an accurate global ab initiopotential energy surface for the x1a8...

JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 11 15 SEPTEMBER 2000

An accurate global ab initio potential energy surface for the X 1A 8electronic state of HOBr

Kirk A PetersonDepartment of Chemistry, Washington State University, 2710 University Dr., Richland, Washington 99352and The Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory,Richland, Washington 99352

~Received 11 April 2000; accepted 21 June 2000!

A global, analytical potential energy surface for the ground electronic state of HOBr has beendetermined using highly correlated multireference configuration interaction wave functions andexplicit basis set extrapolations of large correlation consistent basis sets. Theab initio data havebeen fit to an analytical functional form that accurately includes both the HOBr and HBrO minima,as well as all dissociation asymptotes. Small adjustments to this surface are made based on thelimited experimental data available and by indirectly taking into account the effects of spin–orbitcoupling on the OH1Br dissociation channel. Vibrational energy levels are calculated variationallyfor both HOBr and HBrO up to the OH1Br dissociation limit using a truncation/recoupling method.The HOBr isomer is calculated to contain 708 bound vibrational energy levels, while the HBrOminimum lies above the OH1Br dissociation limit but is calculated to have 74 ‘‘quasibound,’’localized eigenstates. Infrared intensities for all of these vibrational transitions are also calculatedusing MRCI dipole moment functions. The assignment of the HOBr states is complicated by strongstretch–bend resonances even at relatively low energies. In contrast to the HOCl case, these statemixings made it particularly difficult to assign the relatively intense OH overtone bands abovev152. The vibrational density of states of HOBr at the OH1Br dissociation limit is determined tobe 0.16 states/cm21. Comparisons to recent work on HOCl using similar methods are madethroughout. ©2000 American Institute of Physics.@S0021-9606~00!30235-5#

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I. INTRODUCTION

Due to the particularly efficient ability of brominecontaining species to catalytically remove stratospheozone,~see, e.g., Refs. 1 and 2! there has been significaninterest in their characterization. Hypobromous acid has bproposed to participate in stratospheric ozone depletionthe cycle3–5

Br1O3→BrO1O2

BrO1HO2→HOBr1O2

HOBr1hn→OH1Br

OH1O3→HO21O2

2O3→3O2

HOBr is formed both by the homogeneous gas phase rtion of the HO2 radical with BrO,4,6

HO21BrO→HOBr1O2

as well as by the hydrolysis of bromine nitrate7,8

BrONO2~aq!1H2O→HOBr~aq!1HNO3~aq!

on or in aerosol particles either at night in the stratospherunder other low light conditions, such as Arctic haze evein the Arctic troposphere. The removal of HOBr in the lowstratosphere~,25 km! is dominated by its photolysis

HOBr1hn→OH1Br,

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while at higher altitudes the reaction with atomic oxygen9

O~3P!1HOBr→OH1BrO

becomes more important. Of course, heterogeneous remprocesses are also prevalent, especially in the troposphwhere the dissolution of HOBr in aerosol particles containg HBr, HCl, or H2SO4 can lead to aqueous Br2 orBrCl.7,10,11These latter species are then easily photolyzedproduce reactive bromine radicals.

Several experimental studies have concentrated onphotolysis and stability of HOBr due to its importance in tcatalytic removal of ozone in the atmosphere. Many of thhave dealt with the determination of its UV/visible absortion spectrum and cross sections in the gas phase,12–17 in-cluding the absorption band near 440 nm correspondingtransition to its lowest lying triplet state.14 The HO–Br dis-sociation energy, and hence the heat of formation of HOhas been determined by Ruscic and Berkowitz18 to be<48.4560.42 kcal/mol by monitoring the appearancthreshold of Br1 from HOBr. The HO–Br near-thresholdphotodissociation dynamics of HOBr have been investigaby Sinha and co-workers19 with characterization of the OHproducts by laser induced fluorescence combined with poization and sub-Doppler spectroscopy. The HO–Br dissotion energy arising from that work, 49.2561.0 kcal/mol, wasslightly larger than the upper bound obtained by Ruscic aBerkowitz ~though within their quoted uncertainty!.

In order to facilitate atmospheric monitoring of HOBseveral high resolution spectroscopic studies have also b

8 © 2000 American Institute of Physics

to AIP copyright, see http://ojps.aip.org/jcpo/jcpcpyrts.html

4599J. Chem. Phys., Vol. 113, No. 11, 15 September 2000 Potential energy surfaces of HOBr

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TABLE I. A comparison of HOBr spectroscopic constants calculated from MRCI, MRCI1Q, and CCSD~T!near-equilibrium potential energy functions with the aug-cc-pVTZ basis set.a

r e(OH)~Å!

Re(BrO)~Å!

ue(HOBr)~deg!

v1

~cm21!v2

~cm21!v3

~cm21!De(OH1Br)~kcal/mol!

MRCI ~ecp! 0.9653 1.8435 102.24 3803.2 1201.2 620.7 48.2MRCI1Q ~ecp! 0.9666 1.8416 102.53 3792.6 1188.1 620.3 50.3MRCI1Q 0.9665 1.8420 102.73 3794.1 1189.0 624.6 50.7CCSD~T! 0.9666 1.8408 102.96 3788.0 1181.6 625.8 51.7

aThe diffusef (O) and Br andd(H) functions were not included in these calculations.

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carried out on this species. All three vibrational fundametals have been observed for both HOBr and DOBr.20–24 Incontrast to HOCl, however, where numerous high-lyiovertones and combination bands have been characterizeto the OH1Cl dissociation limit, only the first overtone othe BrO stretch21 (2n3) for HOBr and then213n3 combi-nation band23 of DOBr have been reported. Analysis of thpure rotational spectra25 of HOBr has led to an accurate etimate of its equilibrium structure,22 as well as the permanendipole moment of DOBr.

There have been relatively few theoretical studiesHOBr that included dynamical electron correlation effecOne of the earliest studies was that of McGrath aRowland,26 who calculated a heat of formation value usiGaussian-2 theory. The coupled cluster study of Lee27 em-ployed a TZ2P basis set to determine the equilibrium strture, harmonic frequencies, and relative energetics of HOand its less stable isomer HBrO. Large atomic natural orb~ANO! basis sets were also used in that work to more acrately predict the heat of formation and isomerization eneof HOBr. Anharmonic near-equilibrium potential energfunctions of HOBr have been determined by Palmieriet al.28

using multireference configuration interaction wave funtions and a cc-pVTZ basis set, as well as by the presauthor29 using the coupled cluster singles and doubles wperturbative triples method, CCSD~T!, with a large correla-tion consistent basis set. The CCSD~T! method was alsoused recently by Li and Francisco30 to characterize the equilibrium spectroscopic properties of HOBr, HBrO, and tisomerization transition state. The electronic spectrumHOBr has been investigated previously by Franciscoet al.31

and more recently by Balint-Kurti and co-workers32 and Leeet al.33 ~HOBr and HBrO!.

The present study stems from a more extensive invegation into the photodissociation dynamics of HOBr thatcludes the first three singlet states and lowest two tripstates. This work reports on the ground electronic stateHOBr using accurate multireference configuration intertion wave functions and explicit extrapolations of the onparticle basis set to the complete basis set limit. The ofour electronic states have been computed at the idenlevel of theory and these results will be reported at a ladate. Section II describes the details of the calculations wSec. III describes the analytical fit to the global potentenergy surface~PES!, minor adjustments to theab initioPES, and the calculation of the vibrational eigenstatesinfrared band intensities of HOBr and HBrO. The concsions are summarized in Sec. IV.

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II. COMPUTATIONAL DETAILS

The ab initio electronic structure calculations usedcharacterize the ground state potential energy surfaceHOBr were nearly identical to those carried out previoufor HOCl.34–36 A series of three basis sets derived from tcorrelation consistent sets of Dunning and co-workers37,38

were used at every geometry considered. Specifically thcorresponded to the standard cc-pVDZ, cc-pVTZ, andpVQZ basis sets augmented with diffusespd ~for Br and O!and sp ~for H! functions from the correspondinaug-cc-pVnZ sets38,39 ~resulting sets denoted AVDZ, AVTZand AVQZ, respectively!. In order to include some treatmenof scalar relativistic effects for the bromine atom, a relatistic effective core potential~ECP! from the Stuttgart group40

was used on Br. The contractedspd functions that corre-sponded to the Br 1s2s2p3s3p3d Hartree–Fock~HF! coreorbitals were, of course, removed from the above basis sand the 4s4p HF functions were recontracted in the presenof the ECP. Table I shows results at the MRCI/AVTZ levof theory~see below! comparing the spectroscopic constanof HOBr obtained in calculations both with and without aECP. The effects are observed to be small, as suggesteprevious Dirac–Fock benchmark calculations41–43 on HBr,BrF, and Br2. Note that these observations are very differefrom the recent work of Balint–Kurti and co-workers32

where different basis sets were used to compare resultsand without an ECP. As in previous work on HOCl,34–36 theregular convergence behavior of the correlation consisbasis sets used in this work was exploited by extrapolathe total energies at each geometry to the complete basi~CBS! limit using the expression44

En5E`1Ae2~n21!1Be2~n21!2, ~1!

wheren is the cardinal number of the basis set~2, 3, 4 forAVDZ, AVTZ, and AVQZ, respectively! andE` is the totalenergy at the approximate CBS limit. Recent studies hindicated that this functional form is among the most acrate for these sizes of basis sets.45,46As demonstrated belowaccounting for basis set truncation errors in this mannersults in more accurate geometries and asymptotic energeven in comparison to results obtained with the relativlarge AVQZ basis set.

Electron correlation was treated at the internally cotracted multireference configuration interaction~MRCI! levelof theory47,48 with the addition of the multireference analoof the Davidson correction49–51 for higher excitations(MRCI1Q). The orbitals for the MRCI calculations wer


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4600 J. Chem. Phys., Vol. 113, No. 11, 15 September 2000 Kirk A. Peterson

determined in state-averaged complete active spaceconsistent field calculations~SA-CASSCF!. The active spacewas of the full valence type, i.e., 14 electrons in 9 orbitaThe O1s orbital was constrained to be doubly occupied inconfigurations and was obtained in a preceding SA-CASScalculation that held the lowest three orbitals doubly ocpied (O 1s, 2s, and Br 4s) in order to resolve the O 1s and2s orbitals~see, i.e., Ref. 52! Since the present study is paof a more extensive investigation into the photodissociatof HOBr, the state-average in the CASSCF calculations csisted of all singlet and triplet states correlating with the O(X 2P)1Br (2P) dissociation limit, i.e., (1 – 3)1A8,(1 – 3)1A9, (1 – 3)3A8, and (1 – 3)3A9, for a total of 12states. Equal weights were used, except for the third stateach symmetry since they become very high in energyshortRBrO distances and caused convergence problems inCASSCF. Thus the weights for these states were smoodecreased from values of 1/12 at longRBrO distances to zeroat RBrO53.474 bohr. The reference function for the intenally contracted MRCI was identical to that used in tCASSCF and resulted in 302 configuration state functi~CSFs! for the X 1A8 state. Only the valence electrons wecorrelated. With the AVQZ basis set this resulted in just o600 000 variational parameters. TheMOLPRO suite of elec-tronic structure programs53 was used throughout the presework.

Also included in Table I are comparisons betweensults obtained with MRCI, MRCI1Q, and CCSD~T! wavefunctions with the AVTZ basis set. The1Q correction isobserved to have a relatively small effect on the equilibrigeometry, with the largest differences between MRCI aMRCI1Q being;0.002 Å inRe~BrO! and 0.3° inu~HOBr!.The OH stretch and bending harmonic frequencies, howeare decreased with the addition of the1Q correction byabout 10 cm21, which are then in better agreement with tCCSD~T! results~and subsequently in better agreement wexperiment as can be inferred below!. Addition of the David-son correction is also observed to be particularly advageous in regards toDe~HO–Br!, where the MRCI1Q valueis larger than the MRCI one by 2.1 kcal/mol.

III. RESULTS AND DISCUSSION

As a validation of the theoretical method chosen inpresent work, including the basis set extrapolation procednear-equilibrium potential energy functions were initiacalculated for HOBr, HBrO, and the HOBr→HBrO transi-tion state~TS!. A total of 41 geometries were sampled in thregion of each of the two minima and 27 points for thegion of the PES near the TS. These data were then fipolynomials in simple internal displacement coordinatThe resulting equilibrium geometries, harmonic vibrationfrequencies, and relative energetics as a function of basiat the MRCI1Q level of theory are shown in Table II. Ineach case, the calculated spectroscopic constants smoconverge with basis set toward the CBS limit values. In geral, the difference between the AVQZ and CBS resultssmall, although for instance the OH1Br dissociation energyincreases by 1.4 kcal/mol and the BrO equilibrium distanin HOBr and HBrO both decrease by about 0.004 Å. Bo


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the HOBr→HBrO isomerization energy and barrier heigare well converged with the AVQZ basis set. At the CBlimit the calculated MRCI1Q value for De(HO–Br) islower than experiment19 by about 1.5 kcal/mol, which is verysimilar to previous work34 at the same level of theory foHOCl. The BrO1H and HBr1O(1D) dissociation energiesboth agree with experiment to nearly within their experimetal uncertainties. The calculated MRCI1Q/CBS equilibriumgeometry for HOBr is in excellent agreement with the valuestimated from experiment,22 i.e., r e(OH) is too short byabout 0.002 Å andRe(BrO) is too long by;0.001 Å, whileu~HOBr! is slightly too small by about 0.2°. In the caseHBrO, it is interesting to note that its equilibrium BrO distance is significantly shorter than that of HOBr by more th0.1 Å. Not surprisingly, the same behavior has beenserved previously for the HOCl/HClO pair.36 As discussed indetail by Leeet al.,54 this can be attributed to the hypervalecharacter of the bonding in HBrO and HClO. At the isomeization transition state, the BrO distance is stretched by ab0.05 Å compared to HOBr, while, as previously noted byand Francisco,30 the OH distance is about halfway betweethose of HOBr and HBrO.

The near-equilibrium results shown in Table II cancompared to those obtained in previousab initio studies.Nearly all of the previous work used basis sets of similar sor smaller as the AVTZ one used in this work, which genally resulted inRe(BrO) values that were too long by 0.010.02 Å. The exception is the large basis set CCSD~T! studyof Ref. 29, which is in very good agreement with the presMRCI1Q results. The MRCI value forue obtained by Palm-ieri et al.28 with the cc-pVTZ basis set, 101.0°, is nearly 2smaller than experiment~and the present AVTZ result! andis presumably due to the lack of diffuse functions in thbasis set. The recent CCSD~T! study of HOBr, HBrO, andthe intervening transition state by Li and Francisco30 is ingood agreement with the results shown in Table II for tequilibrium structures. In their largest basis set calculatio6-31111G(3d f ,3pd), they obtained a CCSD~T! equilib-rium isomerization energy of 58.9 kcal/mol and a barrheight of 78.6 kcal/mol. Their value for the isomerizatioenergy is identical to the CCSD~T!/ANO4 value calculatedpreviously by Lee.27 These can be compared to thMRCI1Q/CBS values of the present work of 61.1 and 79kcal/mol, respectively. Due particularly to the more complebasis sets and more balanced correlation treatment usethe present work~the CCSDT1 diagnostic has been shown iRef. 27 to be twice as large for HBrO as for HOBr!, theseprevious CCSD~T! values forDEisom andDEb may be some-what too small. In an attempt to confirm this, neaequilibrium CCSD~T! potential energy functions were calculated with the AVTZ basis set. The resulting isomerizatibarrier height and isomerization energy of 78.1 and 5kcal/mol, respectively, are smaller than the MRCI1Q/AVTZvalues shown in Table II by 0.7 and 1.5 kcal/mol. Hencedifferences between the present MRCI1Q and previousCCSD~T! results is more of a correlation effect rather thimbalances in their basis sets, which is in direct contrasthe HOCl case.36 The harmonic vibrational frequencies oHOBr and HBrO obtained in the present work are genera



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TABLE II. Spectroscopic constants~Å, deg, cm21, and kcal/mol! of HOBr, HBrO, and the HOBr→HBrOtransition state from near-equilibrium potential energy functions at the MRCI1Q level of theory with a seriesof correlation consistent basis sets.

AVDZ AVTZ AVQZ CBSa Expt.

HOBrEmin(a.u.) 288.895 711 289.007 154 289.049 176 289.073 731r e(OH) 0.9731 0.9666 0.9641 0.9625 0.9643b

Re(BrO) 1.8731 1.8416 1.8332 1.8287 1.8279b

ue(HOBr) 102.26 102.53 102.69 102.78 103.05b

v1(OH) 3747.2 3792.6 3805.7 3806.1v2(bend) 1179.9 1188.1 1199.4 1202.8v3(BrO) 606.3 620.3 631.4 635.9De(OH1Br) 48.3 50.3 52.5 53.9 55.661.0c

De(BrO1H) 100.1 102.2 103.3 104.0 103.661.4d

De(HBr1O) 106.8 109.9 111.3 112.1 113.461.0d

HBrOEmin(a.u.) 288.799 641 288.910 196 288.951 952 288.976 351r e(HBr) 1.4588 1.4571 1.4563 1.4558Re(BrO) 1.7609 1.7214 1.7135 1.7095we(HBrO) 105.49 106.09 106.31 106.40v1(BHr) 2361.0 2298.8 2313.3 2326.3v2(bend) 783.5 821.8 827.1 830.4v3(BrO) 652.6 690.2 696.6 699.7DEisom 60.3 60.8 61.0 61.1

HOBr→HBrO TSEmin(a.u.) 288.773 72 288.881 52 288.923 06 288.947 37r e(OH) 1.780 1.771 1.743 1.719Re(BrO) 1.915 1.890 1.880 1.877ue(HOBr) 45.9 45.9 46.3 46.7DEb 76.6 78.8 79.1 79.3

aObtained by fitting the total energies to Eq.~1!. See the text.bReference 22.cReference 19.dSee the footnotes to Table III.

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in good agreement with previous values, except in thcases where the BrO distance was calculated to be sigcantly too long, which led to BrO stretching harmonic frquencies that were too small by 10–20 cm21.

In order to cover the global surface for HOBr,ab initio

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eifi-calculations were carried out at a total of 1259 geomet@each geometry treated with 3 basis sets and then extrlated to the CBS limit via Eq.~1!#. Initially many of thesewere confined to a grid defined by

r OH@a0#51.4,1.6,1.83,2.0,2.2,2.6,3.0,

RBrO@a0#52.65,2.85,3.05,3.25,3.474,3.65,3.85,4.35,4.85,5.35,6.5,8.5,10.0,

uHOBr@deg#50.01,20,40,60,80,103.2,120,140,160,179.99,

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but where geometries with values ofr HBr,1.5a0 were omit-ted. This grid was then extended by computing mamore points corresponding to longer OH distances, e.g.,HBrO isomer and the HBr1O entrance channel. In additionall of the data obtained above in the calculation of the neequilibrium potential functions were also used in the costruction of the global surface in order to better defineminima and isomerization transition state. As in previowork on HOCl,34,36 in addition to the explicitly calculated
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data a small number of points~244! for long OH distances(r OH.3 a0) at u values between 100° and 180° were otained by extrapolating cuts ofr OH that were fit with thegeneralized Morse oscillator function,55,56

V5Ve1De@12e2b~r !Dr #2, ~2!

where b(r )5aDr 21bDr 1c and Dr 5r OH2r e,OH. Forthese extrapolations the values ofDe were constrained by the


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energy of BrO1H at the same level of theory. The totnumber of data points included in the analytical fit procedwas 1503.

A. Analytical representation of the global surface

The analytical fit was based on a many-body expansio57

in the three bond lengths,

VHOBr~R1 ,R2 ,R3!5V~1!1VOH~2!~R1!1VHBr

~2! ~R2!1VBrO~2! ~R3!

1VHOBr~3! ~R1 ,R2 ,R3!, ~3!

whereR1 , R2 , and R3 are the OH, HBr, and BrO separations, respectively. The sum of the one-body terms,V(1)

5H(2S)1O(3P)1Br(2P), was computed as a supermoecule withR15R35100a0 . The two-body, diatomic potentials were also computed on the triatomic PES with the thatom separated by 100 bohr. These diatomic potentials,responding toX 2P OH1Br(2P), X 1S1 HBr1O(1D), andX 2P BrO1H(2S), were fit to the switched-MLJ~modifiedLennard-Jones oscillator! function of Hajigerorgiou and LeRoy,58

V~r !5Ve1DeF12S r e

r D 6

e2bMLJs

~z!zG2

, ~4!

wherez5(r 2r e)/(r 1r e), and

bMLJs ~z!5 f s~r !F (

m50

M

bmzm2b`G1b` . ~5!

In Eq. ~5! the switching functionf s(r ) is defined byf s(r )51/@eas(r 2r s)11# with as being the damping strength parameter andr s was typically set to;1 bohr longer than themaximumr data point used in the fit. The value ofb` can berelated58 to the C6 dispersion coefficient, b`

5 ln@2De(re)6/C6#. Using the London formula~see, e.g., Ref.

59! and experimental values for the atomic polarizabilitand ionization potentials,60 the C6 values were fixed to~atomic units! 9.134~OH!, 38.845~BrO!, and 32.274~HBr!.In addition, the values ofDe were fixed to the results fromaccurate polynomial fits to near-equilibrium data. In the cof OH, 17 points were fit withM58 to a root-mean-squar~RMS! deviation of just 0.003 kcal/mol, while for BrO, 1points were fit (M56) with a RMS error of 0.04 kcal/molAs noted previously for the HCl potential energy curve in tcase of HOCl~see, e.g., Ref. 36! the ground state of HOBcorrelates with HBr(X 1S1)1O(1D), but at long HBr dis-tances this surface leads to ground state oxygen atom.resulting small barrier occurring in the HBr potential, whicarises from interactions with upper excited states near diciation, is not accounted for in this work~doing so wouldgreatly complicate the form of the resulting three-body ptential!, and the low-lying energies are smoothly connecto the ground state atomic asymptote via Eq.~4!. Thus forHBr just 12 points were fit (M55) to a RMS error of 0.04kcal/mol. The minimum of this potential correspondsHBr1O(1D), and the O(3P–1D) MRCI1Q/CBS splittingobtained in this work, 45.10 kcal/mol, is in very good agrement with the experimental value61 of 45.15 kcal/mol~spin–orbit averaged value!.


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The three-body potential,VHOBr(3) , was obtained by sub

tracting the one and two-body contributions at eachab initiogeometry. Because of the rather complicated topology ofground state surface as shown previously for the very simHOCl system,36 i.e., two minima, an intervening saddlpoint, and conical intersections with other electronic sta~see Ref. 36!, an accurate fit to within a few tenths ofkcal/mol by an analytical function is a challenging task. Ater much experimentation, it was found that in order to otain the most accurate fit for both HOBr and HBrO, as was all three atom–diatom dissociation channels (OH1Br,BrO1H, HBr1O), a switched multicenter representatiosimilar to that used by Mladenovic and Schmatz62 for theHCO1/HOC1 system was found to yield the most satisfatory results. Refering to the coordinate system of Fig. 1,three-body term was expressed as

VHOBr~3! 5@Va

~3!1Vb~3!#x, ~6!

where

Va~3!5(

i 51

2

(lmn

dilmnr ilr3

mh inV i~R12R2!. ~7!

The stretching coordinates,r i( i 51 – 3), were taken to be63

r i5Rie2b i ~Ri2Ri

0!, ~8!

where the reference geometries,Ri0, were approximately

equal to the equilibrium bond lengths in the two-body potetials. The angular functionsh i corresponded to damped Legendre polynomials,

h in5Pl

n~cosu i !•G i11, ~9!

where the damping functions,

G i5H 12@12tanh$g2~R222R2

0!%# for i 5112@12tanh$g1~R122R1

0!%# for i 52~10!

helped to smooth any spurious oscillations in the asymptregions. In Eq.~7!, the function that smoothly switches between the HOBr (R1,R2) and HBrO (R2.R1) regions ofthe PES,V i(R12R2), is defined by

V i~R12R2!5 12$12~21!d2i tanh@k~R12R2!#%, ~11!

where the optimal value of the switching strength paramek, was found to be 0.55. Stronger switching strengths wobserved to result in the introduction of unphysical featu

FIG. 1. Coordinate system for HOBr used in the analytical fit.


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into the PES. The highest degree ofr andh terms in Eq.~7!were 9 and 7, respectively, fori 51, and 6 and 4, respectively, for i 52, which resulted in 363 linear paramete(dilmn).

As discussed previously in detail for HOCl,34,36there areseveral conical intersections present on the ground stateof HOBr. The most prominent of these occurs at linear HOconfigurations (u150), and theVa

(3) function alone is notcapable of accurately fitting this region. The additional funtion Vb

(3) has been added to account for this, as well asother intersection at linear HBr–O geometries (u250), andhas the form

Vb~3!5(

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2

(lmn

djlmnr jl r3

mh jnJ j , ~12!

where the functionsJ j are cusplike functions for the conicaintersections atu j50° analogous to those used previousfor HOCl.64 The addition ofVb

(3) contributed 33 additionaterms to the fit. Finally the last term of Eq.~7!, x, is a cutofffunction that makes the three-body contribution exactly zfor small atom–atom separations,

x~R1 ,R2 ,R3!

5H expS a1

d12R11

a2

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a3

d32R3D ; for Ri.d i

0; for Ri<d i

.

~13!

The short-range repulsion is then represented only bytwo-body potentials. This term was essential to avoidoccurrence of deep, unphysical wells at short range, ecially in the BrO coordinate. It should be noted that the suin Eqs.~7! and~12! have the usual constraints63 so thatVHOBr

(3)

is defined to be zero at all dissociation asymptotes.In the fitting of the three-body potential, unequal weigh

were assigned to the data based on the same weightingtion used previously for HOCl.36 In contrast to this previouswork, however, the HBrO minimum was not given any spcial weighting in the present case. The final fit of 15MRCI1Q/CBS energies resulted in the following RMS erors as a function of the energy above the HOBr minim~all values in kcal/mol!,

0<V<30 RMS error50.09,

30,V<60 RMS error50.19,

60,V<100 RMS error50.50.

The RMS error for all 1503 points was just 1.1 kcal/mol aincluded several points as high as 300 kcal/mol aboveHOBr minimum.

B. Characteristics of the analytical PES

Equipotential contour plots of the fitted PES are dplayed for HOBr internal coordinates in Figs. 2 and 3. Quatatively these are very similar to those shown previousl36

for HOCl. The conical intersection atuHOBr5180° betweenthe lowest1S1 and1P states is easily observed in Fig. 2~a!


ESr

-e

o

eee-s

nc-

-

e

--

and the dissociation of HOBr to OH1Br proceeds without abarrier. Figure 2~b!, which displays the angular dependenof the r OH coordinate at fixedRBrO , clearly shows both theHOBr and HBrO minima and the intervening transition staas well as the minor conical intersection at 0°, which aarises from an intersection of low-lying1S1 and1P states.As was also the case for HOCl, there is a barrier inBrO1H coordinate for HOBr angles near 70° atr OH dis-tances of;4 a0 . This is also a result of an interaction witan excited1A8 state. Figure 3 shows the radial dependencer OH and r BrO near the equilibrium angle of HOBr~103°!,where very little coupling between the two stretching codinates is observed. A contour plot of the PES atuHOBr

FIG. 2. Equipotential contour plots of the fitted HOBr PES for fixed~a!r OH51.82 a0 and ~b! r BrO53.34 a0 . The contour increments are 5 kcamol with the zero of energy corresponding to completely separated grostate atoms.


d5ted


FIG. 3. Equipotential contour plots of the fitted HOBr PES for fixeu(HOBr) of ~a! 103°, ~b! 180°, and~c! 33°. The contour increments arekcal/mol with the zero of energy corresponding to completely separaground state atoms.

tg.ec

te

mre

al

i-

mesnt.

ted

enteions

dr-al

om

5180° @Fig. 3~b!# exhibits barriers of;15 kcal/mol forBr1OH and;10 kcal/mol for H1OBr linear approaches. Au533°, which is near the equilibrium angle of HBrO, Fi3~c! demonstrates that HOBr is purely repulsive with respto dissociation to OH1Br @see also Fig. 2~a!#, while HBrO isclearly metastable. Equipotential contour plots of the fitPES as a function ofwHBrO are shown in Fig. 4 for fixedr HBr

~4a! and RBrO ~4b!. The approach of O(1D) to HBr is ob-served to be attractive for all angles, except nearwHBrO

5180° ~oxygen oriented toward the Br end of HBr!. Figure4~b! is clearly analogous to Fig. 2~b! with respect to display-ing both the HOBr and HBrO minima near their equilibriuBrO distances. In addition, the approach of H to BrO ispulsive at bothwHBrO5180° and 0° with a barrier@see alsoFig. 2~b!# at wHBrO5;70°.

Equilibrium geometries and vibrational frequencies cculated for the analytical,ab initio PES are shown in TableIII. The equilibrium geometry of HOBr is essentially ident


t

d

-

-

cal to the values obtained from the CBS near-equilibriupotential shown in Table II, where the OH and BrO distancare slightly smaller and larger, respectively, than experimeThe anharmonic vibrational frequencies of HOBr calcula~see below for details! with the ab initio PES are in goodagreement with the accurate experimental values.20–22 TheOH stretch fundamental, however, is too large by 28.5 cm21,and the bend and BrO fundamentals differ from experimby 113.7 and 4.7 cm21, respectively. The larger error for thOH stretch is due to missing dynamical electron correlateffects in the MRCI1Q wave function, which also manifestitself in the somewhat too short equilibrium value ofr OH.The equilibrium structure of HBrO calculated on the fittePES ~Table III! is also nearly identical to the CBS neaequilibrium values of Table II. The fundamental vibrationfrequencies are calculated to be 2176, 785, and 694 cm21 forthe HBr stretch, bend, and BrO stretch, respectively. Frcomparison to the results on HOBr and HBr~see below!, the


tuith

-

6

o

ie

lie

al/to

e

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hentthe5.4

reu-will

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y

l/u


vibrational fundamentals of HBrO should be accuratewithin about 10–20 cm21. Recent experimental work by Chand Li65 proposed the observation of the HBrO isomer wvibrational frequencies of 2333 and 668 cm21. The observedtransition at 2333 cm21, however, is well outside the expected error limits of the presentab initio value~2176 cm21!and cannot be assigned to HBrO. The observed band atcm21 could possibly be assigned to the~001! BrO stretchingfundamental of HBrO, but this would imply an error of226cm21, which would be much larger than expected basedthe HOBr results.

The lowest vibrational level of HBrO is calculated to l58.5 kcal/mol above the~000! level of HOBr, and places it

FIG. 4. Equipotential contour plots of the fitted HOBr PES for fixed~a!r HBr52.75 a0 and ~b! r BrO53.25 a0 . The contour increments are 5 kcamol with the zero of energy corresponding to completely separated grostate atoms.


o

68

n

7.2 kcal/molabovethe OH1Br dissociation limit~9.4 kcal/mol with the adjusted PES, see below!. This is in contrast toHClO, where its lowest vibrational level was calculated tobelow the OH1Cl dissociation limit by 3.4 kcal/mol.36 Theisomerization transition state is calculated to lie 76.3 kcmol above HOBr when zero-point vibrations are taken inaccount ~17.8 kcal/mol above HBrO!. Anharmonic vibra-tional calculations for the TS were carried out with thMULTIMODE code ~see below for details!, which yielded animaginary frequency of 1087i cm21 at the TS. This can becompared to the value of 1124i cm21 calculated previously36

for the HOCl→HClO TS ~note that an incorrect value wainadvertently given in Ref. 36!. The equilibrium energies othe atom–diatom asymptotes relative to the HOBr minimare identical to the dissociation energies given in TableComparison of the vibrationally corrected values with eperiment, however, shows an overestimation ofD0(OH1Br)and D0(BrO1H) that is primarily due to the lack of spin–orbit effects in the present calculations~see below!. Both theequilibrium bond lengths and vibrational frequencies for tdiatomics are of similar accuracy compared to experime66

as observed for HOBr. The fundamental frequency forOH radical, however, is larger than experiment by just 1cm21, while that of HBr is too large by 11.8 cm21.

C. Adjustments of the ab initio PES

As shown in Table III, the fittedab initio PES results infundamental vibrational frequencies for HOBr that aslightly too large in comparison with experiment. Particlarly in the case of the OH stretching mode, these errorspresumably become unacceptably large for the higher~yetunobserved! overtones and combination bands. To improthe agreement with experiment for the fundamental vibtional states and provide more accurate predictions for higenergy states, small adjustments were made to the PESlowing the same strategy as in previous work on HOCl.34,36

First the HOBr minimum was shifted to the estimated expemental equilibrium geometry of Cohenet al.22 Secondly, thecoordinates were scaled67–69 as

Ri5a i~Ri2Rie!1Ri

e , ~14!

where theRi are the three internuclear distances andRie their

experimental equilibrium values. The three scaling paraetersa i ~0.991 80, 0.991 60, 0.992 35! were determined bytrial and error to give anharmonic vibrational energiesgood agreement with the known fundamental vibrationsboth HOBr and DOBr.20,23 Since the HBrO isomer has nobeen observed experimentally, no scaling has been attemfor this region of the PES, and both the geometry shift ascaling were smoothly switched off asR1 ~i.e., r OH) becamegreater than 3a0 .

The third adjustment was to correct for the HO–Br dsociation energy, which has been determined by Locket al.19

to be 17.2276350 cm21 (49.361 kcal/mol). Note that this is2 kcal/mol lower than the MRCI1Q/CBS value given inTable III. Much of this difference is due to the neglectspin–orbit coupling in the presentab initio calculations; dis-sociation to the2P3/2 state of the bromine atom is lower b

nd


.9.2.2

22

s.


Downloaded 22

TABLE III. Properties of the global fitted MRCI1Q/CBS and adjusted potential energy surfaces~all values for79Br). Values in parentheses include zero-point vibrational corrections.a

DE~cm21!

r e(OH)~Å!

Re(BrO)~Å!

r e(HBr)~Å!

ue(HOBr)~deg!

we(HBrO)~deg!

v1

~cm21!v2

~cm21!v3

~cm21!

HOBrab initio 0.0 0.9626 1.8287 102.79 3643.4 1176.3 624adj. 0.0 0.9643 1.8279 103.05 3614.9 1162.8 620Expt.b 0.0 0.9643 1.8279 103.05 3614.9 1162.6 620

HBrOab initio 61.1~58.5! 1.7101 1.4558 106.25 2175.7 785.3 694.adj. 61.1~58.6! 1.7101 1.4558 106.27 2175.2 785.7 694.

HOBr→HBrO TSab initio 79.3~76.3! 1.7248 1.8772 1.4309 46.58 61.10 2757.6 1087.4i 579.9adj. 79.3~76.3! 1.7327 1.8768 1.4278 46.39 61.48 2738.5 1100.8i 576.7

OH1Brab initio 53.9~51.3! 0.9684 3585.0adj. 51.9~49.2! 0.9701 3557.0Expt.c (49.361.0) 0.9697 3569.6

BrO1Hab initio 104.0~97.1! 1.7232 704.3adj. 104.0~97.1! 1.7232 704.3Expt.d (95.361.4) 1.7207 715.9

HBr1O(1D)ab initio 112.1~107.9! 1.4151 2570.3adj. 112.1~108.0! 1.4151 2570.3Expt.e (109.261.0) 1.4144 2558.5

aThe experimental dissociation energies include all zero-point vibrational and spin–orbit coupling effectbReference 22 for the equilibrium geometry, Ref. 22 forv1 , Ref. 21 forv2 , and Ref. 20 forv3 .cReference 19 forD0 and Ref. 66 for the OH spectroscopic constants.dDissociation energy obtained from a thermodynamic cycle employingD0(HO–Br) ~Ref. 19!, D0(OH) ~Ref.66!, andD0(BrO) ~Ref. 81!. The equilibrium bond length of BrO represents an average between the2P3/2

~Ref. 82! and 2P1/2 ~Ref. 83! values. The fundamental vibrational frequency corresponds to the2P3/2 value~Ref. 84! 1Dve(1/223/2)/2 from Ref. 85.

eDissociation energy obtained from a thermodynamic cycle employingD0(HO–Br), D0(OH), D0(HBr) ~Ref.66!, and the O(3P–1D) splitting ~Ref. 61!.

lre

rf-

ue

–he

reg

O

fuhi

infer

in

esBr.se

nott di-

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3.51 kcal/mol~Ref. 61! than thej-averaged limit~molecularspin–orbit coupling in OH adds an additional 0.2 kcal/mo!.This effect, however, is mitigated somewhat by the undetimation of D0 at the MRCI1Q/CBS level of theory~see,i.e., Table II!. This situation is very different from similawork on HOCl,34 where the combination of spin–orbit efects and errors in theab initio treatment resulted in aD0

within just 0.24 kcal/mol of the accurate experimental valIn order to make this relatively large adjustment to theabinitio D 0 of HOBr in a physically realistic manner, spinorbit coupling calculations were carried out on tHOBr→OH1Br dissociation path for fixedr OH51.83a0

and u(HOBr)5103.2°. In these calculations, which wesimilar in principle to recent work on the spin–orbit splittinof the halogen atoms~F, Cl, and Br!,70 the cc-pVTZ,cc-pVTZ1p, and cc-pCVTZ basis sets were used for H,and Br, respectively. For these calculations, anyf-type polar-ization functions were omitted from the basis sets. Theone and two-electron Breit–Pauli operator was used witthe interacting states method as implemented in theMOLPRO

program system. The spin–orbit eigenstates were obtaby diagonalizingHel1HSO in a basis of eigenfunctions oHel . The electronic wave functions employed in the det


s-

.

,

lln

ed

-

mination of the spin–orbit matrix elements were obtainedfrozen core singles-only MRCI~FOCI! calculations with atotal of 12S2 states, i.e., all of the singlet and triplet statcorrelating with the ground electronic states of OH andThe orbitals for these calculations were identical to thodescribed in Sec. II. Since the FOCI wave functions doyield very accurate state separations, the most importan

agonal elements ofHel were replaced by MRCI1Q/CBS val-ues, i.e., those corresponding to the lowest five electrostates (X 1A8, A 1A9, B 1A8, a 3A9, andb 3A8). The remain-ing diagonal elements were obtained as relative splittifrom these MRCI1Q/CBS energies using the FOCI resultSince the present calculations do not include core eleccorrelation effects, which have been shown to be veryportant in the case of Br atom,70 the lowering of theasymptotic energy due to spin–orbit coupling is less thanexperimental value by 185 cm21 ~1113 cm21 vs 1298 cm21!.In addition, while the effects of spin–orbit coupling resultan energy lowering of the ground state at the equilibriugeometry by;80 cm21 ~0.23 kcal/mol!, nearly all of thecoupling is completely quenched atRBrO distances,1.5* r e(;5 a0). An offset function, which was subsequently added to the BrO two-body energy, was then c


y

et

r

foal

r,7icd

iosere

ac

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oeenofto

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atns–6

vee

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he


structed that had the sameRBrO dependence as the energdifference between the originalRBrO cut and the lowestspin–orbit eigenstate, but scaled to reproduce the experimtal HO–Br dissociation energy. This function was chosenhave a value of zero at distances less than or equal toRBrO

53.474a0 and had the final form~bond distances in bohwith the resulting offset energy in kcal/mol!

Voff~R3!522.04$1/@0.48e24.37~R325.60!

11.15e20.87~R325.14!11#%. ~15!

The effect of this offset on the calculatedRBrO cut is shownin Fig. 5. Of course, this offset should not be appliedHBr–O configurations and hence is decayed exponentiwith HBr distance ~i.e., for r HBr,3.4a0) to mimic thequenching of the spin–orbit coupling in HBr.

Properties of this adjusted surface are also shownTable III. The zero-point vibrational energies for HOBHBrO, and the TS are calculated to be 2765, 1870, and 1cm21, respectively. In regards to the asymptotic energetonly the relative energy of the OH1Br products are changeappreciably from the unadjustedab initio PES. In addition,the geometry and vibrational frequencies of the transitstate are also slightly different due to the BrO energy offand the coordinate scaling. In particular, the imaginary fquency is increased slightly to 1101i cm21. Since the totaleffect of all adjustments was very minor, the adjusted surfis very similar to the originalab initio PES.

D. Calculation of vibrational eigenstates

The variational calculation of the HOBr and HBrO vbrational bound states (J50) was carried out using atruncation/recoupling method as described in deelsewhere.35 In these calculations the standard body-fixHamiltonian in atom-diatom Jacobi coordinates was used

FIG. 5. Illustration of the modification of the original potential along tHO–Br coordinate@r OH51.83 a0 ,u~HOBr!5103.2°# based on spin–orbitcoupling calculations.


n-o

rly

in

18s,

nt-

e

il

H3D521

2m

]2

]R221

2mAB

]2

]r 2 1S 1

2mR2 11

2mABr 2D 2

1V~R,g,r !, ~16!

where in the case of HOBr,m is the reduced mass of Br tthe center of mass of OH andmAB is the reduced mass of thdiatom defined by O and H. For HBrO, the diatom was takto be BrO andR is the distance of H to the center of massBrO. The details for these calculations are very similarthose carried out previously for HOCl/HClO.35,36For the cal-culation of the eigenstates of HOBr up to the OH1Br disso-ciation limit, at total of 8500 3D basis functions were founto be sufficient to reasonably converge the highest enebound states~i.e., within a few wave numbers!. The 3D basiswas constructed by recoupling 14 one-dimensional wfunctions forr OH, defined on an interval from 1 to 6 bohwith 1600 two-dimensional wave functions inR–g coordi-nates, whereR ~distance of Br to the center of mass of OH!was defined on the interval from 2.5 to 12 bohr andg is theJacobian angle. The two-dimensional wave functions wobtained by diagonalization of a reference 2D Hamiltonin the direct product basis of 130R by 60g wave functions.Calculations for both79Br and 81Br were carried out forHOBr. In the case of HBrO, the basis set origin was placedthe TS geometry and a total of 12 000 3D basis functiowere used. The box size was defined by intervals of 1.5bohr inR and 2–8 bohr forr BrO . Lastly, 250 2D wave func-tions in R–g coordinates were recoupled with 70 1D wafunctions for r BrO . The 2D basis was constructed from thdirect product of 70R by 70 g wave functions.

A total of 708 bound states (J50) were calculated forHOBr using the adjusted PES. The assignment of the eigstates was facilitated by inspection of coordinate expectavalues from the variational calculations, plots of the vibrtional wavefunctions, as well as by inspection of the expsion coefficients from vibrational calculations using theMUL-

TIMODE VSCF-CI code.71–74 The MULTIMODE calculationsutilized the state mixing technique75 ~V–CI! based on a vir-tual state expansion in a basis of eigenstates of a referVSCF Hamiltonian. These allowed the straightforward asignment of 89 states for HO79Br and 82 states for HO81Br.

TABLE IV. Dunham parameters~cm21! for HOBr and HBrO ~adjustedPES!.

Constant HO79Br HO81Br H79BrO

v1 3762.93 3760.60 2258.58v2 1186.11 1185.65 823.53v3 623.61 630.96 701.23x11 270.332 269.659 233.038x22 25.892 25.536 24.550x33 24.525 24.556 24.831x12 212.107 29.503 251.958x13 2.576 3.136 14.483x23 27.364 27.221 210.997y112 22.0351 21.9710y113 20.9637 21.0953y112 22.0465 23.1895 3.4970y233 0.2286 0.3379 20.3112y123 21.4083 21.8464 4.0698


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TABLE V. Selected vibrational eigenstates~cm21! and infrared intensities~km/mol! of HOBr ~adjusted PES!. Experimental values in parentheses.

HO79Br HO81BState (v1v2v3) Band origin Intensity Band origin Intensity

001 620.2 2.264 618.9 2.251~620.2!a ~619.1!a

010 1162.8 43.600 1162.7 43.606~1162.6!b ~1162.5!b

002 1231.8 0.259 1229.2 0.257~1232.4!b ~1229.8!b

011 1774.9 0.029 1773.6 0.029003 1834.8 0.019 1831.0 0.019020 2311.6 3.906 2311.4 3.906012 2379.3 0.014 2376.7 0.015021 2916.9 0.020 2915.5 0.020013 2975.7 0.001 2971.8 0.001030 3444.5 0.066 3444.2 0.066022 3514.4 0.025 3511.7 0.024014 3563.9 0.003 3558.8 0.003006 3593.8 0.002 3586.5 0.001100 3614.8 55.018 3614.8 55.020

~3614.9!c ~3614.9!c

101 4236.1 0.068 4234.8 0.068040 4563.0 0.026 4562.7 0.026110 4754.3 0.224 4754.3 0.223102 4848.2 0.021 4845.6 0.020111 5365.4 0.001 5364.1 0.001103 5451.3 0.008 5447.4 0.008120 5876.1 0.129 5876.0 0.129104 6045.4 0.021 6040.3 0.021121 6480.0 0.017 6478.6 0.016105 6630.6 0.006 6624.4 0.006060 6758.4 0.002 6757.8 0.002130 6971.3 0.834 6971.0 0.837

03610281016d 6972.5 0.006 6963.63 0.0002122 7075.1 0.817 7072.7 0.504200 7084.0 5.889 7083.8 6.205131 7571.3 0.006 7569.8 0.006201 7702.0 0.062 7700.6 0.062140 8059.4 0.006 8059.0 0.006210 8204.3 0.074 8204.2 0.074202 8311.9 0.009 8309.3 0.009211 8809.8 0.002 8807.5 0.001125d 8811.6 0.002150 9137.8 0.002 9137.3 0.002220 9292.1 0.003 9291.9 0.003221 9891.3 0.001 9889.7 0.001152 10298.3 0.004 10295.4 0.002

2301300d 10309.2 0.102 10309.0 0.1043001230d 10428.3 0.114 10428.2 0.112

136 10428.5 0.002231d 10915.7 0.007 10914.2 0.007301 11033.8 0.015 11032.3 0.014232d 11510.9 0.002 11508.2 0.001302 11632.3 0.007 11629.2 0.007303 12230.8 0.002 12226.8 0.002304 12816.3 0.009 12811.2 0.009305 13396.6 0.003 13388.5 0.002

?1400d 13430.3 0.025 13429.5 0.02213434.2 0.004

4001?d 13494.5 0.029 13494.1 0.015158d 13501.9 0.003 13490.4 0.007

13498.8 0.011330d 13656.8 0.024 13656.6 0.024261d 14026.0 0.002 14024.2 0.002331d 14092.5 0.008 14090.9 0.008

40113311261d 14242.2 0.007 14240.7 0.007332d 14683.5 0.001 14680.6 0.001402d 14825.4 0.002 14822.6 0.002


These eigenstate energies were then fit to within RMS erof 1.4 cm21~79Br! and 2.4 cm21~81Br! with standard Dunhamexpansions

G~v1 ,v2 ,v3!5(i

v ini1(i< j

xi j ninj1 (i< j <k

yi j ninjnk

1¯, ~17!

whereni5v i112. ~For HOBr v1 is the OH stretch,v2 is the

bend, andv3 is the BrO stretch.! The results of these fits arshown in Table IV. It should be noted that these coefficieare effective values and should not be equated to the unear-equilibrium spectroscopic constants. Use of these Dham expansions then facilitated the assignment of mmore bands and was particularly useful in the interpretatof heavily mixed eigenstates.

Selected eigenstates of HO79Br and HO81Br are shownin Table V along with the current state assignments. Tisotope splittings are generally very regular and amounonly about 1 cm21 per quantum of BrO stretch. As expectethere is nearly no effect on the OH stretch or bending moAs has been discussed in detail previously for HOCl,76,77

there are two types of vibrational resonances that canexpected to occur in HOBr, a 1:2 Fermi resonance betwthe bend and OBr stretch and a 3:1 resonance betweenbend and OH stretch. In the case of HOCl the former donated the spectrum while the latter was relatively unimptant. The existence of these resonances can decreasnumber of ‘‘good’’ quantum numbers from three (v1 ,v2 ,v3)to two, v1 and the polyad quantum numberP52v21v3 , orjust one, namely, 3v11P. From a cursory inspection of several HOBr vibrational wave functions, the 1:2 Fermi resnance is also important in HOBr and some of these groings can be easily observed in Table V. In fact this resonacomes into play at much lower energies for HOBr thanHOCl. At very low energies assignments can easily be maas evidenced by the nodal patterns of theab initio vibrationalwave functions shown in Fig. 6 for polyad@v1 ,P#5@0,6# asa function of the JacobiR andg coordinates. At only slightlyhigher energies, however, U-shaped or ‘‘horseshoe’’ famiof wave functions begin to emerge76,77as shown in Fig. 7 forpolyad@0, 10#, which starts at just 5668 cm21. Characteriza-tion of these wave functions is well outside the scope of twork, but has been investigated in detail for HOCl.76,77 Inaddition, since thev2 fundamental in HOBr is about 100

TABLE V. ~Continued.!

HO79Br HO81BState (v1v2v3) Band origin Intensity Band origin Intensity

4031333d 15408.2 0.002 15404.2 0.0024041334d 15984.6 0.003 15979.5 0.003

335 16405.8 0.002500d 16409.7 0.012 16409.9 0.011

3601500d 16560.2 0.006 16559.9 0.006430d 16758.6 0.002 16758.2 0.002

aReference 20.bReference 21.cReference 22.dTentative assignments due to strong state mixing.


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esa

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is

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as


cm21 smaller than that of HOCl, the 1:3 nonlinear resonanbetween the OH stretching and bending modes stronglyturbs the higher energy vibrational bands in HOBr, particlarly for v1>3, e.g., mixing between the~300! and ~230!levels. The simple Dunham model indicates that the septions of the zeroth-order (v1,0,0) and (v121,3,0) eigen-states decrease as 170, 110, 60, 25, and 10 cm21 for v1

51 – 5. This results in many uncertain assignments at higenergies due to these strong state mixings, and the attemassign vibrational quantum numbers other than the sinpolyad number 3v11P is very questionable in these case

FIG. 6. Ab initio vibrational wave functions calculated using the adjusPES belonging to the polyad@v1 ,P#5@0,6#. The vertical axis is theRJacobi coordinate (2.86a0,R,4.71 a0) while the horizontal axis is thecosine of the Jacobi angle (21.0,cosg,0.96). The energy~in cm21! andstate number are given for each level. The members of this polyad are eassigned from pure bending to pure BrO stretch levels2~030!, ~022!, ~014!,and ~006!.


er--

a-

ert tole.

The ~500! level is the highest bound OH overtone and li;800 cm21 below the OH1Br dissociation limit~6;350cm21!. This is in contrast to HOCl where the~600! level wasmeasured78 to lie 167 cm21 below the dissociation limit.

In various statistical theories of unimolecular reactidynamics,79 an important quantity is the vibrational densiof states,r(E). In the present case, a calculation of all t(J50) bound states of HOBr leads to a straightforwaevaluation of its sum of states,N(E), and its first derivative,r(E)5dN(E)/dE. In the present work, the density of statis obtained by double-sided numerical differentiation withstep size of 500 cm21.62 The derivative~density of states! atthe dissociation limit is obtained by the usual single-sidformula with the same increment, i.e.,@N(Ediss)2N(Ediss

2500)#/500. The density of states at the dissociation limitcalculated in this manner to be 0.16 states/cm21. There is asmall dependence, of course, in how this derivative is calated. A polynomial fit toN(E) over the last 2000 cm21

below dissociation leads to a density of states at the disciation limit of 0.15 states/cm21. The values calculated foHOBr are essentially identical to the density of states preously derived for HOCl of 0.2 states/cm21.35 The state countand density of states as a function of vibrational energyplotted in Fig. 8.

In the case of HBrO, where the lowest vibrational enerlevel lies above the OH1Br dissociation limit, 74 quasi-bound localized eigenstates were calculated to lie belowenergy of the isomerization transition state. This diffeslightly from the HOCl/HClO case, where the first three vbrational states of HClO were truly bound with respectOH1Cl. As in HOBr, inspection of coordinate expectatiovalues andMULTIMODE expansion coefficients led to the intial assignment of 51 out of 74 states. These were then~RMS deviation50.71 cm21) to a Dunham expansion, whicled to the coefficients shown in Table IV. Nearly all of thremaining eigenstates of HBrO could then be assignedselected number of these are shown in Table VI. Whilestates shown in Table VI are well localized within the HBrpotential well, a plot ofr HBr and r OH expectation values vsstate number, Fig. 9, demonstrates that a few states do ex

ily

ade

ethen-2.

FIG. 7. Ab initio vibrational wave functions calculatedusing the adjusted PES belonging to the poly@v1 ,P#5@0,10#. The coordinates are identical to thosof Fig. 6. The energy~in cm21! and state number aregiven for each level. While the first few members of thpolyad are easily assignable, i.e., the first two are~050! and~042! states, the higher energy members coverge toward the U-shaped wave function of level #4


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into the classically forbidden region under the TS. Neaidentical behavior was reported previously for HClO.

E. Infrared intensities

Dipole moments for HOBr and HBrO were calculatedexpectation values at the MRCI/AVQZ level of theorThose for HOBr were confined to the grid outlined in SeIII, while those of HBrO were calculated at the 41 neaequilibrium points employed for the potential energy funtions of Table II. In both cases the calculated dipole mments were rotated into Eckart reference frames,80 and theresultingmx andmy components were then fit either by cubsplines~HOBr! or polynomials in simple displacement coodinates~HBrO!. The effects of using a spline fit for HOBwere checked against near-equilibrium analytical fits anderrors were small and similar to those noted previouslyHOCl.35 Dipole moment matrix elements were computeding the eigenfunctions of the adjusted PES as discusseRef. 35. The dipole moments of HOBr in its vibrationground state are calculated to be20.080 and 1.4037 D forthe ma andmb components, respectively. These are in goagreement but slightly larger than those calculated prously at the CCSD~T! level of theory ~20.004 and 1.393D!,29 as well as the experimental values for DOBr by Koet al.,25 ma50.000(10) andmb51.384(10) D. Analogous toHOCl, the differences in the dipole moments betweHO79Br and HO81Br are completely negligible (;1026 D).

The infrared band intensities for both the79Br and 81Brisotopomers of HOBr are shown in Table V. Only transitiowith intensities greater than 0.001 km/mol are shown. Tfundamental band intensities are calculated to be 55.0, 4and 2.3 km/mol for thev1 , v2 , andv3 bands, respectivelySimilar to the HOCl case, the intensities of thev1 and v3

bands are somewhat smaller than the CCSD~T! values of

FIG. 8. Quantum sum of states,N(E), and density of states,r(E), calcu-lated for HOBr.


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Ref. 29 ~67, 42, and 10 km/mol!. There appears to besignificant amount of intensity borrowing from the pure Ostretch overtone bands starting at~200!. For example, theintensity of the~028! band is unusually large, 0.006 km/mobut it is smaller by over a factor of 20 upon substitution79Br with 81Br, which evidently detunes this resonance. T~130! and ~122! bands also appear to ‘‘borrow’’ intensitfrom the ~200! state. As mentioned earlier, at relatively loenergies it is already very difficult to make clean assigments based onv1v2v3 quantum numbers, and from TabIV it is obvious that the strong state mixing results in signicant intensity borrowing as well.

The ma and mb components of the dipole moment oHBrO in its vibrational ground state are calculated to23.392 and 0.582 D, respectively. These are similar to th

FIG. 9. Expectation values ofr OH and r HBr for HBrO eigenstates vs statenumber.

TABLE VI. Selected localized eigenstates~cm21! and infrared intensities~km/mol! of H79BrO ~adjusted PES!.

State (v1v2v3) Band origin Intensity

001 697.15 20.933010 785.75 1.872002 1378.10 1.425011 1470.99 0.178020 1567.72 0.292003 2051.95 0.010012 2145.32 1.086100 2175.18 91.403021 2243.79 0.136030 2345.19 0.079101 2886.64 0.618022 2906.51 0.030110 2919.71 0.121111 3624.62 0.017103 4277.59 0.035200 4285.78 0.652210 4986.76 0.463201 5011.00 0.353043 5038.13 0.013122 5054.50 0.027


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calculated previously for HClO,36 23.36 and 1.01 D, at thesame level of theory. As shown in Table VI, the stronginfrared transitions are those for the fundamentals, whichcalculated to be 91.4, 1.9, and 20.9 km/mol forv1 , v2 , andv3 , respectively. The value calculated for thev1 ~HBrstretch! band is about a factor of 3 larger than thev1 bandintensity in HClO. In contrast to HClO, however, the~012!level mixes only weakly with the~100! state, leading to anintensity of just 1.1 km/mol.

IV. CONCLUSIONS

A accurate, global potential energy surface for HOBr hbeen constructed using highly correlated multireferencewave functions and explicit basis set extrapolations tocomplete basis set limit. The analytic functional form faitfully reproduces theab initio data and results in an accuradescription of both HOBr and HBrO, as well as all atomdiatom dissociation asymptotes. The resulting PES is appriate for the study of the spectroscopy and unimolecudecomposition dynamics of HOBr, as well as reactive sctering calculations. After making small adjustments basedthe limited experimental data, vibrational energy levelsHOBr were calculated variationally up to the OH1Br disso-ciation limit. Where possible, assignments of these levwere made, but strong stretch–bend resonances stronglymany of the bands, destroying the usual vibrational quannumbers. None of the HBrO vibrational states are calculato be bound with respect to the OH1Br limit, but there are74 states which are localized in the HBrO potential wePermanent dipole moments and infrared intensities hbeen calculated for both HOBr and HBrO. The strong infred intensities calculated for the fundamental transitionsHBrO may facilitate the detection of this species if it cansuccessfully produced.

In regards to the O(1D)1HBr reaction, the 0 K exother-micity calculated on the adjusted PES for OH1Br products,258.8 kcal/mol, is smaller than the experimental va(260.061 kcal/mol) by just slightly more than the expermental uncertainty. In contrast, for the BrO1H productchannel, the adjusted PES yields aDH(0 K) of 210.9 kcal/mol, which is less exothermic by 361.4 kcal/mol than ex-periment. The latter error is due to a combination of tneglect of spin–orbit effects in BrO and residual errors inMRCI1Q wave function.

The analytical adjusted PES can be obtained on reqfrom the author.

ACKNOWLEDGMENTS

This work was partially supported by the Chemical Sences Division in the Office of Basic Energy Sciences ofU.S. Department of Energy under Contract No. DE-AC076RLO 1830 in the William R. Wiley Environmental Molecular Sciences Laboratory at the Pacific Northwest Ntional Laboratory. The partial support of the NationScience Foundation under CAREER award No. CH9423162 is also gratefully acknowledged. The author wolike to thank Dr. Sergei Skokov and Dr. Joel Bowman fmany helpful discussions, as well as for generously prov


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ing their truncation/recoupling code and theMULTIMODE pro-gram. The Pacific Northwest National Laboratory is a muprogram national laboratory operated by Battelle MemoInstitute for the U.S. Department of Energy under ContrNo. DE-AC06-76RLO 1830.

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an accurate global ab initiopotential energy surface for the x1a8...

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