J. Phys. Chem. 1996, 100, 9235-9241
9235
Proton Transfer Properties of Imidazole Steve Scheiner* and Manyin Yi Department of Chemistry, Southern Illinois UniVersity, Carbondale, Illinois 62901 ReceiVed: January 2, 1996; In Final Form: March 19, 1996X
The imidazole molecule is paired with NH3 in order to examine the proton transfer properties of the former by ab initio methods. The primary minimum on the surface is ImH+‚‚‚NH3 wherein the inter-nitrogen distance in the H bond is 2.89 Å. A second well appears in the surface, corresponding to Im‚‚‚+HNH3, and the barrier between the two minima is rapidly enlarged, when the latter distance is elongated. When the NH3 is displaced from the N lone pair direction of the imidazole in the plane of the latter, the greater proton-attracting power of the imidazole relative to NH3 is enhanced; the opposite is observed when the NH3 is pulled out of the imidazole plane. This distinction is explained simply on the basis of the dipole and quadrupole moments of imidazole. The ability of imidazole to act as a proton shuttle from one molecule to another is examined by placing one NH3 molecule on either side. Taking H3NH+‚‚‚ImH‚‚‚NH3 as a starting point, the simultaneous transfer of two protons to form H3N‚‚‚HIm‚‚‚H+NH3 must overcome a large energy barrier. A stepwise process, passing through the H3N‚‚‚HImH+‚‚‚NH3 intermediate, is greatly favored energetically. If the central imidazole is permitted the freedom to translate between the two NH3 molecules, it is possible for the latter to be quite some distance apart. The imidazole will first approach within about 2.65 Å of the donor H3NH+ ion. The transfer to imidazole can then take place with little or no energy barrier. The protonated imidazole will then move close to the receptor NH3 before depositing the proton with it. In most cases, the largest energy barrier is associated not with the proton transfers, but with the motion of the imidazole cation. The barrier for this translation grows as the ultimate donor and acceptor NH3 molecules are moved further apart.
I. Introduction The imidazole group (Im) exhibits particularly versatile chemistry. Imidazole and some of its derivatives form a class of nucleophilic and general base catalysts.1,2 In its incarnation as the functional group of the histidine residue, imidazole is commonly associated with protein subunits that act to transport protons from place to place.3-6 The unique structure of imidazole, containing two virtually identical N atoms, permits it to pick up a proton on one of its N atoms to form a cation and deliver another hydrogen from the other N to a second site. In fact, this sort of shuttling action has been proposed as part of the catalytic mechanism of a number of enzymes,7-9 and is consistent with the proton conductivity properties of imidazole in the solid state where long H bonded chains are present.10 Quantum chemistry has been applied to investigate some of the aspects of imidazole as an element in a proton-relay mechanism. The ability of the His side chain to pick up a proton from one protein residue and deliver it to another in the catalytic mechanism of serine proteinases was evaluated by an approximate ab initio molecular orbital method.11,12 It was learned that such transfers were probably viable, provided the imidazole is able to properly position itself in each case. A semiempirical study examined the transfer of a proton between two imidazole species and indicated that the resulting ion pair might form only in a medium with large dielectric constant.13 Later ab initio computations suggested a second well might exist in the gas phase, but the corresponding configuration is more than 40 kcal/ mol less stable than the neutral dimer.14 Protonating the dimer changes the situation a great deal. The transfer of a proton between the two Im molecules in ImH+‚‚Im has in its path an energy barrier of some 9 kcal/mol. Ab initio calculations also formed infinite chains of Im molecules15 and obtained an energy barrier of 35 kcal/mol for the simultaneous displacement of all protons from one Im to the next in the chain. X
Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00057-3 CCC: $12.00
The purpose of the present communication is to examine the proton transfer properties of the imidazole group on a fundamental level. Section III pairs imidazole with a single partner (NH3) in a proton-bound H bonded dimer. In keeping with numerous other studies that illustrate a sensitivity of the energetics of proton transfer to the geometry of the hydrogen bond,16-19 the transfer is examined for a range of distances and angles separating the imidazole from its partner. In the next section, one NH3 molecule is placed on either side of imidazole, and the latter’s ability to shuttle a proton from one to the other is examined. Of particular interest is the question of the synchronicity of the motion of the two protons and their influence upon one another. This situation is idealized in that all three entities are fixed in position. Section V relaxes this constraint and permits the central imidazole to move freely between the two NH3 molecules. In this way, it is possible to ascertain the optimal mechanism of proton shuttling over any arbitrary distance between the ultimate proton donor and acceptor. All calculations are carried out at the ab initio level, using the Gaussian-94 package of codes.20 II. Monomers In any investigation of proton transfer phenomena, it is crucial that the theoretical method be capable of treating properly the intrinsic attraction of a proton toward each of the entities involved. The proton affinities calculated for NH3 and imidazole (Im) are listed in Table 1 for several levels of theory. The results indicate that the addition of the polarization functions on the H atoms tends to raise the proton affinity of both NH3 and Im; correlation has a lowering effect on this property. The basis set labeled 6-31+G*(*) is intermediate between 6-31+G* and 6-31+G** in that the p functions are placed not on all the hydrogen centers but only on those involved directly in the H bonds. Since only one hydrogen of NH4+ © 1996 American Chemical Society
9236 J. Phys. Chem., Vol. 100, No. 22, 1996
Scheiner and Yi
TABLE 1: Proton Affinitiesa (All Entries in kcal/mol) SCF/6-31+G* SCF/6-31+G*(*)b SCF/6-31+G** MP2/6-31+G* MP2/6-31+G*(*)b MP2/6-31+G** exptc
NH3
Im
∆
205.9 208.2 207.8 204.0 208.2 206.6 204.0
222.3 232.8 225.1 215.7 228.3 220.2 223.4
16.4 24.6 17.3 11.7 20.1 13.6 19.4
a Calculated by adding vibrational and translational corrections to the electronic energy contribution, followed by a correction of -RT to account for the change from energy to enthalpy. b 6-31+G* augmented by p functions added only to hydrogen centers involved directly in the H bonds. c From ref 21.
Figure 1. Geometries and energetics of stationary points along the proton transfer potential between NH3 and imidazole. Distances shown are in Å and energies in kcal/mol. Nitrogen atoms are shaded more darkly than carbon.
will act as a bridge in our model systems below, one of its hydrogens has these functions added. Both of the hydrogens bonded to nitrogen in C3H3N2H2+ (protonated imidazole) participate in H bonds so the 6-31+G*(*) basis adds p functions to these hydrogens. The computed proton affinities reproduce the experimental quantities in the last row of Table 1 reasonably well. The results for the smaller NH3 molecule are particularly good, approaching the experimental value within only a few kilocalories. There is somewhat more scatter in the computational estimates of the proton affinity of imidazole. The last column reports the difference in proton affinity between NH3 and Im, the most important quantity for our purposes. Experimental measurements find Im to be the stronger base by 19.4 kcal/mol. The calculations verify the higher proton affinity of Im, with the difference covering a range between 12 and 25 kcal/mol. The closest agreement with experiment is associated with the 6-31+G*(*) basis set at the MP2 level. Hence, the bulk of the computations reported below were carried out with 6-31+G*(*), in which p functions have been added to the bridging hydrogens only. Bearing in mind the theoretical overestimate of the proton affinity difference at the SCF level with this basis set, the results reported below may be expected to contain a small bias for placing a proton on the imidazole as compared to NH3. III. Dimer Because of its greater basicity, the imidazole retains the excess proton when paired with ammonia (Am). Figure 1 reports the salient characteristics of the geometries of the important stationary points on the surface of the Im‚‚H+‚‚Am complex, computed at the SCF level. As depicted in Figure 1a, the bridging proton is located 1.028 Å from the nitrogen atom of Im, as compared to 1.865 Å from the N of ammonia in the global minimum, ImH+‚‚‚Am. This structure is bound by 18.3 kcal/mol, relative to isolated ImH+ and Am. There is a secondary minimum on the potential energy surface which
TABLE 2: SCF Energetics of Proton Transfer (kcal/mol) for the Im‚‚H+‚‚Am System R(N‚‚N), Å
∆Ea
E† (ImH+fAm)b
E† (ImrH+Am)c
adiabaticd
8.8 7.7 10.0 11.7
9.2 9.9 19.6 31.5
0.4 2.1 9.6 19.9
2.7 2.9 3.1
a E(Im‚‚‚+HAm) E(ImH+‚‚‚Am). b E(Im‚‚+H‚‚Am) E(ImH+‚‚‚Am). c E(Im‚‚+H‚‚Am) - E(Im‚‚‚+HAm). d R allowed to vary along proton transfer coordinate.
corresponds to the transfer of the proton across to the ammonia. Im‚‚‚+HAm lies 8.8 kcal/mol higher in energy than ImH+‚‚‚Am, reported as ∆E in the first row of Table 2. A small energy barrier of 0.4 kcal/mol prevents the spontaneous decay of Im‚‚‚+HAm to ImH+‚‚‚Am via a proton transfer. The internitrogen distance in this transition state to back transfer is 2.585 Å, shorter than the 2.894 and 2.686 Å of ImH+‚‚‚Am and Im‚‚‚+HAm, respectively. Consistent with Hammond’s postulate,22 the transition state resembles the higher energy Im‚‚‚+HAm as compared to ImH+‚‚‚Am. As a principal example, the bridging proton is closer to the Am N atom than to that of Im (1.192 vs 1.394 Å). The barrier to decay of Im‚‚‚+HAm to its more stable congener ImH+‚‚‚Am is low enough (0.4 kcal/mol) that it is unlikely to contain even a single vibrational level. It is likely that this barrier would disappear entirely if correlation were added to the energetics or if zero-point vibrations were included. For that reason, one may consider the proton transfer potential of this complex to be of asymmetric, single-well type for all intents and purposes. It may be supposed, however, that a true double-minimum potential would be realized were the Im and Am subunits pulled further apart from one another. As one example, when the two N atoms are held at the same distance (2.9 Å) in the proton transfer transition state as in the global minimum ImH+‚‚‚Am configuration, the barrier for transfer to the ammonia climbs from 9.2 to 19.6 kcal/mol. The sensitivity of the energetics of proton transfer to the separation between the Im and Am molecules is reported in some detail in Table 2. ∆E refers to the preference of the bridging proton for the more basic imidazole, as compared to ammonia, i.e., the difference in energy between the two wells in the proton transfer potential. In the asymptote of very long separation, this quantity would of course reduce to the difference in proton affinity between Am and Im. The energy barriers to transfer are denoted, E†, with appropriate notation in the following parentheses to indicate the direction. These barriers climb quickly as the H bond is elongated, as compared to a more gradual increase of ∆E with R. Note that these barriers take a single R(N‚‚N) distance and hold this quantity fixed throughout the proton transfer process, as distinguished from a so-called adiabatic transfer, in the first row of Table 1, wherein the two N atoms are permitted to move toward and away from one another as the transfer progresses. The proton transfer energetics are sensitive not only to the length of the H bond but also to its angular characteristics as well.17,23-25 In the fully optimized geometry of ImH+‚‚‚Am, the H bond is very nearly linear. That is, the bridging hydrogen lies within 3° of the N‚‚N axis in all configurations considered. Moreover, the lone pair of the ammonia, assumed collinear with the C3 rotation axis of the molecule, points directly toward the bridging hydrogen. While such an idealized linear geometry may be appropriate in the gas phase bimolecular situation, the structural restraints imposed when the H bond occurs within the context of a macromolecule such as a protein would normally prevent such perfect alignment. Indeed, bent H-bonds
Proton Transfer Properties of Imidazole
J. Phys. Chem., Vol. 100, No. 22, 1996 9237
TABLE 3: SCF Energetics of Proton Transfer (kcal/mol) for Angularly Distorted Configurations with R ) 2.9 Å R, deg
∆E
E† (ImH+f Am) In-Plane Bends 19.6 21.7 29.3
E† (Imr H+Am)
a
no restraint 20 40
10.0 10.4 12.8
no restraint 20 40
Out-of-Plane Bends 10.0 19.6 9.5 19.7 8.4 20.6
9.6 11.3 16.5 9.6 10.2 12.2
a
Mode reported pulls Am in direction toward second N atom of Im. Results for motion in opposite direction are identical to within several tenths of kcal/mol.
are the rule rather than the exception in proteins.26 For that reason, various types of angular distortion were imposed on the H bond connecting the Im and Am subunits and proton transfer potentials computed. The first distortion mode examined is of in-plane type in the sense that the NH3 molecule is displaced off of the original H bond axis, holding it within the plane of the Im molecule. The inter-nitrogen distance is set to 2.9 Å, fixing the Am N atom, but the NH3 molecule retains the freedom to pivot around this atom. The proton transfer profile is then computed, permitting optimization of all other parameters. The out-of-plane distortions are similar except that the NH3 is pulled straight up, perpendicular to the Im plane. Table 3 lists the salient characteristics of the proton transfer potentials, for a given angle of distortion R and with R fixed at 2.9 Å. As in the earlier case, ∆E refers to the energetic preference of the proton for association with the Im as compared to the Am. The upper section of Table 3 illustrates that this preference is enhanced as the NH3 is displaced from the lone pair direction of the imidazole nitrogen, remaining within the Im molecular plane. This trend is reversed when the ammonia is pulled out of this plane in that ∆E becomes less positive as R is increased. There are other distinctions between the inplane and out-of-plane distortions as well. These differences are evident when focusing on the depth of the Im‚‚‚+HAm well, as characterized by the height of the barrier for transition to the lower energy ImH+‚‚‚Am configuration, in the last column of Table 3. Whether the distortion is in or out of the plane, this barrier is increased by the deformation. However, the rate at which the barrier climbs is quite different in the two cases. Whereas a 40° distortion raises this barrier by 7 kcal/mol for an in-plane mode, the increase is only 2.6 kcal/mol when the Am is pulled out of the Im plane. Similarly, smaller barrier increments are observed in the ImH+f Am transfers in the preceding column of Table 3. In fact, the barrier for transfer in this direction barely changes at all when the ammonia is displaced out of the imidazole molecular plane. These distinctions can be most easily understood on the basis of the electrostatic interactions between the neutral Im and positively charged HNH3+ in the Im‚‚‚+HAm configuration. The interaction between the molecular dipole moment of the neutral imidazole and the charge on HNH3+ is illustrated in Figure 2a where the former moment may be seen to be approximately collinear with the lone pair direction of the pertinent N atom. Displacement of the HNH3+ away from this direction, either within or out of the plane of the Im, would have an approximately equivalent destabilizing effect. The difference arises when considering the interaction between the ion and the quadrupole moment of the imidazole. As indicated in Figure 2b, the elements of the traceless quadrupole matrix are positive in a direction approximately perpendicular to the internal
Figure 2. Schematic diagram indicating interaction between the positive charge of HNH3+ and the (a) dipole and (b) quadrupole moment of imidazole in the Im‚‚‚+HAm configuration.
N- -N line of Im and negative out of the molecular plane. (The element collinear to the N--N line very nearly vanishes.) One may consider the negative sign of the out-of-plane element as a simple manifestation of the π-electron cloud above and below the molecular plane. In any event, it is evident from Figure 2b that a displacement of the HNH3+ unit within the Im plane will destabilize the system by bringing this ion into closer proximity with the positive in-plane element of the quadrupole moment of Im. In contrast, a stabilizing effect will arise when HNH3+ is pulled out of the Im plane due to a closer approach of this cation to the negative poles of the out-of-plane quadrupole moment of Im. In summary, both the dipole-ion and quadrupole-ion interactions act to destabilize the Im‚‚‚+HAm configuration when the HNH3+ is displaced from the H bond axis within the Im plane. An out-of-plane distortion, on the other hand, results in a stabilization of the quadrupole-ion term which counteracts the destabilization of the dipole-ion interaction, resulting in a considerably more gradual increase in energy. These suppositions are confirmed by the computed energetics of the system. The 20° and 40° in-plane deformations of the Im‚‚‚+HAm configuration destabilize the system by 1.7 and 7.1 kcal/mol, respectively, as compared to only 0.8 and 3.1 kcal/ mol for similar out-of-plane distortions. The energy of the other well in the transfer potential, ImH+‚‚‚Am, is virtually independent of whether the distortion is of the in-plane or out-of-plane variety. The deformation energies for 20° and 40° are respectively 1.3 and 4-5 kcal/mol in either case. IV. Proton Shuttling with Stationary Im The ability of the imidazole species to act as a proton shuttle in certain circumstances provides a motivation to examine this aspect of the group’s behavior. Ammonia molecules were used as prototype proton-accepting or -donating groups; one NH3 was placed in the proximity of each of the two N atoms of imidazole. Full geometry optimization led to a structure consisting of a cationic ImH+ surrounded by two neutral ammonias, denoted as Am‚‚HImH+‚‚‚A. (In the following, both H atoms that are subject to transfer are indicated explicitly in our notation.) The two symmetrically equivalent H bonds are each quite linear, with R(N‚‚N) ) 2.925 Å. The total interaction energy between the three subunits amounts to 17.5 kcal/mol for each of the two H bonds. This value is slightly smaller than the 18.3 kcal/mol binding energy of the single H bond in HImH+‚‚Am; the bond is also slightly longer in the trimer, as compared to 2.894 Å in the dimer. This bond weakening is a manifestation of negative cooperativity, since the central HImH+ is acting as proton donor to both Am molecules. A configuration that results from transfer of both of the Im protons to the ammonias, yielding AmH+‚‚Im-‚‚H+Am, wherein the central anion is flanked by a pair of cations, lies 54.7 kcal/ mol higher in energy. This geometry is not a true minimum, however, since vibrational analysis leads to two imaginary frequencies. The structure which would be expected were only one of the two protons of HImH+ to transfer, AmH+‚‚ImH‚‚Am, does not represent a minimum on the potential energy
9238 J. Phys. Chem., Vol. 100, No. 22, 1996
Figure 3. Contour surface of the potential energy of AmH+‚‚ImH‚‚Am system. r1 and r2 refer to the distances of the two bridging hydrogens from the relevant N atom of the central imidazole. R(N‚‚N) is set equal to 2.9 Å in each H bond. Contour increments are 5 kcal/ mol.
surface either. Attempts to locate this configuration decayed in each case to the global minimum Am‚‚HImH+‚‚Am. In order to examine the shuttling capacity of the imidazole species, the two NH3 groups were positioned a set distance away from the central Im. The nitrogens of the ammonia molecules were placed directly along the N-H axis of the protonated HImH+, with R(N‚‚N) set to 2.9 Å. The two bridging hydrogens were moved in uniform increments between the two N atoms, holding the remainder of the geometry of the complex fixed. Energies were thus computed for a grid of proton positions. These energies are presented as a contour surface in two dimensions, where r1 and r2 represent the distances of the two hydrogens from the pertinent N of Im. The minimum near the lower left corner of Figure 3, with small values of both r1 and r2, corresponds to the Am‚‚HImH+‚‚Am configuration, the lowest energy point on this surface. There are local minima in the upper left and lower right corners, which refer respectively to the equivalent AmH+‚‚ImH‚‚Am and Am‚‚HIm‚‚H+Am configurations. These structures are 14.7 kcal/mol higher in energy than Am‚‚HImH+‚‚Am because, in the first place, Im is more basic than Am. Second, the central position of the Im makes it a better location for the excess positive charge since it can interact with molecules on both sides of it. The shuttling action of Im would serve to bring a proton from a group on one side of it to another on the other side. Such activity can be modeled by the double proton transfer, passing from AmH+‚‚ImH‚‚Am to Am‚‚HIm‚‚H+Am. In other words, we are interested in the energetics of going from the upper left corner of Figure 3 to the other minimum in the lower right. A simultaneous transfer of both protons would correspond to a straight path between these two minima. Such a line would traverse a region of high energy in Figure 3. For this reason, it is unlikely that this path would be followed: i.e., the two protons would not transfer simultaneously. More likely would be a pathway that passes through or near the lower left corner as this region is of low energy. One possibility would be for the first proton to transfer completely (AmH+‚‚ImH‚‚Am f Am‚‚HImH+‚‚Am), after which the second proton could be displaced from the Im to the Am (Am‚‚HImH+‚‚Am f Am‚‚HIm‚‚H+Am). Of course, these two transfers do not have to be completely sequential, i.e., the second proton can begin its transfer prior to the completion of the
Scheiner and Yi
Figure 4. Energetics of transfer of the second proton in the AmH+‚‚ImH‚‚Am triad as a function of position of the first proton. r1 refers to the distance of the first proton from the Im (see Figure 3). The barrier to transfer of the second proton from Im to the second Am is indicated by E† (ImHb f Am), with an analogous notation for the reverse transfer barrier. ∆E denotes the difference in energy between the two wells in the transfer potential. The corresponding value for the simple HIm‚‚H+‚‚Am diad is represented by asterisks.
motion of the first. The principal conclusion is that there must be at least some delay between the displacement of the first and second protons. It is also worth stressing that it is highly unfavorable for the ImH to begin to lose its proton before the first proton approaches the imidazole. Such a process would pass through the upper right region of Figure 3, near the unstable AmH+‚‚Im-‚‚H+Am configuration, which is computed to be 49.6 kcal/mol higher in energy than the lowest minimum Am‚‚ HImH+‚‚Am. The contour plot of Figure 3 is quite similar in character to that developed for the protonated homotrimer of water: H2OH+‚‚HOH‚‚OH2.27 In that case, the central molecule contained only one heavy atom. Enlarging this chain to the pentamer by adding another water molecule to each end, thereby reducing end effects, had little effect on the overall shape of the potential energy surface for transfer of the two protons. Similar conclusions were reached when the central water molecule was replaced by HCOOH, wherein the carbonyl O played the role of proton acceptor and the hydroxyl group was the donor.28 One may conclude that the necessity to place the proton transfers in sequential order, and avoid making their motions simultaneous, is a common feature of multiple proton transfers. The use of a larger and more complex species like imidazole as the protonshuttling unit, in which the two protons reside on different atoms, does not circumvent this limitation. Whereas the contour surface suggests that the two proton motions would tend to be sequential, the data do not imply that the position of one proton has no influence on the transfer energetics of the other. On the contrary, any displacement of the first proton toward the Im facilitates the transfer of the second. This trend is illustrated explicitly in Figure 4 which indicates the dependence of the energetics of transfer of the second proton, in terms of the position of the first. More specifically, the two protons in the initial configuration are identified as AmHa‚‚ImHb‚‚Am, and the barrier for transfer of Hb to the amine is reported as the upper solid curve in Figure 4. It is immediately evident that this barrier drops as Ha is moved closer and closer to the central Im, i.e., as r1 becomes
Proton Transfer Properties of Imidazole
J. Phys. Chem., Vol. 100, No. 22, 1996 9239
smaller. The effect amounts to a change in barrier from 31 kcal/mol when r1 ) 1.9 Å to 22 kcal/mol when Ha is within 1.0 Å of the imidazole. Note that all of these barriers, even those for very small r1, are somewhat higher than the value of 19 kcal/mol in the ImH+‚‚Am diad (the asterisk in Figure 4). This observation indicates the addition of the second NH3 on the other side of the Im acts to raise the barrier, i.e., retain the proton on the Im. Concomitant with the ImH f Am barrier reduction that occurs as the Ha proton approaches from the other side is the lowering of ∆E, indicated by the broken curve in Figure 4. This quantity represents the energetic preference of the ImHb‚‚Am configuration as compared to Im‚‚HbAm. A smaller value for ∆E indicates a push of Hb toward the amine, also consistent with the closer proximity of the Ha proton. A final measure of this same trend is the increasing barrier for back-transfer, i.e., Im r HbAm, which would also act to retain the Hb proton on the amine. V. Proton Shuttling with Mobile Im The prior calculations addressed a highly idealized situation wherein all three species were anchored in place and only protons were permitted to move. Moreover, the three groups were perfectly aligned with regard to maintaining linearity of both H bonds. The action of the histidine residue within the context of a protein is envisioned to include a certain amount of flexibility of motion of its imidazole ring. That is, it is supposed that the Im can move to some extent between the proton-donating and -accepting groups. In order to more accurately model this situation, calculations were carried out in which the two NH3 groups were anchored in place a certain set distance from one another and the intervening Im was allowed to move freely between them as described in more detail below. The entire process we seek to model is as follows. We wish to move a proton from the charged H+NH3 species to a neutral NH3 some distance away. A neutral imidazole is placed between these two groups and is free to move back and forth between them. Several key parameters are used to monitor the energetics of the entire process. The first parameter is a measure of the position of the imidazole ring; specifically, R0 refers to the distance between one N atom of Im and the nitrogen of the ammonia to which it forms a H bond. The energetics of the AmH+‚‚ImH‚‚Am system are presented in Figure 5 for the case where the two ammonia nitrogens are positioned 7.8 Å distant from one another. The curve in the figure labeled a refers to the AmH+‚‚ImH‚‚Am proton configuration, taken as the starting point for the eventual transfer to the other ammonia. Curve a illustrates that the energy rises as the ImH is pulled away from its minimum-energy position with R0 ) 2.65 Å. This energy increase is rather gradual since the weakening of the H bond between AmH+ and ImH is compensated in part by a shorter and hence stronger H bond between ImH and the other Am. The transfer of the proton from the left AmH+ to the neutral ImH results in the Am‚‚H+ImH‚‚Am configuration. The dependence of the energy of this structure (b) upon the position of the central H+ImH unit is indicated by the appropriately labeled curve in Figure 5. As curve b lies below that of AmH+‚‚ImH‚‚Am, it is evident that the proton transfer to the Im is an exoergic process for any given separation between Am and Im. The transition-state energies for proton transfer from AmH+ to ImH are indicated by the curve labeled c in Figure 5. Consistent with prior calculations, this barrier rises quickly with increasing H bond length; in this case, the latter length
Figure 5. Energetics of a number of configurations. The nitrogens of the two ammonias are separated by 7.8 Å. R0 refers to the distance between the H bonded nitrogen of Im and the Am to which it is closer. (When Im crosses the Am- - -Am midpoint, the identity of the pertinent Am changes.) Open circles on curve b represent the situation when the Im and Am are close enough together that there is no stable Am‚‚HIm‚‚H+Am configuration, as it would collapse to Am‚‚HImH+‚‚Am with no barrier.
corresponds to R0. Due to the rapidly rising barrier, the most opportune moment for the proton to transfer from AmH+ to ImH would occur when R0 is small, i.e., when the ImH has moved close to the AmH+. In fact, this process can take place without any barrier at all for R0 less than 2.65 Å or so. Once the proton has been transferred to the ImH, the displacement of the HImH+ toward the other Am is characterized by the energetic profile b in Figure 5. This curve passes through a minimum when R0 is equal to 3.0 Å (where HImH+ is equally distant from the two Am subunits). Further motion to take HImH+ within proximity of the receptor Am requires no more energy than would this same group moving back to the original donating Am group, perhaps 4-5 kcal/mol. Once optimally located for proton transfer, with R0 once again equal to 2.65 Å (this distance now refers to the nitrogen on the right), the transfer can take place with no energy barrier. The only energetic cost of this transfer is the 8 kcal/mol or so needed to overcome the less basic character of Am as compared to Im. The segment of curve b containing the open circles refers to even closer approaches of the ion and the neutral Am in the Am‚‚H+ImH‚‚Am configuration. Note that this curve rises quickly, indicating the two groups are being “squeezed” together and undergoing steric repulsion. With the loss of the energy barrier to proton transfer when R0 < 2.65 Å, the proton transfer potential contains only a single minimum, corresponding to Am‚‚HImH+‚‚Am. Unless the two groups are separated by more than 2.65 Å, the proton will not “stick” to the Am but will spontaneously decay back to Am‚‚HImH+‚‚Am. In summary, the energy profiles in Figure 5 provide a possible scenario for transferring the excess proton from AmH+ to another Am some 7.8 Å distant from the first. Beginning with the AmH+‚‚ImH‚‚Am configuration, the neutral ImH is attracted by the positive charge of the AmH+. Once there, the ImH can acquire this proton in an exoergic process with little or no energy barrier. Swinging across from one Am to the other requires no energy; the H+ImH passes through a minimum-energy position midway between these two groups. The only endoergic process involves the H+ImH releasing its proton to the Am. While no energy barrier is present when the two groups are within 2.65 Å of one another, the transfer itself is endoergic by some 8
9240 J. Phys. Chem., Vol. 100, No. 22, 1996
Figure 6. Same as Figure 5, but with two ammonias separated by 12.0 Å.
kcal/mol. (A longer H bond would add to this endoergicity and impose an energy barrier as well.) The preceding analysis was based on a separation of the two Am groups by 7.8 Å. Analogous computations on the slightly longer distance of 8.8 Å yielded much the same results. As an example of a larger gap, computed curves for 12.0 Å, comparable to those in Figure 5, are presented in Figure 6. There are certain similarities between the two situations. As in the above case, the ionic AmH+ draws the ImH toward it and the barrier to proton transfer from AmH+ to ImH disappears for close approach of these two groups. The transfer potential collapses into a single well here for the slightly longer distance of 2.71 Å. As before, the transfer from AmH+ to ImH is exoergic by about 7 kcal/mol. This process is more exoergic for longer separations, but then one must overcome an energy barrier that rises rapidly as this H bond elongates (cf. curve c). When the two Am were separated by 7.8 Å, the protonated H+ImH preferred a position midway between them. The situation is different when the interamine distance is 12 Å in that the H+ImH clearly prefers association with one Am or the other. Crossing from one to the next requires overcoming an energy barrier of 9 kcal/mol. But it should be noted that even at the top of the barrier, the energy of the system is no higher than it was originally in the AmH+‚‚ImH‚‚Am configuration (curve a). Once this barrier has been traversed, the H+ImH can release its excess proton to the receptor Am, but again this will occur most facilely when the two groups are fairly close to one another. A 2.71 Å separation is probably optimal as the transfer takes place with no energy barrier, although the process is endoergic by 7 kcal/mol. Comparison of this process with that occurring for R1 ) 7.8 Å is similar in many respects. Particularly similar are the energetic and geometric aspects of the proton transfers. The principal distinction resides in the motion of the charged H+ImH between the two amines. Instead of the essentially free motion when the amines are close together, a separation of 12 Å introduces a 9 kcal/mol barrier into the path of the H+ImH. The magnitudes of the barriers for the two elementary reactions of this entire process are mapped in Figure 7 as a function of the distance separating the two amine groups. The proton transfer barriers are taken as the energy required to displace the bridging proton from the imidazole in Am‚‚HImH+‚‚Am to the amine to form Am‚‚HIm‚‚H+Am. More specifically, since the barrier is sensitive to the R0 separation
Scheiner and Yi
Figure 7. Calculated energy barrier that must be overcome to transfer a proton (pT) from H+ImH to Am and barrier to motion of H+ImH between two Am subunits. Results are plotted against the inter-nitrogen distance, R1, of the two Am subunits.
between Im and Am, the value shown is the minimum, obtained just at the point where the Am‚‚HIm‚‚H+Am configuration emerges as a second minimum in the potential, and the bridging proton can remain on the Am. The appropriate curves in Figure 7 illustrate that this quantity is fairly insensitive to the distance between the amines. That is, regardless of how far apart the two amines are, the H+ImH can move close enough to Am so that it can deliver its excess proton, at the same energetic cost in each case. The latter endoergicity is about 8 kcal/mol at the SCF level but is only 2-3 kcal/mol after inclusion of electron correlation. The energy barrier that the H+ImH must overcome in its translation across from one Am to the other is, on the other hand, very much dependent upon the distance between these two amine groups. For R1 less than about 9 Å, this motion occurs with no barrier at all. But as the two amines become further separated, the placement of the H+ImH midway between the amines becomes progressively destabilized relative to a close association with one or the other. At the SCF level, the energy barrier for the H+ImH motion climbs from 0 at 9 Å to 9 kcal/ mol when R ) 12 Å and then up to 15 kcal/mol for R ) 18 Å. The MP2 barriers climb even more quickly as the two amines are separated. The latter more rapid increase at the correlated level may be due to the stronger H bonds that are typically associated with electron correlation. Comparison of the curves representing the energy barriers for proton transfer and for H+ImH displacement provides certain insights into the factors controlling the entire protonshuttling process. Focusing first on the MP2 data, for all interamine distances longer than 9 Å, the barrier for motion of the H+ImH is higher than the proton transfer energy requirement. One could hence conclude that the former will be the rate-determining step. That is, any endoergicity involved in moving the proton from one group to another (only about 2-3 kcal/mol at this level) is outweighed by the energy needed to extract the H+ImH cation from the first Am and move it over to the other. And again, the latter barrier rises rather quickly as the two amines are separated. These observations apply to the SCF level calculations as well, except that the crossover point occurs somewhat later, around R ) 12 Å. For inter-amine distances less than this, the endoergicity of the proton transfer process is greater than the energy barrier for displacement of the H+ImH.
Proton Transfer Properties of Imidazole This sort of interrelation between two different phenomena is supported by recent observations of human carbonic anhydrase.29 The His-64 side chain normally acts as a proton shuttle in this enzyme. When Arg-67 is replaced by His, the proton shuttling continues but at a much reduced rate as compared to His-64. The authors conclude that the rate-determining factor derives from the energy barrier to attaining the correct alignment of the His and its associated donor and acceptor groups and is not due to the energetics of proton transfer from one group to the next. They believe that once the proper alignment has been achieved, the 64 and 67 positions for His are equally effective as proton conduits. This analysis is consistent with our own findings based on Figure 7. When the donor and acceptor groups are further apart than a critical distance, the motion of the protonated imidazole has associated with it a higher energy barrier than does the proton transfer to or from this residue. Another point of coincidence is in the low barrier to proton transfer. Our own calculated MP2 value is less than 5 kcal/mol (see Figure 7), as is the barrier extracted from the experimental data.29 It is estimated that some 11 kcal/mol is required in the enzyme to properly orient the His side chain so as to enable the proton transport to occur. This value falls well within the range predicted by our computations for a similar sort of motion of Im. Acknowledgment. We are grateful to Professor Silverman for sending us a preprint of his group’s manuscript and for interesting discussions. This work was supported by the National Institutes of Health (GM29391). References and Notes (1) Bender, M. L.; Bergeron, R. J.; Komiyama, M. The Bioorganic Chemistry of Enzymatic Catalysis; Wiley-Interscience: New York, 1984; p 312. (2) Stewart, R. The Proton: Applications to Organic Chemistry; Academic Press: Orlando, FL, 1985; Vol. 46, p 313. (3) Cain, B. D.; Simoni, R. D. J. Biol. Chem. 1989, 264, 3292. (4) Lightowlers, R. N.; Howitt, S. M.; Hatch, L.; Gibson, F.; Cox, G. Biochim. Biophys. Acta 1988, 933, 241.
J. Phys. Chem., Vol. 100, No. 22, 1996 9241 (5) Howitt, S. M.; Gibson, F.; Cox, G. B. Biochim. Biophys. Acta 1988, 936, 74. (6) Vik, S. B.; Antonio, B. J. J. Biol. Chem. 1994, 269, 30364. (7) Silverman, D. N.; Lindskog, S. Acc. Chem. Res. 1988, 21, 30. (8) Zhong, S.; Haghjoo, K.; Kettner, C.; Jordan, F. J. Am. Chem. Soc. 1995, 117, 7048. (9) Lesburg, C. A.; Christianson, D. W. J. Am. Chem. Soc. 1995, 117, 6838. (10) Kawada, A.; McGhie, A. R.; Labes, M. M. J. Chem. Phys. 1970, 52, 3121. (11) Scheiner, S.; Kleier, D. A.; Lipscomb, W. N. Proc. Natl. Acad. Sci. U.S.A. 1975, 72, 2606. (12) Scheiner, S.; Lipscomb, W. N. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 432. (13) Chojnacki, H.; Lipinski, J. AdV. Mol. Relax. Interact. Processes 1980, 18, 149. (14) Basch, H.; Krauss, M.; Stevens, W. J. J. Am. Chem. Soc. 1985, 107, 7267. (15) Bre´ das, J. L.; Poskin, M. P.; Delhalle, J.; Andre´, J. M.; Chojnacki, H. J. Phys. Chem. 1984, 88, 5882. (16) Scheiner, S. Acc. Chem. Res. 1985, 18, 174. (17) Scheiner, S. Acc. Chem. Res. 1994, 27, 402. (18) Chu, C.-H.; Ho, J.-J. J. Am. Chem. Soc. 1995, 117, 1076. (19) Jaroszewski, L.; Lesyng, B.; McCammon, J. A. J. Mol. Struct. (THEOCHEM) 1993, 283, 57. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Stewart, J. J. P.; Head-Gordon, M.; Gonzalez, G.; Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 1995. (21) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. Gas-Phase Ion and Neutral Thermochemistry; American Institute of Physics: New York, 1988; Vol. 17. (22) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334. (23) Chu, C.-H.; Ho, J.-J. J. Phys. Chem. 1995, 99, 16590. (24) Chu, C.-H.; Ho, J.-J. Chem. Phys. Lett. 1994, 221, 523. (25) Cybulski, S. M.; Scheiner, S. J. Phys. Chem. 1989, 93, 6565. (26) Baker, E. N.; Hubbard, R. E. Prog. Biophys. Mol. Biol. 1984, 44, 97. (27) Scheiner, S. J. Am. Chem. Soc. 1981, 103, 315. (28) Scheiner, S. In Proton Transfer in Hydrogen Bonded Systems; Bountis, T., Ed.; Plenum: New York, 1992; p 29. (29) Ren, X.; Tu, C.; Laipis, P. J.; Silverman, D. N. Biochemistry 1995, 34, 8492.
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