Theoretical Study of Hydrogen Bonded Complexes of Ammonia and

Departments of Physics and Chemistry, University of Missouri Columbia, Columbia, ... Stabilization energies, counterpoise-corrected energies, and zero...
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J. Phys. Chem. B 2004, 108, 19582-19588

ARTICLES Theoretical Study of Hydrogen Bonded Complexes of Ammonia and Hydrogen Cyanide† Patricia L. Moore Plummer* Departments of Physics and Chemistry, UniVersity of MissourisColumbia, Columbia, Missouri 65211 ReceiVed: May 8, 2004; In Final Form: July 22, 2004

Ab initio and density functional electronic structure calculations have been used to examine the association of ammonia with HCN. The split-valence diffuse-polarized 6-311++G(d,p) was the primary basis set employed. Clusters with up to two molecules of HCN and from two to four molecules of NH3were considered. Several stable hydrogen bonded mixed clusters have been identified that exhibit cyclic structures in which the NH3 molecules serve as both hydrogen donors as well as hydrogen acceptors. Stabilization energies, counterpoisecorrected energies, and zero point vibration energies are reported for the stable clusters. Cooperative effects on cluster stability are discussed.

1. Introduction The concept of hydrogen bonding was introduced in the early 1920s1 and has been a subject of much theoretical and experimental study since that time. Until the 1960s the studies focused on hydrogen bonds formed by O-H, N-H, and F-H groups. Increases in sensitivity in detection methods have added acidic C-H groups to the list of proton donor groups. It has long been known that both H2O and HF readily form hydrogen bonds in the gas phase, both as acceptors and as donors of the hydrogen in the bond. On the other hand, in the gas phase NH3 will vigorously accept a hydrogen bond, but the lack of evidence for NH3 acting as a hydrogen donor led Klemperer and coworkers2 in 1987 to title a paper “Does ammonia hydrogen bond?” Nearly 20 years earlier, Stillinger and co-workers3 were among the first researchers to employ accurate SCF calculations to study hydrogen bonding in water clusters. A principle aim of their study was to examine the origin and magnitude of cooperative effects on cluster stabilization and the dependence of these effects upon distances and orientations of the constituent monomers. A decrease in the hydrogen bond length in going from dimer to trimer was one structural evidence of cooperativity in hydrogen bonding. They identified a definite “cooperative effect” in the linear water trimer that was strongest when the hydrogen bonds are sequential and the central molecule participates in two hydrogen bonds, serving as both a donor and as an acceptor in the bonding. The observation of a dependence of the sign and magnitude of three body effects on bonding pattern was surprising as water had been regarded as an equally willing acceptor or donor in hydrogen bond formation, in contrast with the behavior observed for ammonia. Later more extensive calculations4 have shown that the minimum energy structure for the water trimer has a cyclic structure in which each molecule exhibits the preferred donor-acceptor conformation first identified by Stillinger et al. †

Part of the special issue “Frank H. Stillinger Festschrift”. * E-mail: [email protected].

Even with the renewed interest of the last two decades in the hydrogen bond, there is still considerable debate as to its physical nature. Electrostatic models for hydrogen bonds have played a prominent role in both theoretical and experimental discussions of this interaction and “strong” hydrogen bonds such as those found in (HF)2 are clearly dominated by electrostatic interactions. However, there are an increasing number of examples where the nonelectrostatic effects play a significant, if not dominant role. Advances in experimental techniques for producing and measuring properties of hydrogen bonded and other weakly bound systems have greatly increased the interest in these systems as has the need for more accurate representations of the hydrogen bond in diverse environments to predict molecular properties of biologically important molecules and aggregates. Increases in computer memory and speed, together with improvements in software, have provided the ability to undertake accurate electronic energy calculations on ever larger molecular clusters, thereby permitting consideration of three-body and higher order interactions in the analysis of the hydrogen bond. The system chosen for the present study can provide new insights and add to our knowledge and understanding of the nature of the attractive interaction in weakly bonded molecular clusters. Specifically, mixed clusters of HCN and NH3 present a challenge in several distinct arenas. First, even though both molecules are polar, most of their interactions are considerably more complex than purely electrostatic. Second, neither molecule can be considered as a strong Lewis acid, willingly donating a hydrogen for hydrogen bond formation. As noted above, it has been questioned whether NH3 will ever act as the donor in hydrogen bonding. The recently reported structure for the ammonia dimer5 suggests a certain degree of hydrogen bonding but not a linear hydrogen bond. Third, these calculations of NH3 dimer5 and those of the related dimer and dimer ions of NH4+ have commented6 on the importance of dispersion energy in these systems compared to more classical hydrogen bonded systems such as the H2O or HF dimers. Fourth, extensive basis sets including polarization and diffuse functions on hydrogen

10.1021/jp048018+ CCC: $27.50 © 2004 American Chemical Society Published on Web 09/14/2004

Complexes of Ammonia and Hydrogen Cyanide

J. Phys. Chem. B, Vol. 108, No. 51, 2004 19583

Figure 1. Heterodimers of HCN-NH3: (left) dimer1; (right) dimer2. Nitrogens are darkest gray; hydrogens are white.

Figure 2. Optimized structure for 1:3 cluster (left). Sample starting configuration (right).

as well as the heavy atoms are required to correctly order structures by energy when NH3-NH3 interactions are present. Previously, we had examined structures and energies for the heterodimers7 of NH3 with HCN and showed that NH3 did serve, although reluctantly, as a hydrogen donor. In view of the cooperative effect of hydrogen bonding observed in many homogeneous systems, it is of interest to learn whether the NH3 becomes a less reluctant donor in the presence of a more extended hydrogen bond network. But there is a question as to whether larger clusters will be stable given the weakness of the bonding in the ammonia dimer and the even weaker HCNHNH2 heterodimer. If the larger clusters are stable, are the nonadditive effects such as increasing bond stability and decreasing hydrogen bond lengths found by Stillinger et al.3 for water clusters, and subsequently by others for a variety of homogeneous clusters, present in systems of mixed clusters? Another tantalizing question concerns the change from covalent to ionic bonding in small aggregates or clusters. In the condensed phase ammonia and hydrogen cyanide exist as an ion pair, CN- and NH4+. In clusters involving ammonia and hydrogen halides, proton transfer occurs when two or more ammonia molecules “solvate” an HX molecule. Because HCN is often considered a pseudo halide, can it be “convinced” to give up its proton in the presence of two or three NH3 molecules? 2. Computational Methods The electronic structure calculations were done using the Gaussian 03 quantum mechanical packages.8 Analyses of the calculations were aided by graphical display of the results. The software packages GausView 039 and Molden10 were used to examine the structural and vibrational data for the stable clusters and to produce the figures. Beginning with the optimized geometries obtained previously for the two distinct HCN-NH3 heterodimers, the initial larger clusters were constructed by adding ammonia groups in a variety of ways. For example, two of the starting geometries for four molecule clusters have an ammonia dimer attached to either of the heterodimers. Figure 2 depicts one such initial configuration. Because the association of ammonia molecules is weak and the hydrogen bond between ammonia and the N of HCN is also very weak, inclusion of electron correlation is essential for describing the structure and bonding present in the mixed clusters of HCN and ammonia. The density functional methods have been shown to provide an economical method to reliably include electron correlation

in electron structure calculations. The hybrid density functionals have been increasingly employed for this purpose. The choice of B3LYP11 as the density functional method to be used in this study is justified by increasing evidence of its reliability to study hydrogen bonded systems.12 In the past the use of DFT approaches have been questioned when applied to very weak hydrogen bonds or van der Waals systems where dispersion forces dominate. But in the case of polar molecules where dispersion is expected to play a minor role,13 the use of a flexible basis with the hybrid B3LYP is increasingly the method of choice. For comparison, the clusters were also examined with MP2 because this method14 has been shown to be effective and accurate in determining the equilibrium structure and binding energy for many hydrogen bonded and other weakly bound clusters and is often considered a standard for these systems. Specifically, the stationary points located with B3LYP were fully reoptimized with MP2 and the structures and stabilization energies compared with the B3LYP results. As stated earlier, the choice of basis sets used to describe weakly bound clusters is very important. Although adding polarization functions to standard double-ζ bases is generally sufficient to provide a reasonable description of “moderate” to “strong” hydrogen bonds,7 weak hydrogen bonds and van der Waals clusters require additional flexibility in the basis set. For a proper description of Rydberg bonds and to allow for polarization and dispersion stabilization, diffuse functions are needed on the hydrogens as well as the heavy atoms.5a The triple split-valence basis with polarized and diffuse functions, 6-311++G(d,p),15 satisfies these requirements and has proved reliable in previous studies of weakly associated systems, including the Rydberg dimer6a (NH4)2 and (HCN)n oligomers.16 The use of basis sets containing diffuse functions with density functional methods requires added care in the computations. Thus in the B3LYP calculations the evaluation grid was expanded in terms of both additional radial shells and added grid points per shell. Also the SCF convergence criterion was tightened. The initial structures were then fully optimized at the B3LYP level using the standard split-valence diffuse-polarized 6-311++G(d,p) basis. Stationary points were evaluated by examining the associated Hessian matrix. The geometries thus identified as stable minima at the B3LYP/6-311++G(d,p) level were used as the initial geometry for optimization at the MP2/

19584 J. Phys. Chem. B, Vol. 108, No. 51, 2004

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TABLE 1: Energy (au) and Hydrogen Bond Lengths (Å) for H3NHCN as Functions of Basis Set and Correlation Levela basis MP2/fc/fullb MP3 MP4(SDQ) MP4(SDTQ) CISD R(N- - -H)c

6-31G(d) energy (au) 0.52774 0.53379 0.54917 0.56206 0.48197

0.53912 0.54883 0.56001 0.57721 0.49089 2.0536

6-311G(d,p)

6-311++G(d,p)

6-31+G(3df,2p)

0.67920

0.63031

0.68691

0.69345

2.0553

2.1311

2.1266

2.0583

Energy is equal to -149.000000 - x, where x is the number in the table. b Numbers in bold font are the results of MP optimization including core electrons, MP)Full. c Hydrogen bond length calculated at MP2 level. a

6-311++G(d,p) level. Except where specifically noted, the frozen core approximation was used in the MP calculations. The weak binding, together with the potentially large amplitude motions in these mixed clusters due to many lowfrequency intermolecular vibrational modes, makes the calculation and inclusion of corrections for zero point vibrational energy (ZPVE) important. Therefore ZPVE are calculated and reported for all systems. The correction for basis set superposition error (BSSE) in the cluster energies for stationary states is calculated using the counterpoise procedure (CP) first described by Boys and Bernardi17a and implemented in Gaussion 03 using the procedure of Dannenberg et al.17b 3. Results and Discussion 3.A. Dimers. Because results7 of calculations for the heterodimers have been discussed previously, they are included here primarily to facilitate comparisons of the variation in dimer hydrogen bond lengths due to basis set effects, especially the addition of diffuse functions on the hydrogens. The geometries and stabilities of the heterodimers serve as reference points for understanding and identifying the origin of any changes in hydrogen bond parameters found for the larger clusters. The heterodimer with HCN as the H-donor is referred as dimer1; dimer2 has NH3 as the H-donor. Specifically, for dimer1, examination of the results from the previous calculation7 (see results summarized in Table 1) show that the hydrogen bond length remains essentially unaltered by the following changes to the basis set: polarization functions added to the hydrogens a diffuse function added to the heavy atoms additional splitting of the valance shell increasing the number of polarization functions on the heavy atoms On the other hand, adding diffuse functions to the hydrogens increased the hydrogen bond length by about 4% in the MP2 optimizations. With the 6-311++G(d,p) basis, both the B3LYP and MP2/monomer geometries are in excellent agreement with experiment, the largest deviation occurring in the CN bond, which is just over 1% too long. The MPn hydrogen bond lengths are slightly reduced when core electrons are included in the correlation optimization. When corrected for ZPVE, the stability of each of the dimers is reduced relative to previously reported values7 (see Tables 4 and 5). This reduction is greater for the MP2 results and for dimer2. The reduced stability may be in large part attributed to the increase in monomer-monomer separation when diffuse functions are added to the hydrogens and thus would be expected to have a greater effect on dimer2. The minimum energy structures for the two heterodimers are shown in Figure 1. 3.B. Larger Clusters. Two types of mixed clusters are considered, denoted as 1:N (N ) 3, 4) and 2:2 where the first number indicates the number of HCN’s in the cluster and the second the number of NH3’s. Thus we have two distinct four-

molecule clusters. In the first, 1:3, two molecules of ammonia are added to a heterodimer. In the second, a 2:2 cluster, a dimer of heterodimers is constructed, which contains two molecules of HCN and two molecules of NH3. The largest cluster studied contained five molecules; one of HCN and four of NH3,1:4. The clusters that contain a single molecule of HCN, the 1:N clusters, are discussed first. 1:3 Cluster. In the search for stable structure(s) for the 1:3 cluster a number of initial configurations were constructed by adding two ammonia molecules in a variety of orientations and bonding sites to one of the heterodimers. For each starting configuration, all geometric parameters were fully optimized with all symmetry constraints turned off. Regardless of the initial structure, upon final optimization the resulting lowest energy potential surface minimum located had a cyclic structure with each of the ammonia molecules participating in two hydrogen bonds and each acting as both a hydrogen donor and a hydrogen acceptor. The nitrogens of the four molecules lie in a plane (see Figure 2 and Table 2). Convergence was exceedingly timeconsuming as the potential surface surrounding the ammonias is exceedingly flat with respect to relative H2NH- -NH3 orientations. Optimizations where the energies were converged to very tight limits still had large displacements in the NH3 hindered rotations and thus had to be continued until all forces were essentially zero (2 or more orders of magnitude less than the TIGHT cutoff in Gaussian03). As the different starting configurations converged to slightly differing ammonia orientations, the geometries of the stationary points were further refined until the resulting structures could be superimposed and differed by less than 0.0002 Å in bond length, ca. 1° in bond angle, and less than 0.000001 au in energy. Because the potential energy surface appears to be quite flat for various internal motions, and the motions asymmetric, the vibrations associated with them are expected to be highly anharmonic. To further assess the effects of basis set and level of correlation on this cluster, single point energy calculations at the MP2/6-311++G(d,p) geometry were carried out for higher levels of electron correlation. Energies were also calculated for two correlation consistent basis sets18 with diffuse functions, aug-cc-pvdz and aug-cc-pvtz, at the same geometry. These results are reported in Table 3. Computer resources did not permit geometry optimization at the higher correlation levels nor more extensive basis set trials, as the single CCSD(T)/augcc-pvtz//MP2/6-311++G(d,p) failed to complete in 1000 h on a 4 processor DEC-ALPHA/ES40. This lack of data limits conclusions somewhat, but we note that there is a smaller energy change in going from MP2 to CCSD(T) for the 6-311++G(d,p) basis than for the comparably sized aug-cc-pvdz basis. 1:4 Cluster. The starting configuration for the 1:4 cluster had two ammonia molecules in a roughly dimer configuration5 H-bonded to each end of the HCN molecule. As for the 1:3 cluster, optimization resulted in a cyclic structure, again with each ammonia participating in two hydrogen bonds and acting

Complexes of Ammonia and Hydrogen Cyanide

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TABLE 2: Properties of Hydrogen Bonds (Bond Length, Å; Bond Angle, deg) [N- - -H-C]

[CN- - -H-N] [H3N- - - -H-NH2]

B3LYP MP2 B3LYP MP2

B3LYP

MP2

1:N Clusters H3NHCN R ∠B-H-A HCNHNH2 R ∠B-H-A (NH3)3HCN R ∠B-H-A ∠NNNN (NH3)4HCN R ∠B-H-A

2.0904 2.1311 179.9 179.8 2.4384 2.4358 173.7 180 1.9633 1.9957 2.4832 2.4015 2.1885 166.8 167.1 164.8 164.3 176.4 2.1223 169.1 0.9 0.05

2.2013 176.3 2.1392 167.9

1.9489 1.9800 2.2931 2.3167 2.1733 171 171.2 164.6 150.7 176.7 2.1417 178.5 2.0957 171.8

2.1986 165.9 2.1379 175.8 2.1072 167

2:2 Clusters (H3N)3 (HCN)2 R 1.9987 1.9984 ∠B-H-A 166.7 166.5 ∠NNNN 0.03 (H4N)2(CN)2 R 1.6785 1.6802 ∠B-H-A 167.1 167.1 ∠NNNN 0.004

2.0293 2.0293 168.7 168.2 0.009

2.3222 2.3209 152 152.1

2.3119 2.3118 148.3 148.2

1.6288 1.6292 169.6 169.6 0.007

1.6927 1.6934 167.1 167.1

1.748 1.7485 167.2 167.2

a First pair of columns refer to C- - -H bond, and the second pair to the N- - -H bond.

TABLE 3: Single Point Energy (au) for (NH3)3HCNa basis aug-cc-pvdz 6-311G(d,p) 6-311++G(d,p) aug-cc-pvtz

MP2

MP3

0.431344 0.468481 0.465988 0.483049 0.511306 0.672618 0.700099

MP4(SDQ)

CCSD

CCSD(T)

0.473575

0.481000 0.513522

0.527820 0.709138

0.526922 0.556928

a Energy is equal to -262.000000 - x, where x is the number in the table. At MP2/6-311++G(d,p) geometry.

Figure 3. Optimized structure for the 1:4 cluster.

as both a donor and an acceptor (see Figure 3). But unlike the 1:3 cluster, the nitrogens no longer lie in a plane. The ammonia group which is second neighbor to the HCN on the N end of the molecule buckles out of the plane, somewhat reminiscent of the structure of cyclopentane. The nonplanarity of the N’s is greater for the MP2 results. Examination of hydrogen bond lengths (Table 2) as ammonias are added to the cluster clearly shows a shortening consistent with cooperative effects. The magnitude of the decrease is

essentially the same for the B3LYP and the MP2 results. The cyclic structures of the four and five molecule clusters result in hydrogen bonds that are substantially nonlinear. This is not unexpected both because of the asymmetric nonlinear hydrogen bonding found for the NH3 dimer5 and because of strain in the cyclic structure. The greatest distortion, and also the longest bond, occurs for the bond to the N of the HCN molecule. For both the 1:3 and 1:4 clusters described above the starting configurations had the terminal nitrogens separated by 7.99.2 Å (see Figure 2 for a typical starting configuration). A variety of rotational orientations of the terminal ammonia groups were also considered as was variation in the ∠CN-H(N) (dimer2 H-bond) angle of 167° to 178°. Examination of intermediate structures in the optimization suggests that the impetus toward cyclization originates with the ammonia(s), which is(are) hydrogen bonded to the N of HCN. The angle ∠CN-H begins to decrease and the ammonia(s) begin(s) to move toward the ammonia bound at the H end of HCN. The hydrogen bond is also bending and the H-NC distance is decreasing. As this “translation” is taking place, the ammonias are undergoing librational motion to facilitate the formation of a new hydrogen bond between the initially free ends of the cluster. Natural population analysis19 (NPA) was carried out for the 1:3 and 1:4 clusters. Contrary to expectations, the charge on the H of HCN did not increase significantly with increasing cluster size. The hydrogens donated by an ammonia to another ammonia exhibited the greatest positive charge among hydrogens participating in hydrogen bonds. The same trends in charge for the hydrogen bonded hydrogens were found for both NPA and Mulliken population analysis. 2:2 Clusters. Returning now to the second type of cluster, 2:2, which contains two molecules of HCN and two molecules of NH3, only a single starting configuration was studied. Initially, the four molecules were roughly centered on the vertexes of a rectangle with the HCN’s occupying diagonally opposite corners and with their dipoles oppositely aligned. The ammonias were then placed in the remaining corners oriented with an N-H bond pointed toward an N of HCN and the N lone pair toward the H of HCN. This crude starting point was optimized with AM1 before starting a B3LYP optimization. No symmetry constraints were invoked and the initial structure was slightly nonplanar in terms of the heavy atoms. A stationary point was located more readily than for the four molecule cluster containing only one molecule of HCN, probably due to the stronger HCN-NH3 interaction as compared with an NH3-NH3 interaction. The optimized structure is shown in Figure 4. Examination of the hydrogen bond lengths given in Table 2 again shows remarkable similarity between the B3LYP and the MP2 results. The hydrogen bonds have shortened by about 5% from the heterodimer lengths and have bent more than 10°. In many respects, the decrease in hydrogen bond lengths and deviation from linearity exhibited by this 2:2 cluster are similar to the trends observed for the 1:3 cluster. The charges associated with the hydrogens in the hydrogen bonds are also essentially the same as in the 1:N clusters. The stability of this 2:2 cluster can be attributed to the increase in the strength of the hydrogen bond having NH3 as an H-donor (see Table 5). The final cluster in this study is also a 2:2 cluster in which the fragments are molecular ions. The starting point for this system was obtained from the minimum energy structure of the previously described 2:2 cluster by moving the hydrogen from each HCN group along its hydrogen bond to a position 1 Å from the ammonia nitrogen. This initial configuration was

19586 J. Phys. Chem. B, Vol. 108, No. 51, 2004

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Figure 4. Optimized structures for the 2:2 clusters: neutral cluster (left); ion pair cluster (right).

TABLE 4: Energies (au) of Stationary Statesa total energy DFT(B3LYP) -56.582723 -56.920355 -93.454505 -92.888477 -150.048577 -150.047474 HCNHNH2 -150.039784 -150.039606 (NH3)3HCN -263.232915 (cyclic) -263.229790 (NH3)4HCN -319.824597 (cyclic) -319.820322 [H3NHCN]2 -300.107827 (cyclic) -300.105345 [NH4CN]2 -300.075332 (cyclic) -300.074326 NH3 NH4+ HCN CNH3NHCN

a

TABLE 5: Cluster Stabilization Energya E0

cluster

MP2

DFT(B3LYP)

MP

-56.415234 -56.755685 -93.203221 -92.634105 -149.630308 -149.628132 -149.622100 -149.621491 -262.483049 -262.475634 -318.908760 -318.898110 -299.274184 -299.267115 -299.236494 -299.227276

0.034263 0.049491 0.016359 0.004835 0.053294

0.034821 0.050153 0.014216 0.004502 0.053397

0.051898

0.051945

0.127705

0.128546

0.164771

0.166224

0.108643

0.108601

0.110387

0.110117

Counterpoise-corrected energies are displayed in bold font.

allowed to optimize in the standard waysno symmetry constraints and tight SCF convergencesresulting in the minimum energy structure shown on the right in Figure 4. Notice that though the NH distance is slightly longer in the NH-C bonds than for the NH-N bonds, the H’s are clearly associated with the ammonia. The minimum energy structure has the H’s shifted by nearly 1 Å from their previous bonding sites on the carbons. Both Mulliken and natural population analyses support the conclusion that this structure has four ionic bonds between pairs of NH4+ and CN- ions. 3.C. Cluster Energy and Stabilization. The total energy, the counterpoise-corrected energy, and the zero point vibrational energies, Eo, for the clusters are given in Table 4 for both the B3LYP and MP2 calculations. To facilitate comparisons and computation of stabilization energies, the total and ZPVE energies are also reported for the monomer fragments. All of the energies are the optimized values using the 6-311++G(d,p) basis. The stability of the clusters reported in Table 5 is defined as the energy of the cluster minus the sum of energies of the constituent monomers, corrected for ZPVE. The ZPVE has not been scaled because much of the potential energy surface is anharmonic for the low-frequency intermolecular modes and the scaling is more appropriate for more nearly harmonic motions. In addition, scaling factors are different for B3LYP and MP2 calculations. In Table 5, we also report a value for the cooperativity effect, the increase in stability that can be attributed to nonadditive effects of having multiple hydrogen bonds in the cluster. The cooperative effect is defined, in the spirit of Scheiner,20 as

∆ECE ) ∆Ecluster - Σ∆Edimer

B3LYP

H3NHCN -5.45 -0.80 HCNHNH2 (NH3)3HCN -13.30 (NH3)4HCN -16.19

CEb

〈EHB〉c

MP2

CE

〈EHB〉

1:N Clusters

-4.70 -0.46 -7.77 -3.33 -16.55 -9.51 -3.24 -19.95

-3.53 -4.14 -4.66 -4.50

2:2 Clusters -6.45 -4.08 -16.79 -3.80 -4.20 [H3NHCN]2 -16.30 [NH4CN]2 -217.14 -252.50 (+4.03)d (+6.81) a All calculated with 6-311++G(d,p) and corrected for zero point vibrational energy. b CE is a cooperative effect and is defined as ∆EN - Σ(∆Ei), where ∆EN is the cluster stabilization and ∆Ei is dimer stabilization energy for (NH3)HCN, HCN(HNH2) or (NH3)2; ∆E for (NH3)2 was taken as 1.76 kcal/mol from Lee and Park.4a c 〈EHB〉 is defined as the stabilization energy devided by the number of hydrogen bonds in the cluster. d Energy in parentheses refers to the neutral molecule asymptote [2NH3 + 2HCN].

where the sum is over the dimers that make up the cluster. Thus, for example, the 1:4 cluster consists of one dimer1, one dimer2, and three ammonia dimers whereas the neutral 2:2 cluster is made up of two of dimer1 and two of dimer2. Looking at the table, we find that cooperative effects calculated in this way account for a large fraction of the stability in these clusters. Further evidence of a significant cooperative effect comes from the decrease in hydrogen bond lengths (see Table 2) as the number of cluster H-bonds increases. Another measure of cooperativity is the average energy of the hydrogen bonds in the cluster, i.e., ∆Ecluster/n, where n is the number of hydrogen bonds in the cluster. This average H-bond energy, 〈EHB〉 is also given in Table 5. Recalling that the dissociation energy5 for the ammonia dimer is ca. 1.76 kcal/ mol and that for the weaker of the heterodimers, dimer2, it is less than 1 kcal/mol, an average H-bond energy in the range of 3.5-4.5 kcal/mol for the 1:N and 2:2 clusters is clear evidence of enhanced stability, which can be attributed to the hydrogen bonding network. Data for the ionic 2:2 cluster are included in Table 5, but because the bonding is not hydrogenic, no attempt has been made to estimate cooperative effects nor average hydrogen bond energies. This [NH4CN]2 cluster is stable by more than 200 kcal/ mol relative to dissociation into ions. It appears to reside in a local minimum on the potential energy surface, which is metastable with respect to the asymptote for the neutral molecules. There are evidently barriers, whose height and shape we have not yet fully investigated, that separate this ioncontaining cluster from the neutral 2:2 cluster and from dissociation to neutral monomers. The stabilization energies reported in Table 5 have not been CP-corrected (although the interested reader can easily do so). The magnitude of the correction varied widely with cluster and

Complexes of Ammonia and Hydrogen Cyanide with correlation method despite the fact that the basis set was the same in all calculations and the geometries determined by the B3LYP and MP2 methods were quite similar. A problem of the standard counterpoise correction procedure overcorrecting cyclic geometries has been noted.21 Furthermore, as the size of basis sets available for use in cluster calculations has gotten larger, the use of counterpoise-corrected energies for calculation of interaction energies has been increasingly questioned. A recent result22 for (HF)3 has shown that the electronic stabilization energy of the cyclic minimum energy structure is underestimated by more than 10% at the MP2/aug-cc-pVDZ level. For this system, the already too low dynamic electron correlation contribution to the electronic stabilization energy is further reduced by the counterpoise correction. Others have argued that the full CP correction should not be applied at the MP2 level because it “overcorrects” the BSSE. For the aug-cc-pVXZ family of basis sets the uncorrected MP2 interaction energy is in significantly better agreement23 with that calculated at the basis set limit than when CP corrected. This is especially true for X ) D, T. It has been argued17b that many apparent ambiguities, and possible discrepancies, can be resolved by exchanging the single point CP correction for computing a CPoptimized surface. This led to the examination of the CPoptimized surface for several of the clusters in this study. For example, for dimer2, the difference in BSSE between the single point CP and CP-optimized surface is 8 × 10-6 and 3.5 × 10-5 au for B3LYP and MP2, respectively. For the 1:3 cluster the MP2 difference is 1.1 × 10-4 au. For the 1:4 cluster the B3LYP the difference is 2.9 × 10-4 au. Though the BSSE correction was reduced somewhat and some hydrogen bond lengths minimally increased in this sample study, these results did not clearly identify an optimum approach to deal with BSSE for these clusters. Hence further work is planned in the attempt to clarify how, how much, or whether to include corrections for BSSE in this mixed cluster system. 4. Conclusions The mixed clusters of ammonia and hydrogen cyanide exhibit clear evidence of cooperative effects of hydrogen bonding in this system. The hydrogen bonds are shorter, and the overall stability of the cluster is greater than the sum of the hydrogen bonds analyzed in terms of dimer fragments. [The CH-N bond decreases by >5% between the 1:1 and 1:3 cluster, and a further 1% between the 1:3 and 1:4 cluster. The N-N separations in the ammonia-ammonia bonds decrease in excess of 1% between the 1:3 and the 1:4 cluster.] This answers the question as to whether the cooperative effects of the type described by Stillinger et al.3 for water trimers would be seen in mixed clusters which are associated by weaker hydrogen bonds. Perhaps the most surprising result of this study was the seeming ease with which the clusters cyclized, because the formation of the ring requires the creation of an ammoniaammonia hydrogen bond that is very “floppy” and weak in the gas-phase dimer.5 When the hydrogen bonds formed between ammonia molecules in the clusters containing HCN are compared with that in the ammonia dimer, it is seen that (1) the N-N separation, and hence the hydrogen bond, are shorter and (2) the conformation moves toward a linear, i.e., less distorted, hydrogen bond. The presence of the HCN molecule “encourages” the ammonia to become a hydrogen donor to form a new bond in the cluster, which in turn, enhances the overall cluster stability. Thus the second question as to whether ammonia will hydrogen bond, i.e., serve as both a hydrogen donor and acceptor, can be also be answered with a resounding “Yes”.

J. Phys. Chem. B, Vol. 108, No. 51, 2004 19587 The goal of observing the transition from hydrogen bonding to ionic bonding was not achieved with the cluster sizes examined in this study. However, a minimum on the potential surface corresponding to a fully ionized tetramer has been identified, and there is a barrier in the potential surface that serves to stabilize the ion cluster preventing recombination of the ion pairs. This suggests that this tetramer is a “threshold” for the transition in bonding. The studies of HCl with water and ammonia conclude that “while four water molecules may not be sufficient to ionize a single hydrogen chloride molecule, the same four water molecules can easily ionize four hydrogen chloride molecules.”24,25 The same trend could well hold true for the ammoniashydrogen cyanide system. In any case, there is no doubt that ammonia becomes a more willing donor when it is between two HCN molecules; this in turn can weaken the C-H bond, thus encouraging proton transfer to the ammonia. Some questions relating to the requirements on basis sets and computational techniques for studying weakly hydrogen bonded molecular clusters have also been examined. The effects of electron correlation on the stability of the mixed clusters of HCN and NH3 are significant. For these clusters the self-consistent field binding energy accounts for only about 65% of the corresponding MP2 value. For comparison, for HCN dimers, where the interaction is primarily electrostatic, HF level results account for about 96% of the stability. But even here, second-order electron correlation effects are essential to characterize the total two-body interaction terms.16 At the opposite extreme, for the ammonia dimer only about 55% of the stability is accounted for by the HF level results. Comparison of the results of MP2 and B3LYP calculations for the structures and stabilization energies for the mixed clusters of ammonia and hydrogen cyanide supports the viability of B3LYP with flexible basis sets to provide an accurate description of the interactions in weakly hydrogen bonded systems. Thus these results are consistent with a number of previous studies that have concluded that hybrid functionals, especially B3LYP produce accurate hydrogen bond lengths and binding energies13,16 for both strong and weak hydrogen bonds, often in better agreement with experiment than the MP2 results.13 We further conclude that the 6-311++G(d,p) basis provides the necessary flexibility to predict structures and relative stabilities for these mixed clusters. The counterpoise correction for BSSE appears to pose a problem for these clusters showing atypical variation which was seemingly independent of cluster size. Future work will examine these CP results further in the attempt to determine if they are unique to this system of clusters or pose questions for other larger mixed cluster systems as well. Both basis set effects and method of handling electron correlation should be considered as sources for the apparent nonconvergence of the counterpoise correction for BSSE. Study of the transition from hydrogen bonding to ionization will also continue. Attempts to produce an ion pair in the clusters containing a single HCN were unsuccessful. In all cases the hydrogen returns to the CN group (ion recombination) upon optimization. Thus the barrier to ion recombination found for the tetramer, [NH4CN]2 will be investigated in detail as will the bonding in other N:N clusters. Additionally, we will continue to examine the “solvation” effects of ammonia on hydrogen cyanide in the gas phase and in solution employing self-consistent reaction field theory.26 Of special interest is whether immersing the cluster(s) in liquid ammonia facilitates the transfer of H/H+ from HCN to NH3.

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