J. Phys. Chem. 1995, 99, 16590-16596
16590
Effects of Formaldehyde Substituents on Potential Energy Profiles for Proton Transfer in [ABCO-H-OCXH]' Chih-Hung Chu and Jia-Jen Ho* Department of Chemistry, National Taiwan Normal University, 88 sec. 4, Tingchow Rd., Taipei, Taiwan 11 7, ROC Received: June 12, 1995; In Final Form: August 21, 1995@
Ab initio methods are used to discover the effects of formaldehyde substituents on potential hypersurfaces for proton transfer in the equilibrium complex (ABCO-H-OCXH)+ in which A, B, and X are electronreleasing or -withdrawing groups. The potential profiles span the full range from symmetric double well, asymmetric double well, to single well, depending on the substituents. A symmetric double well corresponds to a complex with two equivalent subunits such as (FCHO-H-OCHF)', whereas in (HFCO-H-OCH?)' only one minimum structure is obtained in the entire potential surface. When the protonation energies of the two subunits are not greatly different an asymmetric double well might form. A ratio o to represent the extent of the difference of protonation energies between the two subunits in the complex was introduced to illustrate the formation of an asymmetric double well for calculated several complexes. To determine which conformation of the two wells has lower energy, the magnitude of the addition of binding energy of the conformation and the protonation energy of the subunit nearer the central proton is a crucial factor. The bigger is the magnitude of the conformation, the deeper is the well. A deeper right well in either the trans or cis conformer of (CH,FCHO-H-OCH*)' can be clarified easily with this magnitude as a parameter. It would be puzzling if only one term of energy (either binding energy of the conformation of two wells or protonation energy of the two subunits) were used. The difference of the magnitudes in two wells represents the potential gap between the two wells. The geometries of complexes varied from the parent complex (H2CO-H-OCH*)+ are discussed briefly based on the direction of the dipole moment in the substituted HXCO subunits. The thermodynamic properties AH', AS", and AGO of the association reaction ABCOH' (ABCO-H-OCXH)+ at several temperatures are evaluated according to standard thermodynamic formulae that incorporate the vibrational frequencies of the various species.
+
-
Introduction Proton transfer involved in chemical and biological processes has been extensively investigated. Experimental measurements yielded a linear correlation between the bond dissociation energy and the difference between the proton affinities of the proton donor and of the proton acceptor.2 Blatz et al.' measured the concentrations of the H-bonded form and of the protontransferred form of a Schiff base quantitatively as a function of temperature through the absorbance of the species. Deuterium isotope fractionation6 in the gas phase of proton-transfer reactions between DO- and substituted 2-propenes have also been measured. Quantum chemical calculations were employed to supplement the experimental work; this approach has the advantage that it yields both energies and structures of the intermediates and transition states. Such a calculation supplies directly the activation energies and is independent of a dynamic model to correlate rates with The transition structures and energy barriers of intramolecular proton transfer between oxygen atoms in negatively charged systems such as hydrogen peroxide and glycolate anion and the tautomerization of formamide were calculated.'0.'' The energy barriers are significantly diminished when water molecule participates in these reactions. Using modest basis sets at the Hartree-Fock level Scheiner et al. systematically investigated proton transfer between groups of varied complexity in small and in more complicated systems involving transfer between oxygen and other Evleth and c o - w ~ r k e r s 'investigated ~ proton transfer between CH4, NH3, H20, HCCH, and HCN and
* To whom correspondence should be addressed. Abstract published in Advance ACS Abstracts, October 15, 1995.
0022-365419512099-16590$09.00/0
their conjugated bases. Recently, Gronert?" reported results of high-level ab initio calculations of proton transfer of first- and second-row nonmetal hydrides with their conjugated bases. Many protonated aldehyde ions (RCHO),H+ were observed with unknown structures.?' In our previous ca1culationsz2.23we investigated optimized structures and energy profiles of proton transfer in (HCH0)2H+ and (CH3CHO)?H+ion complexes; in its equilibrium geometry each calculated ion complex had a nonlinear 0 - H - 0 conformation and the central proton moved from beneath the 0-0 axis to above during proton transfer. According to new findings of structure and energetics of proton transfer in a similar system with hydrogen replaced by various substituents,?4 the position of substitution and character of substituent strongly affected the proton affinity, dipole moment, and the energy barrier of proton transfer. In the present work, we extend our investigation to the potential energy profiles of proton transfer under the influence of substitution in a more complicated complex (ABCO-HOCXH)+, in which A, B, and X denote positions of substituents. These systems yield potential-energy surfaces for proton transfer that span the range from symmetric double well through an asymmetric double well to a single well, for varied substituents. The results provide a good basis for generalizations.
Methods of Calculation All calculations were carried out using the ab initio Gaussian92 quantum mechanical package;25geometries were optimized with the gradient schemes included therein. To investigate proton transfer in the complex (ABCO-H-OCXH)', proton affinities of the subunits in the complex were obtained first by
0 1995 American Chemical Society
Potential Energy Profiles for Proton Transfer
J. Phys. Chem., Vol. 99, No. 45, 1995 16591
TABLE 1: Protonation Engery (kcallmol) of Formaldehyde and Its Derivatives HF
MP2
/*
B1 ;
species
uncorr
cod
uncorr
cod
expta
HCHO FCHOd CH3CHOd CH3FCO (trans). CH3FCO (cis)f CH2FCHOd
182.68 167.84 195.16 180.61 183.30 186.45
181.71 167.19 194.26 179.97 182.51 185.60
175.22 161.16 188.17 174.23 177.03 179.66
172.89 184.0(177.2)c 159.32 185.88 195.3(188.9)c 172.33 174.99 177.52
a Experimental proton affinity, corrected for computed zero-point vibrational energy and contributions from translational and rotational terms. Values in parentheses lack these corrections. Correction by basis set superposition error (BSSE). See ref 29. The protonation atom (H") is located at the opposite side of F (or CH3 or CH2F) with respect to the C - 0 axis. e The protonation atom (Hm)is located at the opposite side of F and at the same side of CH3 with respect to the C - 0 axis. 'The protonation atom (Hm)is located at the opposite side of CH3 and at the same side of F with respect to the C - 0 axis.
computing the difference between the energies of the molecules ABCO and OCXH on the one hand and the respective protonated species ABCOH+ and HOCXH+ on the other, with all geometries fully optimized. Zero-point vibrational energies and thermal correction terms were taken into account in the comparison with the experimental data. The polarized splitvalence 4-3 lG* basis set26was used with geometry optimization at the Hartree-Fock level. To consider the effect of electron correlation, we employed second-order Moller-Plesset perturbation theory (MP2).27 The basis set superposition error (BSSE) inherent in computation of molecular interaction energies was corrected via the Boys-Bemardi counterpoise technique.28The advantages of the 4-31G* basis set are that it is demonstrated to yield satisfactory results compared with experiment29and that it is widely used to calculate energy barriers for proton transfer in similar s y ~ t e m s . ' ~ . ' ~ .As ' ~ ,shown ~ ~ . ~ ~in Table 1, the calculated relative proton affinities, using 4-31G* at the HF level, agree satisfactorily with experiment, more accurately than results calculated with the 4-31G** basis set and geometry optimized at the MP2 level, mentioned in our previous work.24 The accuracy of HF/4-3 lG* treatment of proton affinities was further confirmed in a calculation including a larger basis set and electron correlation at the MP4 level (MP4/4-31G**). The data are not shown in here. Generally, the use of the basis set 4-31G*, without polarization orbitals on H atoms appears not to be judiciously chosen, as in these ions polarization forces between the two entities are important. Furthermore, the dispersion forces (which enter at the MP4 level) between the central proton and the other entities are not negligible at the equilibrium distances. That the calculation (HF/4-31G*) without considering both polarization and dispersion forces yields such good results for proton affinities in agreement with experiment is believed to arise fortuitously from a balance between these two errors. As we consider a transfer between two molecules in (ABCO-H-OCXH)+, it is important that our theoretical approach render precisely their relative proton affinities, known from experiment. Therefore, we are confident to use 4-31G* and to calculate at the Hartree-Fock level in our systems. The positions of substituents in (ABCO-H-OCXH)+ and some parameters are explained in Figure 1 (the left subunit is tagged L, right R, and middle m). The parameter R denotes the inter-oxygen separation and a, p, and 6 the angles (CLOLHm),(CRORHm),and (OROLHm),respectively; A and B represent the substituents located on the same (cis) and opposite (trans) sides of the central proton (H"), respectively, with respect to the CL-OL axis. The subunits (formaldehyde monomer and its derivatives) of the complexes were investigated first, followed
\
\
I
H
Figure 1. General geometry of fully optimized complexes (ABCOH-OCHX)'; the left subunit is tagged L, the right R, and the middle proton m. A, B, and X represent positions of substitutions for hydrogen atoms. H
HF 8-1 13,75706 MP2=-114,05656
n
H
HF =-153.078816
HF =-153,079393
MP2=-153.49710
MP2=-153.49763
HF =.114.04817 MP2=-114.33578
Figure 2. Optimized structures of (A) aldehyde (B) formaldehyde together with their protonated counterparts. The experimental data of bond lengths and angles for aldehyde32and f ~ r m a l d e h y d eare ~ ~ listed in parentheses as a comparison.
by calculations of optimized structures of protonated derivatives. The results appear in Figures 2 and 3 with energies computed at the SCF and MP2 levels. The search of configuration space of the protonated complexes was carried out by moving the central proton between the two subunits and the character of all minima and transition structures was confirmed with analytical second derivatives.
Results and Discussion Geometries. The protonation energy of formaldehyde decreases from 182.68 to 167.84 kcal/mol with a F atom substituent, whereas it increases to 195.16 kcallmol when a hydrogen atom is replaced by a methyl group, described in our previous work.24 Interestingly, when both hydrogens are replaced by an electron-donating methyl group and an electronwithdrawing fluorine atom the protonation energy varies with the orientation of these two substituents. The cis disubstituted protonated formaldehyde in Figure 3B in which the F atom and Hm are located at the same side with respect to the C - 0 bond exhibits attraction between Fd- and d+Hmand increases the protonation energy to 183.30 kcallmol. In contrast, the trans
Chu and Ho
16592 J. Phys. Chem., Val. 99, No. 45, 1995 F
H
F HF =-251.51485
HF =.251.56023
MP2=-252,11003
MP2=-252.15865
HF =-251.81198 MP2=-252 39633
HF =-251.848M MP2=-252.43628
HF =-251.85233 MP2=-252.44676
Figure 3. Optimized structures of the subunits and their protonated counterparts; (A) the subunit with CHzF substituent, (B) with CH3 and F two substituents, which has trans and cis protonated analogues (bond lengths/A, angleddeg, SCF and MP2 energieshartree).
disubstituted counterpart lacks a similar effect between F and H"; instead, it shows a small steric effect between the methyl group and Hm when they are located at the same side with respect to the C - 0 bond. Therefore, the protonation energy decreases to 180.6 kcal/mol, compared to protonated formaldehyde (Figure 2B, 182.68 kcal/mol). When one hydrogen of the formaldehyde is substituted with a CH2F group (Figure 3A), as we intended to merge the electron-releasing and -withdrawing characters in one substituent, the protonation energy becomes 186.45 kcal/mol, which is greater than for the disubstituted cisor truns-CH3FCO and H2CO but smaller than for CH3CHO. That the fluorine atom is located at p carbon relative to proton Hmand that the electron-releasing character of methyl group is simultaneously decreased is accountable for the calculated result. The BSSE corrections at the HF level, listed in Table 1, are about 1 kcal/mol and increase to 2 kcal/mol at the MP2 level. These values are less than 1% of the protonation energies and have no effect on the relative energies of the derivatives. The methods of calculating potential energy hypersurfaces for proton transfer are fully described p r e v i o ~ s l y . ~The ~ potential profiles all have a symmetric double well in complexes with two equivalent subunits, listed in the first three rows of Table 2 , along with the geometry parameters of the two local minima and the transition structure. In calculation of energies of transition structures the constraint of fixed R(OL-OR) was removed in the process of structural ~ p t i m i z a t i o n . ~The ~,~~ difference in energy between the transition structure and the right (or left) local minimum provides a measure of the transition barrier of proton transfer from either side of the minimum, listed as E#, in the last column in Table 2. The E# value so calculated is significantly decreased. It also may be noted that the barriers of the disubstituted complexes with two similar moieties (B and X positions both being occupied by F or CH3) are larger than the parent counterpart. As an explanation of this phenomenon, in the aldehyde complex (CH$HO-H-OCHCH3)+, the transfer of the central proton is slightly more difficult than for the formaldehyde analogue as the proton affinity of aldehyde exceeds that of formaldehyde. The energy barrier is therefore slightly greater, 1.73 kcal/mol. For the complex (HFCO-HOCHF)+, the proton affinity of HFCO is much smaller than that of CH3CHO or H2C0, but the energy barrier increases to
2.38 kcavmol. A possible explanation is that the H-bond length, 2.543 8, is significantly greater than the length 2.510 8, or 2.516 A in the analogous proton-bound dimer (H2CO-H-OCH*)+ or (CH3CHO-H-OCHCH3)+. The distance of transfer of a proton from the left minimum ( I L = 1.000 A) to the right (IL = 1.573 A) is much longer than for the formaldehyde counterpart, in which r ~ = . 1.018 8, to r ~ = . 1SO9 8,. Therefore it is more difficult to break the left OL-Hm bond during the movement of a proton without compensation of energy from the formation of the right OR-Hm bond. It is of interest to observe the variation of R(O0) during the transfer of a proton in the complexes. The R value in the left or right well of each complex is greater by about 5% than that of the transition structure. A similar effect was observed by Scheiner et a1.'* in the system containing a triple bond (HCCH and HCN), in which the contraction of the complex occurred when the proton moved from the equilibrium geometry to the transition structure. The two moieties of the complex at first move toward each other, reach their smallest distance at the transition structure, and then split apart to form the other local minimum. Structural variation during proton transfer in symmetric complexes (A-H-A)' such as for the first three entries in Table 2 is symmetric such that each corresponding parameter of the left complex is equal to that of the right complex (t, I R , a, and p of the left equals I R , I L , @, and a of the right , respectively). The process is equivalent to interchange of the two subunits in the complex; the transition structure has the central proton Hm located at the mid point of the 0-0 axis, belonging to the C2h point group. Based on the varied dipole momentI3 was explained briefly the alteration of a and @ angles in our previous report. The deviation of the a angle for conformations at the right well from the parent complex , as well as that of the /3 angle for conformations at the left well, is strongly related to the electron-donating or -withdrawing character of the substituents and to their positions of substitution in the subunits. The direction of the dipole moment tums clockwise 34.6" from the horizontal axis of the OCH2 molecule (Figure 4) with an electron-withdrawing substituent (F atom), but counterclockwise 7.4" with an electron-donating substituent (CH3). The a angle in the conformation at the right well, (ABCO-HOCXH)+ with various substituents at the A, B, and X positions, is adjusted appropriately according to the direction of the dipole moment of the substituted subunits (ABCO) to match the proper charge-dipole interaction in the complex. Methyl substitution in both subunits, (CH3CHO-H-OCHCH3)+, decreases slightly the a angle about 1" compared to the parent complex (133.2'). In contrast, F-atom substitutions, FCHOH-OCHF, greatly increase the a angle by 12.5" to 145.7', due to the clockwise shift of the dipole moment axis. The presence of both F and CH3 substituents in one subunit of the complex, trans (CH3FCO-HOCH#, further increases the a angle to 148.1', as the degree of clockwise tum is the greatest, 39.6". Whereas, the a angle is greatly reduced to 127.3' in the cis counterpart, resulting from the same degree but opposite turn of the dipole moment axis. The alteration of the p angle in the conformation at the left well, (ABCOH-OCXH)+, can be rationalized similarly. Potential Hypersurfaces. The potential profiles of proton transfer varying with the complexes from a symmetric double well through a single well to an asymmetric double well are plotted in Figure 5. The broken line of a symmetric double well (Figure 5A) represents the transfer potential of the parent complex (H2CO-H-OCH2)+, in which the two subunits are equivalent to each other and in which the transition structure
J. Phys. Chem., Vol. 99, No. 45, 1995 16593
Potential Energy Profiles for Proton Transfer
TABLE 2: Optimized Geometries of Wells and Transition Structures in the Potential Energy for Proton Transfer in (ABCO-H-OCXH'l'' species R rL rR a P 6 HF/4-31G* (au) E (kcal/mol) H2CO-H-OCH2 (L) 2.510 1.018 1.509 115.2 133.2 8.1 -227.851651 1.43b 0.0 -227.849367 (TS) 2.383 1.192 1.191 121.3 121.3 -227.851651 1.43' (R) 2.511 1.509 1.018 133.2 115.2 -6.0 CH3CHO-H-OHCCH3 (B, X = CH3) (L) 2.516 1.011 1.523 114.2 132.2 8.3 -305.895487 1.73 (TS) 2.380 1.190 1.190 120.2 120.2 0.0 -305.892737 (R) 2.516 1.523 1.011 132.3 114.2 -5.9 -305.895486 1.73 FCHO-H-OHCF (B, X = F) (L) 2.543 1.000 1.571 115.0 145.8 10.8 -425.403363 2.38 0.0 -425.399568 (TS) 2.378 1.189 1.189 124.9 124.9 -425.403365 2.38 (R) 2.545 1.573 1.000 145.7 115.0 -6.8 FCHO-H-OCH2 (B = F) (R) 2.575 1.625 0.991 148.6 114.5 -326.63323 CH3FCO-H-OCH2 trans (B = F, A = CH3) (L) 2.532 1.012 1.523 117.6 132.0 3.4 -365.650217 1.48 (TS) 2.379 1.169 1.210 124.2 120.3 -1.1 -326.647852 (R) 2.532 1.573 0.999 148.1 114.0 -8.1 -365.652337 2.81 CH3FCO-H-OCH2 cis (A = F, B = CH3) (L) 2.504 1.030 1.476 117.9 135.7 2.7 -365.651994 0.56 (TS) 2.393 1.145 1.248 121.0 123.1 -0.3 -365.651101 (R) 2.525 1.527 1.014 127.3 115.2 -5.2 -365.655334 2.66 CH2FHCO-H-OCH2 (B = CH2F) (L) 2.534 1.005 1.550 114.7 134.6 9.3 -365.613205 2.30 (TS) 2.381 1.209 1.172 123.4 119.8 -1.2 -365.609535 (R) 2.515 1.558 1.004 145.2 113.7 -8.8 -365.611875 1.47 All distances in angstroms; angle in degrees. See text for the definition of substitutional position. E# = energy difference between left local minimum (L) and transition structure (TS). E# = energy difference between right local minimum (R) and transition structure (TS). H
(E)
6
\
/
F
0
c-0
/
4 -
w
. 3
@ h
d = 2.64
d = 2.36
e = 0.0
e = 34.6
H
\
c-0
(C)
(D) cH3
/
\\ /
F
c-0
/
04
8
Q
= -7.4
08
10
12
14
16
18
20
rd4
c
d = 2.94
06
&
d = 3.05 0 = 39.6
Figure 4. Direction (8) and magnitude ( 6 ) of calculated dipole moments of formaldehyde and its substituted counterparts (dipole moment/D and angleldeg). has the central proton midway between the two oxygens. Whereas, in (HFCO-H-OCH# only one minimum is obtained in the entire potential energy surface represented by the dotted curve in Figure 5B. Owing to a large difference of proton affinities (14.84 kcal/mol) between these two subunits, the central proton is considerably farther from the formyl fluoride, Q = r(OLHm)= 1.625 A, compared to 0.991 8, for the distance between Hm and OR. We therefore designate this structure (FHCO-HOCHz)+. When hydrogen of the HFCO subunit is further replaced by the electron-donating CH3 group such as in the complex (CH3FCO-H-OCH*)+, to decrease the large difference of proton affinities between the two subunits (to 2.07 kcaymol from 14.84 kcaymol), an asymmetric double well for proton transfer reforms, the solid curve Figure 5C. The configuration of the shallow left well corresponds to (CH3FCOH-OCH*)+ and that of the deeper right to (CH3FCOHOCH*)+,due to the slightly greater proton affinity of OCH2 moiety. The location of transition structure in the potential
Figure 5. Potential-energy profiles for proton transfer in substituted complexes that span from symmetric double well through a single well to an asymmetricdouble well, depending on the substituents: (A) parent complex (H2CO-H-OCH2)+, (B) (FHCO-H-OCH#, and (C) (CH3FCO-H-OCH2)+. surface, according to Hammett's3' principle, shifts toward the greater of the two minima. The binding energies of each complex are listed in Table 3 at both HF and MP2 levels. When the complex has two local minima in the transfer potential then the binding energy for the left equilibrium is defined as AE = E(ABC0H-OCXH)+ - E(ABCOH)+ - E(0CXH) and that of the right as AE = E(ABC0-HOCXH)' - E(ABC0) - E(HOCXH)+. This binding energy represents the bonding strength between ABCOH' and OCXH or between ABCO and HOCXH+ of the complex, and is normally related to the equilibrium distance R ( O 0 ) and the type of substituents. We reported decreased binding energies in the system (HXCO-H-OCH2)+, in which X = F, CH3, and C1, relative to the parent complex; the consequences were attributed to the unequal interaction of the two subunits towards the proton, which lengthened either the OR-Hm or the OL-Hm bond and made the H-bond weaker by 3-5 kcal/mol. When the B and X positions are occupied by CH3, the binding energy of the complex increases from 29.13 to 29.93 kcal/mol, whereas that of the fluorine disubstituted counterpart decreases to 25.19 kcaumol. Q in the monofluoro-
16594 J. Phys. Chem., Vol. 99, No. 45, 1995
TABLE 3: Binding Energies (kcaYmol) of (ABCO-H-OHCX)Cu HF species uncorr cor+ 29.13 21.48 A, B, X = H 29.93 28.30 B, X = CH3 B,X=F 25.19 24.01 B=F 23.39 22.10 28.31' 26.59 B = F, A = CH? (trans) 21.5Id 26.15 A = F, B = CH3 (cis) 26.74' 25.16 29.45d 21.65 B = CHzF 27.71' 26.12 30.66d 29.14 B = CH2C1 21.12' 25.69 29.31d 26.26 B = CHCl2 28.16' 26.56 24.74d 23.36 B = CC13 28.83' 27.30 23.64d 22.33
Chu and Ho n
F
MP2
uncorr 32.44 33.09 26.12 25.16 31.23 30.02 29.93 33.04 30.44 33.48 39.10 32.91 30.80 29.21 31.65 21.13
corr 28.88 29.41 24.38 22.66 21.87 21.28 26.88 29.15 21.35 30.45 26.45 29.05 21.61 26.13 28.23 24.42
\
/
H
1179
2%
oxH7z--+gg SCF=-365.651994
1220
C 4 Z H
1 0 8 4 1 '17'
H F
1.Q77i ,.2,0\
" See text for the definition of substitutional position. Correction by basis set superposotion error (BSSE). Binding energy AE = E(ABCOH-OCH# - E(ABCOH+)- E(H2CO). Binding energy AE = E(ABC0-HOCH2)' - E(ABC0) - E(H2COH'). 6
I
4
h
1 1 077
\
lg2
1273
1527
H SCF =-365.655334
121 0
\
1 0 7 y : 1 5 0
o
n
H
2 10
0
1 -
0 0
u
0
H
1
1
and difluoro-substituted complexes is 1.625 and 1.573 8, (Table 2), respectively, significantly greater than for the parent analogue, 1.509 A; it is logical to have smaller binding energies in these more stretched fluoro-substituted systems. Nevertheless, the larger binding energy of the dimethyl-substituted counterpart with a slightly longer r~ (1.523 A) may be due to the electron-releasing methyl groups at both ends of the complex, which increases the basicities of oxygen atoms of the subunits and produces a stronger H-bond. Our previous results illustrated that, in an asymmetric double well, the well corresponding to the proton being closer to the subunit of greater proton affinity was the deeper. For example, as the proton affinity of trans protonation of CH3FCO (Table 1) is smaller than that of OCH2 by 2.07 kcallmol the right-potential well of trans complex (CH3FCO-HOCH2)+ with proton nearer OCH2 is deeper by 1.33 kcal/mol than the corresponding left well in which the proton is closer to the CH3FCO subunit (the solid curve in Figure 6). Nevertheless, this argument is not obeyed in the cis counterpart. The conformation in the right well in which the proton is closer to the OCH2 of smaller proton affinity by 0.62 k c d m o l than the cis-protonated CH3FCO is still deeper by 2.10 kcal/mol relative to the left well, shown by the dotted
Figure 7. Optimized equilibrium structures of cb(CH3FCO-HOCH2)+ at (A) the left well, (C) the right well, and (B) the transition structure of proton-transfer potential energy profile. (SCF energies/ hartree). curve in the same figure. An explanation of this conflict is obtained through introduction of binding energies listed in Table 3. The binding energy in the left well structure (CH3FCOHOCH# is 26.74 kcal/mol and that of the corresponding right well (CH3FCO-HOCH2)+ is 29.45 kcdmol. This greater value 2.71 k c d m o l in the right well indicates stronger interaction between CH3FCO and HOCH2+ than for the other two moieties in the left well and is sufficient to compensate the proton affinity difference (0.62 kcal/mol) between CH3FCO of cis protonation and OCH2. Another aspect that provides support of this explanation arises from the observation of conformations of the cis complex in Figure 7. The equilibrium conformations of the left and right wells are represented in Figure 7A,C, respectively. The energy needed to cleave the structure in Figure 7A into two corresponding subunits (CH3FCOH+ OCH3 is greater than that in Figure 7C into CH3FCO +HOCH2 if the lengths of the bonds Hm-OR in Figure 7A (1.476 A) and OL-Hm in Figure 7C (1.527 A) are the only factors to be considered in relating to the dissociation energy. Cleavage of the OL-Hm bond in Figure 7C associated with the breaking of the F6-&+Hminteraction thus requires more energy, whereas this phenomenon does not appear in the split of the Hm-OR bond in Figure 7A. This argument upholds that the conformation in Figure 7C is located in a deeper well. This interaction also gives an apparent decrease of the potential energy in the system; the entire transfer profile (Figure 6) of the cis complex is lower than that of the trans counterpart. In contrast, for the trans
+
+
J. Phys. Chem., Vol. 99, No. 45, 1995 i6595
Potential Energy Profiles for Proton Transfer
TABLE 4: Protonation Energy (kcal/mol) and o Value of Several Calculated Complexes complexes EL^ ER~ IEL- ERI 0 (%I [H~CO-H-OCHZ]' 182.68 182.68 0.00 0.00 0.00 0.00 [HFCO-H-OCFH]+ 167.84 167.84 0.00 0.00 [HClCO-H-OCClH]+ 174.31 174.31 0.00 0.00 [CH3CHO-H-OHCCH3]+ 195.16 195.16 [CH3FCO-H-OCH2]+ (cis) 183.30 182.68 0.62 0.34 [CH3FCO-H-OCH#
(trans)
well typecS/D D D D D D
180.61
182.68
2.07
1.13
D
[ (CH2Cl)HCO-H-OCH21+
186.02
182.68
3.34
1.83
D
[(CHCl2)HCO-H-OCHz]+
179.07
182.68
3.61
2.02
D
[(CH2F)HCO-H-OCH2]+
186.45
182.68
3.17
2.06
D
[FHCO-H-OCHCI]'
169.70
173.4
3.70
2.18
D
[(CC13)HCO-H-OCH2]+
174.81
182.68
7.87
4.50
D
[(CHF~)HCO-H-OCHI] +
174.56
182.68
8.12
4.65
D
[FHzN-H-OCH~]'
193.65
182.68
10.97
6.00
D
[ClHCO-H-OCHz]+
169.70
182.68
12.98
7.65
D
E# (kcal/mol)
1.43 2.38 2.73 1.73 0.56d 2.66' 1.48 2.81 2.55 0.80 1.54 1.73 2.30 1.47 0.43 3.30 0.73 3.41 0.65 3.28 0.41 8.76 0.06 4.47
167.84 182.68 OCH2]+ 14.84 8.84 S [H3N-H-OCH2]+ 218.20 182.68 35.52 19.4 S Protonation energy of the left subunit in the complex. Protonation energy of the right subunit in the complex. Type of well for potential energy profile of proton transfer; S for single and D for double. Energy difference between left local minimum (L) and transition structure (TS). e Energy difference between right local minimum (L) and transition structure (TS). [HFCO-H-
complex having no F-Hm interaction to decrease the energy, the enhanced steric effect between CH3 and Hm at the same side of the molecule increases the energy of the system. To understand the variation of potential profiles for proton transfer with various equilibrium protonated complexes (AH-B)+ discussed above is one purpose of this work. The formation of an asymmetric double well or a single well in the complex (A-H-B)+ for A f B depends on the difference of protonation energies between the two subunits A and B. A formula gives the per cent quantity w ,
sum for the conformation in the well, the deeper is the well. The example of the cis complex (CH3FCO-H-OCH2)+ in the preceding section that has a deeper right well is explained easily according to this argument. This magnitude is greater for the right well (212.13 kcaVmol = binding energy (BE) 29.45 kcal/ mol protonation energy (PE) of OCH2 182.68 kcaVmo1) than for the left well (210.04 kcaymol = BE 26.74 kcal/mol PE of CH3FCO at cis position 183.30 kcaymol). In the (CH2FHCO-H-OCH# complex the greater magnitude for the left well 214.16 kcaVmo1 = BE 27.71 kcal/mol PE of CH2FHCO 186.45 kcaVmol than for the right well 213.34 kcav mol = BE 30.66 k c d m o l PE of OCH2 182.68 kcal/mol, resulting in a deeper left well, confirms the above argument. In addition, the difference of the left and right magnitudes represents the potential gap between the two wells. The last two entries in Table 4 have larger w values; for this reason neither a second minimum nor a transition structure is found through all conformation space.
+
+
+
+
in which E(A) and E(B) represent the protonation energies of subunits A and B respectively, and min(E(A),E(B)) represents the smaller protonation energy of the two. Our calculated results show that when w was less than 8% an asymmetric double well for proton transfer appeared in an equilibrium complex (AH-B)+. For example, the protonation energy of NH3 is 218.20 kcaVmo1, significantly larger than that of OCH2. As the calculated w is about 19%, a single well is predicted in the equilibrium complex (NH3-H-OCH2)+. When one hydrogen of NH3 is replaced with a fluorine atom, the protonation energy of NH2F decreases to 193.65 kcal/mol and w is calculated to be only 6%; as a consequence, an asymmetrical double well appears in the equilibrium complex (NHzF-H-OCH#. Several other protonated complexes (A-H-B)+ were calculated; the corresponding results appear in Table 4. The w values for most selected complexes are smaller than 8%, and the corresponding profiles of proton-transfer potential of the complexes in the equilibrium conformation appear as a double well. To determine which conformation of the two local minima has a lower energy in an asymmetric double well, the magnitude of the sum of binding energy of the conformation and protonation energy of the subunit nearer the central proton in the conformation is a decisive factor. The larger is the magnitude of this
Conclusion The w value 8% in determining the well type of asymmetric double well from a single well is an arbitrary generalization from our calculated results for the complexes presented in Table 4. However, in other complex systems, for w greater than 8% an asymmetric double well might occur, or a single-well potential might form for w smaller than 8%. Indeed, if w is too large the transfer of proton becomes terminated, such that there is only one minimum in the entire configuration space. A double well is generally formed if protonation energies of the two subunits differ not too much. Figures 2 and 3 show opening of the bond angle at the carbonyl carbon atom after protonation. Recently this behavior has been utilized by X-ray crystallographyof H-bonded systems. As is well-known, X-ray does not locate the well position of the proton but the bond angle at the atom at which the proton is residing becomes larger. Thus in this way the position of the proton may be 10calized.~~
16596 J. Phys. Chem., Vol. 99, No. 45, 1995
Chu and Ho
-
TABLE 5: Thermodynamic Properties of Binding Reactions ABCOH+ + HXCO (ABCO-H-OCXH)+ Evaluated at Several TemDeraturee substituent
1K
10K
none B, X = CH3 B, X = F B=F
-27.67 -28.99 -24.20 -22.00
-27.73 -29.05 -24.24 -22.04
100K
300K
500K
1OOOK
-27.40 -28.20 -23.37 -21.38
-26.47 -27.25 -22.40 -20.39
-23.78 -24.56 -19.70 -17.67
AH' (kcal/mol)
none B, X = CH3 B, X = F B=F
-0.45 -5.99 -4.65 -2.02
none B, X = C H 3 B,X=F B=F
-27.67 -28.98 -24.19 -22.00
-27.99 -29.09 -24.29 -22.17
ASo (cal/mol) -17.86 -31.75 -24.27 -33.74 -22.90 -32.67 -20.32 -31.58 AGO -27.55 -28.81 -24.01 -21.84
-31.14 -31.24 -30.05 -29.74
-29.79 -29.80 -28.57 -28.23
(kcal/mol) -24.81 -18.06 -25.71 -18.83 -21.02 -14.36 -19.01 -12.46
-11.58 -12.35 -8.11 -6.28
-27.47 -27.51 -26.24 -25.86 3.69 2.95 6.54 8.19
fl These data are evaluated through standard thermodynamic formulas that incorporate the vibrational frequencies of the various species.
-
To understand the thermodynamic properties of the association reaction ABCOH+ HXCO (ABCO-H-OCXH)+, we calculated AH", and AS", and AGO of the reaction at various temperatures, presented in Table 5. As predicted theoretically, the enthalpy of the reaction decreases with increasing temperature, indicating that the intermolecular modes of the complex at small wavenumbers become increasingly populated as temperature increases, which is not possible for the separate monomers. The enthalpy of the monomers depends less on temperature below 300 K than the enthalpy of the complex. That AS" becomes less negative with increased temperature also results from the increased entropy of the complex in which the population of those intermolecular vibrational modes increases. These results are similar to those reported for the acetylene system by Scheiner et al.'* The sequence of entropies of the association reactions with various substituents occupying the A, B, and X positions at higher temperatures follows the opposite trend of the magnitude of binding energies of the complexes; i.e. the sequence of reaction entropies is (CH3CHOH-OCHCH3)' < (HCHOH-OCH2)' < (FCHOHOCHF)+ < (FHCOH-OCH*)+. The "looseness" of the complex correlates with the magnitude of the entropy of the reaction; Le., the complex with a larger population in the lower intermolecular vibration modes is associated with a smaller binding energy. The Gibbs free energy of the reaction, AGO, reaches its thermoneutrality point at a temperature greater than 500 K, indicating that the above association reactions can best occur (spontaneously) at a temperature less than 500 K.
+
Acknowledgment. We are grateful to the computer center at National Taiwan Normal University where the Gaussian
package and the computer time are provided. Support for this research from the National Science Council of the Republic of China (NSC 85-21 13-M-003-014) is also gratefully acknowledged. We are also indebted to the reviewer for helpful suggestions concerning the manuscript.
References and Notes (1) Blatz, P. E.: Tompkins, J. A. J. Am. Chem. Soc. 1992, 114, 3951.
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