Theoretical Study for Solvent Effect on the Potential Energy Surface for the Double Proton Transfer in Formic Acid Dimer and Formamidine Dimer

Transcription

1 J. Phys. Chem. A 1997, 101, Theoreticl Study for Solvent Effect on the Potentil Energy Surfce for the Doule Proton Trnsfer in Formic Acid Dimer nd Formmidine Dimer Je-Hyun Lim, Eok Kyun Lee, nd Yongho Kim*, Deprtment of Chemistry nd Institute of Nturl Science, Kyung Hee UniVersity, Yongin-Kun, Kyunggi-Do , Kore, nd Deprtment of Chemistry, Kore AdVnced Institute of Science nd Technology, Yosong-Ku, Dejon, Kore ReceiVed: August 23, 1996; In Finl Form: Decemer 6, 1996 X Doule proton trnsfers in formic cid dimer nd formmidine dimer were studied s prototypes of multiple proton trnsfer. The potentil energy surfce (PES) for the doule proton trnsfer ws studied using initio quntum mechnicl methods. The solvent effect on the PES ws lso included using the Onsger selfconsistent rection field model. In the gs phse, the trnsition stte for the doule proton trnsfer in the formic cid dimer complex hs D 2h symmetry, ut in wter it is chnged to C 2V structure, when the Hrtree- Fock (HF) level of theory is used. When the density functionl theory is used, the trnsition stte hs D 2h symmetry with nd without solvent. However the rrier height depends very much on the electron correltion. The doule proton trnsfer occurs synchronously in ll the cses. For the formmidine dimer complex, the trnsition stte hs C 2V symmetry in the gs phse, nd it chnges to C s symmetry in wter t the HF level of theory. The C 2V structure ecomes n intermedite in wter, which mens tht doule proton trnsfer occurs synchronously. In the density functionl theory for the gs phse, the trnsition stte hs D 2h symmetry, nd it chnges to C 2V structure in solution. However the doule proton trnsfer occurs synchronously in oth cses. These results suggest tht the correltion is very importnt to the PES for doule proton trnsfer, not only in the gs phse ut lso in solution. Introduction Proton trnsfer is one of the simplest nd the most fundmentl rections in chemistry, nd it is importnt in oxidtionreduction rections in mny chemicl nd iologicl rections, so it hs een studied extensively. 1,2 However most of the studies of proton trnsfer hve een done for single proton trnsfer, in which one proton is trnsferred during the rection. Multiproton trnsfers, in which more thn one proton is trnsferred, either synchronously or synchronously, hve not een extensively studied. There re mny exmples of multiproton trnsfer such s proton rely systems in enzymes, certin proton trnsfers in hydrogen-onded wter complexes, nd proton trnsfers in prototropic tutomerisms. 3 A proton rely is thought to ccount for the high moility of the proton in wter. Limch et l. hve studied the doule proton trnsfer in prototropic tutomerisms for mny formmidine systems nd porphyrins using the dynmic NMR technique. 4-8 They reported rtes nd the kinetic isotope effects for oth concerted 7,8 nd stepwise 4-6 doule proton trnsfers. However there is little theoreticl work on the dynmics of multiproton trnsfers. To study the dynmics of such systems, one must hve detiled informtion out potentil energy surfces ner the trnsition stte nd the criticl configurtion. This pper presents such informtion for the formic cid nd formmidine dimers. Formic cid dimer (FAD) is one of most extensively studied systems oth experimentlly nd theoreticlly since it forms strong hydrogen onds, so it is firly esy to mesure its IR nd Rmn frequencies. 9,10 It is lso one of the simplest exmples of multiproton trnsfer system in which the constituents re held together y two hydrogen onds, so it cn e used s model of mny chemiclly nd iologiclly importnt multiproton trnsfers. Recently we hve reported Kyung Hee University. Kore Advnced Institute of Science nd Technology. X Astrct pulished in AdVnce ACS Astrcts, Ferury 15, S (96) CCC: $14.00 direct dynmics study for the doule proton trnsfer in FAD. 11 Amidine compounds re importnt to mny medicl nd iochemicl processes. 12 They ply crucil role in the iosynthesis of imidzole nd purines nd the ctolism of histidine. Formmidine hs een studied experimentlly nd theoreticlly s prototype of this clss of compounds. In ddition to serving s model for hydrogen trnsfer rections in ses of nucleic cids, formmidine hs een extensively studied theoreticlly since it forms homodimers nd hydrogen onds with wter. Intrmoleculr nd intermoleculr hydrogen trnsfer hve een studied theoreticlly for vrious formmidine systems. 4,5,13-16 Proton trnsfers in formmidine dimer cn e considered prototype of multiproton trnsfer. They cn lso provide informtion out hydrogen onding, s well s the proton rely mechnism in enzymes. 3 Becuse of the smll mss of the proton, quntum mechnicl tunneling is often very importnt in this rection. The shpe of the potentil energy surfce (PES) ner the trnsition stte nd the criticl configurtion hs influence on the tunneling proility. Most of the erlier theoreticl studies hve focused on the geometric chnge on dimeriztion, nd the energetic stiliztion due to the hydrogen onds in the gs phse. 16 The chrcteristics of the PES, such s the dimeriztion energy nd the rrier for the doule proton trnsfer, strongly depend on the level of the theoreticl clcultion, the size of the sis set, nd the inclusion of correltion energy. 14,16 However most proton trnsfers occur in solution, so the chrcteristics of the PES will vry with the properties of the solvent. Therefore it is necessry to understnd how solvtion processes influence the PES. In this study we investigted the solvent effect on the PES for the doule proton trnsfer in formic cid dimer nd in formmidine dimer, using the Hrtree-Fock (HF) level of initio quntum mechnicl clcultion, including the selfconsistent Onsger rection field. Since electron correltion plys n importnt role in determining the chrcteristics of the 1997 Americn Chemicl Society

2 2234 J. Phys. Chem. A, Vol. 101, No. 12, 1997 Lim et l. PES for the proton trnsfer rection in the gs phse, 16,18 it is necessry to consider the correltion effect in solution too. The density functionl theory hs een successfully pplied to the proton trnsfer rections, nd it grees well with other methods including high-level electron correltion. 19 Recently Ruiz-López et l. hve studied solvent effects on the proton trnsfer using density function theory including the self-consistent Onsger rection field, nd they showed tht the solute s correltion energy could e gretly modified in the solvtion process. 20 We hve performed density functionl theory clcultions to investigte the chnge in the PES, compred with the HF clcultion without the correltion effect, in the gs phse nd in solution. Clcultions All electronic structure clcultions were done using the GAUSSIAN 94 quntum mechnicl pckges. 21 Geometries for formic cid (FA), formmidine (FD), stle formic cid dimer (FAD), formmidine dimer (FDD), nd the trnsition sttes for the doule proton trnsfer in formic cid dimer nd formmidine dimer were optimized t the Hrtree-Fock (HF) level of theory using the 6-31G(d,p) sis set. Density functionl theory clcultions were lso performed. Becke s three-prmeter 22 grdient-corrected exchnge with the Lee- Yng-Prr 23 grdient-corrected correltion (B3LYP) using the 6-31G(d,p) sis set ws employed. The self-consistent Onsger rection field model 24 ws used to optimize structures nd to clculte energies for vrious dielectric constnts. Frequencies were clculted for ll ound nd trnsition stte structures. The imginry frequency t the trnsition stte hs een monitored with the vrition of the dielectric constnt. In the Onsger rection field theory, 24 the solute in sphericl cvity is surrounded y polrizle medium with dielectric constnt ɛ. A dipole in the solute induces dipole in the medium, nd the electric field pplied to the solute y the solvent dipole will interct with the solute dipole to produce net stiliztion. In the quntum mechnicl theory, the solvent effect is tken s perturtion term, H 1,in the Hmiltonin of the isolted solute, H 0 : 25,26 The perturtion term (H 1 ) represents the coupling etween the rection field vector, RB nd the electric dipole moment opertor, µ: The rection field, RB, is proportionl to the electric dipole moment, µ: The proportionlity constnt, g, is the Onsger fctor, which determines the strength of the rection field. It depends on the dielectric constnt of the medium, ɛ, nd on the rdius of the cvity, 0 : The effect of the rection field y the solvent perturtion is incorported s n dditionl term in the Fock eqution: The energy is given y H ) H 0 + H 1 (1) H 1 )-µ RB (2) RB)-g µ (3) 2(ɛ - 1) g ) 3 (2ɛ + 1) 0 (4) F ) F 0 - gµ µ (5) E ) Ψ H 0 Ψ - 0.5µ RB (6) where Ψ is the full wve function of the molecule. These selfconsistent rection field (SCRF) equtions re solved itertively. The cvity rdius is the only djustle prmeters in solvent effect clcultion, nd the choice of the rdius hs een discussed extensively The simplest method to otin the rdius is to clculte it from the solute molr volume (V m ): in which V m is given y experiment nd N A is Avogdro s numer. When the experimentl molr volume is not ville, the moleculr gretest dimension could e used to estimte the rdius. 26 In this pproch, the dimeter of the molecule is clculted from the lrgest internucler distnce y dding the vn der Wls rdii of the two end toms involved. Then, the rdius otined y this pproch is incresed y 0.5 Å to ccount for the vn der Wls rdii of the surrounding solvent molecules. In this study, the rdius ws clculted from the moleculr volume of the optimized structure in the gs phse, on the ssumption tht the structure is sphericl, nd incresed y 0.5 Å to consider the surrounding solvent molecules. This method is implemented in the GAUSSIAN 94 initio quntum mechnicl pckge 21 tht ws used for ll electronic geometry clcultions. The dimeriztion energies for the hydrogen-onded complexes were clculted from the difference in energies etween the dimer nd two monomers. The sis set superposition error (BSSE) my e importnt in the clcultion of the dimeriztion energies. 29 The BSSE ws corrected y the Boys nd Bernrdi counterpoise correction scheme, 15,30 where E m (M) nd E d (M ) re the energies of the monomer in its own sis set nd in the sis set of the dimer, respectively, nd M nd M denote the optimized geometry of monomer nd the geometry of the monomer in the optimized dimer, respectively. The reorgniztion energy (E reorg ), i.e., the energy ssocited with the trnsition from the optimized geometry of monomer to the geometry tht the monomer hs in the dimer, should lso e included in the correction of the BSSE. The corrected dimeriztion energy is determined s follows: where E(D) is the energy of dimer. 0 3 ) 3V m /4πN A (8) BSSE ) 2[E m (M) - E d (M )] + E reorg (9) E reorg ) 2[E m (M ) - E m (M)] (10) E d (corr) ) E(D) - 2E m (M) + BSSE (11) ) E(D) - 2E d (M ) + E reorg Results nd Discussion Formic Acid Dimer. The geometries for FA, FAD, nd the trnsition stte (FADTS) for the doule proton trnsfer were optimized t the HF level of theory nd t the B3LYP density functionl level. They re shown in Figure 1. FAD hs C 2h symmetry in the gs phse with two hydrogen onds. The O-H ond length in FAD is Å longer thn the O-H ond length in FA due to the hydrogen ond t the HF level of theory. The sme ond length t the B3LYP level of theory is Å longer thn tht in FA. The ond distnce for the hydrogen ond in the density functionl theory is Å, which is out 0.2 Å shorter thn tht t the HF level of theory. The experimentl distnce for the hydrogen ond is Å, 17 which grees very well with the B3LYP results. The density functionl theory predicts slightly lrger ond lengths for ll onds except the hydrogen ond in FAD. A trnsition stte structure with

3 Doule Proton Trnsfer in Formic Acid Dimer J. Phys. Chem. A, Vol. 101, No. 12, Figure 1. Geometries for FA, FAD, nd FADTS. Numers in prentheses re from the geometries otined t the density functionl theory (B3LYP). The unprenthesized numers re from the HF clcultion. FA: r 1 ) 1.182(1.230), r 2 ) 1.322(1.346), r 3 ) 1.085(1.100), r 4 ) 0.949(0.974). FAD: r 1 ) 1.196(1.227), r 2 ) 1.298(1.310), r 3 ) 1.084(1.007), r 4 ) 0.963(1.098); r 5 ) 1.831(1.643), θ ) 173.5(178.9). FDDTS: r 1 ) 1.242(1.264), r 2 ) 1.118(1.210), r 3 ) 1.084(1.098), θ ) 179.1(178.6). Experimentl ond lengths nd ngles re s follows. 17 FA: r 1 ) 1.202, r 2 ) 1.343, r 3 ) 1.097, r 4 ) FAD: r 1 ) 1.217, r 2) 1.320, r 3 ) 1.079, r 4 ) 1.033, r 5 ) 1.663, θ ) 180 (ssumed). Bond lengths re in ngstroms, ngles in degrees. TABLE 1: Dimeriztion Energies, Brrier Heights for the Doule Proton Trnsfer in FAD, nd Imginry Frequencies of FADTS(D 2h ) t Vrious Levels of Theory in the Gs Phse E d E qc ν qd ref HF/STO-3G i 31c HF/6-31G i 31c HF/6-31+G i 31c MP2/6-31G(d,p) i 31c HF/DZ -19.3(-16.8) i 31 HF/DZ+P -14.3(-12.3) i 31 HF/6-31+G(d,p) HF/6-311G(d,p) HF/6-311+G(d,p) B3LYP/cc-pVDZ B3LYP/AUG-cc-pVDZ G2* -16.2(-14.2) 8.94(5.20) 11 MCPF -16.2(-13.9) HF/6-31G(d,p) -15.3(-11.1 e ) 16.6(11.2) 1756i this study B3LYP/6-31G(d,p) -19.6(-13.7 e ) 5.4(1.51) 1195i this study expt Numers in prentheses re with zero-point energy. Reltive energies of FAD with respect to the energies of two FA in kcl mol -1. c Reltive energies of FADTS with respect to the energies of FAD in kcl mol -1. d Rection coordinte frequency in cm -1. e The BSSEs re corrected in ddition to zero-point energy. D 2h symmetry is otined t oth the HF nd the B3LYP level of theories in the gs phse. This result suggests tht the doule proton trnsfer proceeds through concerted mechnism in the gs phse. The geometries from the B3LYP method for FA, FAD, nd FADTS gree etter thn those from the HF clcultion with the experimentl 17 nd high-level initio results including electron correltion. 11 Dimeriztion energies, rrier heights, nd imginry frequencies re listed in Tle 1 for the gs phse. Dimeriztion energies nd rrier heights re chnged very much with the level of theory nd the size of the sis sets. 31 Electron correltion is very importnt in determining dimeriztion energies nd rrier heights. Adding diffuse functions to the sis set does not improve the results t the HF level of theory. The clculted dimeriztion energies, without ny zero-point energy correction, re nd kcl mol -1, from the HF nd the B3LYP methods, respectively. They re nd kcl mol -1, from the HF nd the B3LYP methods, respectively, with zero-point energy correction. The experimentl enthlpy of dimeriztion for FAD is out kcl mol Scheiner hs reported tht the sis set superposition errors (BSSEs) my e importnt in the determintion of the dimeriztion energy for hydrogen-onded complexes. 29 There TABLE 2: Dimeriztion Energies for the Doule Proton Trnsfer in FAD, nd Frequencies of FADTS(D 2h ) t the HF nd B3LYP Level of Theories with the Onsger Rection Field Model t Vrious Dielectric Constnts ɛ E d ν q (B 3g) c ν(b 1u) d gs -15.3(-19.6) 1756i (1195i) 768 (1362) (-19.2) 1756i (1195i) 565 (1282) (-18.8) 1756i (1195i) 120 (1170) (-18.6) 1756i (1195i) 348i (1117) (-18.5) 1756i (1195i) 444i (1075) (-18.4) 1756i (1195i) 487i (1069) (-18.4) 1756i (1195i) 509i (1060) Numers in prentheses re from the B3LYP method. The rrier heights for the doule proton trnsfer in FAD t the HF nd B3LYP levels of theory re 16.6 nd 5.4 kcl mol -1, respectively, nd these vlues re not chnged y solvent effect. The cvity rdii for FA, FAD, nd FADTS(D 2h) re 3.05, 3.69, nd 3.49 Å, respectively, for the HF method, nd 3.04, 3.58, nd 3.47 Å, respectively, for the B3LYP method. Reltive energies of FAD with respect to the energies of two FA in kcl mol -1. The BSSEs re not corrected. c Rection coordinte frequency in cm -1. d The norml mode frequency most sensitive to the solvent polrity. Other frequencies re lmost insensitive to the solvent polrity. my e the BSSEs involved in the dimeriztion energies in Tle 1, which mke the dimeriztion energies less negtive. The counterpoise procedure ws performed to correct the BSSE for the dimeriztion energies in the gs phse. The BSSEs from the HF nd the B3LYP methods re 2.19 nd 4.08 kcl mol -1, respectively. From eq 11, the corrected dimeriztion energies from the HF nd the B3LYP methods re nd kcl mol -1, respectively, with zero-point energy correction. The corrected dimeriztion energy from the B3LYP method grees very well with the experimentl vlue. The rrier heights were clculted from the difference in energies etween FADTS with D 2h symmetry nd FAD. The clculted rrier heights from the HF nd the B3LYP methods re 16.6 nd 5.42 kcl mol -1, respectively. The vlue from the HF method is lrger, ut tht from the B3LYP method is smller thn the rrier height from the G2* level of theory, 11 which is 8.94 kcl mol -1. The B3LYP method slightly underestimtes the rrier height, ut the vlue from the B3LYP method grees with the G2* vlues etter. The geometries of FA, FAD, nd FADTS with D 2h symmetry hve een optimized in solution t vrious dielectric constnts. Dimeriztion energies nd frequencies re listed in Tle 2 for solutions with vrious dielectric constnts. The clculted dimeriztion energy ecomes less negtive s the dielectric constnt increses. The glol dipole moment of FAD is zero ecuse it hs C 2h symmetry, nd this gives zero rection field in eq 3. Therefore there is no stiliztion in energy for FAD y the Onsger self-consistent rection field method (eqs 1-6). The chnge in the dimeriztion energy is due to the stiliztion of the monomer in solution, which mkes the dimeriztion energy less negtive. However the chnge is not lrge: only out 1.6 kcl mol -1 t the HF level of theory, nd 2.3 kcl mol -1 t the B3LYP level of theory. These results suggest tht the strong hydrogen onds in FAD re not wekened very much even in very polr solvent. However this does not tke more specific interctions into ccount. For exmple, formic cid does not dimerize in dilute queous solution. Therefore these results re meningful in solutions such tht solvent provides polr dielectric medium to solute without specific interctions. The clculted imginry rection coordinte frequency with B 3g symmetry is insensitive to the dielectric constnt, ut the frequency with B 1u symmetry is very sensitive; in prticulr the B 1u frequency from the HF method ecomes imginry etween dielectric constnts of 5 nd 10. These results indicte tht the FADTS with D 2h symmetry is not rel trnsition stte,

4 2236 J. Phys. Chem. A, Vol. 101, No. 12, 1997 Lim et l. Figure 2. Norml mode eigenvectors for FADTS(D 2h) optimized t the HF level of theory using the Onsger rection field model for wter. (A) Norml mode eigenvector for the rection coordinte frequency (B 3g). (B) Norml mode eigenvector for the frequency with B 1u symmetry, which is sensitive to the strength of the rection field. TABLE 3: Brrier Heights nd Rection Coordinte Frequencies of FADTS(C 2W ) t the HF Level of Theory with the Onsger Rection Field Model t Vrious Dielectric Constnts ɛ E q ν q (B 2) c ν(a 1) d r e µ f gs g i i i i i i i The structures of FADTS(C 2V) were optimized t ech dielectric constnt with the cvity rdius of 3.49 Å. Reltive energies of FADTS(C 2V) with respect to the energies of FAD in kcl mol -1. c Rection coordinte frequency in cm -1. d Frequencies tht re similr to the norml mode virtion s the B 1u mode in FADTS with D 2h symmetry. e The difference etween two O-H ond lengths (r 1 - r 2 in fig. 4) in FADTS(C 2V) in ngstroms. f Dipole moments in deyes. g In the gs phse, FADTS hs D 2h symmetry. Figure 3. C 2V trnsition stte structure optimized t the HF level of theory using the Onsger self-consistent rection field model for wter nd the eigenvectors for the rection coordinte frequency. ut just sttionry point on the PES, in highly polr solvents t the HF level of theory. The eigenvectors for the B 3g nd B 1u frequencies re shown in Figure 2. The B 3g norml mode of the rection coordinte does not chnge the dipole moment of the FADTS. However the B 1u norml mode virtion chnges the dipole moment of FADTS gretly. The lrge chnge in the dipole moment due to this virtionl motion influences the rection field; therefore the B 1u frequency is sensitive to the strength of rection field, which is relted to the dielectric constnt. The frequency ecomes imginry ecuse the potentil curve for the B 1u virtionl motion is inverted in polr solvent. This is not surprising since the B 1u mode induces lrge dipole moment t the turning point of virtion, where the totl energy cn e reduced y solvtion. The rel trnsition stte structure in medium with the wter dielectric constnt ws clculted t the HF level of theory. It hs C 2V symmetry, s shown in Figure 3. The rection coordinte frequency is 1276i cm -1 nd this is the only imginry frequency. The eigenvector for the rection coordinte is lso shown in Figure 3. The rrier heights, dipole moments, nd the rection coordinte frequencies for the C 2V FADTS t vrious dielectric constnts re listed in Tle 3. The positions of the two protons in flight re shifted continuously towrd one formte residue s the dielectric constnt is incresed. The dipole moment is incresed t the sme time. The rrier height in the high permittivity fluid is reduced y only 0.1 kcl mol -1 compred with the rrier in the gs phse, which suggests tht the solvtion process does not hve ig influence on the rrier height. The energies of the C 2V structure Figure 4. Schemtic three-dimensionl digrm for the solvent effect on the PES for the doule proton trnsfer in FAD t the HF level of theory. R nd P represent the structures for the FAD complex, nd M nd N represent the FADTS(C 2V) structures in wter. The x represents the rection coordinte connecting R nd P, nd the y represents the coordinte for the norml mode virtion with B 1u symmetry perpendiculr to the rection coordinte connecting M nd N. The vriles x nd y re defined in the text. The lines A, B, nd C re schemtic potentil curves for the norml mode virtion with B 1u symmetry in the gs phse, in n intermeditely polr solvent, nd in wter, respectively. The left hlf of the curve C is not shown. The minimum energy rection coordinte in wter is long the line connecting R, TS 2, nd P. t ɛ ) 2 nd 5 re slightly lrger thn those in the gs phse. These results men tht the rection pth vi C 2V FADTS structure is not minimum energy pth t ɛ ) 2 nd 5, so the rel trnsition stte in these cses is the structure with D 2h symmetry. This is consistent with the fct tht the B 1u frequencies in the D 2h structure do not ecome imginry until ɛ ) 10, s shown in Tle 2. The solvent effect on the PES for the doule proton trnsfer in FAD t the HF level of theory is schemticlly shown in Figure 4. The rection coordinte vrile, x, nd the vrile tht represents norml mode with B 1u symmetry, y, cn e defined pproximtely s eqs. 12 nd 13, x ) (r 1 + r 4 ) - (r 2 + r 3 ) (r 1 d + r 4 d ) - (r 2 d + r 3 d ) y ) (r 1 + r 3 ) - (r 2 + r 4 ) (r 1 w + r 3 w ) - (r 2 w + r 4 w ) (12) (13) where r s re ond distnces s defined in Figure 4 nd r d s

5 Doule Proton Trnsfer in Formic Acid Dimer J. Phys. Chem. A, Vol. 101, No. 12, nd r w s re the corresponding distnces in the FAD complex nd the C 2V structure of FADTS, respectively, in wter, which re given in Figures 1 nd 3A. The idel potentil curve, A, in Figure 4, for the norml mode virtion (B 1u ) perpendiculr to the rection coordinte ecomes inverted in polr solvent, s shown in the potentil curves, B nd C. This chnges the minimum energy rection coordinte from the pth vi TS(D 2h ) in the gs phse to the pth vi TS 2 (C 2V ) in wter. The C 2V structure in wter is not n intermedite. It is the trnsition stte with n imginry frequency, which mens tht the doule proton trnsfer occurs synchronously. In the density functionl theory the B 1u frequency is lrger thn tht from the HF level of theory, which mens tht the potentil curve for the B 1u virtionl motion is steeper. It is not inverted even in wter, even though the frequency ecomes smller with incresing the dielectric constnts. This mens tht the potentil curve for the B 1u mode from the B3LYP method is firly stiff. The D 2h structure for FADTS hs only one imginry frequency in ll cses, s shown in Tle 2. The fct tht the imginry frequency is not vried with solvtion indictes tht the minimum energy rection pth for the doule proton trnsfer is not chnged with the permittivity of the medium. This result cn e understood since the doule proton trnsfer, s shown in Figure 2A, does not chnge the dipole moment of rection nd the strength of the rection field. The rection occurs through D 2h trnsition stte oth in the gs phse nd in solution. The solvent effect on the PES from the density functionl theory (B3LYP) is quite different from tht predicted y the HF level of theory. This difference origintes proly from the fct tht the HF level of MO theory does not include electron correltion. Therefore electron correltion is very importnt in determining the rection coordinte for the doule proton trnsfer in solution. Formmidine Dimer. The geometries for FD, FDD, nd the trnsition stte for the doule proton trnsfer (FDDTS) re optimized t the HF level of theory, nd the geometric prmeters re shown in Figure 5. The optimized structure of FDD hs C i symmetry. Truhlr nd co-workers hve reported slightly different optimized structure for FDD ( C 2 structure), 16 ut the difference etween the energies of these structures is less thn 0.1 kcl mol -1, nd the geometries of two conformers re very similr. It is not necessry to consider ll structures for solvent effect study, so we used only the C i structure for the solvent effect clcultion. The D 2h structure of FDDTS from the HF level of theory hs two imginry frequencies oth in the gs phse nd in solution, which mens tht this structure is not rel trnsition stte for the doule proton trnsfer. Ahlerg nd co-workers hve reported tht the C 2V structure is n intermedite t the HF level of theory using the 6-31G(d) sis sets. 16 However, the C 2V structure in this study is trnsition stte with one imginry frequency in the gs phse. The dimeriztion energies, rrier heights, trnsition stte symmetries, nd imginry frequencies, t the vrious level of theories in the gs phse, re listed in Tle 4. Not only the dimeriztion energies nd the rrier heights ut lso the symmetry of the trnsition stte re chnged very much with the level of theories nd the size of the sis sets. The BSSEs in the dimeriztion energies were corrected from the HF nd B3LYP methods using eq 9, nd they re 1.72 nd 3.54 kcl mol -1, respectively. The corrected dimeriztion energies including the BSSEs nd zeropoint energies from the HF nd B3LYP methods re nd kcl mol -1, respectively. The dimeriztion energy nd the rrier height from the B3LYP method gree very well with those from the high-level initio clcultions including electron correltion. Electron correltion chnges the trnsition stte Figure 5. Geometries for FD, FDD, nd FDDTS(D 2h) optimized t the HF nd B3LYP level of theory in the gs phse. Numers in prentheses re from the B3LYP results. Bond lengths re in ngstroms nd ngles in degrees. FD: r 1 ) 1.255(1.277), r 2 ) 1.368(1.376), r 3 ) 0.993(1.009), r 4 ) 1.085(1.099), r 5 ) 1.001(1.020), r 6 ) 0.995(1.012). FDD: r 1 ) 1.266(1.292), r 2 ) 1.345(1.347), r 3 ) 0.991(1.005), r 4 ) 1.086(1.098), r 5 ) 1.001(1.017), r 6 ) 1.006(1.035), r 7 ) 2.103(1.894), θ ) 175.6(174.5). FDDTS(D 2h): r 1 ) 1.302(1.318), r 2 ) 1.277(1.288), r 3 ) 0.996(1.011), r 4 ) 1.086(1.098), θ ) 174.0(174.2). The geometries for FDDTS(C 2V) re optimized t the HF level of theory in the gs phse nd t the B3LYP level of theory in wter. The geometry for FDDTS(C s) is optimized t the HF level of theory in wter. FDDTS- (C 2V): r 1 ) 1.305(1.321), r 2 ) 1.297(1.315), r 3 ) 1.572(1.520), r 4 ) 1.090(1.129), r 5 ) 0.999(1.014), r 6 ) 0.993(1.010), θ ) 174.1(174.0). FDDTS(C S): r 1 ) 1.288, r 2 ) 1.309, r 3 ) 0.992, r 4 ) 1.079, r 5 ) 0.995, r 6 ) 1.029, r 7 ) 1.831, r 8 ) 1.295, r 9 ) 1.313, r 10 ) 1.000, r 11 ) 1.096, r 12 ) 0.998, r 13 ) 1.441, r 14 ) 1.152, θ 1 ) 170.3, θ 2 ) symmetries s well s the dimeriztion energies nd the rrier heights. These results suggest tht electron correltion should e considered in the clcultion of the PES for the doule proton trnsfer in FDD, not only in the gs phse ut lso in solution. The dimeriztion energies, the rrier heights, nd the rection coordinte frequencies in medi of vrious dielectric constnts t the HF level of theory re listed in Tle 5. The dimeriztion energies re reduced out 3.3 kcl mol -1 y solvtion, ecuse the energy of FD is lowered y solvtion, ut tht of FDD is not, ecuse of its zero dipole moment. The C 2V structure of FDDTS ecomes n intermedite in solution, ecuse the imginry frequency disppers in solvent with ɛ ) 2.0, s shown in Tle 5. This result mens tht the doule proton trnsfer in solution occurs vi stepwise mechnism, with n intermedite of C 2V symmetry, t the HF level of theory. Since the positions of the two protons re lredy shifted towrd the nitrogens of one monomer unit in the gs phse, the dipole moment of the trnsition stte is firly lrge, out 4.6 D. As the dielectric constnts re incresed, the ridging protons re shifted further; therefore the dipole moment of the C 2V intermedite tht is formed y single proton trnsfer ecomes even lrger, s listed in Tle 5. This stilizes the FDDTS(C 2V ) nd reduces the rrier height out 4.1 kcl mol -1. Since the C 2V structure is n intermedite nd the proton trnsfer occurs stepwise, there must exist two trnsition sttes for ech step of the rection. The trnsition stte for the single proton trnsfer t the HF level of theory ws clculted in wter, nd it hs C s symmetry, s shown in Figure 5. The other trnsition stte is just the mirror imge of this structure, nd the rrier height is kcl mol -1 in wter. The C 2V intermedite in wter is only kcl mol -1 lower in energy thn the C s trnsition stte. The concerted doule proton trnsfer in the gs phse hs switched to stepwise in wter with out 3.4 kcl mol -1 of

6 2238 J. Phys. Chem. A, Vol. 101, No. 12, 1997 Lim et l. TABLE 4: Dimeriztion Energies, Brrier Heights, Trnsition Stte Symmetry, nd Imginry Frequencies for the Doule Proton Trnsfer in FDD in the Gs Phse E d E qc TS symm ν qd ref HF/STO-3G C 2V 1311i 16 HF/3-21G C 2V 1494i 16 HF/6-31G C 2V 432i 16 HF/6-31+G C 2V 146i 16 HF/6-31G(d) -11.2(-9.6) 25.4(23.0) C s 328i 16 MP2/6-31G(d,p)//HF/6-31G(d,p) -15.4(-13.9) 13.8(8.1) D 2h 16 SAC2/6-31G(d,p)//HF/6-31G(d,p) 11.0(5.3) D 2h 16 HF/6-31G(d,p) -11.4(-8.14 e ) 23.8(21.5) C 2V 231i this study B3LYP/6-31G(d,p) -16.6(-12.1 e ) 11.7(6.78) D 2h 1462i this study Numers in prentheses re with zero-point energy. Reltive energies of FDD with respect to the energies of two FD in kcl mol -1. c Reltive energies of FDDTS with respect to the energies of FDD in kcl mol -1. d Rection coordinte frequency in cm -1. e The BSSEs re corrected in ddition to zero-point energy. TABLE 5: Dimeriztion Energies, Brrier Heights for the Doule Proton Trnsfer in FDD, nd Frequencies of FDDTS(C 2W ) t the HF Level of Theory with the Onsger Rection Field Model t Vrious Dielectric Constnts ɛ E d E qc ν(b 2) d r e µ f gs i The cvity rdii for FD, FDD, nd FDDTS(C 2V) re 3.40, 3.99, nd 3.89 Å, respectively. Reltive energies of FDD with respect to the energies of two FD in kcl mol -1. The BSSEs re not corrected. c Reltive energies of FDDTS(C 2V) with respect to the energies of FDD in kcl mol -1. d Rection coordinte frequency in cm -1. This ecomes nonimginry in solution. e The difference etween two N-H ond lengths (r 3 - r 4 in FDDTS(C 2V) of Figure 5) in ngstroms. f Dipole moments in deyes. dvntge in energy y solvtion. The ond distnces, r 14 nd r 13 in FDDTS(C s ) of Figure 5, re nd Å, respectively, which suggest tht the C s structure is more similr to the C 2V intermedite thn to FDD(C i ). The geometries for FD, FDD, nd FDDTS, optimized t the B3LYP level of theory, re lso shown in Figure 5. The hydrogen ond length in FDD, r 7, is out 0.21 Å shorter thn tht from the HF method. This indictes tht the hydrogen onds from the B3LYP method re stronger. This result is consistent with the results for the FAD, in which the dimeriztion energy otined from the B3LYP method is more negtive thn tht from the HF method, s shown in Tle 2. The geometry for the FDDTS in the gs phse hs D 2h symmetry, with n imginry frequency s shown in Figure 5. The rrier height nd the dimeriztion energy in the gs phse re nd kcl mol -1, respectively, which gree very well with previous high-level initio clcultion including the electron correltion. 16 There re two imginry frequencies for the FDDTS(D 2h ) in solution for ll dielectric constnts of 2 nd ove, which shows tht FDDTS(D 2h ) is not rel trnsition stte. The trnsition stte given y the B3LYP clcultion for the doule proton trnsfer in solution hs C 2V symmetry, nd this structure is lso shown in Figure 5. The rrier heights nd imginry frequencies t vrious dielectric constnts re shown in Tle 6. The dimeriztion energy is less negtive y out 2.8 kcl mol -1. This occurs ecuse only the energy of FD is lowered y solvtion, s mentioned efore. The imginry frequency of the FDDTS(C 2V ) in solution ecomes much smller with incresing dielectric constnt, ut it still remins imginry in wter. This mens tht FDDTS(C 2V ) is not n intermedite even in wter, nd it is rel trnsition stte for the concerted doule proton trnsfer. The rrier height is reduced y out 0.82 kcl mol -1 in medium with the wter dielectric constnt TABLE 6: Dimeriztion Energies, Brrier Heights for the Doule Proton Trnsfer in FDD, nd Frequencies of FDDTS t the B3LYP Level of Theory with the Onsger Rection Field Model t Vrious Dielectric Constnts D 2h compred with tht in the gs phse, which suggests tht dielectric solvtion does not hve much influence on the rrier height in the density functionl theory. Limch et l. hve mesured Arrhenius ctivtion energy for the doule proton trnsfer in N,N -is(p-fluorophenyl)formmidine dimer in THF, which is 4.52 kcl mol The clculted therml energies for FDD nd FDDTS(C 2V ) t the B3LYP level of theory in medium of ɛ ) 10, including virtionl, rottionl, nd trnsltionl energies, re nd kcl mol -1, respectively, t 298 K. The enthlpy of ctivtion, estimted from the therml energies nd the rrier height, is 4.95 kcl mol -1, which grees very well with the experimentl vlue. A schemtic digrm of the potentil energy surfce for the doule proton trnsfer in formmidine dimer is shown in Figure 6. Imginle rection pths for the doule proton trnsfer re from R(C i )top(c i ) vi either TS(D 2h ), TS(C 2V ), or I(C 2V ). At the HF level of theory in the gs phse, the doule proton trnsfer occurs synchronously vi TS(C 2V ); however in solution, the proton trnsfer occurs synchronously vi I(C 2V ). There re two trnsition sttes, oth with C s symmetry, t the top of the dshed lines in Figure 6. These two trnsition sttes hve mirror imge reltion. At the density functionl level of theory, in the gs phse, the doule proton trnsfer occurs synchronously vi TS(D 2h ). In solution, it occurs synchronously too, ut vi TS(C 2V ). The C 2V structure is not n intermedite in this cse. The two theories (HF nd B3LYP) produce quite different results oth in the gs phse nd in solution. Most importntly, the HF method predicts stepwise rection pth for the doule C 2V ɛ E d ν(b 3g) c ν(b 1u) d E qe ν(b 2) f gs i 446 g g i 107i i i 464i i i 553i i i 597i i i 620i i i 631i i The cvity rdii for FD, FDD, FDDTS(D 2h), nd FDDTS(C 2V) re 3.40, 3.88, 3.84(D 2h), nd 3.67(C 2V) Å, respectively. The rrier height, which is the reltive energy of FDDTS(D 2h) with respect to the energy of FDD, is kcl mol -1, nd this is not chnged with dielectric constnts. Reltive energies of FDD with respect to the energies of two FD in kcl mol -1. The BSSEs re not corrected. c Rection coordinte frequency of FDDTS(D 2h) incm -1. d The norml mode frequency of FDDTS(D 2h) most sensitive to the solvent polrity. Other frequencies re lmost insensitive to the solvent polrity. e Reltive energies of FDDTS(C 2V) with respect to the energies of FDD in kcl mol -1. f Rection coordinte frequency of FDDTS(C 2V) incm -1. g In the gs phse, the trnsition stte hs D 2h symmetry.

7 Doule Proton Trnsfer in Formic Acid Dimer J. Phys. Chem. A, Vol. 101, No. 12, theory with the SCRF method cn e used to study the medium effect successfully. Acknowledgment. This work ws supported, in prt, y grnt from Kyung Hee University, nd the Cry R&D Fund, 1997, from SERI. Figure 6. Schemtic three-dimensionl digrm for the solvent effect on the PES for the doule proton trnsfer in FDD. R nd P represent the structures for the FDD complex, nd M nd N represent the C 2V structures in wter. The x represents the rection coordinte connecting R nd P, nd the y represents the coordinte for the norml mode virtion with B 1u symmetry perpendiculr to the rection coordinte connecting M nd N. The vriles x nd y re defined in the text. The lines A, B, nd C re schemtic potentil curves for the norml mode virtion with B 1u symmetry in the gs phse- (B3LYP), in polr solvent(b3lyp), nd in wter(hf), respectively. The left hlf of the curve C is not shown. The minimum energy rection coordinte from the HF method in wter is long the dshed line connecting R, I, nd P. proton trnsfer in solution, ut the B3LYP method predicts concerted pth. These differences re proly due to the fct tht the HF level of MO theory does not include electron correltion; therefore these results suggest tht the electron correltion is very importnt in clculting the PES for the doule proton trnsfer, not only in the gs phse ut lso in solution. Since very mny importnt proton trnsfer rections occur in solution, it is crucil to understnd how the PES is modified y polr solvent. This study shows tht correltion should e included in estimting the PES for doule proton trnsfer in solution. Concluding Remrks The PESs for the doule proton trnsfer in formic cid dimer nd in formmidine dimer hve een studied t the HF nd the density functionl levels of theory, with nd without medium effect. The doule proton trnsfer in formic cid dimer occurs synchronously with D 2h trnsition stte oth in the gs phse nd in solution t the B3LYP level of theory. At the HF level of theory, however, the trnsition stte is chnged from D 2h structure in the gs phse to C 2V structure in solution, even though the doule proton trnsfer occurs synchronously. The doule proton trnsfer in formmidine dimer occurs vi concerted mechnism through D 2h trnsition stte in the gs phse, nd C 2V trnsition stte in solution in the density functionl theory. At the HF level of theory, however, the mechnism of the doule proton trnsfer chnges with solvent. In the gs phse, the doule proton trnsfer occurs vi concerted mechnism through C 2V trnsition stte, ut in solution it occurs vi stepwise mechnism through C s trnsition stte nd C 2V intermedite. The solvent effect on the PES for doule proton trnsfer is very importnt. 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