J. Phys. Chem. 1996, 100, 13455-13461
13455
Proton Transfer in Ionic Hydrogen Bonds James A. Platts* Department of Chemistry, UniVersity of Wales, Cardiff, P.O. Box 912, Cardiff CF1 3TB, U.K.
Keith E. Laidig Department of Medicinal Chemistry, UniVersity of Washington, Seattle, Washington 98195 ReceiVed: February 7, 1996X
Correlated electronic structure calculations, coupled with atoms in molecules analysis, have been employed in a study of proton transfer in ionic hydrogen bonds. The isoelectronic series FHF-, H3O2-, H5O2+, and N2H7+ are used as models for such processes. Calculations at the MP2/6-311++G** level on the minimum energy structure and the transition state for proton transfer give an estimate of the barrier to proton transfer. Decomposition of the resulting charge distributions and energetics using Bader’s techniques provides a deeper understanding of the electronic factors determining proton transfer barriers. It also indicates a fundamental difference between anionic and cationic hydrogen bonds.
Introduction Proton transfer (PT) reactions are both very common and very important throughout chemistry,1 for example playing a crucial role in enzymatic reactions.2 Their importance has led to a growing interest in the computation of the relevant potential energy surfaces (PESs)3 via ab initio molecular orbital methods. Such studies have become widespread enough for the effects of basis sets and electron correlation on the calculated PT barriers to be apparent. One important finding is that the inclusion of at least some correlation is necessary to obtain realistic PT barriers. While the published studies have established the level of theory necessary for the calculation of barriers to PT, less emphasis has been placed on the underlying processes governing the observed behavior in such systems. Several studies have demonstrated that charge flows in the direction opposite to that of the proton,4 on the basis of both theoretical calculations and infrared spectroscopy. However, the energetic consequences of this charge flow can only be estimated; we will show that in some cases the energetics of proton transfer are counterintuitive. We have chosen to focus on the hydrogen-bonded ions FHF-, H3O2-, H5O2+, and N2H7+ as model systems. Not only do these ions have the advantage of small size but they also allow the use of symmetry in finding the appropriate transition state (TS), since in all cases the TS has higher symmetry than the equilibrium geometry. However, the use of these systems raises a problem in that the first three have a symmetrically placed central proton when a suitably high level of theory is employed,3a,b,5 while N2H7+ has only a very small barrier to PT when electron correlation is included in the calculations. Thus, the first three ions have no PT barrier at their equilibrium configurations, while the barrier in the latter is of a size similar to typical integration errors found in the atoms in molecules (AIM) decomposition we wish to use. This problem may be circumvented by observing that, as the hydrogen bond is lengthened, existing PT barriers increase and single-well PESs tend to become double-welled. This approach has been employed before in theoretical studies of PT reactions,3a,b,d where the hydrogen bond length was fixed at a value that results in a substantial PT barrier, i.e. up to 30 kJ X
Abstract published in AdVance ACS Abstracts, July 15, 1996.
S0022-3654(96)00384-X CCC: $12.00
mol-1. We shall use this approach here, taking the hydrogen bond lengths used in the previous studies on FHF-, H3O2-, and H5O2+, and using one that gives a similar barrier for N2H7+. In this manner, PT barriers that are amenable to AIM analysis are obtained. We feel this approach is justified since our primary interest lies in modeling PT in “real” systems with double-well PESs. We present an analysis of PT reactions using Bader’s atoms in molecules (AIM) techniques. In this way we can build upon previous studies,4 gaining further insight into the origin of the barriers to PT. AIM analysis provides us with not only atomic charges but also higher multipole moments such as atomic dipoles and quadrupoles which describe the distribution of electronic charge within an atom. Atomic energies are also obtained from AIM analyses, allowing the identification of local energy changes in the system. While a myriad of methods are available to compute atomic charges and several atomic multipole partitioning schemes have been proposed, AIM analysis is the only method capable of delivering atomic energetics. Computational Section All ab initio constrained optimizations and TS searches employed the MP2(FC)/6-311++G**6,7 level of theory, as implemented in the GAUSSIAN92 package8 running on the University of London Computing Centre’s CONVEX C3800. No zero-point energy corrections have been applied to the calculated PT barriers. Symmetry constraints were used throughout this study, not only to speed up the calculations but also to facilitate the location of the TSs, since higher symmetry in the TS is a feature of all four systems. For the minima, FHFwas assumed to be C∞V, H3O2- and H5O2+ to be Cs, and N2H7+ to be C3V, in line with previous studies3,5 (see Figure 1). The TS searches employed the point groups D∞d, C2h, C2h, and D3d, respectively. In this manner we were able to use the normal optimization algorithm to locate the appropriate TSs. Decomposition of the resulting electron distributions and energies into atomic contributions was carried out following the techniques developed by Bader and co-workers.9 In particular, the programs EXTREME and PROAIMV (part of the AIMPAC10 suite of programs) were employed. These © 1996 American Chemical Society
13456 J. Phys. Chem., Vol. 100, No. 32, 1996
Platts and Laidig
TABLE 1: MP2/6-311++G** Molecular Properties (Å, deg, and Hartrees)a FHFmin rXAXB rXAHA rXBHB rXAHT XBXAHA XAXBHB E VNE
H3O2TS
2.600
2.600
1.004
1.300
-200.0165 -533.4757
-200.0087 -532.6647
H5O2+
N2H7+
min
TS
min
TS
min
TS
2.740 0.958 0.963 1.027 100.8 107.7 -151.9561 -427.8890
2.740 0.962 0.962 1.370 98.7 98.7 -151.9447 -427.1763
2.740 0.975 0.966 1.043 110.6 115.8 -152.8708 -443.7763
2.740 0.970 0.970 1.370 112.4 112.4 -152.8611 -443.0088
2.746 1.021 1.019 1.119 110.6 113.1 -113.2149 -356.3205
2.746 1.020 1.020 1.373 111.9 111.9 -113.2104 -355.8737
a XA is the heavy atom in the acid fragment; XB is the heavy atom in the base fragment; HA is the “external” hydrogen on the acid fragment; HB is the “external” hydrogen on the base fragment; HT is the “internal” hydrogen.
Laplacian of the charge density, ∇2F, reveals much about the chemistry of a system. Where ∇2F is negative (solid lines), density is locally concentrated, whereas regions of positive ∇2F (dashed lines) correspond to local charge depletion. It has been repeatedly shown9 that a negative Laplacian in internuclear regions corresponds to “shared” interactions, such as covalent bonds, while a positive ∇2F is indicative of “closed-shell” interactions, such as ionic bonds and hydrogen bonding. Results
Figure 1. Labeling and axis system employed.
techniques are based around the formal definition of a quantum mechanical subsystem, one which obeys the same quantum mechanical laws as does the total system in all formulations of quantum mechanics (including the vital property of obeying the virial theorem). Bader has shown that such a subsystem is defined by the “zero-flux surface” in the gradient vector field, i.e. the surface with normal nˆ (r) in real space which obeys the equation
∇F(r)‚nˆ (r) ) 0 for all points on the surface. The region of space Ω bounded by this surface, along with the nucleus it contains, is identified as an atomic basin. Integration of the property density associated with an operator A, FA, over Ω gives the atomic expectation value for that operator. Atomic properties computed in this fashion may include populations, energies, volumes, multipole moments,11 polarizabilities, and magnetic susceptibilities.12 The atomic populations and energies have been checked to ensure they sum to the correct molecular value; this is particularly important here as the systems are not at equilibrium, so the Hellman-Feynman forces on the nuclei are not zero. Critical point (CP) searches used EXTREME, and Laplacian plots were produced with GRID.10 CP analyses involve finding those points where the gradient of the charge density, ∇F, vanishes. A (3,-1) or bond CP is the minimum on the line of maximal charge density between two nuclei and is invariably found between two interacting atoms. The properties of the charge density at such points (F, ∇2F, and ) provide a powerful tool for the classification of bonding interactions.13 The
The results of the constrained optimizations and TS searches, using the heavy atom separation indicated, are reported in Table 1. Use of these separations results in PT barriers for FHF-, H3O2-, H5O2+, and N2H7+ of 20.32, 30.04, 25.52, and 11.84 kJ mol-1, respectively. These values are in general agreement with those found in published calculations at a similar level (differences arise from our optimization of all but the XX distance). The use of arbitrary interatomic separations means little emphasis should be placed on the absolute magnitude of these barriers. Previous studies3a,b indicate that more electron correlation, such as MP4 or QCISD(T), barely changes such barriers. Also included in Table 1 are the total electron-nuclear potential energies, VNE, which show that the barriers arise out of a decrease in this attraction as the protons shift. Some trends are apparent in the geometrical parameters; for example, the “internal” XA-HT bond is considerably longer than the “external” ones. The results of the AIM analysis are reported in Tables 2 (populations and energetics) and 3 (multipole moments), with bond critical point properties in Table 4. (i) FHF-. In FHF- electronic charge flows in the direction opposite the proton’s movement, i.e. from FB to HT and FA. Most of the transferred density is accepted by HT, whose ability to stabilize density within its own basin is clearly enhanced by moving toward FB. Despite accepting density, FA is destabilized by the PT process, while both other atoms are stabilized as they approach one another. The destabilization of FA as the proton moves away is therefore the source of the barrier to PT in FHF-. A deeper understanding of the energy changes can be gained by considering the inter- and intraatomic stabilizations. Intraatomic stabilization, VNEO, is defined as the attraction of an atom’s electron density for that atom’s nucleus; interatomic stabilization, VNE - VNEO, is the difference between the total atomic electron-nuclear attraction and the intraatomic stabilization. Together with the repulsive potential energy, VREP, these quantities determine the overall atomic energetics. The change in interatomic stabilization dominates the energy change in FA; the increased distance to the positively charged HT leads to a reduction in the Coulombic attraction between these atoms. Similarly, the dominant energy changes in FB and HT are interatomic, stabilizing one another as they approach. A large intraatomic destabilization is also observed in FA, which is
Proton Transfer in Ionic Hydrogen Bonds
J. Phys. Chem., Vol. 100, No. 32, 1996 13457
TABLE 2: Atomic Populations and Energetics at the Minimum Energy and Transition State Geometries (au)a XA
XB
HA
HB
HT
FHFN E VNEb VNEO VREP
9.8226(+0.0043) -99.9880(+0.1188) -266.8180(+1.7011) -243.5852(+0.4472) +66.8512(-1.4575)
9.9111(-0.0842) -99.7747(-0.0948) -264.5974(-0.5195) -243.2238(+0.0858) +65.0578(+0.3359)
N E VNE VNEO VREP
9.2480(-0.0055) -75.5189(+0.1288) -210.1480(+1.7539) -184.7124(+0.5604) +59.1130(-1.4914)
9.3387(-0.0962) -75.2824(-0.1077) -207.8210(-0.5731) -184.1440(-0.0080) +57.2594(+0.3622)
H3O20.4893(+0.0415) -0.4082(-0.0168) -3.3816(-0.2233) -0.7735(-0.0361) +2.5647(+0.1890)
0.5626(-0.0318) -0.4358(+0.0107) -3.7091(+0.1042) -0.8342(+0.0246) +2.8370(-0.0833)
0.3613(+0.0921) -0.3017(-0.0035) -2.9803(-0.5618) -0.5909(-0.0427) +2.3586(+0.5539)
N E VNE VNEO VREP
9.1792(-0.0282) -75.7438(+0.0770) -216.8161(+1.5580) -185.2217(+0.3981) +65.3317(-1.4008)
9.1791(-0.0281) -75.5948(-0.0720) -214.6220(-0.6361) -184.7891(-0.0345) +63.5362(+0.4947)
H5O2+ 0.3040(+0.0349) -0.2945(-0.0243) -2.2900(-0.2319) -0.5521(-0.0462) +1.7005(+0.1829)
0.3745(-0.0356) -0.3422(+0.0234) -2.7506(+0.2287) -0.6434(+0.0451) -2.0656(-0.1822)
0.2847(+0.0578) -0.2589(+0.0060) -2.5273(-0.3663) -0.4936(-0.0194) +2.0090(+0.3777)
N E VNE VNEO VREP
8.0820(+0.0002) -55.1729(+0.0493) -165.2845(+0.8765) -134.5013(+0.2206) +54.9389(-0.7775)
8.0936(-0.0114) -55.0566(-0.0670) -163.8341(-0.5739) -134.1570(-0.1237) +53.7214(+0.4400)
N2H7+ 0.5340(+0.0315) -0.4242(-0.0170) -3.7777(-0.1688) -0.8375(-0.0337) +2.9285(+0.1524)
0.5960(-0.0305) -0.4566(+0.0154) -4.1426(+0.1781) -0.9025(+0.0313) +3.2286(-0.1477)
0.4345(+0.0084) -0.3430(+0.0268) -3.6456(+0.0257) -0.6815(+0.0307) +2.9587(+0.0275)
a
0.2667(+0.0793) -0.2536(-0.0162) -2.3626(-0.5582) -0.4637(-0.0576) +1.8550(+0.5253)
Values in parentheses are changes on going to the TS. b See text for definitions of VNE, VNEO, and VREP.
TABLE 3: Atomic Multipole Moments at the Minimum Energy and Transition State Geometriesa XA
XB
HA
HB
FHF-
HT
q MZ QXX QZZ
-0.8226(-0.0043) -0.2377(+0.2966) -0.1757(-0.1811) +0.3514(+0.3622)
-0.9110(+0.0842) -0.0332(-0.0257) -0.3954(+0.0386) +0.7808(-0.0772)
q MX MZ QXX QZZ
-1.2480(+0.0055) -0.0729(+0.0486) -0.0697(+0.1654) +1.1429(+0.4820) +0.4374(-0.0366)
-1.3387(-0.0962) -0.0209(+0.0452) -0.1938(+0.0981) +1.9372(-0.3123) +0.3570(+0.0438)
H3O2+0.5017(-0.0415) -0.2039(-0.0304) +0.0326(+0.0015) -0.0575(-0.0186) +0.0326(-0.0072)
+0.4374(+0.0318) +0.2532(-0.0189) -0.0795(+0.0454) -0.0918(+0.0157) +0.0339(+0.0059)
+0.6387(-0.0921) -0.0024(+0.0024) -0.1114(+0.1114) -0.0843(-0.1233) +0.1729(+0.2749)
q MX MZ QXX QZZ
-1.1792(+0.0282) -0.2894(+0.0331) -0.0868(+0.1104) -0.4759(-0.2037) +0.0495(+0.0362)
-1.1791(+0.0281) +0.2227(+0.0336) -0.0957(+0.0721) -0.8212(+0.1416) +0.0454(+0.0404)
H5O2+ +0.6960(-0.0349) -0.0572(-0.0075) +0.0385(+0.0107) -0.0034(-0.0021) +0.0105(-0.0021)
+0.6255(+0.0356) +0.0697(-0.0007) -0.0643(+0.0151) -0.0053(-0.0002) +0.0049(+0.0035)
+0.7153(-0.0578) -0.0012(+0.0012) -0.0852(+0.0852) -0.0050(-0.1347) +0.1039(+0.1725)
q MZ QXX QZZ
-1.0820(-0.0002) -0.0929(-0.0300) +0.2947(+0.1685) -0.5895(-0.3370)
-1.0936(+0.0114) +0.1421(-0.0192) +0.5641(-0.1009) -1.1283(+0.2018)
N2H7+ +0.4660(-0.0315) +0.0549(+0.0103) +0.0845(+0.0086) -0.0352(-0.0064)
+0.4040(+0.0305) -0.0755(+0.0103) +0.1020(-0.0089) -0.0487(+0.0071)
+0.5655(-0.0084) -0.0827(-0.1010) -0.0050(-0.1347) +0.1039(+0.1725)
a
+0.7332(-0.0793) -0.0831(+0.0831) -0.0538(-0.0907) +0.1075(+0.1815)
See Figure 1 for the axes employed.
surprising given that an increase in electron population is observed. The source of this destabilization is apparent in the atomic multipole moments and their changes on PT. Prior to proton transfer, FA in FHF- has a large negative z-dipolesindicating polarization of density toward HT and FBs(see Figure 1 for the axes employed), a result of the attractive influence of HT. As the influence of the proton falls, this dipolar polarization is removed, and FA has a small positive z-dipole in the TS. Thus F’s density distribution is almost centered on its nucleus. To lessen the electron-electron repulsion that arises, FA undergoes a massive quadrupole polarization, pushing density away from the molecular axis and forming a torus of density around the molecular axis. The movement of density away from the nucleus reduces the electron-nuclear attraction and is the cause of the observed intraatomic destabilization. The moments on HT behave in a similar fashion; it is dipole
depolarized (to zero by symmetry) and quadrupole polarized perpendicular to the molecular axis. The increase in population results in intraatomic stabilization, but it is interatomic effects that dominate here. FB, on the other hand, is dipole polarized toward the approaching HT. The bond CP data in Table 4, along with the Laplacian plots of Figure 2, show the changes in density properties caused by PT. It is clear that at equilibrium FHF- has a “typical” H-bond, with one covalent (high F and negative ∇2F) and one ionic (low F and positive ∇2F) interaction. At the TS both interactions are apparently ionic, with large regions of positive ∇2F separating all atoms. Despite this, the Laplacian is negative at the associated CP, indicating that this point lies within the valence shell of charge concentration (VSCC) of HT. Similar results have been found experimentally for an anionic O‚‚‚H‚‚‚O bond14 (see below).
13458 J. Phys. Chem., Vol. 100, No. 32, 1996
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TABLE 4: Critical Point Properties for “Internal” X-H Bondsa FHFmin
H3O2TS
min
H5O2+ TS
F ∇2F
0.2644 -1.7771 0.0000
0.1124 -0.0611 0.0000
0.2875 -1.9158 0.0191
XA-HT 0.1139 -0.0688 0.0351
F ∇2F
0.0501 +0.1243 0.0000
0.1124 -0.0611 0.0000
0.0461 +0.1041 0.0793
XB‚‚‚HT 0.1139 -0.0688 0.0351
N2H7+
min
TS
min
TS
0.2662 -1.8542 0.0172
0.1061 -0.0939 0.0323
0.2461 -1.1817 0.0000
0.1277 -0.1579 0.0000
0.0440 +0.1004 0.0630
0.1061 -0.0939 0.0323
0.0677 +0.0693 0.0000
0.1277 -0.1579 0.0000
a F is the value of the charge density at the CP; ∇2F is the second derivative of the charge density here; is the ellipticity of the bond, defined as λ1/λ2 (the ratio of the two negative curvatures of the charge density).
Figure 2. -∇2F distributions in FHF- at (a, top) minimum energy geometry and (b, bottom) transition state geometry.
Figure 3. -∇2F distributions in H3O2- at (a, top) minimum energy geometry and (b, bottom) transition state geometry.
(ii) H3O2-. This anion behaves in a fashion generally similar to FHF-, although the picture is complicated somewhat by the presence of terminal hydrogens. Both oxygens lose density as the proton shifts; this is much more pronounced in OB. Electron density is transferred from the base fragment (OB and HB), mostly to HT, with an increase observed in the acid HA. The origin of the loss in population of OB is analogous to that of FB in FHF-, while that in OA results from its reduced effective electronegativity. Without the assistance of HT to stabilize density within its basin, OA relinquishes charge to HA. The loss in population of OB is analogous to that in FB in FHF-; that in OA results from its reduced electronegativity which allows HA to withdraw density from it. The largest energy changes occur in the oxygen atoms: OB is stabilized and, as in FHF-, the barrier to PT originates in the destabilization of the acid heavy atom. Stabilization of HA and destabi-
lization of HB is observed, while the increased attraction and repulsion in HT are very nearly balanced. As in FHF-, interatomic effects dominate the changes in atomic energies; in particular the destabilization of OA arises out of the reduction in the stabilizing influence of HT. As they approach one another, OB and HT are interatomically stabilized (with an accompanying increase in their repulsive energies). Similarly, interatomic changes dominate the energetics of HA and HB. Intraatomic energy changes are only important in OA, wherein a large quadrupole polarization leads to a loss in VNEO, mirrorring the behavior of FA in FHF-. The behavior of HT is also similar to that observed in FHF-, with dipole depolarization but large quadrupole polarization. Table 4 and Figure 3 show a picture broadly similar to that found in FHF- above, with one covalent and one ionic bond at equilibrium changing to two ionic interactions at the TS. One
Proton Transfer in Ionic Hydrogen Bonds point apparent in Figure 3 is the alignment of a lone pair on OB with the HT direction, which is clearly the most stable orientation. Also, unlike in the FHF-, HT is highly elongated in the TS, reflecting its quadrupole polarization noted above. (iii) H5O2+. In this cation, both oxygens’ populations are decreased, as are those of the HB’s, while HA and HT gain density. Overall density is transferred from base to acid, and the trend of electron density flow in the direction opposite the proton movement is maintained. Energetically, OA is destabilized and OB is stabilized, largely through interatomic effects. Intraatomic destabilization of OA is again found: this could be ascribed to the same quadrupole polarization effects as described above, but the large loss of electron population also plays a part. The stabilization of OB is almost all due to interatomic effects, though a small intraatomic stabilization results from its dipole and quadrupole depolarization. The energy changes in the external hydrogens are more important here than in the previous two systems (bearing in mind that there are two each of HA and HB). As a consequence, the barrier to PT cannot be assigned purely to the destabilization of OA. The acid hydrogens take advantage of the lower effective electronegativity of OA, pulling density from this atom. In doing so that are stabilized inter- and intraatomically, while the base hydrogens are similarly destabilized. Overall though, these changes are not as large as in the heavy atoms, so that the acid fragment is destabilized and the base fragment is stabilized by proton transfer. The energetics of HT are curious: it is destabilized on moving to the central position, despite substantially increasing its population. It increases both its inter- and intraatomic stabilizations by moving closer to OB and accepting density. However, the increase in its repulsive energy is greater than in its attractive energy, giving it a net atomic destabilization. The PT barrier thus arises out of the destabilization of both OA and HT. The results in Figure 4 and Table 4 for H5O2+ are remarkably similar to those for H3O2- and further support the picture of a typical H-bond going to two ionic interactions. HT aligns itself with a lone pair on OB at equilibrium, and HT is polarized along the O‚‚‚O axis in the TS. Both TSs have small, negative values of the Laplacian at the bond CPs: this appears to be a consequence of the very small size of HT rather than being indicative of covalent bonding. (iv) N2H7+. The situation here is apparently dominated by the behavior of the hydrogens. NA’s population hardly changes, the basic NB loses some density, and HT gains a similar amount of density. These changes are dwarfed by those in the six external hydrogens, where around 0.1e are transferred from HB to HA. The PT energetics have similarly large contributions from the external hydrogens, so much so that the acidic NH3 fragment is actually stabilized as the proton leaves. The acidic NA is destabilized by both inter- and intraatomic effects, due to the removal of HT’s stabilization and its huge quadrupole polarization, respectively. Its attached hydrogens are stabilized, mostly interatomically as they move slightly closer to NA, with a smaller intraatomic contribution resulting from their increased population. The base NB has a large interatomic stabilization from the approaching proton, but the intraatomic contribution is much larger than in the other systems, due to its dipole and quadrupole depolarization. HT increases its population, but in doing so is very strongly quadrupole polarized. This leads not only to intraatomic destabilization but also to increased repulsion, which results in substantial atomic destabilization. Since both NH3 fragments are stabilized, this is the source of the PT barrier here.
J. Phys. Chem., Vol. 100, No. 32, 1996 13459
Figure 4. -∇2F distributions in H5O2+ at (a, top) minimum energy geometry and (b, bottom) transition state geometry.
Here, the bond CP data and Laplacian plots (Figure 5) show very different behavior from the previous three systems. At equilibrium the system is “normal”, with NA-HT covalent and NB‚‚‚HT ionic. Figure 5b, however, is striking in its dissimilarity to the other TSs. Whereas two ionic interactions are typically found at the TS, here the region of negative ∇2F is continuous over [N‚‚‚H‚‚‚N], indicating two coValent N-H bonds exist at the TS. Such negative Laplacian values have been found before for symmetric [N‚‚‚H‚‚‚N]+ hydrogen bonds in proton sponges.15 Discussion One obvious feature of the atomic properties, common to all four systems, is that electronic charge density flows in the direction opposite the proton’s movement. Florian and Scheiner’s study, which employed Mulliken and APT charges, reached the same conclusion. This charge flow results from an equalization of the population of the fragments which must accompany the formation of a symmetric TS. In the initial hydrogen bond the acid group has a lower population than the base group, a situation which must be removed on going to the symmetrical TS by transferring density from base to acid. The changes in atomic population bear no simple relation to the atomic energy changes; that is, those atoms that gain electrons are not necessarily stabilized. So, the use of atomic charges to infer energy changes, which has been suggested with NBO charges,16 is not straightforward for PT processes. The overall energy changes are dependent on the arbitrary heavy atom separation employed and hence do not show consistent behavior over the four systems. One feature present in all systems is the drop in the total electron-nuclear potential energy
13460 J. Phys. Chem., Vol. 100, No. 32, 1996
Figure 5. -∇2F distributions in N2H7+ at (a, top) minimum energy geometry and (b, bottom) transition state geometry.
at the TS. Another common feature is the destabilization of the acid heavy atom as the proton leaves, along with the stabilization of the base heavy atom. Despite these similarities, the behavior on PT differs greatly across this isoelectronic series [HnX2], n ) 1, 3, 5, 7. Two possible reasons for these differences are the presence or absence of external hydrogens and the total charge on the systems. These results demonstrate that the external hydrogens are important in determining the total energy change, acting as “reservoirs” and “sinks” for density. If this were the origin of the differences, we would expect FHF- to have anomalous behavior. In fact FHF- and H3O2- act in a very similar fashion, as do H5O2+ and N2H7+. Thus it seems that it is rather the total charge on the system that determines its behavior on PT, perhaps because electron density is more easily transferred in the electron rich anionic species. In the anionic systems, the barrier to PT arises from the destabilization of the heavy atom from which the proton moves. This destabilization is a result of decreased VNE in this atom, rather than increased repulsion. The reduction of the stabilizing influence of the positive hydrogen and the quadrupolar polarization of density are the sources of the diminished electronnuclear attraction. In the cationic systems the energetic changes are less clear-cut; the acidic heavy atom is again destabilized, but this is offset much more by the accompanying stabilization of the attached hydrogens. Unlike in the anionic systems, the central hydrogen is destabilized as it is transferred, making a substantial contribution to the PT barrier. Bond CP data and Laplacian plots in the X‚‚‚H‚‚‚X region appear to support the results of high-resolution X-ray diffraction experiments on similar systems. Anionic O‚‚‚H‚‚‚O H-bonds
Platts and Laidig in sodium hydrogen succinate and dichloromaleate14,17 show properties similar to those reported here. In both cases the VSCC of the proton was found to be polarized in the O‚‚‚O direction. This has been taken as possible evidence of structural disorder about the central position; but the presence of this feature (Figures 3b and 4b) in our calculations provides evidence to the contrary. Also, the O‚‚‚H CPs are found experimentally to lie within the VSCC of the central proton, resulting in negative Laplacian values, despite the ionic nature of the interaction. The elongation of H’s VSCC is the likely cause of this unusual result, though the very small bonded radius of the HT here leads to the CP lying within its basin. It is informative to compare the bond CP data for the very strong ionic H-bonded systems studied here with those found for more conventional H-bonds. In a recent study,18 the same level of theory was employed for the complexes of HF with H2O, H2S, H2CO, and H2CS. H-bond strengths of between 20 and 40 kJ mol-1 were calculated, compared with upward of 100 kJ mol-1 for ionic H-bonds. As has been reported previously,19 H-bond strength is correlated with the value of F at the corresponding CP. The results presented here add further weight to this conclusion: the strong, ionic H-bonds have at least twice the density at the CP than do the weaker, neutral H-bonds. However, there seems to be no such correlation between H-bond strengths and ∇2F at the bond CP here, since Laplacian values found in the ionic H-bonds are very similar to those observed in neutral H-bonds. The atomic properties reported in this study could find use in the fields of molecular modeling and molecular dynamics, particularly in biological systems and studies on solvent effects where proton transfer reactions are important. More specifically, the use of simple point charge models to represent electrostatic interactions is limited at best. The higher multipoles obtained from an AIM analysis allow a much more accurate estimate of electrostatic properties to be made, and furthermore these results provide concrete data on the polarization effects often ignored in molecular dynamics models. Conclusions We have identified the origin of barriers to proton transfer in the ionic hydrogen bonds contained in FHF-, H3O2-, H5O2+, and N2H7+ to be decreased electron-nuclear attraction concentrated mainly in the acid heavy atom. This is dominated by the reduction of the stabilizing influence of the transferred proton, with a smaller contribution from the polarization of the density within this atom’s basin. In doing this we have shown that anionic and cationic proton transfer behave in distinct ways. In the former, the barrier arises out of the destabilization of the acidic heavy atom as the proton leaves. In the latter, this same effect occurs but to a lesser degree, with the destabilization of the transferred proton making a large contribution to the barrier. In the cationic systems the external hydrogens’ behavior is important, acting as “sinks” and “reservoirs” for electron density. We have demonstrated that, in general, changes in atomic charge do not correlate with changes in atomic energy, since changes in higher multipole moments are large. Finally, we have shown that a typical transition state has an isolated valence shell of charge concentration (VSCC) for the transferred proton, while in N2H7+ the VSCC is continuous over all atoms. Acknowledgment. The authors thank Dr. S. T. Howard for his constructive criticism of the manuscript and Dr. P. R. Mallinson for providing preliminary results of experimental X-ray diffraction charge density studies.
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J. Phys. Chem., Vol. 100, No. 32, 1996 13461 (9) (a) Bader, R. F. W.; Nguyen-Dang, T. T. AdV. Quantum Chem. 1981, 14, 63. (b) Bader, R. F. W. Atoms in Molecules; A Quantum Theory; Oxford University Press: Oxford, 1990. (c) Bader, R. F. W. Chem. ReV. 1991, 91, 893. (10) Biegler-Ko¨nig, F. W.; Bader, R. F. W.; Tang, T. H. J. Comput. Chem. 1982, 3, 317. (11) (a) Bader, R. F. W.; Cheeseman, J. R.; Laidig, K. E.; Wiberg, K. B.; Breneman, C. J. Am. Chem. Soc. 1990, 112, 6530. (b) Bader, R. F. W.; Chang, C. J. Phys. Chem. 1989, 93, 5095. (c) Bader, R. F. W.; Carroll, M. T.; Cheeseman, J. R.; Chang, C. J. Am. Chem. Soc. 1989, 109, 7968. (d) Laidig, K. E. J. Phys. Chem. 1993, 97, 12760. (12) (a) Laidig, K. E.; Bader, R. F. W. J. Chem. Phys. 1990, 93, 7213. (b) Howard, S. T. Mol. Phys. 1995, 85, 395. (c) Keith, T. A.; Bader, R. F. W. Chem. Phys. Lett. 1993, 210, 223. (d) Bader, R. F. W.; Keith, T. A. J. Chem. Phys. 1994, 99, 3683. (13) Bader, R. F. W.; Essen, H. J. Chem. Phys. 1984, 56, 1943. (14) Mallinson, P. R.; Woz´niak, K. Personal communication. (15) (a) Platts, J. A.; Howard, S. T.; Woz´niak, K. J. Org. Chem. 1994, 59, 4647. (b) Howard, S. T.; Platts, J. A.; Alder, R. W. J. Org. Chem. 1995, 60, 6085. (c) Platts, J. A.; Howard, S. T. Submitted to J. Org. Chem. (16) Glendening, E. D.; Feller, D.; Thompson, M. A. J. Am. Chem. Soc. 1994, 116, 10657. (b) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (17) Mallinson, P. R.; Frampton, C. S. Acta Crystallogr., Sect. C 1992, 48, 1555. (18) Platts, J. A.; Howard, S. T.; Bracke, B. R. F. J. Am. Chem. Soc. 1996, 118, 2726. (19) Carroll, M. T.; Bader, R. F. W. Mol. Phys. 1988, 65, 695.
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