ARTICLE pubs.acs.org/JPCA
Charge-Displacement Analysis of the Interaction in the AmmoniaNoble Gas Complexes Giovanni Bistoni,† Leonardo Belpassi,*,†,‡ Francesco Tarantelli,*,†,‡ Fernando Pirani,† and David Cappelletti§ †
Dipartimento di Chimica, Universita di Perugia, 06123 Perugia, Italy Istituto CNR di Scienze e Tecnologie Molecolari (ISTM-CNR), c/o Dipartimento di Chimica, Universita di Perugia, Via Elce di Sotto 8, I-06213 Perugia, Italy § Dipartimento di Ingegneria Civile e Ambientale, Universita di Perugia, 06125 Perugia, Italy ‡
ABSTRACT: We carry out an accurate ab initio study of the interaction between ammonia and the whole series of noble gas atoms and relate the results to those of high-resolution scattering experiments that provide access to the average radial dependence of the interaction potential. The chargedisplacement calculations show that charge transfer is a non-negligible, strongly anisotropic, component of the interaction, governing some basic features of the potential energy surfaces especially for the heavier systems. A comparison is made with the analogous binary complexes of H2O with the waterH2 system (Belpassi, L.; et al. J. Am. Chem. Soc. 2010, 132, 13046), supporting the conclusion that charge transfer plays a peculiarly special role in water’s intermolecular interactions.
’ INTRODUCTION The extent and role of charge-transfer (CT) effects in weak intermolecular interactions involving hydrogenated molecules constitute a long debated and still unsettled question (see, for example, refs 19). A full, detailed description of the nature of the hydrogen bond requires an account of the critical balancing of electrostatic, charge transfer, induction, dispersion, and exchange (or size) repulsion interaction components. This represents for a long time a fundamental and broad field of research.10,11 One aim of the research is to establish and generalize a correct partition of the intermolecular forces involved, based on the nature of the various interaction contributions. Quantitatively identifying, among the others, the CT component is a particularly elusive task, but it is crucial in order to develop models founded on solid grounds and useful for the description of the force fields operating in complex systems of technological interest. Experimental and theoretical studies squarely aiming at this goal, starting with complexes of small hydrogenated molecules like water and ammonia, thus appear particularly desirable. There are also other specific reasons of interest in these systems since there is evidence that weakly interacting complexes of water and ammonia in the gas phase lead to collisional complexes, either stable or metastable, that can play relevant roles in atmospheric chemistry and physics.12 In particular, complexes involving water and air components have been suggested as possible contributors to the absorption of solar radiation in the infrared region,13 thus affecting the energy balance of the earth's atmosphere. Ammonia was the first polyatomic molecule detected in the interstellar space, and since this discovery, NH3 has proved to be an invaluable spectroscopic tool in the study of the interstellar medium.14 It is an excellent probe of the physical conditions of dense molecular gas and a good molecular cloud r 2011 American Chemical Society
thermometer15 (see ref 16 and references therein). The detailed characterization of dynamical and optical properties of these weakly interacting species is still unsatisfactory17 since it requires the knowledge of reliable full potential energy surfaces (PESs). In this context, the modeling of various components of the overall noncovalent interaction is an issue of general and great interest.18 Systems involving closed shell hydrogenated molecules, interacting with other nonpolar closed shells, are generally thought to bind through van der Waals (vdW) forces, which we define here as due to the combination of short-range size repulsion with longrange dispersion attraction (note that different definitions may be available in the literature) to which induction effects often add. High resolution molecular-beam scattering experiments, showing appreciable shifts in the position of quantum interference effects on the cross-section,19 have, however, in some cases, suggested otherwise. Similar experimental findings, combined with very accurate ab initio calculations involving charge-displacement analysis,20,21 have finally shown that even the waternoble gas complexes cannot be classified as conventional noncovalent vdW systems: an appreciable (i.e., measurable) fraction of the interaction energy is due to CT. The latter was clearly demonstrated to be stereospecific, showing maximum strength for the noble gas (NG) approaching water on the hydrogen side.20,21 Recently,22 we have studied in detail the waterH2 system, for which an electrostatic component (due to the permanent dipolepermanent quadrupole interaction) is operative. A significant and far more intriguing CT stereospecificity was discovered for this prototype Received: September 14, 2011 Revised: October 31, 2011 Published: November 21, 2011 14657
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The Journal of Physical Chemistry A complex. In particular, when hydrogen approaches water from the side of the latter’s hydrogen atoms, with the H2 axis perpendicular to the water plane, some millielectrons are transferred from H2 toward H2O, as found in the NG case.20,21 But when the hydrogen molecular axis is pointed toward the oxygen atom along the C2v symmetry axis of water, the reverse effect occurs, with water acting as the electron donor. In other words, we observed in the embryo the amphoteric character of water. The investigation of these intermolecular interactions has been recently extended to the ammoniaNG systems with new high-resolution molecular beam scattering experiments, performed by using rotationally hot ammonia molecules scattered by NG atoms.23 This has provided a direct probe of the intermolecular interaction on an absolute scale. The methodology of such experiments is the same as that used for the investigation of the interaction of water and hydrogen sulphide molecules with other closed shell neutral species.19,21,22,2426 The adopted experimental conditions have permitted, in the case of NH3NG, the clear observation of an oscillatory pattern (except for NH3 He), associated with the glory quantum interference effect, superimposed to a smooth average crosssection component. The analysis of the experimental data has revealed the presence of an interaction component, which adds to the vdW plus induction interaction, and has permitted to estimate its strength. This stabilization component of the spherically averaged potential is about 34 meV in the case of the NH3Xe, corresponding to 15% of the total interaction. Complementing this experimental study, we discuss here the results of accurate ab initio charge-displacement investigations that explain and characterize the origin of this small but measurable energy. Most of the theoretical calculations on NH3NG systems reported in the literature investigated the PES. Some of these calculations have been performed a long time ago (see refs 2733 and references therein) using both supermolecular calculations and many body symmetry adapted perturbation theory. A notable exception is the recent work of Wen and J€ager34 that reports a highly accurate ab initio PES for NH3Xe at the coupled-cluster level with double and perturbatively included triple excitations, CCSD(T), with a large basis set. To our knowledge, no recent, systematic, and accurate comparative ab initio study of the NH3NG series is available. We have, therefore, carried out such a detailed study using the coupledcluster theory. Some characteristic cuts of the PES have been computed and will be discussed in detail, along with the determination of the most stable nuclear configurations determined by full geometry optimization.
’ COMPUTATIONAL DETAILS All calculations have been carried out at the coupled-cluster level of theory3537 with single, double, and perturbatively included triple excitations (CCSD(T)) using augmented correlation consistent polarized valence basis sets up to quintuple-zeta (aug-cc-pVxZ, with x = D, T, Q, 5).3840 We shall refer to these basis sets as AVxZ, with x = D, T, Q, 5. For Xe, relativistic effects have been taken into account through the use of small-core pseudopotentials.41 All the ab initio calculations have been carried out using the program MOLPRO.42 For all NH3NG complexes, we have investigated in detail the basis set convergence for the determination of both the equilibrium geometry and the corresponding interaction energies. The basis set superposition error (BSSE) on the interaction
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Figure 1. CCSD(T)/AV5Z optimized interaction energies for the NH3 NG complexes for Θ = 60° as a function of the angle Φ. BSSE correction is included.
energies has been evaluated by using the counterpoise correction of Boys and Bernardi,43 but the geometry optimizations have been carried out for the non-BSSE-corrected energy. The geometry of the ammonia was kept fixed at its equilibrium structure (angle HNH of 106.7° and NH bond length of 1.012 Å), as in ref 34. The geometry of the complex is defined by a set of spherical coordinates (r,Θ,Φ) with an origin at the center of mass (c.m.) of the ammonia and r representing the NG-c.m. distance. Θ is the dihedral angle between a symmetry plane of NH3 and the plane containing ammonia’s C3 axis and the NG atom. Θ = 0 corresponds to NG lying in the half-plane containing one NH bond. Φ is the angle between the c.m.NG radius and the C3 axis, with Φ = 0 corresponding to NG lying on the C3 axis on the hydrogen side.
’ GEOMETRY OPTIMIZATIONS AND INTERACTION ENERGIES Experimental and previous theoretical information on the structure and most stable configurations of NH3NG suggests that the absolute minima of the PESs correspond to a Θ = 60° structure, with NG lying on the symmetry half-plane not containing a NH bond (see ref 34 and references therein). We thus restrict our analysis to the section of PES that is obtained by fixing Θ = 60° with Φ varying in the full range from 0 to 360° (by 20degree steps) and reoptimizing r at each point. Note that this slice of the PES provides a good sampling of the interaction, with the NG atom probing regions close to a hydrogen atom, between two hydrogens, and close to nitrogen. For example, along this path, Φ > 180° corresponds to NG lying on the mirror half-plane containing a NH bond, i.e., it is the same as a configuration with Θ = 0 and Φ0 = 360° Φ. For these calculations, we used the AV5Z basis set at the CCSD(T) level of theory. The PES sections obtained, corrected for BSSE, are reported in Figure 1. It can be seen that all complexes show a similar interaction energy pattern. In all cases, the main minimum occurs for Φ in the range 90105° corresponding to a configuration with the NG atom lying beside the nitrogen atom and between two hydrogens. The minimum for the two lightest NGs is clearly less pronounced, and there is a larger gap between the binding energy of these two atoms and that of the heavier ones. All the curves except that of the heavier Xe show a secondary minimum for Φ = 250280°, i.e, with NG lying on the opposite side of ammonia compared 14658
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Table 1. CCSD(T) Optimized Geometrical Parameters and Corresponding Interaction Energies E (meV) of the NH3NG Complexes at Θ = 60° with Different Basis Setsa He
Ne r
Φ
E
Ec
2.5
3.32
96
11.9
3.5
3.7
3.23
93
11.8
6.3
4.5
4.1
3.25
92
11.2
7.4
4.4
4.2
3.26
93
9.1
7.9
basis
r
Φ
E
AVDZ
3.29
99
5.3
AVTZ
3.22
92
4.8
AVQZ
3.25
91
AV5Z
3.23
91
Ec
Main Minimum
Secondary Minimum AVDZ
3.53
262
4.9
1.8
3.60
273
11.4
2.8
AVTZ
3.50
261
3.8
2.5
3.47
278
12.5
3.2
AVQZ
3.55
260
3.2
2.9
3.57
276
9.8
5.2
AV5Z
3.57
260
3.1
2.9
3.53
259
7.3
6.1
Ar basis
r
Φ
E
Kr Ec
r
Φ
E
Xe Ec
r
Φ
E
Ec
Main Minimum AVDZ 3.59 96
20.7 10.1 3.69 94
25.7 10.2
3.89 105 26.7 11.7
AVTZ 3.55 94
21.9 15.0 3.70 94
24.3 17.6
3.86 105 27.4 20.1
AVQZ 3.55 94 AV5Z 3.60 94
20.1 17.1 3.70 94 19.7 17.8 3.70 94
23.1 20.2 22.4 20.8
3.87 105 25.7 23.1 3.89 105 25.2 23.9
Secondary Minimum AVDZ 3.83 279 23.2 6.3
3.95 280 25.2 6.6
AVTZ 3.83 280 20.8 11.2 3.95 279 23.1 13.3 AVQZ 3.87 275 16.9 13.5 3.94 261 19.2 15.9 AV5Z 3.87 274 16.1 13.9 3.93 257 18.1 17.0
The term r is in Å and Φ is in degrees. Ec (meV) are the interaction energies corrected for BSSE. a
with that of the main minimum. In all cases, the curve maximum (smallest binding energy) is located at Φ = 0, and in all cases except Xe, a second maximum is also observed at Φ = 180°, i.e., with NG located on the C3 axis directly above nitrogen. Note further how these PES cuts tend to flatten in the region above Φ = 180°, especially for the heavier NGs. In the case of Xe, the secondary minimum is absent, and at Φ = 180°, its PES shows a flex. Wen and J€ager34 suggested that the secondary minimum is absent because the larger electron cloud of the Xe atom leads to a stronger repulsive interaction with the closest H atom. We will return on this interesting point in the next section, suggesting that another phenomenon can contribute to this peculiar feature of the NH3Xe system. It is worth noticing here that the geometrical patterns found for NH3NG differ remarkably from those of the corresponding water complexes,20 in that the NG atoms prefer to approach water on the side of an OH bond, tending progressively to line up with the OH bond itself as the NG size increases. Keeping Θ = 60° fixed, we performed a full optimization of the distance r and of the angle Φ with all basis sets. The resulting geometrical parameters and the corresponding interaction energies at the main and secondary minima are reported in Table 1. The various basis sets, with the exception of the small AVDZ, give very similar geometries. The largest variations with the basis set are observed for the He and Ne complexes, where the interaction
Figure 2. CCSD(T)/AV5Z optimized distance r as a function of the angle Φ for the NH3NG complexes. Θ is fixed at 60°.
energies are smaller (see Figure 1). The complexes with He, Ne, Ar, and Kr have their main minimum for an almost identical (within 3 degrees) angle of approach Φ, very close to 90°, while this is larger by about 15° in the Xe case. The Φ values corresponding to the secondary minimum differ more pronouncedly for the various NGs, and the distances are significantly larger (by 0.20.3 Å). This clearly reflects the hindrance by the nearby H atom, which lies between NG and the NH3 c.m. The interaction energies have been obtained as the difference between the energy of the complex and that of the isolated fragments. The table shows that obtaining accurate interaction energies for these weakly bound systems requires very large basis sets: convergence in the BSSEcorrected results (to within about 10%) is obtained only with the AVQZ basis. In Figure 2, we show a plot of the optimized distance r as a function of the angle Φ. Clearly, they parallel relatively closely the corresponding PES sections of Figure 1, with a larger binding energy corresponding to a shorter distance. The curves for the three more strongly bound, heavier, NGs are nearly parallel and separated by an almost constant shift, essentially reflecting the different atomic size. By contrast, the curve for He shows much more pronounced oscillations, getting closest to ammonia at equilibrium but as far as Ar when He is on either side on the C3 axis. The distance of approach is generally larger in the region Φ > 180° because of the presence of the H atom pushing the NG away. The minimum distance of approach is for Φ = 90100° and (except for He) the longest is for Φ = 300°, which is very close to the angle of a NH bond. In the case of He, the maximum distance is for Φ = 0. It is interesting to compare further the potential energy profiles of Figure 1 and the distance profiles of Figure 2, which appear to be correlated. Indeed, the minimum distance of approach is observed at about the same Φ values of the equilibrium structures, and the distance profiles also show a secondary minimum in the same region of the energy secondary minimum. This correlation suggests, as may be expected, that the interaction is dominated by vdW forces. The correlation between energy and distance appears increasingly less stringent as NG size increases, and for Xe, a secondary minimum in the distance is still found, while no such minimum exists for the energy. This suggests that other interaction components may play an increasingly important role for the heavier NG atoms. As mentioned in the introduction, one of the main purposes of the present work is to use our theoretical results to compare with, 14659
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Table 2. Theoretical CCSD(T)/AV5Z (BSSE Corrected) and Experimental Isotropic Well Depth ε and Equilibrium Distance rm for the AmmoniaNG and KrNG Systemsa theoreticalb system
experimentalc
ε (meV) rm (Å) ε (meV) rm (Å)
vdW + inductionc ε (meV)
rm (Å)
NH3He
2.22
3.69
2.45
3.70
2.77
3.58
KrHe
2.40
3.74
2.67
3.70
2.98
3.66
NH3Ne
5.19
3.59
5.55
3.67
5.66
3.62
KrNe
5.45
3.70
6.16
3.66
6.25
3.70
NH3Ar KrAr
13.3 13.1
3.80 3.95
13.6 14.33
3.83 3.91
12.7 14.08
3.86 3.92
NH3Kr
16.3
3.91
17.7
3.94
15.7
3.97
KrKr
15.6
4.07
17.30
4.01
17.61
4.03
NH3Xe
19.5
4.09
21.5
4.11
18.4
4.14
KrXe
18.0
4.26
19.95
4.20
20.63
4.18
The experimental estimated uncertainty is of 35% for ε and 12% for rm. The estimates of a simple vdW + induction model of the potential are also reported for comparison. b This work. c See ref 23. a
and explain, the experimental data we obtained by scattering experiments for the absolute interaction energies of the NH3 NG complexes. 23 The latter refer to rotationally hot ammonia molecules and therefore reflect an average energy over all possible relative orientations of the interacting species, which are obviously overestimated by the theoretical results at the equilibrium geometry of Table 1. The full ab initio PES of the complexes is not available, and therefore, an accurate theoretical prediction of the rotationally averaged well depths cannot be made. However, as we said above, the Θ = 60° section of the PES provides a sampling of various qualitatively different orientations. Accordingly, a rough theoretical estimate of the observed potential well depth (ε) and position (rm) may be obtained by simply averaging the computed results over the curves of Figures 1 and 2. In Table 2, these averages are compared with the experimental data and with the estimates of a simple vdW + induction model.23,44 (The model refers to classical induction, not the perturbation-theory induction term which includes CT.8) For each NH3NG complex, we also show in the table the data for the corresponding KrNG adduct. Kr and ammonia have very similar polarizability, so the KrNG results are useful to assess the value of the comparison in case of a similar interaction where only vdW forces are at work and where no averaging is needed. Clearly, the averaging procedure consistently reduces the NH3NG interaction energies and enlarges the distances compared with the values at the optimized geometries (see Table 1). The agreement of the theoretical estimates with the experimental determinations is good; in fact, it is within the experimental error bar for all systems. To make the comparison more significant and illustrate some important conclusions regarding the nature of the interaction, we show in Figure 3 the computed and experimental ratio of the potential well depth for the NH3NG complexes compared to that of the corresponding KrNG ones, plotted versus the NG polarizability. The theoretical data for this relative measure of the interaction are in remarkable agreement with the experimental ones, in most cases within the estimated experimental error,23 and most importantly, the trends match each other extremely well. As can be seen, the ratio increases along the NG series, meaning that the interaction strengthens increasingly for the
Figure 3. Ratio ε/ε0 of the potential well depth of the NH3NG binary complexes to that of the corresponding KrNG systems, plotted as a function of NG polarizability, the key quantity on which vdW intermolecular interactions depend. Shown are the experimentally determined and theoretically estimated values, together with those derived using simple vdW + induction correlation formulas.23,44 The estimated uncertainty on the latter is evidenced as a gray band.
heavier NH3NG complexes compared to that of the pure vdW KrNG ones. This increase is not due to the induction term. Indeed, as the figure clearly shows, an essentially constant ratio, well outside of the respective error bars, would be predicted by applying the correlation formulas44 describing the vdW + induction model used to derive the values reported in Table 2 and presented in ref 23. Similar findings were reported for the waterNG complexes and were related to CT effects.20,21 Indeed, since the only component missing in the model is CT, the above comparison suggests again that a CT component in the interaction plays an increasingly stabilizing role along the NH3NG series. This stabilization appears to be absent or negligible for He and Ne and reaches 34 meV (i.e., roughly 1520% of the interaction) for Xe.23 Note that essentially identical conclusions regarding the magnitude of the stabilization energy are reached by confronting the long-range attraction region of the experimentally derived interaction potential (where CT is absent) with the well region, without reference to any vdW or induction model.23 In the following sections, we shall study in detail the extent and role of CT in the NH3NG complexes and correlate it with the features of the PES in relation with the experimental findings and to our previous results for the analogous H2ONG series.20,21
’ CHARGE DISPLACEMENT ANALYSIS To study the electron density changes characterizing the bond between ammonia and the NGs, we shall adopt the chargedisplacement (CD) analysis we have successfully used to study intermolecular interactions and chemical bonding in several diverse contexts.20,22,4547 The CD function is defined as ΔqðzÞ ¼
Z ∞ ∞
dx
Z ∞ ∞
dy
Z z ∞
ΔFðx, y, z0 Þdz0
ð1Þ
where ΔF is the electron density difference between the interacting complex and the isolated constituent fragments (in the present case, ammonia and the NG) placed in the same positions. z is a suitably chosen axis, which here is that joining the NG with the c.m. of ammonia. At each point along z, Δq measures the net 14660
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Figure 4. Contour plots of the electron density changes and corresponding CD curves Δq accompanying the formation of the NH3Ar complex at the two minima of the PES (Φ = 94° and Φ = 274°) and at the two axial stationary points (Φ = 0° and Φ = 180°). In the contour plots, the dashed red lines denote negative values (density depletion), and the solid black lines are positive contours. The contour values range from (0.05 to (1.0 me/bohr3 in steps of 0.05. The red circles on the CD curves correspond to the projection of the nuclear positions on the integration axis z, which has an origin at the c.m. of NH3 and joins this to the NG. The blue line marks the isodensity boundary.
electron charge that, upon formation of the complex, has been displaced from right to left across the plane perpendicular to the axis through z (thus, where Δq is negative, the electron charge has correspondingly moved from left to right). The CD function provides a useful snapshot of the features of the interaction across the whole molecular region, especially insightful to compare different interaction geometries. It does not, of course, provide, per se, a definition of CT between the fragments, as this cannot be unambiguously defined, in any method, without adopting some convention (see for example refs 8 and 4851 and references therein). It is helpful, however, especially in weakly bound systems, for assessing the presence and qualitative extent of CT, as the curve obviously suggests CT when it is appreciably different from zero and does not change sign in the region between the fragments, whereas the situation may be uncertain (in both magnitude and direction) if the curve crosses zero. To be able to define CT in this approach, we need to take the CD value at some specific point z between the fragments, i.e., define a plane separating them. We have usually chosen the point along z where the electron densities of the noninteracting fragments become equal (isodensity boundary). This choice is reasonable, at least for small systems, (we have noticed, for instance, that the isodensity boundary is usually close to the
minimum of the total molecular density between the fragments and also close to the bond critical point50 when there is one) but of course arbitrary, as there is no true way, for example, to precisely separate CT from polarization of the fragments. Again, the shape and slope of the CD function itself, in particular around the chosen separation point, helps to assess the reliability of our (or any other) choice. If the curve is sufficiently flat between the fragments, the choice of the separation point is not critical, while more caution and analysis may be required otherwise. A further assessment of CT, and its associated energy, comes from the study of its dependence on the interfragment separation, as it must show exponential falloff. We have investigated this point in detail in previous work, showing that indeed the calculated CT exhibits exponential decay, and the associated stabilization energy matches both experimental observations and accurate ab initio calculations.22 In the present work, the electron density used to evaluate eq 1 has been calculated using CCSD and the AVQZ basis. At such level of treatment, the CD curves are expected to be fully converged.20 We shall consider the ammonia complexes with the three heavier NG atoms, for which a measurable stabilization energy has been detected. Let us begin with NH3Ar in the nuclear arrangements corresponding to the main and secondary minima of the PES. The corresponding contour plots of the electron 14661
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Figure 5. Contour plots of the electron density changes and corresponding CD curves Δq accompanying the formation of the NH3Kr complex at the two PES minima (Φ = 94° and Φ = 257°) and at Φ = 0° and 180°. For notation and details, see Figure 4.
density change taking place upon bond formation and the respective CD curves are shown in the upper panels of Figure 4. In the main minimum configuration, the density deformation contour plot shows that the Ar electron cloud is markedly polarized by the presence of ammonia. This polarization, however, is essentially oriented in the direction of ammonia’s dipole and thus nearly perpendicular to the z axis. As a result, the CD curve is flat and close to zero everywhere. The slight nonorthogonality between the Ar polarization axis and the z axis is reflected in the slightly larger deviation from zero of the CD curve around the Ar site. Clearly, the curve shows no appreciable CT between the interacting species here. Note that this is a completely different pattern from that observed at the equilibrium configuration of the H2OAr complex, where the CD curve clearly lets us conclude that a CT of more than 2 me takes place from Ar to water.20 At the secondary minimum configuration, Ar is on the opposite side of ammonia, in the half-plane containing an H atom. Also here, the Ar electron cloud is strongly polarized, but now a lobe of density accumulation extends between the fragments and crosses their isodensity boundary. Note that some appreciable charge rearrangement also takes place in the ammonia region, where there is a small but visible density depletion around the hydrogen atom closer to the approaching Ar. This is accompanied by polarization at the N site. The corresponding CD curve is slightly but clearly negative everywhere, indicating without ambiguity a small net CT from left to right, i.e., in the
direction going from the NG toward NH3. The minimum CT in the region between the fragments is 0.7 me at 1.9 Å from ammonia’s c.m. At the isodensity boundary, CT is only slightly larger, 0.8 me, and it remains about the same in the whole interfragment region at least up to the position of the nearby hydrogen (0.9 me). It is interesting to analyze briefly the two other peculiar stationary points of the NH3NG complexes, where the NG lies on ammonia’s C3 (i.e., dipole) axis at Φ = 0 (hydrogen side) and Φ = 180° (nitrogen side). The CD analysis results for the complex with Ar are reported in the bottom panels of Figure 4. One might have expected that, at these two points, direct induction effects due to ammonia’s dipole would be maximized roughly equally but, as the figure clearly illustrates, the two situations are instead surprisingly extremely different. At Φ = 0, polarization of Ar is nearly absent, even less than at the minima studied above, where the dipole is nearly orthogonal to the z axis. The CD curve shows that at the Ar site (maximum CD magnitude) only about 2 me have moved toward ammonia, indicating that the presence of the hydrogen atoms on the Ar side has strong effects on the density deformation of the complex. Also in this case, the CD curve is negative in the whole region between the fragments. At the isodensity boundary, CT from Ar to ammonia is 0.7 me, a value similar to that found at the secondary minimum above. A completely different pattern is observed for the nuclear arrangement at Φ = 180. Here, Ar is also 14662
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Figure 6. Contour plots of the electron density changes and corresponding CD curves Δq accompanying the formation of the NH3Xe complex at the PES minimum (Φ = 105°) and at Φ = 300°, 0°, and 180°. For notation and details, see Figure 4.
pointing toward ammonia along the C3 axis but on the side of the N atom, with hydrogen atoms far away. Now the density calculations show the strong polarization of Ar in the direction of the ammonia dipole, which might have been expected, with 13 me transferred toward the intermolecular region at the Ar site. In this case, the CD curve remains close to zero and in fact changes sign twice in the interfragment region (at about 1.8 and 0.8 Å from the c.m.), leaving some ambiguity as to the extent and consequences of CT. At the isodensity boundary, CT is 0.5 me from NH3 to Ar. This small but non-negligible value is quite interesting and may be taken to show that the NG may locally accept electrons under the influence of the electric field due to ammonia’s dipole. Of course, in this case, a proper estimate of the extent and direction of CT, if any, is problematic and depends on the definition of a boundary between the interacting species. We may point out that the choice of the isodensity boundary appears particularly conservative toward suggesting CT in the NH3 f NG direction because the NH3 dipole pushes the Ar electrons away from the interfragment zone. The NH3Kr complex exhibits very similar CD patterns to NH3Ar, and they are shown in Figure 5. As for the NH3Ar case, we may conclude that CT is essentially absent at the main minimum, while it takes place from the NG to ammonia at the secondary minimum and at Φ = 0. CT at the isodensity boundary is 0.4 and 0.7 me, respectively, again very similar to the Ar case. At Φ = 180°, the analysis is qualitatively again identical, but CT
from ammonia to the NG appears to be even more pronounced here, with a value of 1.1 me at the isodensity boundary, which is more than twice that for Ar. As might have been expected on the basis of the differences in geometrical and PES features, the CD analysis for the case of Xe (see Figure 6) evidence some differences from the previous ones, which may help to explain the PES features, and in particular the lack of a secondary minimum. The differences are especially evident at the equilibrium structure, which occurs at Φ = 105°, i.e., about 1015° larger than for the lighter NGs. Xe polarization due to the presence of ammonia is here in a direction roughly parallel to the NH bonds, and the density rearrangement exhibits a different pattern. As a result, the net balance of polarization along the XeNH3 direction has a sign opposite to that of the lighter NGs, so that the CD curve is positive around Xe and distinctly different from zero. At the Xe site itself, about 3 me have been pushed from right to left. In fact, the CD curve remains positive across the whole complex, indicating a net CT from the NH3 region to the Xe region. At the isodensity boundary, the CD value is 1.2 me. When Xe approaches NH3 along its C3 axis (Φ = 0° and Φ = 180°), the qualitative pattern of density rearrangement is similar to that seen in the Ar and Kr cases. At Φ = 0° (hydrogen side), NG polarization is again relatively small, with only about 4 me shifted from the left to the right side of Xe. This value is about twice that for Ar due to the correspondingly larger polarizability of Xe. However, at the isodensity boundary, CT 14663
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The Journal of Physical Chemistry A from Xe to NH3 is only about 0.5 me, i.e., slightly smaller than in the Ar and Kr cases. At Φ = 180°, Xe polarization is again much more pronounced, with about 20 me shifted to the left of the Xe site. Here, CT from ammonia at the isodensity boundary is 2.3 me, about four times larger than in the Ar case. In Figure 6, we also report the CD analysis for the Φ = 300° configuration (as always, with Θ fixed at 60° and r optimized) in which Xe points roughly toward an H atom in the direction of the NH bond. This arrangement is interesting in order to make a comparison with the corresponding water complex, where Xe placed on an OH bond axis corresponds to the absolute minimum of the PES. Not unexpectedly, the qualitative pattern of density and charge displacements is similar in the ammonia and water cases.20 Xe is strongly polarized along the z direction, with the density accumulation lobe extending to the region between the fragments and appreciably crossing their isodensity boundary. A significant charge rearrangement also takes place in the ammonia region and there is a density depletion around the hydrogen atom closer to the approaching Xe, while charge accumulates in the NH bond region. The CD curve is negative everywhere, indicating a net CT from the NG region to the ammonia region. However, the quantitative differences between the NH3 and H2O complexes are significant and provide insight. Xe polarization in the ammonia complex is much less pronounced, and the CD curves provide a measure of this; while about 17 me have shifted to the right of Xe in the water complex, only about 10 me have moved in the NH3 case. In addition, while CT from Xe to ammonia is about 1.4 me at the isodensity boundary, it is nearly three times as large (3.9 me) from Xe to water. These results, taken together with the different features of the PES and equilibrium geometries, support the conclusion that CT in the water complexes plays a special role not seen in other hydrides. More extensive comparative studies of the kind presented here will surely add useful information in this regard.
’ STEREOSPECIFICITY OF CHARGE TRANSFER AND ENERGY STABILIZATION In the previous section, we have seen that, depending on orientation, CT may take place in different directions in the NH3NG complexes, with ammonia acting alternatively as the electron acceptor or donor. It may be interesting to present a concise quantitative illustration of this and attempt to correlate it to some of the features of the PES. This will also illustrate a useful approach to combining experimental and theoretical results in order to gain insight into these intermolecular interactions. In Figure 7, we report a plot of CT estimates, taken at the isodensity boundary, along the PES cut of Figure 1. Although numerically slightly different, values taken at any other reasonable point between the fragments would provide essentially the same picture. The figure captures CT anisotropy quite clearly and shows expected qualitative similarities, but significant quantitative differences, between the three complexes. It is clearly confirmed that ammonia is the electron acceptor when the NG approaches on the hydrogen side and the electron donor on the nitrogen side. CT in the former direction is maximized for Φ = 4050° and, especially, Φ = 300°. The former corresponds to NG approaching roughly between two hydrogens on a HNH plane, the latter to NG pointing directly toward a hydrogen atom along a NH bond. CT is very much the same for all three complexes in the former orientation (about 0.60.7 me) and somewhat more differentiated in the latter (11.5 me), with the
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Figure 7. CT at the isodensity boundary between ammonia and the heavier NGs along the PES section of Figure 1. Positive values denote CT from NH3 to the NG.
heavier Xe donating about 0.5 me (50%) more than Ar. CT practically vanishes for all complexes for Φ = 8090°. This is close to the most stable configuration of the Ar and Kr complexes, which may be thus seen as determined mostly by the balance of vdW and induction forces, but about 15° away from the most stable configuration of NH3Xe, where CT from ammonia to Xe is larger than 1 me. On the opposite side, CT crosses zero for Φ = 250260°, which is again very close to the secondary minimum of the PES found for Ar and Kr. The maximum of NH3 donation always occurs for NG approaching nitrogen on the C3 axis (Φ = 180°), where it is much larger for Xe (over 2 me) than for Kr (about 1 me) and Ar (about 0.5 me). It is interesting to underline that the above CT pattern clearly does not appear to correlate strongly with the features of the PES section along the same path (Figure 1), in particular the most stable configurations do not correspond to the regions of largest CT. This is in utter contrast with what we have found for the waterNG complexes, where such correlation between increasing CT and increasing binding energy appeared evident.20,21 It would, therefore, appear that while CT can crucially contribute to determine the geometry of the water complexes, it is generally too small, compared to other forces, to do so in the ammonia adducts. (One should consider, for example, that the polarizability, which governs the vdW component, is about 1.5 times larger for ammonia than for water.) Consistently with this surmise, we note that in the NH3Xe case, where CT is largest, some peculiarities of the PES that we have noted above may indeed be in relation with CT. For example, the steeply increasing CT above Φ = 90° may be at the origin of the increased equilibrium value of Φ compared to Ar and Kr. Similarly, the stabilization associated with the relatively much larger CT in the region around Φ = 180° may be responsible for the flattening of the PES noted earlier and, consequently, for the disappearance of the secondary PES minimum. We can put the above considerations on a firmer basis by using the experimentally determined CT-induced stabilization energies for NH3 NG mentioned earlier. These are 0.7 ( 0.7 meV, 2.1 ( 0.9 meV, and 3.6 ( 1.0 meV for NG = Ar, Kr, and Xe, respectively.23 Since the experimental data refer to the orientationally averaged interaction, to put these in relation with the computed CT, we need to obtain a rough estimate of the average CT magnitude, which we can do by simply averaging over the curves of Figure 7. This gives average CT values of 0.53, 0.74, and 14664
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The Journal of Physical Chemistry A
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Figure 8. Comparison of the ab initio CCSD(T)/AV5Z PES section for NH3Xe (E) with the energy obtained by subtracting the estimated CT contribution (ECT).
1.13 me for Ar, Kr, and Xe, respectively. If we simply assume direct proportionality between CT and stabilization energy ECT ¼ kΔq
ð2Þ
we get values of k equal to 1.3 ( 1.3, 2.8 ( 1.2, and 3.2 ( 0.9 meV/me for Ar, Kr, and Xe, respectively. It is remarkable that a similar value, 2.5 meV/me, was obtained for the waterH2 complex.22 This result may finally provide some sort of independent verification of the surmise that CT is largely responsible for the peculiar features that characterize the NH3Xe PES compared to the lighter NGs. To this end, we report in Figure 8, along with the NH3Xe PES section of Figure 1, the curve obtained from it by subtracting the CT contribution in eq 2. The latter contribution is simply the absolute value of the Xe CT curve of Figure 7 multiplied by k = 3.2 meV/me, as determined above. This clearly suggests that, without a CT contribution to the potential, the principal PES minimum of NH3Xe would be shifted to a smaller Φ value, and the PES would exhibit, in line with that of the lighter systems for which CT is less important, an evident secondary minimum around Φ = 260°.
’ CONCLUSIONS Prompted by high-resolution scattering experiments providing the absolute-scale of the radial (spherically averaged) interaction between NH3 and the noble gas series, we have carried out, for the whole series of NH3NG binary complexes, state-ofthe-art ab initio calculations of some crucial sections of the potential energy surface and of the electron density changes that accompany the interaction. This has also entailed a thorough basis-set convergence study of the computed equilibrium geometry of the adducts, their interaction energies, and the basis-set superposition error. The spherically averaged equilibrium distances and binding energies agree remarkably well with the experimental determinations. The theoretical results have established that, for the whole series of complexes, the PES minimum corresponds to the configuration in which the NG lies on a symmetry plane of ammonia on the side of a pyramidal face. The radius that joins ammonia’s center-of-mass to the NG is nearly orthogonal to the C3 axis for all systems except NH3Xe, for which the angle is somewhat larger. This arrangement, especially for the heavier NGs, differs substantially to that found for the analogous water
complexes, where the NGs tend, increasingly, to approach water along an OH bond. A secondary minimum is also found for the lighter NGs lying on the opposite side of NH3, but this becomes shallower as the NG size increase, until it disappears altogether for Xe. The charge-displacement analysis has revealed that a nonnegligible charge-transfer component characterizes the ammonia NG interaction and increases along the NG series. This is entirely consistent with the analysis of the experimental data, which has evidenced the emergence, in the potential well region, of an increasingly stronger attractive interaction component than the one implied by the long-range vdW and induction forces. CT is pronouncedly anisotropic and, very interestingly, even its direction changes with orientation: ammonia acts as an electron acceptor when NG approaches from the region of the hydrogen atoms and as an electron donor on the nitrogen side. One peculiar consequence of this is that CT turns out to essentially vanish precisely for those nuclear arrangements close to the principal minima of the PES. In other words, the energy stabilization provided by CT is, on balance, not large enough to affect the geometry of the complexes, which is thus largely determined by vdW and induction forces. This is again in contrast with the indications emerging in the waterNG case, where a clear correlation was found between larger CT and larger binding energy. By comparing the theoretically estimated CT with the experimentally determined stabilization energy, we have obtained an estimate of the effective energy contribution per unit charge transferred. This agrees extremely well with that recently calculated for the waterH2 complex. This has permitted a demonstration that, in partial contrast with the findings above and confirming the subtle and often unsuspected importance of CT in these weak interactions, CT becomes strong enough in the Xe complex to be entirely responsible for some of the peculiarities that distinguish its PES from those of the lighter systems, such as the larger equilibrium angle and the lack of a secondary minimum. The present results add a further insightful contribution to the accumulating knowledge and understanding of weak interactions involving hydrogenated molecules.52,53 Further comparative studies of this kind, in combination with direct, high-resolution experiments, will be useful to reveal the nature of other interactions of water and ammonia, for example, with methane or CCl4. The latter may be important toward the fundamental characterization of the halogen bond.54
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (L.B.);
[email protected] (F.T.).
’ ACKNOWLEDGMENT This work was supported by the MIUR (PRIN project no. 2008KJX4SN_003) and by the Fondazione Cassa Risparmio Perugia (project no. 2010.011.0501). ’ REFERENCES (1) Kollman, P. A.; Allen, L. C. Chem. Rev. 1972, 72, 283–303. (2) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899–926. (3) Isaacs, E. D.; Shukla, A.; Platzman, P. M.; Hamann, D. R.; Barbiellini, B.; Tulk, C. A. Phys. Rev. Lett. 1999, 82, 600–603. 14665
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