Ref. 13. An earlier quadratic and cubic force field has been reported in Ref. 12. c These values were fixed to preliminary values of the present ab initio work. d Reference 25. to calculate the derivatives of the dipole moment function with respect to dimensionless normal coordinates. 59 The resulting linear and quadratic terms are shown in Table VI for both OClO and OBrO. For both species the fundamental band intensities may be well approximated by just the linear terms, since the second derivatives are generally smaller by comparison. An exception to this, especially for OBrO, may be in the case of the 1 band, where the diagonal second derivative, 11, as well as 13, is more than half the size of 1. Some of the terms shown in Table VI for OClO can be compared to derivatives derived experimentally by Ortigoso et al. 60 absolute values, , , and D. In each case our theoretical derivatives 0.094, 0.17, 0.22 are just below the lower end of their stated uncertainties. From the observed 2 1 overtone and 1 3 combination bands, Ortigoso et al. 60 also derived values for the dipole moment second derivatives 11 and 13 of and D, respectively. The former is nearly identical to our ab initio value, while the latter would appear to be much too large. Within the double harmonic approximation harmonic force field and linear dipole moment function, absolute infrared intensities S for the fundamental vibrational modes of OClO and OBrO are calculated to be (S 1, S 2, S , 15.7, 68.5, and 1.1, 15.3, 19.7 km/mol, respectively. The OClO values are nearly identical to those of our previous study, 26 except for the 3 intensity which is smaller in this work by nearly a factor of 2. The OClO values can also be compared to the band intensities of Ortigoso et al., , , and 86 9 km/mol. While the 2 band intensity is in excellent agreement, the ab initio 1 and 3 intensities are TABLE IV. Selected icmrci Q vibrational band origins cm 1 and absolute infrared band intensities S km/mol for X 2 B 1 OClO and OBrO. a O 35 ClO O 79 BrO Band icmrci Q Expt S icmrci Q Expt f S b c d b c e e c c c c a Only those bands with calculated intensities greater than km/mol are shown. Results for bands of weaker intensity are available on request. b Reference 15. c Reference 57. Uncertainties are estimated. d Reference 14. e Reference 16. f Reference 6.

7 8870 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson TABLE V. The expansion coefficients a of the icmrci Eckart frame electric dipole moment functions x and y for the electronic ground states of OClO and OBrO in a.u.. D y ijk ( D y jik ) D x ijk ( D jik x ) i j k OClO OBrO OClO OBrO a The dipole moments were fit to quartic polynomials in internal displacement coordinates, i.e., x ijk D x ijk r i 1 r j 2 k, and were expanded about the same geometries as those of Table I. The dipole moments are expressed in an Eckart frame where at the reference geometry the positive y axis bisects the valence angle and r 1 is in the positive xy quadrant, i.e., the x-axis corresponds to the A principal axis and the y axis corresponds to the B principal axis. Positive signs for the equilibrium moments are consistent with positive polarities along the x and y axes. TABLE VI. First and second derivatives of the icmrci Eckart frame dipole moments in Debye with respect to dimensionless normal coordinates for the electronic ground states of OClO and OBrO. O 35 ClO O 79 BrO a component a b component a a Refers to the A and B principal axes. The B principal axis corresponds to the C 2 symmetry axis. smaller than the experimentally derived ones by about 20% 25%. Fully anharmonic, rotationless dipole moment matrix elements have also been computed for all the vibrational states shown in Table IV, and the derived absolute infrared band intensities are shown in this same table. For the fundamental bands, very little difference is seen in comparison with the less accurate double harmonic values noted above even for OBrO. The experimentally derived absolute IR intensities for the 2 1 and 1 3 bands, and km/mol, respectively, were reported by Ortigoso et al. 60 These can be compared to the values shown in Table IV of 0.52 and 3.3 km/mol. From the IR spectra of OClO in neon matrices, Müller and Willner 61 obtained band intensities relative to the 3 band. Their results are in good agreement with those of Ortigoso et al. They also observed the 2 3 overtone and the combination band with intensities relative to the 3 of 0.09 and 0.03, respectively. The ab initio relative intensities see Table IV are 0.14 and 0.11, respectively. As indicated in Table IV, the 3 3 overtone band should also have enough intensity to be observable. For OBrO both the 1 and 3 band intensities are calculated to be much weaker than in OClO. Qualitatively this can be understood by comparing plots of the dipole moment functions of OClO and OBrO, which are shown in Figs. 1 a and 1 b, where the stretching dependence is depicted. For both the a and b components, the EDMFs are fairly nonlinear and there are extrema located close to the equilibrium geometries. In the case of the b component of OBrO this is even more pronounced than in OClO, which accounts for the large drop in intensity of the 1 band compared to OClO. The calculated intensities of the 2 1 and 1 3 bands of OBrO, however, are very similar in magnitude to those of OClO. Other bands of OBrO that should carry significant intensity include the 1 2, 2 3,2 3, and 3 3. B. A 2 A 2 OClO and C 2 A 2 OBrO Calculated spectroscopic constants for the first excited 2 A 2 states of OClO and OBrO are shown in Table VII where they are compared to the available experimental results. For both OClO and OBrO the excitation energies of the excited states are very accurately reproduced, differing from experiment by just 0.03 and 0.02 ev. In the case of the equilibrium structures, the A state equilibrium geometry for OClO is of similar accuracy as was observed for the ground state, i.e., the bond length to within a few må and the angle within a couple tenths of a degree. For OBrO, only an estimated equilibrium geometry has been obtained experimentally, 6 and

8 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson 8871 FIG. 1. The stretching dependence of the X 2 B 1 OClO left and OBrO right icmrci electric dipole moments in Debye for the a a and b b components. Bond distances are in bohr. while the derived bond angle from the work of Miller et al. 6 agrees very well with our calculated value, their bond length would appear to be too short by Å their estimated uncertainty was 0.01 Å. The accuracy of the quadratic part of the ab initio potential of OClO can be assessed by comparing the calculated A-reduced centrifugal distortion constants with those determined by Hamada et al. 62 footnote to Table VII. Excellent agreement is observed. The rotational structure of the C 2 A 2 X 2 B 1 system of OBrO has not yet been characterized, hence the calculated spectroscopic constants given in Table VII should provide accurate estimates for the effects of vibration-rotation and centrifugal distortion in future rotational analyses of this band system. In the (A,C) 2 A 2 X 2 B 1 absorption spectra of OClO and OBrO, expected progressions in both the symmetric stretch ( 1 ) and bend ( 2 ) were observed. In the case of OClO, however, there was an unusually strong activity in the antisymmetric stretch, 3. This was first attributed by Coon et al. 63 as evidence for a C s -distorted equilibrium geometry in the A 2 A 2 state, implying a double-minimum in the stretching potential. However, the later work of Richardson et al. 57 and especially Brand et al. 64 modeled this effect by intensity borrowing through anharmonic coupling of 3 with the strong progressions of the 1 band. The model of a double minimum potential was again employed in the spectroscopic work of Hamada et al. 62 and most recently by Ri-

9 8872 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson TABLE VII. Spectroscopic constants of the A 2 A 2 and C 2 A 2 excited states of OClO and OBrO, respectively, calculated from the icmrci Q PEFs compared to experimental values. a O 35 ClO O 79 BrO Constant icmrci Q Expt icmrci Q Expt g T e ev b r e Å c e deg c A e (cm 1 ) B e (cm 1 ) C e (cm 1 ) A 1 MHz A 2 MHz A 3 MHz B 1 MHz B 2 MHz B 3 MHz C 1 MHz C 2 MHz C 3 MHz A 0 (cm 1 ) c B 0 (cm 1 ) c C 0 (cm 1 ) c D N (MHz) c 14.8 D NK (MHz) c 85.6 D K (MHz) c 419. d 1 (MHz) c 6.52 d 2 (MHz) c (cm 1 ) d (cm 1 ) d (cm 1 ) x 11 (cm 1 ) , e 2.76 d x 22 (cm 1 ) e x 33 (cm 1 ) , e d x 12 (cm 1 ) , e 3.55 d x 13 (cm 1 ) , e 5.47 d x 23 (cm 1 ) , e 2.22 d cm e 3.74 G 000 (cm 1 ) (cm 1 ) d (cm 1 ) d (cm 1 ) f a Values in parentheses were derived from the variationally calculated vibrational energy levels using the full icmrci Q PEFs, e.g., x ( 1 ) /2 and x 12 ( 1 2 ) 1 2. The centrifugal distortion constants correspond to the S-reduced form of the Hamiltonian. b Obtained from the T 0 of 2.61 ev from Ref. 19 and our icmrci Q G 000 values. c Reference 62. The structure corresponds to the values obtained for the 000 level. The A-reduced centrifugal distortion constants of Ref. 62 in MHz 10 3, N 18, NK 67, K 825, N 6.0, K 88, can be compared to ab initio values of N 17.5, NK 67.2, K 844, N 5.8, K d Reference 19. e Reference 57. f Estimate from Ref. 62. g Reference 6. The T e value was obtained from the experimental T 0 of ev and a zero-point energy obtained from the present ab initio values. chard and Vaida. 19 In our previous ab initio study of this system, 26 a one-dimensional cut along the asymmetric stretching coordinate was calculated with similar wave functions as used in the current work. These results indicated that a double minimum did not exist in the A 2 A 2 state of OClO, but since the full three-dimensional potential was not calculated, the source of the anomalous 3 intensities was not fully resolved. The results shown in Table VII and below in Table IX based on the accurate 3d PEFs of this work definitely support the anharmonic coupling model, 64 namely that the strong activity of the asymmetric stretch is caused by strong anharmonic coupling between the two stretching vibrations. This is evidenced by reproducing the large positive value of the x 33 anharmonicity constant, as well as the accurate calculation of the 1, 2, and 2 3 see below bands compared to experiment. There is also good agreement between the ab initio value for the 3 fundamental and the estimate of Hamada et al. 62 based on an analysis of Coriolis

10 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson 8873 FIG. 2. Potential energy contours in cm 1 of the icmrci Q PEF for the stretching coordinates of X 2 B 1 left and A 2 A 2 right OClO. The first contour is drawn at 500 cm 1 and the contour intervals are 500 cm 1. Bond distances are in bohr. perturbations in the spectrum. Qualitatively, the strong anharmonicity of the stretching potential in the excited state of OClO can be seen in Fig. 2, where contours of both the ground and excited state PEFs of OClO are plotted. It should be noted that unlike the ground state results, there are significant differences between the vibrational constants obtained through second-order perturbation theory and variationally with the full PEF. In particular, both the x 33 and x 13 anharmonicity constants are much smaller though still large when derived from the variational calculations. These smaller values are also in much better agreement with the constants derived experimentally. Not surprisingly, this effect also manifests itself in the calculated 1 band origin, where the value obtained from the variational calculations is larger than the perturbation theory result by over 12 cm 1. Both the 1 and 2 band origins are then within 10 cm 1 of experiment. In the C 2 A 2 X 2 B 1 absorption spectrum of OBrO, 6 there was no evidence of activity in the 3 stretch, and the lower degree of coupling compared to OClO between the two stretches can be observed qualitatively in Fig. 3. In addition, the values of x 33 and x 13 Table VII calculated by FIG. 3. Potential energy contours in cm 1 of the icmrci Q PEF for the stretching coordinates of X 2 B 1 left and C 2 A 2 right OBrO. The first contour is drawn at 500 cm 1 and the contour intervals are 500 cm 1. Bond distances are in bohr.

11 8874 J. Chem. Phys., Vol. 109, No. 20, 22 November 1998 Kirk A. Peterson TABLE VIII. Calculated icmrci Q quartic internal coordinate force fields for the A 2 A 2 and C 2 A 2 excited states of OClO and OBrO, respectively in aj Å n rad m. Term a OClO OBrO f rr f f rr f r f rrr f f rrr f rr f rr f r f rrrr f f rrrr f rrrr f rrr f rrr f rr f rr f r TABLE IX. Selected icmrci Q vibrational band origins cm 1 for A 2 A 2 OClO and C 2 A 2 OBrO. Band O 35 ClO O 79 BrO icmrci Q Expt a icmrci Q Expt b a The force constants are defined such that V(q r,q R,q ) V e (1/2!) ij f ij q i q j (1/3!) ijk f ijk q i q j q k (1/4!) ijkl f ijkl q i q j q k q l, where q r r 1 r 1e, q R r 2 r 2e, and q e. The force fields in terms of dimensionless normal coordinates are available on request from the author. perturbation theory are not markedly different from those derived from the variational band origins, which is in strong contrast to the OClO results. This presumably indicates a lack of near-resonant terms involving 1 and 3 in OBrO. As shown in Table VII, the icmrci Q PEF yields accurate values for the harmonic frequencies of the symmetric modes of OBrO, differing by at most 2 cm 1 from the experimentally derived values. The experimental analysis of Miller et al. 6 also derived values for a few of the anharmonicity constants in the excited state. The ab initio values for x 11 and x 12 are in good agreement, but their result for x 22 would appear to have the wrong sign. The calculated value of x 33 shown in Table VII for OBrO is also positive as in OClO, but less than half its magnitude. The accuracy of the present PEF is further demonstrated by the excellent agreement with the measured values of 1 and 2, where the ab initio values are within 10 cm 1 of experiment. It should be noted that in contrast to OClO, the variational calculations of the vibrational spectrum show only relatively small differences from the perturbation theory results. Quartic internal coordinate force fields are shown in Table VIII for the excited 2 A 2 states of both OClO and OBrO. In general there are strong similarities between the OClO and OBrO values, but not unexpectedly several of the OClO quartic terms, especially f RR, are significantly larger than those obtained for OBrO. Low-lying vibrational band origins calculated variationally using the full 3D PEFs of Table I are shown in Table IX for the first excited 2 A 2 states of OClO and OBrO. As observed for the ground states, most of the errors are systematic and originate in the harmonic force field. Our best estimate of the 3 band origin of OClO is 427 cm 1 based on the a Taken from the vibronic data of Ref. 19, except for the estimate of 3 which is due to Hamada et al. Ref. 62. b Reference 6. The uncertainties in these values are estimated at 3 cm 1. error in our calculated value for 2 3. This is in very good agreement with the estimate of Hamada et al. 62 IV. CONCLUSIONS Accurate three-dimensional, near-equilibrium potential energy and dipole moment functions have been calculated for the ground states and first excited 2 A 2 states of the OClO and OBrO radicals. From the analytical potential energy functions, spectroscopic constants were calculated for each state and variational calculations were employed to obtain accurate vibrational band origins for the fundamentals and low-lying overtones and combination bands. For the electronic ground states, errors compared to experiment were found to be on the order of 5 cm 1. In the excited states, the errors increased to only about 10 cm 1 for the fundamentals. In the A 2 A 2 state of OCIO, strong anharmonic coupling was calculated between the two stretching modes. This was proposed to account for the anomolously strong activity of the asymmetric stretch in its UV absorption spectrum. Evidence for a double minimum in this electronic state was not found. Accurate absolute infrared intensities for the electronic ground states of both species were also derived from the analytical electric dipole moment functions. Good agreement with respect to experiment was generally noted for OCIO, and the intensities of the OBrO fundamental bands were calculated to be much weaker than in OCIO. ACKNOWLEDGMENTS The support of the National Science Foundation under CAREER award No. CHE is gratefully acknowledged. The author would like to thank Dr. H. S. P. Müller for communication of experimental results prior to publication.

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