Theoretical Investigations of the Gas-Phase Dimers (CH 4, HX), X ) F, Cl, Br

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1 J. Phys. Chem. A 1998,, Theoreticl Investigtions of the Gs-Phse Dimers (CH 4, HX), X ) F, Cl, Br Asit K. Chndr* nd Minh Tho Nguyen* Deprtment of Chemistry, UniVersity of LeuVen, Celestijnenln 0F, B-3001 LeuVen, Belgium ReceiVed: April 8, 1998; In Finl Form: June 5, 1998 Ab initio clcultions hve been crried out t the MP)full level with G(3df,p) bsis functions to determine the equilibrium geometries nd binding energies of the 1:1 gs-phse complexes between CH 4 nd HX (X ) F, Cl, Br). Single-point MP4 clcultion t the MP optimized geometry hs lso been performed to include the effect of higher order electron eltion in the binding energy. Contrry to the erlier experimentl nd low-level theoreticl investigtions, it is observed tht the nonconventionl hydrogen-bonded structure is the most stble complex for ll the three hydrogen hlides. This occurs when the proton of HX forms wek hydrogen bond to the center of one of the methne tetrhedrl fces to form symmetric top C 3V dimer. Symmetry-dpted perturbtion theory (SAPT) nlysis hs been crried out to understnd the nture of the forces involved in the bonding nd lso to exmine how different interction energy components vry with the chnge in intermoleculr distnce. It hs been observed tht the binding energy of the (CH 4, HX) dimer decreses in the order > HCl > HBr. 1. Introduction The complexes between methne nd hydrogen hlides re of recent experimentl nd theoreticl interest. 1-5 From the pulsed-nozzle Fourier trnsform microwve spectroscopy, Legon nd co-workers observed tht the equilibrium structure of the (CH 4, ) dimer is different from the equilibrium structure of the (CH 4, HCl) nd (CH 4, HBr) 4 dimers. In the cse of the complex, the equilibrium structure is conventionl hydrogenbonded structure, where the fluorine tom of forms wek bond with the hydrogen tom of CH 4 (structure of Figure 1), wheres in the cse of HCl nd HBr, it is the nonconventionl structure, b in Figure 1, which is the most stble. The proton of HCl or HBr forms wek hydrogen bond to the center of one of the methne tetrhedrl fces to yield symmetric top C 3V dimer CH 4 HX. Similr observtion ws mde erlier by Dvis nd Andrews 1 from infrred spectroscopy experiments on noble gs mtrixes nd b initio clcultions t the Hrtree- Fock level with 6-31G(d,p) bsis functions. Subsequent theoreticl clcultions by Nguyen et l. 6 t the MP/6-311G(d,p) level of theory supported the observtions mde from the experiment bout the contrsting behvior of (CH 4, ) nd (CH 4, HCl) dimers. However, the theoreticl clcultions t the sid level fil to explin the observed low-frequency shift of the H-X stretching vibrtion in the complex compred to the free HX. Moreover, Legon nd co-workers estimted tht the (CH 4, ) dimer should hve greter binding strength thn the (CH 4, HCl) dimer, wheres theoreticl clcultions t MP/6-311G(d,p) predict much weker complex compred to the HCl complex. Thus experiment nd theoreticl clcultions t the MP/6-311G(d,p) level predict the sme overll optimum geometry of the (CH 4, ) dimer. But, they differ significntly with respect to the other observtions mentioned bove. These disgreements between experiment nd theoreticl clcultions might hve two origins. First, to obtin resonble equilibrium * Corresponding uthor. Emil: sit.chndr@chem.kuleuven.c.be. Fx: Figure 1. Possible structures for the (CH 4, HX) dimers, X ) F, Cl, Br. structure for very wek complex, one needs to include electron eltion nd bsis set tht is flexible enough to tke cre of ll the importnt interction energy components. Second, the experimentl geometry is lwys vibrtionlly verged, nd thus one-to-one comprison between experiment nd theoreticl clcultion does not mke ny sense. Now, the bsis sets used in erlier theoreticl studies re obviously not suitble for studying wek moleculr complex. It is well-known tht diffuse functions nd multiple polriztion functions re indispensble for the study of wek complexes. 7 Moreover, nticipting tht the dispersion energy might ply n importnt role in these wek complexes, it is necessry to include higher ngulr momentum polriztion functions in the bsis set. In view of the bove-mentioned disgreement between theoreticl nd experimentl observtions for the (CH 4, ) complex, we feel tht it is necessry to study this system by more ccurte theoreticl techniques. In ddition, present study hs been extended to the HCl nd HBr complexes with CH 4 t the sme level of theory for resonble comprison of these complexes. To our knowledge, there hs been no theoreticl study to dte on the (CH 4, HBr) system. Interction energy component nlysis bsed on symmetry-dpted perturbtion theory (SAPT) S (98) CCC: $ Americn Chemicl Society Published on Web 07/31/1998

2 6866 J. Phys. Chem. A, Vol., No. 34, 1998 Chndr nd Nguyen hs been performed to understnd the forces involved in these dimers nd how they differ from one complex to the other. Moreover, SAPT nlysis hs lso been performed for both conventionl nd nonconventionl forms of the (CH 4, ) dimer to understnd how they differ in the nture of interction.. Computtionl Detils Geometries of the monomers, CH 4 nd HX (X ) F, Cl, Br), nd dimers (CH 4, HX) were fully optimized t second-order Moller-Plesset perturbtion theory (MP) level including ll the electrons nd using two bsis sets: G(d,p) nd G(3df,p). The bsis sets were tken directly from the Gussin progrm librry. Hrmonic vibrtionl frequencies were clculted t the sme level of theory nd using the sme bsis set to chrcterize the sttionry point nd to clculte the frequency shift due to complex formtion. Single-point MP4)full/ G(3df,p)//MP)full/ G(3df,p) clcultions were lso performed for the nd HCl complexes with CH 4 to include the higher order electron eltion effect on binding energy. MP4 clcultions for the HBr complex could not be performed owing to limittions in our computer resources. Single-point MP)full/ G(3df,pd) clcultions using f- nd d-exponents s proposed in ref 7 (f(c) ) 0.11, f(f) ) 0.75, f(cl) ) 0.15, nd d(h) ) 0.1) were lso performed on (CH 4, ) nd (CH 4, HCl) dimers. All the supermoleculr b initio clcultions were performed by using the Gussin 94 progrm. 8 Interction energy component nlysis ws performed by following the technique of symmetry-dpted perturbtion theory (SAPT), 9, nd clcultions were done by using the SAPT progrm. 11 Bsis set superposition error ws estimted by the counterpoise (CP) method of Boys nd Bernrdi Results nd Discussion 3.1. Structure nd Energetics. Although there re mny possible structures for the dimeric systems (CH 4, HX), erlier theoreticl 6 nd experimentl studies 1-3 identified the structures nd b in Figure 1 re the most probble structures for these complexes. The present study is restricted to these two forms. Experimentl studies predicted tht the structure of the (CH 4, ) dimer is similr to the structure in Figure 1 with conventionl hydrogen bond between the fluorine tom of nd the hydrogen of CH 4. Similr conclusions were reched by theoreticl clcultions t the MP/6-311G(d,p) level. 6 Contrry to these observtions, our clcultions t the MP)full/ G(3df,p) level show tht the nonconventionl structure (structure b in Figure 1) is much more stble thn the conventionl one for the (CH 4, ) dimer. In fct, the structure is found to be trnsition stte with one negtive frequency nd energeticlly fr less stble (by 0.99 kcl/mol) thn the structure b. Single-point MP)full/ G(3df,pd) clcultions using f- nd d-exponents s proposed by Chlsinski nd Szczesnik 7 for better estimtion of dispersion energy show structure b is 1.00 kcl/mol more stble thn structure. The optimized H X distnce in structure is.7 Å, nd the distnce between the crbon tom nd the hydrogen tom of is found to be 4.30 Å. These geometricl prmeters re not much different from those predicted by Dvis nd Andrews, 1 but they differ significntly from those obtined by Nguyen et l. 6 nd Legon nd co-workers. Structure b, where the proton of forms wek bond to the center of one of the tetrhedrl fces with ner C 3V symmetry, is thus found to be the most stble structure for the (CH 4, ) dimer. Similr observtions were lso mde from the MP)full/ G(d,p) level of TABLE 1: Optimum Hydrogen Bond Length, R (See Structure b in Figure 1), Dipole Moment (µ in D), nd Rottionl Constnts (B nd C in GHz) Obtined from the MP)full/ G(3df,p) Clcultions for the (CH 4, HX) Dimers complex R (Å) µ rottionl constnt CH (.51) ( ) ( ) CH 4-HCl.49 (.68) (.94 39) ( ) CH 4-HBr.56 (.76) (.3 9) (. 41) The quntities in prentheses re those obtined from the MP)full/ G(d,p) level of theory. Monomer geometricl prmeters t the MP)full// G(3df,p) level re C-H, Å; H-F, Å; H-Cl, Å; nd H-Br, 1.41 Å. TABLE : Binding Energies (kcl/mol) without ( E) nd with ( E c ) BSSE Correction, ZPVE (kcl/mol), nd Low-Frequency Shift ( ν in cm -1 ) in the H-X Stretching Vibrtion As Obtined from Supermoleculr MP)full/ G(3df,p) Clcultions for the Structure b in Figure 1 complex MP MP4 (structure) E b E c ZPVE E E c ν c CH 4-(b) [.14] d [1.31] (1.43) (0.73) (1.8) (39) CH 4-() [0.75] d [0.31] (0.50) (0.14) CH 4-HCl(b) [3.05] d [1.04] (1.4) (0.46) (0.80) (04) CH 4-HBr(b) (1.07) (0.6) (0.69) (03) Binding energy of the structure in Figure 1 of the CH 4- dimer is lso included in the tble. Vlues in prentheses re those obtined from the MP)full/ G(d,p) level. MP4)full/ G(3df,p) clcultions were crried out t the optimized geometry obtined t the MP)level of theory. b E ) E A + E B - E AB. c Frequencies t the MP level of theory. d Obtined from single-point clcultions t the MP)full/ G(3df,pd) level using the following f- nd d-function exponents for hevy toms nd H-tom, respectively: f(c) ) 0.11, f(f) ) 0.75, f(cl) ) 0.15, nd d(h) ) 0.1. theory. Severl geometry optimiztions for the (CH 4, ) dimer strting from geometry predicted by Legon nd co-workers using different bsis sets were performed. But ny sttionry point similr in geometry to tht predicted by these uthors could not be locted. The equilibrium structures for the (CH 4, HCl) nd (CH 4, HBr) dimers re like tht shown in Figure 1b, which re lso similr to tht predicted from the experiments. Thus ll the three hydrogen hlides form nonconventionl hydrogenbonded complex with CH 4. Tbles 1 nd show the optimized intermoleculr distnce (R in structure b of Figure 1), rottionl constnts, binding energies, nd H-X stretching vibrtionl frequency shift in the complex for ll the three (CH 4, HX) dimers. The most striking observtion from Tble 1 is the chnge in the equilibrium intermoleculr distnce R with the chnge of bsis functions from G(d,p) to G(3df,p). The ddition of extr polriztion functions in the bsis set brings the two monomers closer to ech other by lmost 0. Å. This is surely due to the fct tht the dispersion energy is better estimted in the cse of G(3df,p) bsis set, which will be more cler when we look t SAPT energy component nlysis in the next section. To test the convergence of the optimum intermoleculr distnce R (Figure 1b) with respect to the bsis size,

3 Investigtions of the Gs-Phse Dimers (CH 4, HX) J. Phys. Chem. A, Vol., No. 34, dditionl geometry optimiztions were performed t the MP level for the structure b of CH 4 - using G(d,p), G(df,p), nd G(df,pd) bsis sets. It hs been observed tht the distnce R vries within.30 to.3 Å. The optimum intermoleculr distnce (R o ) of the (CH 4, HX) complexes increses in the order < HCl < HBr. The C X distnces obtined from the experiment for the HCl nd HBr complexes re nd 4.14 Å, respectively, wheres the theoreticl vlues obtined t the MP)full/ G(d,p) level re nd Å nd those t MP)full/ G(3df,p) level re nd Å for the HCl nd HBr complexes, respectively. As mentioned erlier the experimentl geometries re vibrtionlly verged nd re, thus, not directly comprble with the theoreticl vlues. It is expected tht not-removed BSSE during supermoleculr clcultions lso shortens the intermoleculr distnce R. To check this effect, severl single-point clcultions were performed round the supermoleculr optimized vlue of R (.33 Å) for the CH 4 - system. It ws observed tht the BSSE ected supermoleculr interction energy ttins its mximum vlue t R ).37 Å, which is 0.04 Å longer thn the optimum vlue of R obtined from the supermoleculr clcultions. However, it is cler tht the intermoleculr distnces obtined from lrger bsis set clcultions re shorter thn the experimentl vlues, wheres those obtined from the smller bsis set re firly closer to the experiment. Rottionl constnts re lso significntly different from those obtined from the experiment. Monomer geometries re found to be virtully unchnged in the complex. The highest chnge observed for the H-F bond length in the (CH 4, ) dimer mounts to 0.00 Å. In ll the (CH 4, HX) complexes, the C-H b (see structure b in Figure 1) distnce is found to be sme s the C-H distnce in free CH 4, wheres the other three C-H bonds increse by n mount of Å in the complex. It is cler from Tble tht the binding energies of these complexes decrese in the order > HCl > HBr. The sme trend ws predicted by Legon nd co-workers. However, if one ssumes bent geometry (structure in Figure 1) for the (CH 4, ) dimer, then the HCl complex is more stble thn the complex. This is the reson Nguyen et l. 6 hd obtined the HCl complex s fr more stble thn the complex. Tble lso shows tht use of f- nd d-exponents for hevy toms nd H-tom s proposed in ref 7 for better estimtion of dispersion energy hs very little effect on the binding energies obtined by using the G(3df,p) bsis tken directly from the Gussin librry. MP4 results re lso included in the Tble. It is cler tht there is no significnt effect of higher order electron eltion on the binding energies of these complexes. In mtrix isoltion experiment, Dvis nd Andrews 1 observed downshift of 3 cm -1 in the H-F stretching vibrtion following complex formtion, wheres Pulson nd Brnes 13 noticed downshift of 16 cm -1 in the H-Cl stretching mode. MP/6-311G(d,p) clcultions show reverse trend. 6 However, present clcultions indeed show low shift of H-X stretching frequency due to complex formtion with CH 4. The shifts obtined from our best clcultions re 4, 17, nd 8 cm -1 for the, HCl, nd HBr, respectively. The experimentl vibrtionl frequency includes the effect of nhrmonicity nd re, thus, not comprble with the frequencies obtined from hrmonic pproximtions. However, if we ssume tht nhrmonicity would be sme in free H-X nd in the complex, then hrmonic shift should provide n estimte of the frequency shift due to complex formtion. The low-frequency shifts re more Figure. Chnge in reltive energy (E - E o in kcl/mol) with the chnge in intermoleculr distnce R (in Å) for the CH 4-HX (X ) F, Cl, Br) complexes. Energies re clculted t the MP)full level with G(3df,p) bsis functions. t the MP)full/ G(3df,p) level compred to those obtined from the MP)full/ G(d,p) clcultions. For prticulr bsis set, the H-X frequency shift decreses in the order > HCl> HBr, which is lso the order of their interction energy with CH 4. It ws lso observed from our clcultions tht IR-inctive C-H stretching vibrtion of CH 4 becomes wekly ctive in the complex nd the trnsition intensity is highest for the (CH 4, ) dimer. This shows tht the lignd produces enough symmetry in the CH 4 molecule of the complex to mke the C-H stretching mode wekly ctive. The frequencies relted to the vrious vibrtionl modes of the CH 4 submolecule in the (CH 4, HX) complexes remin virtully unchnged to the esponding free CH 4 vlues. Figure displys the intermoleculr potentil for the (CH 4, HX) dimers. The potentil hs been clculted t the MP)full/ G(3df,p) level nd keeping ll the geometricl prmeters but R (Figure 1b) fixed t the respective optimized vlues. 3.. SAPT Anlysis. A prtitioning of the interction energy into vrious physiclly meningful prts such s electrosttic, exchnge repulsion, induction, nd dispersion hs been performed using the symmetry-dpted perturbtion theory (SAPT). Only brief description of the pproch is given here in order to clrify the points relevnt to the present clcultions (for detils bout the SAPT pproch, see refs 14-16). The interction energy in SAPT is defined directly s the sum of physiclly distinct polriztion nd exchnge contributions ) E pol + + E () () pol + + where E pol is the clssicl electrosttic energy nd E () pol is the sum of clssicl induction nd quntum mechnicl dispersion (n) energies nd, n ) 1,, re exchnge ections. The ltter represents the effect of the resonnce tunneling of electrons between the intercting systems. Electron eltion effects on the first-order exchnge contribution were pproximted by ɛ exch ) E (11) exch + E (1) exch + exch (CCSD) The first nd second-order cluster opertors in the expression (1) for re replced by converged coupled-cluster opertors, 17 leding to sum of higher order terms (in terms of intrmoleculr eltion) denoted by exch (CCSD). The effect of monomer electron eltion on electrosttic interction is estimted up to third order nd expressed s

4 6868 J. Phys. Chem. A, Vol., No. 34, 1998 Chndr nd Nguyen (1) ),resp ɛ pol (13) +,resp The interction energies were clculted using the following pproximtions: ) E () pol + ɛ pol ) E () exch + E (11) exch + E (1) exch + exch (CCSD) () -ind () () ) E ind () + E ind () () ) -ind.resp + -ind ) E () disp + E (1) () disp + () () -disp ) -disp Superscripts (ij) in the bove expressions refer to the order of the intermoleculr interction opertor nd the intrmoleculr eltion opertor, respectively (see ref for more detils). Present SAPT clcultions were terminted t second order with respect to the intermoleculr interction potentil. Induction nd dispersion components were estimted up to second order of monomer eltion. The l interction energy of the complex cn be estimted s 18 E int ) E int + where E int is the supermoleculr Hrtree-Fock interction energy nd in the present clcultion E int is expressed s (1) ),resp (13) +,resp + E ind () () + ɛ exch + + () () + + E ex-disp These expnsions ccount for the so-clled response for the perturbtion-induced modifiction of the moleculr orbitls. 18 E int were clculted with dimer-centered bsis set to void ny BSSE. The present SAPT clcultions for the (CH 4, ) nd (CH 4, HCl) dimers were performed by using the G- (df,p) bsis functions. The monomer geometries used in the SAPT clcultions re C-H, Å; H-F, Å; H-Cl, Å. The clcultions were performed t vrious vlues of R for the structure b in Figure 1. The sme nlysis for the HBr complex could not be performed owing to limittions in our computer resources. However, we observed from the SAPT nlysis using smller bsis functions such s G(d,p) tht the generl trend of vrious energy components is the sme for the HCl nd HBr complexes of CH 4. Tbles 3 nd 4 present the vrious interction energy components for the nd HCl complexes of methne t different vlues of R. At shorter R, the repulsive exchnge interctions re more for the HCl complex nd they decy fster thn the complex. Induction forces re not much different for the two complexes, nd they decy lmost in similr wy with the increse in R. E () pol is significntly lrger for the HCl complex when R < R o (R o is the optimum vlue of R). It decys fster thn for the complex, nd the difference between them is very smll t R. R o. Compred to the complex, the dispersion components re substntilly lrger for the HCl complex, prticulrly t smller R. For both the complexes, dispersion is the mjor ttrctive force t equilibrium. At equilibrium (R ).60 Å), the CH 4 -HCl complex is repulsive t the Hrtree-Fock level nd the whole stbiliztion energy TABLE 3: Components of Interction Energy (in kcl/mol) s Functions of the Intermoleculr Distnce R (See Structure b in Figure 1) for the CH 4 - Complex R (Å) ɛ exch ɛ pol E ex-disp sm BSSE ected supermoleculr interction energy (E sm int )tthe MP)full/ G(df,p) level is lso given in the tble. TABLE 4: Components of Interction Energy (in kcl/mol) s Functions of the Intermoleculr Distnce R (See Structure b in Figure 1) for the CH 4 -HCl Complex R (Å) ɛ exch ɛ pol E ex-disp sm BSSE ected supermoleculr interction energy (E sm int )tthe MP)full/ G(df,p) level is lso given in the tble. of the complex comes from the elted prt of the interction energy in which dispersion is the min contributor. At R ).60 Å, the E () ind nd E (1) pol re only -0.0 nd -0. kcl/mol, respectively, for the HCl complex, nd thus the dispersion is the min binding force t equilibrium. The mjor contribution to binding energy t the elted level for the CH 4 - complex lso comes from the dispersion force becuse the (1) contribution from the other two stbilizing components nd E () ind re negligible t equilibrium. The importnce of the dispersion force cn be relized from closer look t the Tbles 3 nd 4. At the Hrtree-Fock level the interction energy minim pper t R ).60 nd 3.00 Å for the nd HCl complexes, respectively, wheres inclusion of higher order (in terms of electron eltion) contributions to electrosttic, induction, exchnge, nd dispersion components (expressed s E int ) brings the minim t R ).40 nd.60 Å for the nd

5 Investigtions of the Gs-Phse Dimers (CH 4, HX) J. Phys. Chem. A, Vol., No. 34, TABLE 5: Vrition of Components of Interction Energy (in kcl/mol) with the Chnge in Bsis Set from G(d,p) (Bsis A) to G(df,p) (Bsis B) for the CH 4 - (t R ).50 Å) nd CH 4 -HCl (t R ).70 Å) Complexes CH 4- CH 4-HCl Bsis A Bsis B Bsis A Bsis B Figure 3. Chnge in Hrtree-Fock interction energy, eltion energy components of interction energy, nd l interction energy (in kcl/mol) for the CH 4-HX (X ) F, Cl) complex. HCl complexes, respectively. But s lredy mentioned, t equilibrium, the contribution from induction nd electrosttic components is negligible t elted level for both the complexes nd thus mjor contribution comes from dispersion. Figure 3 shows clerly the importnce of dispersion forces in determining the minimum vlue of R. Nevertheless the importnce of ɛ exch should lso be emphsized. Without this exchnge contribution, the potentil well t equilibrium would be overestimted by n mount of 0.3 nd 0.17 kcl/mol for the nd HCl complexes, respectively, which is 5% nd % of their stbiliztion energy t equilibrium. This clerly shows the indequcy of Hrtree-Fock plus dispersion (D) model, which neglects this importnt contribution. The interction energy obtined from SAPT nd BSSE ected supermoleculr clcultions t the MP)full/ G(df,p) level is lmost sme. The optimum intermoleculr distnce R obtined from supermoleculr clcultions is shorter thn the SAPT vlue. This is minly due to the effect of BSSE during supermoleculr clcultions, which hs been discussed in previous section. In view of the importnt role the dispersion forces plyed in these complexes, it is now cler tht the bsis set used in erlier studies 1,,6 such s 6-311G(d,p) is not t ll dequte for studying these types of complexes. To emphsize this point further, different energy components were clculted for the nd HCl complexes of methne using nother smller bsis set, G(d,p). The results re listed in Tble 5. At the Hrtree-Fock level the contributions to the binding energy re lmost sme for both the bsis sets. But dispersion contribution chnges considerbly on chnging the bsis set from G- (d,p) to G(df,p) by s much s 33% nd 38% for the nd HCl complexes, respectively. This explins why the equilibrium R vlue decreses substntilly with the increse TABLE 6: Components of Interction Energy (in kcl/mol) for the (CH 4, ) Dimer t the Bent Geometry (Structure in Figure 1) nd t the Equilibrium Nonconventionl Structure (Structure b in Figure 1 nd R ).40 Å) b structure structure b b sm H X,.564 Å; C H b, Å; H CH b,3 ; CH bf, 1. b BSSE ected supermoleculr interction energy (E sm int ) obtined t the MP)full/ G(3df,p) level is given in the lst row. in bsis set. SAPT nlysis ws lso performed for the CH 4 - system (t R ).40 Å) with G(d,p) bsis functions to observe the effect of the f-function on the components of energy. It ws observed tht ll the mjor interction energy components re insensitive to the ddition of f-functions except E (1) pol nd E () disp, but their increment with the ddition of f-function is only 0.04 kcl/mol. Thus t lest in the present cse, the presence of multiple d nd p bsis functions in the bsis set is more importnt thn higher ngulr momentum polriztion function. An interction energy nlysis for both the structures nd b (Figure 1) ws performed for the (CH 4, ) dimer. No equilibrium structure of bent geometry (like structure in Figure 1) could be locted from supermoleculr clcultions t the MP)full/ G(3df,p) level. Structure b ws found to be the most stble dimer t the sid level of clcultions. SAPT nlysis ws crried out ssuming bent structure hving the sme intermoleculr coordintes s mentioned in ref 6 (which is lmost similr to the experimentl structure of ref ). Monomer geometries were the sme s mentioned erlier. The results re displyed in Tble 6. At the Hrtree-Fock level the structure b hs stbiliztion energy of -0.6 kcl/mol, wheres the bent dimer is energeticlly unstble by 0.39 kcl/ mol. These results cn be ccounted for by the substntilly lower E () pol nd E () ind for the bent structure nd their prepondernce over the exchnge forces. The dispersion component is lso much lower for the conventionl hydrogen-bonded structure leding to lrge difference in their stbiliztion energy.

6 6870 J. Phys. Chem. A, Vol., No. 34, 1998 Chndr nd Nguyen 4. Conclusions In the equilibrium geometry of ll the (CH 4, HX), X ) F, Cl, Br, dimers, the proton of H-X forms hydrogen bond with the center of one of the tetrhedrl fces of methne with ner C 3V symmetry. The conventionl hydrogen-bonded structure in which the H-tom of methne forms hydrogen bond with the fluorine of is much less stble, nd t the MP)full/ G(3df,p) level it is trnsition stte. In this context, it is interesting to mention the recent work on the CH 4 -H O dimer. 19 It hs been found tht the fce pproch (similr to Figure 1b, see lso Figure 1 of ref 19) gives rise to the most stble dimer. It ws rgued tht the exchnge repulsion is reltively smll for the fce pproch compred to edge nd Vertex pproch. This llows two monomers for closer contct in the fce pproch, which gives rise to lrger dispersion energy. The present conclusion on the dimeric structure of the (CH 4, HX) system tht the fce pproch gives the most stble dimer is lso long the sme line. SAPT nlysis shows tht the ttrctive forces such s electrosttic, induction, nd dispersion re much higher for the nonconventionl hydrogen-bonded structure when the proton of fces the center of one of the tetrhedrl fces of CH 4. SAPT nlysis lso shows tht dispersion plys n importnt role in determining the equilibrium structure of these complexes. Acknowledgment. A.K.C. thnks the Reserch Council of K.U., Leuven, for postdoctorl fellowship. Thnks re lso due to Prof. P. E. S. Wormer, University of Nijmegen, The Netherlnds, for mny helpful discussions. References nd Notes Dvis, S. R.; Andrews, L. J. Chem. Phys. 1987, 86, () Legon, A. C.; Roberts, B. P.; Wllwork, A. L. Chem. Phys. Lett. 1990, 173, 7. (3) Ohshim, Y.; Endo, Y. J. Chem. Phys. 1990, 93, 656. (4) Atkins, M. J.; Legon, A. C.; Wllwork, A. L. Chem. Phys. Lett. 199, 19, 368. (5) Govender, M. G.; Ford, T. A. J. Mol. Struct.: THEOCHEM 1995, 338, 141. (6) Nguyen, M. T.; Coussens, B.; Vnquickenborne, L. G.; Fowler, P. W. Chem. Phys. Lett. 1990, 175, 593. (7) Chlsinski, G.; Szczesnik, M. M. Chem. ReV. 1994, 94, 173. (8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheesemn, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Rghvchri, K.; Al-Lhm, M. A.; Zkrzewski, V. G.; Ortiz, J. V.; Foresmn, J. B.; Cioslowski, J.; Stefnov, B. B.; Nnykkr, A.; Chllcombe, M.; Peng, C. Y.; Ayl, P. W.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Mrtin, R. L.; Fox, D. J.; Binkley, J. S.; DeFrees, D. J.; Bker, J.; Stewrt, J. P.; Hed- Gordon, M.; Gonzlez, C.; Pople, J. A. Gussin 94, Revision D.3; Gussin, Inc.: Pittsburgh, PA, (9) Jeziorski, B.; Chlsinski, G.; Szlewicz, K. Int. J. Quntum Chem. 1978, 14, 71. () Jeziorski, B.; Moszynski, R.; Szlewicz, K. Chem. ReV. 1994, 94, (11) Jeziorski, B.; Moszynski, R.; Rtkiewicz, A.; Rybk, S.; Szlewicz, K.; Willims, H. L. In Methods nd Techniques in Computtionl Chemistry: METECC-94, Vol. B, Medium Size Systems; Clementi, E., Ed.; STEF: Cgliri, 1993; p 79. (1) Boys, S. F.; Bernrdi, F. Mol. Phys. 1970, 19, 553. (13) Pulson, L. Ph.D. Thesis, University of Slford, UK, Brnes, A. J. J. Mol. Struct. 1983, 0, 59. (14) Moszynski, R.; Koron, T.; Wormer, P. E. S.; vn der Avoird, A. J. Chem. Phys. 1995, 3, 31. (15) Moszynski, R.; Wormer, P. E. S.; vn der Avoird, A. J. Chem. Phys. 1995,, (16) Heijmen, T. G. A.; Koron, T.; Moszynski, R.; Wormer, P. E. S.; vn der Avoird, A. J. Chem. Phys. 1997, 7, 90. (17) Purvis III, G. D.; Brtlett, R. J. J. Chem. Phys. 198, 76, 19. (18) Moszynski, R.; Wormer, P. E. S.; Jeziorski, B.; vn der Avoird, A. J. Chem. Phys. 1994, 1, 811. (19) Szczesnik, M. M.; Chlsinski, G.; Cybulski, S. M.; Cieplk, P. J. Chem. Phys. 1993, 98, 3078.