An ab initio correlated study of the potential energy surface for the HOBr.H 2 OcomplexCristina Maria P. Santos, Roberto Faria, Sérgio P. Machado, and Wagner B. De Almeida Citation: The Journal of Chemical Physics 121, 141 (2004); doi: 10.1063/1.1755191 View online: http://dx.doi.org/10.1063/1.1755191 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/121/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A nine-dimensional ab initio global potential energy surface for the H2O+ + H2 → H3O+ + H reaction J. Chem. Phys. 140, 224313 (2014); 10.1063/1.4881943 Correlated ab initio investigations on the intermolecular and intramolecular potential energy surfaces in theground electronic state of the O 2 − ( X Π g 2 ) − HF ( X Σ + 1 ) complex J. Chem. Phys. 138, 014304 (2013); 10.1063/1.4772653 The HOOH UV spectrum: Importance of the transition dipole moment and torsional motion from semiclassicalcalculations on an ab initio potential energy surface J. Chem. Phys. 132, 084304 (2010); 10.1063/1.3317438 Ab initio potential energy and dipole moment surfaces for H 5 O 2 + J. Chem. Phys. 122, 044308 (2005); 10.1063/1.1834500 Millimeter-wave spectroscopy of the internal-rotation band of the He–HCN complex and the intermolecularpotential energy surface J. Chem. Phys. 117, 7041 (2002); 10.1063/1.1496466

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An ab initio correlated study of the potential energy surfacefor the HOBr.H 2O complex

Cristina Maria P. Santos, Roberto Faria, and Sergio P. MachadoLaboratorio de Quımica Inorganica Computacional, Departamento de Quı´mica Inorganica,Instituto de Quı´mica, Universidade Federal do Rio de Janeiro (UFRJ),Caixa Postal 68563, Rio de Janeiro, RJ, 21.945-970, Brazil

Wagner B. De Almeidaa)

Laboratorio de Quımica Computacional e Modelagem Molecular (LQC-MM), Departamento de Quı´mica,ICEx, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, 31.270-901, Brazil

~Received 19 January 2004; accepted 2 April 2004!

The potential energy surface~PES! for the HOBr.H2O complex has been investigated using second-and fourth-order Møller–Plesset perturbation theory~MP2, MP4! and coupled cluster theory withsingle and doubles excitations~CCSD!, and a perturbative approximation of triple excitations~CCSD-T!, correlatedab initio levels of theory employing basis sets of triple zeta quality withpolarization and diffuse functions up to the 6-31111G(3dp,3d f ) standard Pople’s basis set. Sixstationary points being three minima, two first-order transition state~TS! structures and onesecond-order TS were located on the PES. The global minimumsyn and theanti equilibriumstructure are virtually degenerated@DEele-nuc'0.3 kcal mol21, CCSD-T/6-31111G(3d f ,3pd)value#, with the third minima being;4 kcal mol21 away. IRC analysis was performed to confirmthe correct connectivity of the two first-order TS structures. The CCSD-T/6-31111G(3d f ,3pd)//MP2/6-311G(d,p) barrier for thesyn⇔anti interconversion is 0.3 kcal mol21,indicating that a mixture of thesyn and anti forms of the HOBr.H2O complex is likely toexist. © 2004 American Institute of Physics.@DOI: 10.1063/1.1755191#

I. INTRODUCTION

The water molecules abundance in the stratosphere andits higher absorption capacity of solar and terrestrial radia-tion have placed the hydrated complexes as a main respon-sible of the thermal and chemical changes observed on theEarth’s atmosphere. The water oxidation and the water pho-tolysis forming OH• radicals start many reaction cycles re-lated to the ozone depletion. Since they are present in highamount, the water molecules can be found on its polymericforms1–3 and also interacting with different compounds alsopresent in the atmosphere.4 Among these compounds, we canconsider the halogen species as an important group for studyonce it was directly related to the ozone depletion in thetroposphere and in the stratosphere.5–7 The catalytic reac-tions involving bromine oxide coming from sea salt accumu-lated on the Arctic snow pack, has been responsible for theincreased halogen radicals formation on ice surfaces.8 Theseunexpected higher halogen unstable radical concentrationsand the suggested participation of the ice crystal surfaces oncatalytic troposphere reactions have been justified the studyof the intermolecular interactions in the weakly bonded sys-tems involving halogen species and water molecules, object-ing to describe the solutions and ice surfaces. As the propertyis not strongly dependent to the cluster size, the solvationprocess involving only one water molecule can be consid-ered an important contribution on the hydrated cluster study.

In this context, we present theoretical results of struc-

tures, vibrational frequencies and binding energies obtainedon the association of HOBr and one water molecule, in gas-eous phase. We have used a high correlatedab initio level oftheory, i.e., coupled cluster with single and double excita-tions ~CCSD!, and also including triple excitations nonitera-tively ~CCSD-T!, employing a good quality basis set, assur-ing the reliability of our theoretical results. On the HOXhalogen compounds, the literature reports associations in-volving HOCl and 1, 2, 3, and 4 water molecules,9,10 andHOBr with 1, 2, 3, and 4 water molecules.11,12 The discus-sion of the HOBr.H2O complex has been made based on theinteraction involving the hydrogen of HOBr and the oxygenof water molecule, which is the dominant spatial arrange-ment located on the potential energy surface~PES!. In addi-tion, we also found as a true minima on the PES, besides theH-bonded species, a structure resulting from the interactionbetween the Br and oxygen atom of the water molecule.

II. METHODOLOGY

The PES for the interaction between the HOBr and H2Omonomers was comprehensively investigated using theMøller–Plesset second-order perturbation theory~MP2!13

and standard Pople’s split-valence triple-zeta quality6-311G(d,p) basis sets,14–18 including polarization func-tions on all atoms. Six stationary points being three trueminima ~all harmonic frequencies are real!, two first-ordertransition state~TS! structures~having one imaginary fre-quency! and one second-order TS~exhibiting two imaginaryfrequencies! were located on the PES, and characterizeda!Electronic mail: wagner@netuno.qui.ufmg.br

JOURNAL OF CHEMICAL PHYSICS VOLUME 121, NUMBER 1 1 JULY 2004

1410021-9606/2004/121(1)/141/8/$22.00 © 2004 American Institute of Physics

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through vibrational analysis. In a second step a coupled clus-ter with single and double excitations~CCSD!19 full geom-etry optimization and frequency calculations, using the6-311G(d,p) basis set, were performed for thesynandantiminima and the TS structures connecting them in order toassess the effect of the higher correlation approaches on thestructure and vibrational frequencies. Finally, single pointcalculations, using the fully optimized MP2/6-311G(d,p)geometries, were carried out using a highly correlated treat-ment at the MP4SDTQ~Fourth order Møller–Plesset pertur-bation theory with single, double, triple, and quadrupleexcitations!19 and CCSD-T ~coupled cluster with single,double, and noniterative triple excitations!,20 using basissets ranging from the 6-31111G(d,p) to 6-31111G(3d f ,3pd) quality. The basis set superposition error~BSSE! was accounted for using the counterpoise

method.21,22 For a more detailed discussion on the BSSEcorrection see Ref. 23~for a discussion on the effect of thiscorrection for TS structures see Ref. 24!. In this work thefrozen core option was used so inner-shells were excludedfrom the correlation calculation and, beside the fact that bro-mine is a heavy atom, no relativistic correction was consid-ered.

In order to confirm the correct connectivity of the twofirst-order TS structures an IRC~intrinsic reactioncoordinate!25,26analysis was performed. Starting with the ge-ometry of the TS structure the reaction path was followed inthe forward and reverse directions using a step size along thereaction path of 0.1 amu21/2-Bohr. The MP2/6-311G(d,p)force constants were used.

All calculation were done using theGAUSSIAN 94/98abinitio package27 as implemented on a SUN/Ultra-1, Digital/alpha-500au and SilicomGraphics R14000 workstations at

FIG. 1. Intermolecular geometrical parameters for the M1-syn, M2-anti,TS1a and TS1b structures located on the PES for the HOBr.H2O complex:RH-bond5H...Ow : Hydrogen bond distance~the subscript wI implies that theoxygen atom belongs to the water monomer!; a5Ow¯H–O angle~thehydrogen belongs to the HOBr monomer;b5H–Ow¯H angle~the hydro-gen atom of the water monomer is pointed to the out-of-paper-plane!; f5H–Ow¯O–Br torsion angle~the hydrogen atom of the water monomer ispointed to the out-of-paper-plane!.

FIG. 2. Intermolecular geometrical parameters for the M3I and TS2I struc-tures located on the PES for the HOBr.H2O complex:RBr...O5Br¯Ow :Distance between the Br and oxygen atom~the subscript wI implies that theoxygen atom belongs to the water monomer!; a5O–Br Ow angle; b5H–Ow¯Br angle~the hydrogen atom of the water monomer is pointed tothe out-of-paper-plane!; f5H–Ow¯O–H torsion angle~the hydrogen atomof the water monomer is pointed to the out-of-paper-plane!.

TABLE I. Ab initio fully optimized geometrical parameters and harmonic frequencies for the H2O and HOBr free monomers. Distances in Angstroms, anglesin degrees and vibrational frequencies in units of cm21.

MP2/6-311G(d,p)

MP2/6-31111G

(2d,2p)

MP2/6-31111G

(2d f ,2pd)

MP2/6-31111G

(3d f ,3pd)

CCSD/6-31111G

(2d,2p)

CCSD/6-31111G

(2d f ,2pd)

CCSD/6-31111G

(3d f ,3pd)

CCSD~T!/6-311G(d,p)

CCSD~T!/6-31111G

(2d,2p)

CCSD~T!/6-31111G

(2d f ,2pd)

CCSD~T!/6-31111G(3d f ,3pd) Expt.a,b

Geometrical parameters

H2OROH 0.958 0.958 0.959 0.959 0.956 0.956 0.957 0.959 0.958 0.959 0.959 0.957H–O–H angle 102.4 104.3 104.1 104.0 104.5 104.4 104.3 102.4 104.3 104.1 104.1 104.5HOBrROH 0.965 0.966 0.966 0.966 0.961 0.961 0.961 0.965 0.964 0.964 0.965 0.961RBrO 1.860 1.848 1.828 1.829 1.846 1.826 1.827 1.879 1.861 1.840 1.841 1.834H–O–Br angle 101.2 102.4 102.7 102.9 103.1 103.5 103.8 101.2 102.3 102.7 102.9 102.3

Harmonic frequencies

H2OHOH bend 1667 1661 1646 1624 1688 1674 1654 1682 1679 1665 1641 1648OH sym str 3905 3862 3873 3869 3887 3897 3894 3876 3851 3862 3856 3832OH asym str 4013 3982 3995 3988 3988 4002 3996 3970 3954 3967 3960 3943HOBrBrO str 619 628 657 653 623 654 651 575 594 625 622 620HOBr bend 1167 1199 1202 1171 1220 1222 1195 1165 1201 1206 1175 1163OH str 3840 3799 3821 3819 3865 3886 3882 3835 3817 3836 3831 3610

aExperimental values for H2O from Ref. 38.bExperimental values for HOBr from Refs. 39–42.

142 J. Chem. Phys., Vol. 121, No. 1, 1 July 2004 Santos et al.

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TABLE II. MP2 and CCSD fully optimized geometrical parameters and stabilization energies~in kcal mol21) for the stationary points located on the PES forthe HOBr.H2O complex. Distances in Angstroms and angles in degrees.a

M1MP2/6-311G

(d,p)

M1MP2/6-311

11G(2d,2p)

M1CCSD/6-311G

(d,p)

M1CCSD/6-311

11G(2d,2p)

M2MP2/6-311G

(d,p)

M2MP2/6-311

11G(2d,2p)

M2CCSD/6-

311G(d,p)

M3MP2/6-311G

(d,p)

M3MP2/6-311

11G(2d,2p)

Intramolecular parameters

H2OROH 0.960 0.960 0.958 0.957 0.959 0.959 0.958 0.959 0.959ROH ~out-of-plane! 0.960 0.960 0.958 0.057 0.959 0.959 0.958 0.959 0.959H–O–H angle 103.7 104.9 104.0 105.2 104.0 105.2 104.2 103.1 104.7HOBrROH 0.977 0.977 0.971 0.970 0.976 0.976 0.970 0.964 0.965RBrO 1.852 1.840 1.858 1.841 1.852 1.841 1.858 1.869 1.860H–O–Br angle 100.9 101.9 101.4 102.6 101.3 102.6 101.9 101.2 102.3

Intermolecular parameters

RH-bond 1.790 1.824 1.823 1.858 1.786 1.826 1.817 ¯ ¯

RBr...O ¯ ¯ ¯ ¯ ¯ ¯ ¯ 2.743 2.757a 174.1 177.7 173.9 176.9 176.4 175.2 176.7 176.8 177.4b 113.3 113.3 114.2 114.2 115.6 115.6 116.5 106.9 111.0f 59.2 58.9 58.6 59.7 121.3 116.2 118.1 125.3 122.0db 257.1 259.9 259.3 260.5 2117.8 2121.7 2119.1 2125.4 2122.7DEele-nuc 29.9 27.7 29.2 27.2 29.6 27.5 28.9 25.85 24.61DEele-nuc

BSSE 3.6 1.2 3.2 1.1 3.3 1.2 2.9 2.29 0.85DEzero 2.3 2.1 2.2 2.0 2.2 2.0 2.2 1.37 1.3D0

BSSEc 24.0 24.4 23.8 24.1 24.1 24.3 23.8 22.19 22.46

aFor the atomic labels specification and definitions see Figs. 1 and 2.bThe dihedral angled is similar tof, but measured in relation to the other oxygen atom of the water unit.cD0

DSSEc5DEele-nuc1DEele-nucBSSE 1DEzero.

TABLE III. MP2 and CCSD fully optimized geometrical parameters and stabilization energies~in kcal mol21)for the transition states~bound structures! located on the PES for the HOBr.H2O complex. Distances in Ang-stroms and angles in degrees.a

TS1aMP2/6-311G

(d,p)

TS1aMP2/6-31111G

(2d,2p)

TS1aCCSD/6-311G

(d,p)

TS2MP2/6-311G

(d,p)

TS2MP2/6-31111G

(2d,2p)Intramolecular parameters

H2OROH 0.959 0.959 0.958 0.959 0.959ROH ~out-of-plane! 0.959 0.959 0.958 0.959 0.959H–O–H angle 103.9 105.1 104.1 103.3 104.7HOBrROH 0.976 0.976 0.971 0.964 0.965RBrO 1.852 1.841 1.858 1.869 1.860H–O–Br angle 100.9 102.3 101.5 101.3 102.4

Intermolecular parameters

RH-bond 1.794 1.830 1.825 ¯ ¯

RBr...O ¯ ¯ ¯ 2.740 2.764a 175.4 178.1 176.0 178.8 177.5b 116.2 115.5 115.8 110.3 111.6f 2176.4 160.5 2179.2 58.9 117.2db 257.1 276.7 257.9 254.1 27.9DEele-nuc 29.5 27.4 28.8 25.48 24.39DEele-nuc

BSSE 3.2 1.2 2.8 2.20 0.84DEzero 2.2 2.0 2.2 1.22 1.1D0

BSSEc 24.1 24.2 23.8 22.06 22.45

aFor the atomic labels specification and definitions see Figs. 1 and 2.bThe dihedral angled is similar tof, but measured in relation to the other oxygen atom of the water unit.cD0

DSSEc5DEele-nuc1DEele-nucBSSE 1DEzero.

143J. Chem. Phys., Vol. 121, No. 1, 1 July 2004 The HOBr.H2O complex

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the Laborato´rio de Quı´mica Computacional e ModelagemMolecular ~LQC-MM!, Departamento de Quı´mica, UFMG.

III. RESULTS AND DISCUSSION

In a preliminary work28 three different interactions be-tween the water and HOBr molecules were studied. In thefirst, the interaction between the O atom of the HOBr mol-ecule and hydrogen atom of the water molecule was consid-ered and the calculations showed one structure as a localminimum with a relative energy value higher when com-pared with the other interactions. The results pointed out toan unstable structure, and it will not be considered here.Considering the other interactions, in this preliminary work ithas been found that the complexation of HOBr and H2O cantake place involving a hydrogen bonding between the hydro-gen atom of the HOBr monomer and the oxygen of water~which is expected! and also through a van der Waals bondbetween the Br atom and the oxygen atom of the H2O. Fig-ures 1 and 2 show these two plausible spatial arrangementsalong with the definition of the intermolecular geometricalparameters.

Before presenting the results of the complex it is usefulto discuss the isolated monomers, where gas phase experi-mental data is available, in order to assess the performanceof the theoretical methods used here.

Table I reports bond distances and bond angles, and alsoharmonic frequencies for the HOBr and H2O monomers, atthe MP2, CCSD, and CCSD-T levels of theory using triplezeta quality basis sets ranging from 6-311G(d,p) to 6-31111G(3d f ,3pd). The water HO distance is well predictedin all calculations, however for the description of theH–O–H bond angle a basis set of at least the 6-31111G(2d,2p) quality is necessary. Using the smaller6-311G(d,p) basis set we found a deviation of;2° fromthe experimental value. For the HOBr the behavior is similar.It can be seen that the highest level of geometry optimizationcalculation CCSD-T/6-31111G(3d f ,3pd) leads to the bestagreement with experiment, however, the MP2/6-31111G(2d,2p) level of calculation works very satisfactory andcan safely replace the much more computational expensiveCCSD-T level. Regarding the harmonic frequencies it canalso be seen that the 6-31111G(2d,2p) basis set brings animprovement over the 6-311G(d,p) one. Within the samebasis set there is a sizeable improvement on the agreementwith experiment in the order MP2, CCSD, and CCSD-T forthe water monomer. However, this behavior is not strictlyfollowed in the case of HOBr, where the MP2/6-311(d,p)

FIG. 3. MP2/6-311G(d,p) IRC calculation for the interconversion betweenthe M1-synI and M2-antiI structures of the HOBr.H2O complex through thefirst-orderTS1a structure.

FIG. 4. Side view of the MP2/6-311G(d,p) fully optimizedM1-syn, TS1aandM2-anti structures.

FIG. 5. MP2/6-311G(d,p) IRC calculation for the interconversion betweenthe two equivalentM3 structures of the HOBr H2O complex through thefirst-orderTS2 structure.

FIG. 6. Side view of the MP2/6-31111G(2d,2p) fully optimizedM3 andfirst-orderTS2 structures.

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followed by MP2/6-31111G(2d,2p) exhibit the bestagreement with experiment. The maximum difference be-tween the MP2/6-311G(d,p) frequencies and the other cal-culations is;60 cm21 for H2O and;50 cm21 for HOBr.These results provide an estimate of the precision we canexpect when applying these methods in the study of theHOBr.H2O complex, where no experimental data are avail-able for comparison. It should be noted that the most seriousdisagreement with experiment occurred for the OH stretch-ing mode of HOBr, where a difference of 221 cm21 was

observed for the CCSD-T/6-31111G(3d f ,3pd) frequencycalculation, our highest correlated level of theory implementin theab initio package used for the calculations~GAUSSIAN-

98!. Now we shall return to the HOBr.H2O complex.Tables II and III report the fully optimized geometrical

parameters and stabilization energies for the six stationarypoints located on the PES for the HOBr.H2O complex. Bothtables show that the MP2 and CCSD intramolecular geo-metrical parameters follow the same trend observed for thefree monomers. Table II is related to the M1-syn, M2-anti,

TABLE IV. MP2 and CCSD harmonic frequencies~in cm21) for the stationary points located on the PES for the HOBr.H2O complex. The normal modedescription holds for the M1, M2, and TS1a structures.

M1MP2/

6-311G(d,p)

M1MP2/6-311

11G(2d,2p)

M1CCSD/6-

311G(d,p)

M1CCSD/6-311

11G(2d,2p)

M2MP2/

6-311G(d,p)

M2MP2/6-311

11G(2d,2p)

M2CCSD/6-

311G(d,p)

TS1aMP2/

6-311G(d,p)

TS1aMP2/6-311

11G(2d,2p)

TS1aCCSD/6-311

G(d,p)Intermolecular modes

W1 : HOHwag

55 28 31i 49i 47 37 16 54i 40i 56i

W2 : dimerrock

78 67 71 61 71 67 73 69 68 64

W3 : torsion 235 217 226 207 218 198 210 230 199 216W4 : H-bondstr

238 231 229 225 228 215 218 249 229 236

W5 : HOHW

rock331 294 313 282 294 266 279 239 290 321

W7 : H-bondwag

771 737 740 707 766 731 737 678 682 612

Intramolecular modes

W6 : BrO str 629 639 608 628 631 639 612 631 639 654W8 : HOBrbend

1335 1336 1340 1348 1329 1325 1332 1364 1347 1367

W9 : HOHW

bend1657 1663 1678 1689 1653 1660 1675 1656 1660 1678

W10: OHBr str 3625 3580 3720 3699 3644 3598 3735 3639 3597 3731W11: OHW

sym str3889 3847 3901 3878 3893 3850 3904 3892 3849 3903

W12: OHW

asym str3996 3962 3994 3976 4002 3967 3999 3999 3966 3997

TABLE V. MP2 and CCSD harmonic frequencies~in cm21) for the stationary points located on the PES for theHOBr.H2O complex. The normal mode description holds for the M3, and TS2 structures.

M3MP2/6-311G

(d,p)

M3MP2/6-31111G

(2d,2p)

TS2MP2/6-311G

(d,p)

TS2MP2/6-31111G

(2d,2p)Intermolecular modes

W1 : H– OBr HOHwag 72 77 42i 46iW2 : dimer rock 95 87 97 86W3 : torsion 103 93 98 95W4 : van der Waals-bond stret. 140 129 138 125W5 : HOHW rock 280 270 255 250W6 : HOHwag 329 300 323 292

Intramolecular modes

W7 : BrO str 609 610 609 610W8 : HOBr bend 1152 1181 1148 1181W9 : HOHW bend 1659 1660 1655 1659W10: OHBr str 3849 3810 3852 3812W11: OHW sym str 3886 3846 3888 3847W12: OHW asym str 3995 3965 3999 3966

145J. Chem. Phys., Vol. 121, No. 1, 1 July 2004 The HOBr.H2O complex

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and M3 structures. The M1-syn and M2-anti represent thetwo isomers obtained with the water molecule oriented insynand in anti positions with respect to the bromine, respec-tively. The structure called M3 represents the interaction be-tween the Br and oxygen atom of the water molecule. TheH-bond distance for the M1-syn and M2-anti structures is;1.82– 1.86 Å @MP2/6-31111G(2d,2p) and CCSD/6-31111G(2d,2p) values#, being smaller than the corre-sponding experimental value for the water dimer.29 Thissame behavior was observed on HOCl.H2O and HOBr.H2OH-bond distances.9–12 TheRBr¯O van der Waals distance forthe M3 structure is 2.76 Å@MP2/6-31111G(2d,2p) value#which is 50% longer than the Br–O distance for the HOBr

monomer. The formation of hydrogen bond does not lead tosignificant changes in the monomer geometrical parameters.The water monomer geometry remains virtually unchangedupon complexation, with the maximum variation of 0.011–0.009 Å @MP2/6-31111G(2d,2p) and CCSD/6-31111G(2d,2p) values# occurring for the OH bond distance inthe HOBr subunit. The M1-syn global minimum energystructure has stabilization energy corrected for BSSE andzero-point energy (D0

BSSEc) value of ;4 kcal mol21, whichis almost degenerate with the local minima M2-anti. As ex-pected with the inclusion of the diffuse functions,30 it can beseen that there is a substantial decrease in the BSSE correc-tion on going from the 6-311G(d,p) to the 6-31111G(2d,2p) basis set, which is accompanied by a corre-sponding decrease in theDEele-nucgiving very similarD0

BSSEc

values calculated with both basis sets. The effect of improv-ing the electronic correlation to the CCSD level is to system-atically decrease theDEele-nuc by ;0.5– 0.7 kcal mol21,showing that the MP2 energies are very satisfactory to aprecision of;0.5 kcal mol21. A very welcome result is thegood agreement between the zero-point energies calculatedat MP2 and CCSD levels with the 6-311G(d,p) and 6-31111G(2d,2p) basis sets, with the largest difference being0.3 kcal mol21. Although it is known that for an improveddescription of hydrogen-bonded complexes it is necessarythe inclusion of diffuse functions in the basis set,30 as the useof CCSD~T! level of calculation,31 our D0

BSSEcresults did notshow any discrepancy which prevents the use of theMP2/6-311G(d,p) level of calculation for harmonic fre-quencies.

Two TS structures named TS1a and TS1b were locatedon the PES, but as the TS1b~bifurcated structure! is an un-bound second order TS it is not of relevance and will not beconsidered here in the interconversion between the syn andanti hydrogen bonded structures. The first-order TS1a struc-ture present energy value close to the energy obtained for theM1-syn and M2-anti structures. This low energy differencebetween the TS1a energy and M1 or M2 energy imply thatthere is a free rotation of the proton-acceptor water moleculeabout the O–O line. The nonhydrogen bonded complex, M3structure, is;2 kcal mol21 (D0

BSSEcvalue! above the globalminimum M1-synstructure and so, at room temperature andnormal pressure may not be relevant at equilibrium. The TS2structure, responsible for a tunneling motion, provides a verysmall barrier of less than 0.5 kcal mol21 for an interconver-sion between two equivalent configurations.

Figure 3 shows the MP2/6-311G(d,p) IRC calculationfor the M1-syn⇔M2-anti interconversion through the TS1astructure, with the side view of each structure showed in Fig.4. Figure 5 shows the MP2/6-311G(d,p) IRC calculation forthe TS2 and M3 structures and Fig. 6 exhibits a side view ofeach structure. The reason of performing the IRC calculationfor TS1a and TS2 is to confirm that they are correctly con-nected recpectively to the M1-syn and M2-anti, and M3structures. Analyzing the IRC plots it can be seen that this isreally true. The IRC gave an interesting result particularly forthe TS1a structure that coud not be conceived only on intui-tive chemical grounds. This is an example that

FIG. 7. MP2/6-31111G(2d,2p) intermolecular normal modes for thesyn~a! andanti ~b! dimers.

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care is needed when is searching for TS structure on the PESfor weakly bound complexes.

The MP2 and CCSD harmonic frequencies are reportedin Tables IV and V. The CCSD calculations were performedfor the M1-syn, M2-anti and TS1a structures only, which arethe most relevant ones. The vibration attributions followedthe description given previously by Ying and Zhao.11 Theintramolecular modes follow the same trend observed for thefree monomers with respect to the level of correlation andbasis set. As can be seen from Table IV, the larger shifts inthe monomer frequencies upon complexation~M1-syn andM2-anti structures! occurred for the OHBr stretching andHOBr bending modes. The MP2/6-31111G(2d,2p) andCCSD/6-31111G(2d,2p) shift values for the M1-synstructure are, respectively,2219 and2166 cm21 (OHBr str)and 137 and 128 cm21 ~HOBr bend!. The maximum shiftobserved for the water dimer modes are for the asymmetricstretching mode @220 and 212 cm21, MP2/6-31111G(2d,2p) and CCSD/6-31111G(2d,2p) values, respec-tively#. For the M3 structure the Table V shows that thelargest shift was observed for the symmetric and asymmetricOH stretching of the water monomer, i.e.,216 and217 cm21, respectively@MP2/6-31111G(2d,2p) value#.As the van der Waals intermolecular distance is very largethe monomers are practically unperturbed upon complex-ation.

The intermolecular vibrational modes, which harmonicfrequencies are given in Table IV, are depicted in Fig. 7 forthe M1-synand M2-anti minimum energy structures, show-ing the side and front views, respectively. The low frequencybridge vibration can be promptly recongnized by the H-bondstretching mode~No. 4!. This O–H stretching mode well

represent the large anharmonicity present in the hydogenbonded complexes that was dued to the weakness of the hy-drogen bond and the small mass of hydrogen atoms, causingrelative displacements of individual nuclei from their equi-librium positions.32,33 It can also be observed that modes 1and 5 involve basically a rotation of the water subunit aroundthe H-bond axis and an axis perpendicular to it, respectively,with no participation of the HOBr monomer. The other threemodes~No. 2, 3, and 6! involve a coupled vibration of thehydrogen atom of the HOBr and a rotation of the watermonomer. This analysis can raise an interesing question ofthe validity of the harmonic approximation for such low fre-quency modes. This subject has been addressed for the waterdimer34,35case and is under investigation in our group. It canbe noted from Table IV that the CCSD frequencies for theglobal minimum M1-syn structure is slightly negative butpositive for M2-anti complex. As the lowest frequency has avery small value such fluctuations can take place, and wehave shown in other applications involving weakly bounddimers that by increasing the basis set the lowest frequencyfor the true minimum becomes real.36

Finally, Table VI reports Post-Hartree–Fock highly cor-related single point calculations, using theMP2/6-311G(d,p) geometries and zero-point energies, forfive of the six stationary points located on the PES for theHOBr.H2O complex. The convergence of the BSSE ispromptly seen for the H-bond structures, starting with a highvalue of;3.5 kcal mol21 with the 6-311G(d,p) basis set areaching the lowest value of;1 kcal mol21 with the 6-31111G(3d f ,3pd) basis set, which is still a sizeable value. Itcan be also seen from Table VI that theDEele-nuc valuesvirtually converged with the latter basis set at MP2, MP4,

TABLE VI. Ab initio supermolecule binding energies (DEele-nucgas , in kcal mol21)a for a gas phase isolated complex in the vacuum and the corresponding BSSE

correction values (DEele-nucBSSE , in kcal mol21).b The best CCSD-T stabilization energy value for the HOBr.H2O complex, corrected for zero-point energy

@MP2/6-311G(d,p) value# and BSSE (D0BSSEc in kcal mol21), is given in the last column in brackets.

Single point stabilization energy values@MP2/6-311G(d,p) optimized geometry#Basis set 6-311G(d,p) 6-31111G(d,p) 6-31111G(2d,2p) 6-31111G(2d f ,2pd) 6-31111G(3d f ,3pd)

Correlation level DEele-nucgas DEele-nuc

BSSE DEele-nucgas DEele-nuc

BSSE DEele-nucgas DEele-nuc

BSSE DEele-nucgas DEele-nuc

BSSE DEele-nucgas DEele-nuc

BSSE

MP2: M1syn 29.9 3.6 28.0 2.3 27.6 1.4 27.8 1.3 27.8 1.2MP4~SDQ!: M1syn 29.2 3.3 27.6 2.1 27.1 1.3 27.3 1.2 27.3 1.1MP4~SDTQ!: M1 syn 29.7 3.6 28.0 2.4 27.6 1.4 27.8 1.4 27.8 1.2CCSD: M1 syn 29.1 3.3 27.6 2.1 27.2 1.2 27.3 1.2 27.3 1.0CCSD~T!: M1 syn 29.5 3.5 28.0 2.3 27.6 1.4 27.8 1.3 27.8

27.8c

@24.4#d

1.11.0c

CCSD~T!: M2 anti 29.2 3.1 28.0 2.3 27.4 1.4 27.5 1.3 27.527.5c

@24.2#d

1.11.0c

CCSD~T!: TS1a~first order! 29.2 3.2 27.9 2.3 27.4 1.3 27.5 1.3 27.527.5c

@24.2#d

1.11.0c

CCSD~T!: M3 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ 24.06@22.1#d

0.58

CCSD~T!: TS2 ~first order! ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ 23.83@22.0#d

0.58

aDEele-nucgas 5Eele-nuc

gas (HOBr H2O)2@Eele-nucgas (HoBr)1Eele-nuc

gas (H2O)#.bThe BSSE corrected energies are given by the expressionDEele-nuc

gas-BSSEc5DEele-nucgas 1DEele-nuc

BSSE .cCCSD~T!/6-31111G(3d f ,3pd)//MP2/6-31111G(2d,2p) value.dD0

BSSEc5$DEele-nucCCSD-T/6-31111G(3d f ,3pd)1DEele-nuc

BSSE %1DEzeroMP2/6-311G(d,p) .

147J. Chem. Phys., Vol. 121, No. 1, 1 July 2004 The HOBr.H2O complex

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CCSD, and CCSD-T levels of theory, also showing that thereis little improvement on going beyond MP2 level with theour largest basis set. From these results it can be seen that theelectronic correlation effects are satisfactorily accounted forat the MP2/6-31111G(3d f ,3pd) level and that there is noneed to use higher correlated methods that would describemore appropriately the dispersion contribution to the corre-lation energy. An example of such a case is the weakly boundvan der Walls (PCCP)2 dimer37 where there is a significantdiscrepancy between the MP2 and CCSD-T interaction ener-gies. A more useful quantity is the zero-point BSSE cor-rected interaction energy (D0

BSSEc) which can be experimen-tally accessible. Our best gas phase theoretical values arereported in the last column of Table VI in brackets@CCSD-T/6-31111G(3d f ,3pd) results#. From these re-sults it can be seen that the M1-syn structure is preferredover the M2-anti one by a marginal amount of0.2 kcal mol21 and that there is no barrier at all for the in-terconversion starting from the M2-anti species. In additionthe M3 structure is;2 kcal mol21 (D0

BSSEcvalue! disfavoredin relation to the M2-anti dimer, however having no plau-sible interconversion pathway to theanti or syn minimawithout involving a higher energy TS structure.

IV. CONCLUSION

In this article we reported a high level correlatedabinitio study of the PES for the HOBr.H2O, including har-monic frequency calculations and BSSE correction using thecounterpoise method, employing standard Pople’s basis setranging from 6-311G(d,p) to 6-31111G(3d f ,3pd) andelectron correlation effects up to the CCSD-T level. Thereare six stationary points on the PES, being thesynandantiH-bonded minimum energy structures, along with the first-order TS1a structure connecting the two minima, the mostrelevant ones. An IRC calculation was performed confirmingthat the TS1a is the correct TS structure connecting thesynand anti minima, providing an energy barrier corrected forBSSE and zero-point energy (D0

BSSEc) of only 0.2 kcal mol21

@CCSD-T/6-31111G(3d f ,3pd) value#. We found that forthe HOBr.H2O dimer improving the level of electron corre-lation to the CCSD-T level, using our best basis set, does notmodify substantially the corresponding MP2 energy values,so the MP2 level of correlation is sufficient for the descrip-tion of the HOBr.H2O complex. This result shows that aproper description of the dispersion energy, what would re-quire a high level of correlation theory such as CCSD-T, isnot necessary in this specific case. Our results, therefore,provide a conclusive description of the PES for theHOBr.H2O complex complementing substantially the previ-ous study reported in the literature,11,12 where only thesynandanti isomers were considered.

ACKNOWLEDGMENTS

The authors would like to thank the Brazilian agenciesCNPq ~Conselho Nacional de Desenvolvimento Cientı´fico eTecnologico!, FAPEMIG ~Fundac¸ao de Amparo a` Pesquisa

do Estado de Minas Gerais!, FUJB ~Fundac¸ao Jose´ Bonifa-cio!, and Fundac¸ao Jose´ Pelucio Ferreira for financial sup-port.

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148 J. Chem. Phys., Vol. 121, No. 1, 1 July 2004 Santos et al.

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