J. Phys. Chem. 1995, 99, 14340-14346
14340
Computational Investigations of Reactive Intermediates in the Acid-Catalyzed Proton Exchange in Formamide Julianto Pranata* and Geraldine D. Davis Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas 72701 Received: April 14, 1995; In Final Form: July 17, 1995@
Ab initio calculations at various levels (up to QCISD(T) and MP4/6-31 l+G(d,p)//MP2/6-31G(d)) and Monte Carlo simulations were used to investigate protonated formamide and formimidic acid, which are presumed intermediates in the acid-catalyzed proton exchange in formamide. Both in the gas phase and in aqueous solution, protonation at the oxygen leads to a substantially more stable intermediate than protonation at the nitrogen. Of the two conformers of the 0-protonated intermediate, one is preferred in the gas phase, but they become nearly equal in solution. Among the four conformers of formimidic acid, one is preferred in the gas phase, but in solution another conformer is preferred, with two others within 1 kcal/mol. Thus, solvation plays an important role in determining relative stabilities of these intermediates.
Introduction
00"
The mechanism of acid catalyzed proton exchange in amides' is a fascinating subject, because different levels of sophistication in our reasoning lead to different ideas. The simplest analysis would be to recognize that the amide nitrogen has a lone pair, and thus can be protonated, yielding an N-protonated intermediate exemplified by 1. This intermediate would then simply lose a proton, preferably a different one from the proton that just came in, and the exchange has taken place.
e
U \
t 0 H O
N
1
A more sophisticated analysis would recognize that the oxygen atom of the amide is also a site for protonation. The oxygen has two lone pairs; moreover, unlike the nitrogen's lone pair, these electrons are not involved in amide resonance. Protonation at the nitrogen destroys amide resonance; protonation at the oxygen does not. Thus, the 0-protonated intermediate, exemplified by 2a or 2b, should be a more stable species. H
' 0
2a
2b
One can then argue that protonation at the oxygen enhances the acidity of the amide protons, which is lost to generate a further intermediate, the imidic acid (exemplified by 3a-d). Reversing the steps leads to the proton exchange. This 0-protonation mechanism is more circuitous, but perhaps more consonant with chemical intuition. There does not seem to be any serious disagreement that the first point of this second view is correct, Le., that 0-protonated formamide is the more stable isomer. Available experimental evidence have been so and existing calculation^^-^ s- Abstract published in Advance ACS Absrracts, September 1, 1995.
0022-3654/95/2099-14340$09.00/0
H/
l
%NH
3a
H'
El" %I I H
3b
H
H
' 0
H'
&
%NH
' 0
H'
l%I I
H
3c
3d
also support this view. However, not everyone accepts this as evidence to discount the N-protonation mechanism. A more decisive answer was sought Perrin and co-workers.1~s~9 Pemn's account stated that he initially preferred the 0-protonation mechanism;' however, their studies on acetamide8 led them to conclude that the N-protonation mechanism is the correct one for this particular amide. Subsequently, it was concluded that both mechanisms are possible, depending on the type of amide involved? Amides with electron-withdrawing substituents prefer to follow the 0-protonation pathway, whereas electrondonating substituents will favor the N-protonation mechanism. Despite the elegance and ingenuity involved in this work, the conclusions are reached by indirect reasoning, and the possibility of alternative interpretations remains. It appears that our understanding of this particular reaction may still be enhanced by further investigations. Our eventual goal is a thorough characterization, using computational methods, of the potential energy surface of the reaction. This paper describes our initial efforts which focus on the "stable" reactive intermediates, Le., those structures corresponding to minima on the potential energy surface. All of the structures reported here have been subjected to computation^;^-^^'^-^^ however, we have extended previous calculations by utilizing larger basis sets and higher levels of electron correlation. In addition, one key element missing from the existing computations is the role of solvent effects. We have addressed this issue in the present work using Monte Carlo simulations. Computational Procedures
Ab initio molecular orbital calculation^^^ were performed on the intermediates mentioned above, Le., N-protonated formamide (l),the two conformers of 0-protonated formamide (2a and 2b), and the four conformers of formimidic acid (3a-d). For comparison, calculations on formamide were also performed. Complete geometry optimizations were performed at the RHF/ 3-21G, RHF/6-31G(d), and MP2/6-31G(d) levels; the 3-21G 0 1995 American Chemical Society
Acid-Catalyzed FYoton Exchange in Formamide
J. Phys. Chem., Vol. 99,No. 39, 1995 14341
TABLE 1: Solute Parameters for Monte Carlo Simulations molecule atom 9 u,A E , kcaYmol 1
C
0
2a
2a,A
2a,B
2b
3a Figure 1. Stable bimolecular complexes between N- and 0-protonated formamide and water.
3b
w
Q
3a,A
3c
3a,C
3a,B
w
3d
8 3b,A
Ld
3b,B
3b,C
N 3b,D
3c,A
3c,B
3c,c
3c,D
% ! w
2y? 3d,A
3d,B
3d,C
N H(C) Ha(N Hbr HSN) C 0 N H(C) H(O) HaW) HdN) C 0 N H(C) H(O) HdN) HdN) C 0 N H(C) H(O) H(N) C 0 N H(C) H(O) H(N) C 0 N H(C) H(O) H(N) C 0
3d,D
Figure 2. Stable bimolecular complexes between formimidic acid conformers and water.
calculations reproduced previous ~ o r k . ~Computations ,'~ with larger basis sets, 6-31 lG(d,p) and 6-31 l+G(d,p), and at higher levels of electron correlation, MP4 and QCISD(T), were performed on the MP2-optimized structures. Frequency calculations were performed at the RHF/6-31G(d) level in order to ensure that the structures are minima on the potential energy surface. They also provide data for the calculation of thermodynamic quantities. For this purpose, contributions from translational and rotational degrees of freedom were treated classically. Vibrational frequencies were scaled by a factor of
H(C) H(O) H"
0.570 -0.325 -0.406 0.114 0.355 0.346 0.794 -0.549 -0.900 0.147 0.522 0.500 0.486 0.692 -0.479 -0.780 0.131 0.478 0.498 0.460 0.623 -0.650 -0.877 0.080 0.432 0.392 0.580 -0.624 -0.821 0.059 0.454 0.352 0.626 -0.653 -0.859 0.029 0.429 0.428 0.533 -0.569 -0.707 0.016 0.407 0.320
3.75 2.96 3.25 2.50 0.00 0.00 3.75 3.00 3.25 2.50 0.00 0.00 0.00 3.75 3.00 3.25 2.50 0.00 0.00 0.00 3.75 3.00 3.25 2.50 0.00 0.00 3.75 3.00 3.25 2.50 0.00 0.00 3.75 3.00 3.25 2.50 0.00 0.00 3.75 3.00 3.25 2.50 0.00 0.00
0.105 0.210 0.170 0.020 0.000 0.000 0.105 0.170 0.170 0.020 0.000 0.000 0.000 0.105 0.170 0.170 0.020 0.000 0.000 0.000 0.105 0.170 0.170 0.020 0.000 0.000 0.105 0.170 0.170 0.020 0.000 0.000 0.105 0.170 0.170 0.020 0.000 0.000 0.105 0.170 0.170 0.020 0.000 0.000
0.9, and modes with scaled frequencies below 550 cm-' were treated as classical r0tati0ns.l~ Additional ab initio calculations were performed on bimolecular complexes consisting of the protonated formamide or the imidic acid and one water molecule. These calculations were at the RHF/6-31G(d) . . level, and only selected intermolecular distances and angles were optimized; i.e, the water molecule was constrained to the experimental geometry ( r ( 0 H) = 0.9572 A, L(H-0-H) = 104.52') while the other was constrained to the MPZoptimized geometry. A variety of structures were considered; the successful ones are shown in Figures 1 and 2. Due to the relatively low level of computations, the results should not be considered quantitatively accurate. In addition to performing only a partial geometry optimization, no correction for the basis set superposition errorI6 is included in the calculations. Nevertheless, they allow for a qualitative and preliminary assessment about the hydration of these intermediates. To more accurately assess the effects of solvation, Monte Carlo simulation~'~ were performed on isothermal-isobaric systems consisting of one solute molecule (the protonated amide or the imidic acid) and 264 water molecules, in a cubic box of dimensions ca. 20 x 20 x 20 A3 with periodic boundary conditions. Water molecules were represented by the TIP4P model.'* The solute model used rigid, MP2-optimized geom-
Pranata and Davis
14342 J. Phys. Chem., Vol. 99,No. 39, 1995
TABLE 2: Structural Results from ab Initio Calculation@
c-0 C-N C-H N-Ha N-HdHc)
1
2a
2b
2b
3a
3b
3c
3d
1.172 1.155 1.187 1.565 1.525 1.565 1.072 1.082 1.095 1.023 1.016 1.032 1.023 1.016 1.032
1.292 1.280 1.292 1.285 1.285 1.301 1.069 1.074 1.086 1.007 1.003 1.020 1.007 1.003 1.019 0.974 0.957 0.983 126.6 126.2 126.7 113.6 114.5 113.9 123.8 123.5 123.7 120.6 120.0 119.6 122.5 117.6 115.9
1.294 1.274 1.297 1.278 1.279 1.296 1.071 1.076 1.088 1.009 1.004 1.021 1.005 1.001 1.017 0.971 0.956 0.981 118.9 119.5 118.6 121.3 121.0 121.7 120.3 120.8 120.6 122.3 121.2 121.0 120.1 115.3 113.1
1.212 1.193 1.224 1.353 1.348 1.361 1.084 1.081 1.105 0.998 0.996 1.011 0.995 0.993 1.008
1.373 1.339 1.363 1.246 1.246 1.273 1.068 1.075 1.087 1.013 1.007 1.026
1.361 1.329 1.350 1.245 1.246 1.274 1.074 1.079 1.091
1.376 1.344 1.367 1.242 1.242 1.268 1.073 1.079 1.091 1.013 1.006 1.026
1.369 1.337 1.359 1.242 1.242 1.270 1.080 1.084 1.097
0-H 0-C-N 0-C-H C-N-Ha C-N-Hb(H,)
118.0 117.8 118.0 131.4 129.9 130.6 108.6 108.6 108.1 111.2 112.0 111.9
C-0-H
125.3 124.9 124.8 122.4 122.4 122.9 119.4 119.3 118.9 121.9 121.8 121.9
0.967 0.950 0.976 129.2 129.3 130.2 109.3 110.1 109.5 117.6 113.5 112.2
1.007 1.002 1.020 0.969 0.952 0.980 122.0 122.5 121.6 109.7 110.6 110.5
0.964 0.947 0.973 123.5 124.5 124.5 115.5 115.2 115.5 115.1 111.3 109.7
1.008 1.002 1.021 0.963 0.946 0.971 120.1 120.7 119.1 114.0 114.2 114.4
116.7 115.7 111.8 110.8 110.5 109.2 114.2 110.5 113.8 113.1 111.2 108.1 111.3 111.0 108.8 105.4 109.2 108.8
a The three values shown for each parameter are optimized at RHF/ 3-21G, RHF/6-3 lG(d), and MP2(FULL)/6-31G(d), respectively. Bond lengths are in angstroms and angles in degrees.
etries and OPLS-type parameters for intermolecular interactions, with standard Lennard-Jones u’s and and partial atomic charges obtained by the CHELPG methodZofitted to the RHF/ 6-3 1G(d) electrostatic potential. These parameters are shown in Table 1. Nonbonded interactions were truncated using spherical cutoff distances of 8.5 8, for solvent-solvent interactions and 9.5 8, for solute-solvent interactions, with quadratic feathering over the last 0.5 8,. Each simulation consisted of
lo6 configurations for equilibration followed by 2 x 106-4 x IO6 configurations for averaging. Statistical perturbation theory2’ was used in conjunction with the Monte Carlo simulations for interconversions among the protonated amides (1, 2a, and 2b) and among the imidic acid conformers (3a-d). These simulations allow the calculation of the relative free energies of hydration between pairs of isomers. Each interconversion involved 10- 12 (protonated amides) or 25 (imidic acids) separate Monte Carlo simulations with double wide sampling.22 The ab initio calculations were performed with the Gaussian92 program23on a Silicon Graphics Indigo R4000 workstation. The Monte Carlo simulations were performed with the BOSS programZ4on the Indigo or on a Hewlett-PackardApollo Series 700 workstation.
Results and Discussion Isolated Molecules. Detailed structural data for all the reactive intermediates are shown in Table 2, while energy-related information is shown in Table 3. These results are consistent with expectations based on chemical intuition and on previous experience with these types of calculation^.^^ For example, N-protonation of formamide (1) causes loss of amide resonance, resulting in a shortening of the C - 0 bond and lengthening of the C-N bond. In constrast, 0-protonation (2a and 2b) appears to increase the degree of delocalization, resulting in C-N and C-0 bond lengths that are more nearly equal. In the imidic acids (3a-d) some degree of delocalization is present, but the principal contributing resonance structure is one with a C-N double bond. In formamide, of course, the principal contributing resonance structure is one with a C - 0 double bond. Intramolecular nonbonded interactions appear to have significant influence on the structure. 2a and 3a have the hydroxyl and amide hydrogens rather close to one another, and this result in opening up the 0-C-N angle compared to the other conformers. Comparing the structures at the various computational levels, it is observed that bond lengths at the RHF/6-31G(d) level are shorter by up to 0.03 8, compared to the MP2 values. The
TABLE 3: Energetic Results from ab Initio Calculationss 1 RHF/3-2 1G RHF/6-3 1G(d) MP2(FULL)/6-31G(d) MP2(FC)/6-31 lG(d,p) MP2(FC)/6-31 l+G(d,p) MP4(FC)/6-311G(d,p) MP4(FC)/6-3 11+G(d,p) QCISD(T)/6-3 1l+G(d,p) H v , ~ ~ ~ ~ 998
AG298
-168.29696
2a
-168.32323 (- 16.485) - 169.23550 - 169.26173 (-16.460) -169.71188 -169.72674 (-9.325) -169.80514 -169.82229 (- 10.762) -169.80886 -169.82595 (-10.724) -169.84668 -169.86196 (-9.588) -169.85069 -169.86587 (-9.526) -169.84780 -169.86525 (- 10.950) 39.396 39.627 63.469 60.731 -9.902
2b
formamide
-168.32814 (- 19.566) - 169.26655 (-19.484) -169.73199 (-12.619) -169.82780 (-14.219) -169.83186 (-14.433) -169.86731 (-12.946) -169.86587 (-13.153) -169.86525 (-14.596) 39.812 60.701 -13.354
-167.98490
3a
-167.95178 (20.783) - 168.90801 - 168.90194 (18.047) -169.40538 -169.37780 (17.307) -169.49422 -169.47048 (14.897) -169.50512 -169.48034 (15.550) -169.53176 -169.50868 (14.483) -169.54287 -169.5 1874 (15.142) - 169.51704 - 169.51704 (14.194) 30.894 3 1.383 63.111 60.217 15.500
3b
3c
3d
-167.95683 (17.614) - 168.90801 (14.238) -169.38348 (13.742) -169.47610 (11.370) -169.48680 (11.496) -169.51389 (11.214) -169.52474 (11.377) -169.5231 1 (10.385) 3 1.362 59.864 11.821
-167.95049 (21.593) - 168.90097 (18.656) -169.37655 (18.091) -169.46944 (15.550) -169.48004 (15.738) -169.50766 (15.123) -169.5 1847 (15.311) -169.5 1695 (14.250) 31.229 60.632 15.325
-167.94236 (26.694) - 168.89645 (21.492) -169.37207 (20.902) -169.46574 (17.871) -169.47723 (17.501) -169.50383 (17.526) -169.5 1552 (17.162) -169.5 1395 (16.133) 31.212 60.574 17.207
Rows beginning with the computational method designation display the electronic energies (in atomic units) with relative energies (in kcal/ mol) shown in parentheses. These are relative to 1 for the protonated intermediates and relative to formamide for the imidic acids. The energies geometries. in the first three rows are obtained at geometries optimized at that level, the rest were obtained at the MP2(FULL)/6-3lG(d)-optimized Hv,b298 (in kcal/mol) and s298 (in cal(mo1 K)) were obtained from frequency calculations at the RHF/6-31G(d) level, with appropriate scaling of the vibrational frequencies (see text). The values for AGZ9*use the QCISD(T) energies, and are relative to 1 and to formamide as described above.
Acid-Catalyzed Proton Exchange in Formamide smaller basis set 3-21G actually performs better in this regard. This is consistent with numerous previous results with these types of calculation^.^^ With regard to bond angles, contraction of C-0-H and C-N-H (for the imidic acids) is observed with the larger basis set and inclusion of electron correlation, again consistent with previous observation^.^^ Relative energies of the various conformers can be rationalized by considering the intramolecular charge-charge and dipole-dipole interactions. Thus, 2b is more stable than 2a because 2a have unfavorable electrostatic repulsion between the hydroxyl and amide hydrogen, whereas 2b has a favorable interaction between the amide hydrogen and the oxygen lone pair, almost forming an intramolecular hydrogen bond. The 0-protonated intermediates are more stable than the N-protonated intermediate (l), because of the loss of resonance in 1. Evidence of this is present in the C-N and C-0 bond lengths discussed above and also in the rotation barriers of the C-N bond. In 1, this rotation barrier is 0.7 kcal/mol at the RHF/631G(d) level; in 2a and 2b it is 32 and 39 kcdmol, respectively. These values were obtained by locating and optimizing the transition states along the torsional pathways. The most stable conformer of imidic acid is 3b, which almost has an intramolecular hydrogen bond between the hydroxyl group as the donor and the imide nitrogen as the acceptor. A similar “hydrogen bond” exists in 3c, with the role of donor and acceptor reversed. But, it seems that a hydroxyl oxygen is a worse acceptor than an imide nitrogen and imide is also a worse donor than hydroxyl-this is discussed further below. The overall result is that this is not as good a stabilizing interaction as in 3b. In fact, 3c is not any better than 3a, which is destabilized by having the hydroxyl and imide hydrogens so close together. Countering this effect is the good alignment of bond dipoles in 3a, where the N-H bond dipole is favorably oriented relative to C-0, while 0-H is favorably oriented with respect to C-N; in 3c, the 0-H orientation is not as favorable. The least stable conformer is 3d, which has destabilizing electrostatic repulsions between the lone pairs on oxygen and nitrogen, in addition to unfavorable bond dipole alignments. Relative energies among conformers (2a vs 2b, or 3a-d) are fairly consistent even at the lowest level of theory, except that 3d is predicted to be considerably less stable at the RHF/ 3-21G level. Thus, completely discounting this conformer on the basis of RHF/3-21G calculationsI2 can now be seen to be inappropriate. Inclusion of electron correlation (at least at the MP2 level) is necessary to correctly predict the relative energies between 1 and 2, and larger basis sets also appear to be necessary for the relative energies between formamide and formimidic acid. Comparing the results at the various computational level, it appears that the relative energies have reached consistency within 1-2 kcal/mol at the highest levels attempted. Complexes with a Water Molecule. Ab initio calculations were performed on bimolecular complexes consisting of 1, 2, or 3 and one molecule of water. These studies enable us to obtain some preliminary ideas about the hydration of these intermediates, particularly with regard to hydrogen bonding. These calculations are not at a level that can be considered quantitatively accurate, but the trends in the results should give us some insights. The complexes are illustrated in Figures 1 and 2, while some details of the results are in Table 4. For the protonated intermediates 1, 2a, and 2b, only complexes where the water molecule acts as a hydrogen-bond acceptor were possible; complexes where the water molecule acts as a hydrogen-bond donor ended up dissociating upon optimization. This is not surprising considering the positive charge on the intermediate. Only one type of hydrogen bond
J. Phys. Chem., Vol. 99, No. 39, 1995 14343
TABLE 4: Results for Hydrogen-Bonded Complexeg ~
~~
distance (angstroms) interaction energy (kcavmol) ab initio OPLS ab initio OPLS l,A l,B
2a,A 2a,A 2b,A 2b,B 2b,C 3a,A 3a,B 3a,C 3b,A 3b,B 3b,C 3b,D 3c,A 3c,B 3c,C 3c,D 3d,A 3d.B 3d,C 3d,D
1.746 1.758 1.752 (OH donor) 2.372 (OH donor) 1.805 1.669 1.785 1.821 2.259 2.118 1.928 (OH donor) 2.671 (NH donor)b 2.227 1.910 (water acceptor) 2.162 (water donor) 2.270 1.910 (water acceptor) 2.748 (water donor)b 2.219 3.323 (water acceptor) 2.121 2.374 (water acceptor) 2.717 (water donor)b 1.897 2.208 (N acceptor) 2.871 (0acceptor)b 2.204 (N acceptor) 3.084 (0 acceptor)b 2.279 1.912
1.676 1.672 1.607 2.597 1.685 1.601 1.674 1.693 1.792 1.820 1.728 2.469 1.799 1.794 1.924 1.867 1.703 2.743 1.836 2.040 1.824 1.874 2.707 1.704 1.899 2.784 2.589 1.844 1.871 1.711
-20.3 -21.7 -25.7
-18.0 - 19.0 -22.5
-19.3 -23.7 -17.5 -18.7 -3.1 -5.* -8.9
-17.7 -20.1 -16.8 -17.1 -4.5 -7.3 -9.7
-4.1 -9.3
-5.1 - 10.3
-3.8 -9.1
-4.8 -8.3
-3.7
-6.4
-6.6 -3.8
-7.7 -4.8
-8.8 -6.6
-9.0 -7.7
-5.8
-7.4
-4.0 -8.6
-4.7 -8.6
See Figures 1 and 2 for the structures of the complexes. These distances are probably too great for a proper hydrogen bond (see text). (1
is possible in 1, since only the nitrogen can act as the donor. The two possible orientations (1,A and l,B in Figure 1) have essentially the same interaction energies. 2a and 2b have both the hydroxyl and amide groups that can act as hydrogen bond donors, and the amide group has two hydrogens. All three complexes are present for 2b (2b,A, 2b,B, and 2b,C; Figure 2). In 2a, two of these are replaced by a single complex with hydrogen bonds from both hydroxyl and amide groups (2a,A). Not surprisingly, the doubly-hydrogen-bonded complex is more stable than any singly-hydrogen-bonded ones. Another observation is that the hydroxyl group is a better hydrogen bond donor in this situation. Complexes with a hydrogen bond from the hydroxyl group are more stable relative to complexes with a hydrogen bond from an amide group. There is greater variability in the imidic acids, where either molecule can act as the donor and acceptor. In analyzing these results, let us consider the singly hydrogen bonded structures first. There are complexes where the hydroxyl group acts as the donor (3c,D and 3d,D), where the imide group acts as the donor (3b,C and 3d,C), where the hydroxyl group acts as the acceptor (3a,A and 3b,A), and where the imide group acts as the acceptor (3a,B and 3d,B). The most stable complexes appear to be ones where the hydroxyl group is a donor, followed by those where the imide is an acceptor, while complexes where the hydroxyl is an acceptor or imide is a donor are relatively not as stable. The rest of the complexes can potentially have multiple hydrogen bonds. However, based on the interatomic distances ( ( 2 . 5 A) only two of them actually do (3b,B and 3c,A; Table 4). Furthermore, the additional hydrogen bonds do not seem to confer much additional stability. 3b,B for example has the two most favorable kinds of hydrogen bonds (hydroxyl donor and imide acceptor), but is only slightly more stable than the
Pranata and Davis
14344 J. Phys. Chem., Vol. 99, No. 39, 1995 0.12
-180
1
-160 -140 -120 Interaction Energy (kcalimol)
Figure 3. Solute-solvent energy distribution for aqueous solutions
of protonated formamides. The ordinate represents the mole fraction of solute molecules having a total interaction energy with the solvent shown on the abscissa. complexes with only the hydroxyl-donor hydrogen bond such as 3c,D or 3d,D. We have also used these bimolecular complexes for initial evaluation of the OPLS parameters to be used in the Monte Carlo simulations. Quantitative agreement between the OPLS and ab initio interaction energies is not expected, but the trends should be similar.26 Inspection of the data in Table 4 demonstrates that this is indeed the case for the most part. All the complexes that are found to be stable in the ab initio calculation are also stable in the OPLS model, with one exception. 3d,B is hydrogen bonded between the water hydrogen and the imide group in the ab initio calculations (as shown in Figure 2); the corresponding complex in the OPLS model has the hydrogen bond to the hydroxyl group instead. For the protonated intermediates, the OPLS interaction energies are less negative compared to the ab initio ones. This is not surprising since the simple point charge model used in the OPLS scheme does not allow for charge redistribution in the water molecule caused by the positive charge present in the protonated intermediate. However, the differences between the OPLS and ab initio interaction energies are comparable for the three protonated intermediates; the average differences are 2.5 kcaVmol for 1, 2.4 kcaVmo1 for 2a, and 2.0 kcal/mol for 2b. In contrast, the OPLS interaction energies tend to be more negative for the imidic acids, but once again the differences are comparable between the conformers; the average differences are are 1.2 kcaVmol for 3a, 0.6 kcdmol for 3b, 1.0 kcaVmol for 3c, and 0.9 kcal/mol for 3d. The more negative interaction energies from the OPLS calculations are consistent with trends observed in previous investigations.26 For both types of intermediates, the hydrogen bond distances from the OPLS calculations are shorter than those from ab initio calculations. This is once again a typical result and arises from the need to compensate for the lack of explicit polarization effects in the liquid state simulations.26 In conclusion, it would be justified to compare OPLS-based calculations on 1,2a, and 2b with one another, and also between 3a-d, although of course one should not make direct comparisons between the protonated intermediates with the imidic acids. Monte Carlo Simulations. Monte Carlo simulations were performed to more fully characterize the solvation of the intermediates. In addition to conventional Monte Carlo simulations, which provide information about solvent structure and energetics, simulations were also performed that incorporate statistical perturbation theory (SPT), which allow the calculation of the differences in the free energy of solvation between various isomers. Figure 3 displays the total solute-solvent energy distribution for the protonated intermediates. The distribution may be expected to be similar for 2a and 2b; a similar distribution was
:mja -20 -10 0 10 Interaction Energy (kcal/mol)
-30
-100
20
Figure 4. Solute-solvent energy pair distribution for aqueous solutions
of protonated formamides.
c M
---
1
NHe-OW
NHb.OW
'.-
'a
r
d
0 0.0
2.5
5.0
0 7.5 0.0
2.5
5.0
7.5 0.0
25
5.0
7.5
Distance (angstroms)
Figure 5. Solute-solvent radial distribution functions for aqueous
solutions of protonated formamides. also observed for 1. Figure 4 displays the distribution of average solute-solvent pairwise interaction energies. The well-defined peak around -15 kcdmol can be attributed to hydrogen bonded water molecules. Integration to -10 kcdmol revealed the number of these water molecules (Table 5, fourth column). There are more water molecules bound to the N-protonated intermediate, which is to be expected since this ion has a more localized charge compared to the 0-protonated intermediates. The solvent structure around the solute is presented in the form of radial distribution functions in Figure 5 . Integration to 2.5 8, gives another estimate of the number of hydrogen bonded water molecules (Table 5 , columns 5-10). On average, there is about one water molecule bound to each polar hydrogen ; the number is slightly higher for 1. There is good agreement between the energetic and geometric estimates of the number of hydrogen bonded water molecules, which is gratifying. From the Monte Carlo simulations discussed so far, it would appear that the effects of hydration on 1, 2a, and 2b are quite similar, with 1 being perhaps slightly better hydrated. The results of the SPT calculations (Table 6) are therefore rather surprising. The calculations indicate that, although 1 is indeed better hydrated than 2b (with a free energy difference of 2.3 kcaumol), 2a is the structure that has the most favorable interaction with the solvent. In fact, the difference in the free energy of hydration between conformers 2a and 2b is quite large, 4 kcaVmo1. The reason for this is unclear; the analysis of the conventional Monte Carlo simulation presented above provide no clues. The calculated dipole moments of 2a and 2b are quite similar (2.86 and 2.44 D), so this also does not suggest an explanation. The precision of the SPT calculations is quite good; the hysteresis in the closed thermodynamic cycle 1 2a 2b 1 is only 0.2 kcal/mol, well within the statistical uncertainties of the calculations. Thus, we are reasonably confident in these results. For the imidic acids, Figures 6-8 display the total energy distribution, pairwise energy distribution, and radial distribution functions, respectively. Integration of the radial distribution functions to 2.5 8, provides an estimate of the number of hydrogen bonded water molecules; on the average it is about one for waters acting as hydrogen bond acceptors and donors
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Acid-Catalyzed Proton Exchange in Formamide
J. Phys. Chem., Vol. 99, No. 39, 1995 14345
TABLE 5: Results of Monte Carlo simulatio& total energy
1 2a 2b 3a 3b 3~ 3d
f 1.6
-2763.6 -2766.1 -2753.0 -2691.5 -2679.6 -2704.2 -2685.3
zt 4.7 zt 3.1
k 2.6 f 3.4 f 5.3 i 4.0
solute-solvent energy -140.2 -139.3 -137.7 -38.8 -32.2 -40.5 -40.8
bound water waters bound waters bound waters bound waters bound waters bound waters bound moleculesb to 0‘ to N‘ to H(0)C to H,(N)‘ to H@)’ to H,(N)’
f 1.1 f 0.8 f 1.0 f 0.6 f 0.6 f 1.1 f 1.0
4.1 3.1 3.4 2.5 2.3 2.9 2.1
0.5 0.6 0.6 0.6
1.2 1.1 1.1 1.o
1.2 1.0 1.o 1.o 1.o 1.o
1.o 0.9 0.9 0.9
1.2 1.1 1.3
1.4
0.8
0.9 1.0
Energies in kcal/mol. Obtained from the energy pair distribution function, integrated to -0 kcal/mol for the protonated intermediates and to -4 kcal/mol for the imidic acids. Obtained from the radial distribution functions, integrated to 2.5 A. (i
TABLE 6: Results of free energy perturbation calculations
3
3 0-HW
AG of solvation (kcavmol) -1.5 f 0.2 2.3 f 0.2 4.0 f 0.2 3.2 & 0.2 -0.6 i 0.2 -0.5 f 0.3 -4.2 f 0.3 -3.8 f 0.2 0.3 f 0.2
process
1-2a 142b 2a 2b 3a 3b 3a 3c 3a 3d 3b 3c 3b 3d 3c 3d
---
+
total AGa (kcaumol) -11.4 -11.1 0.5
- 0-HW
3b
~~
-0.5 -0.8 1.2 -0.7 1.6 2.2
Sum of the gas-phase free energy difference (Table 3) and the solvation free energy difference. a
0.12
010
2:s
. . 7.5 0.0
5:O
2:s
OH-OW
h
a M
7:s
- 0-HW 1 --- OH-OW
I ” ] 3d
0-HW
5:O
3a 0.0
2.5
5.0
7.5 0.0
2.5
5.0
7.5
Distance (angstroms)
Figure 8. Solute-solvent radial distribution functions for aqueous solutions of formimidic acid conformers.
-60
-50 -40 -30 -20 Interaction Energy (kcal/mol)
-10
Figure 6. Solute-solvent energy distribution for aqueous solutions of formimidic acid conformers. The ordinate represents the mole fraction of solute molecules having a total interaction energy with the solvent shown on the abscissa.
-12
-8
-4
0
4
8
Interaction Energy (kcal/mol)
Figure 7. Solute-solvent energy pair distribution for aqueous solutions of formimidic acid conformers.
to the imidic nitrogen and about half for waters acting as donors to the hydroxyl oxygen. This reflects the “reluctance” of the hydroxyl oxygen in acting as an acceptor, as discussed earlier. However, the imide-as-donor complexes do not appear to be as disfavored. In any case, the total number of hydrogen bonded water molecules is about the same (3.3-3.5) for all conformers 3a-d.
Integration of the energy pair distribution function (Figure 7) gives another estimate. Unfortunately, the cutoff distance here is not as obvious as in the protonated intermediates; the peak corresponding to hydrogen-bonded water molecules appears more as a shoulder rather than as a distinctly separate peak. The values displayed in Table 5, fourth column, were obtained by choosing -4 kcal/mol as the cutoff. Once again, they appear to be comparable to one another. However, the values do not quite agree with the estimate from the radial distribution functions, no doubt because of the uncertainty in the -4 kcal/mol cutoff. A difference is observed for conformation 3b in the energy distribution function (Figure 6). It is clear from the position of the distributions that the solute-solvent interaction for this conformation is significantly weaker than for the others (see also Table 5 , third column). Results of the SPT calculations also reflect this difference (Table 6). Conformers 3a, 3c, and 3d have similar free energies of hydration; the differences are 0.6 kcdmol or less. In contrast, 3b has a free energy of hydration that is substantially higher by about 3-4 kcdmol. As shown in Table 6, interconversions between all possible pairs of conformers were performed in order to assess the quality of the simulations. The energy values are quite precise. For example, the closed cycle 3a 2b 3c 3a has a hysteresis of 0.4 kcdmol; for the other three-legged cycles they are even smaller. It is interesting that the solvation of 3b is less favorable by just about the right amount to compensate for its greater intrinsic stability. Thus, these calculations predict that in aqueous solution 3a, 3b, and 3c are all within 1 kcdmol of each other with 3c as the most stable conformer. Even the fourth conformer 3d is not too much higher in energy.
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14346 J. Phys. Chem., Vol. 99, No. 39, 1995
Pranata and Davis
Implications to the Mechanism of Proton Exchange. In the gas phase, the intermediate involved in the N-protonation mechanism of proton exchange (1) is calculated to be less stable by about 13 kcal/mol relative to the intermediate in the 0-protonation mechanism (2a or 2b; 2b being more stable by about 4 kcal/mol). In aqueous solution, although 1 is calculated to be better hydrated than 2b, 2a is calculated to be even better hydrated. Interestingly, the difference in the free energy of hydration between 2a and 2b almost exactly cancels out their gas-phase energy difference, so in aqueous solution the conformers 2a and 2b are about equally stable. In any case, 1 is still about 10 kcal/mol higher in free energy in solution. What does this say about the preferred mechanism for proton exchange? Unfortunately, not much. In the first place, any discussion about mechanistic preferences should focus on the transition states, not intermediates. However, it is quite reasonable to assume that the more stable intermediate is reached via the lower-energy transition state. It would be proper to conclude that the 0-protonated intermediate is formed in preference to the N-protonated intermediate, as is known all along. However, to conclude that proton exchange occurs via the 0-protonation mechanism would implicitly assume that this protonation step is the rate-limiting one. It is not at all clear that this should be the case. A definitive answer would require a more complete examination of the reaction pathway. It is our intention undertake this examination in the near future. Acknowledgment. We are grateful to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Geraldine Davis' participation was made possible by a summer undergraduate research fellowship from the National Science Foundation (CHE-9200036). References and Notes (1) Penin, C. L. Acc. Chem. Res. 1989, 22, 268. (2) Berger, A.; Loewenstein, A.; Meiboom, S. J. Am. Chem. SOC.1959, 81. 62. (3) Fraenkel, G.; Franconi, C. J. Am. Chem. SOC.1960, 82, 4478.
'
(4) Molday, R. S.;Kallen, R. G. J. Am. Chem. SOC. 1972, 94, 6739. (5) Martin, R. B. J. Chem. SOC., Chem. Commun. 1972, 793. (6) Bonnacorsi, R.; Pullman, A.; Scrocco, E.; Tomasi, J. Chem. Phys. Lett. 1972, 12, 622. Pullman, A. Chem. Phys. Lett. 1973, 20, 29. (7) Zielinski, T. J.; Poirier, R. A.; Peterson, M. R.; Csizmadia, I. G. J. Comput. Chem. 1982,3,477. (8) Perrin, C. L. J. Am. Chem. SOC. 1974, 96, 5628. Perrin, C. L.; Johnston, E. R. J. Am. Chem. SOC. 1981, 103, 4697. (9) Pemn, C. L.; Lollo, C. P.; Johnston, E. R. J. Am. Chem. SOC. 1984, 106, 2749. Pemn, C. L.; Arrhenius, G. M. L. J. Am. Chem. SOC. 1982, 104, 6693. Perrin, C. L.; Lollo, C. P. J. Am. Chem. SOC. 1984, 106, 2754. (10) Radom, L.; Hehre, W. J.; Pople, J. A. J. Am. Chem. SOC. 1971,93, 289. Radom, L.; Hehre, W. J.; Pople, J. A. J. Chem. Sac. A 1971, 2299. (11) Schlegel, H. B.; Gund, P.; Fluder, E. M. J. Am. Chem. SOC.1982, 104, 5347. (12) Elguero, J.; Goya, P.; Rozas, I.; Catalhn, J.; De Paz, J. L. G. J. Mol. Sruct. (THEOCHEM) 1989, 184, 115. (13) Bond, D.; Schleyer, P. v. R. J. Org. Chem. 1990, 55, 1003. (14) Wiberg, K. B.; Breneman, C. M.; LePage, T. J. J. Am. Chem. SOC. 1990, 112, 61. (15) Hehre, W. J.; Radom. L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (16) Scheiner, S. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH: New York, 1991; Vol. 2, pp 172-179. (17) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Clarendon: Oxford, U.K. 1987. (18) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (19) Jorgensen, W. L.; Tirado-Rives, J. J. Am. Chem. SOC. 1988, 110, 3673. (20) Brenneman, C. M.; Wiberg, K. B. J. Comput. Chem. 1990, 11, 361. (21) Jorgensen, W. L. Acc. Chem. Res. 1989, 22, 184. (22) Jorgensen, W. L.; Ravimohan, C. J. J. Chem. Phys. 1985,83,3050. (23) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92, Rev. E ; Gaussian, Inc., Pittsburgh, PA, 1992. (24) Jorgensen, W. L. BOSS Version 3.1; Yale University: New Haven, CT, 1991. (25) See for example: Frey, R. F.; Coffin, J.; Newton, S. Q.; Ramek, V.; Cheng, V. K. W.; Momany, F. A.; Schafer, L. J. Am. Chem. SOC.1992, 114, 5369. Cao, M.; Newton, S. Q.; Pranata, J.; Schafer, L. J. Mol. Struct. (THEOCHEM) 1995,332, 251. (26) Jorgensen, W. L. Chemtracts: Org. Chem. 1991, 4, 91.
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