Ab initio study of the fluoride–ammonia clusters: F–(NH3)n, n = 1–3

Fluoride–ammonia clusters have been investigated via ab initio calculations at the MP2 level of theory, using Dunning’s augmented correlation consistent basis sets.

Optimised geometries, vibrational frequencies, and enthalpy changes for the ligand association reactions are presented for clusters with one, two, and three ammonias bound to a fluoride anion.

The minimum energy structure for the F–NH3 complex, with Cs symmetry, displays a single hydrogen bond between the ammonia and fluoride anion.

For the F–(NH3)2 cluster, two closely lying minima with C2 and C1 symmetry were predicted.

For F–(NH3)3, four minima were located, with the minimum energy structure having C3h symmetry.

Calculated infrared spectra for the minima are presented to aid in assigning spectra from future experimental studies.


Much progress has been made in recent years towards understanding the interactions between ions and solvent molecules.

Such endeavours have obvious importance for more detailed descriptions of molecular interactions, and for describing ion solvation in bulk contexts.1

Advances have been made in both experimental and theoretical methodologies.

On the experimental front, photoelectron, infrared, and microwave spectroscopy of gas phase ion complexes and clusters have furnished qualitative, or in some cases quantitative, structural information2–23.Ab initio calculations of ion–solvent complexes have proved useful in rationalising experimental observations, and in guiding future experiments.24–27

Due to its obvious importance, the solvation of ions (particularly halide anions) by water has received much attention.

Both experiment15,16,28–30 and theory28,31–35 concur that the structures adopted by halide–water clusters depend on the balance of ion–solvent and solvent–solvent interactions.

For example, in the fluoride–water clusters the anion–solvent binding forces dominate, resulting in the anion being situated in the interior of the structure.28

For clusters involving the larger halides, the solvent–solvent attractive interactions play a more significant role in determining the cluster structure, the result being solvent–solvent bonds and asymmetric structures where the anion binds to the surface of the solvent network.

Experimental evidence, provided by IR spectra of Johnson and co-workers, was the absence of bands in the spectra due to free or non-bonded O–H oscillators,29 and the introduction of ring modes similar to those seen for the neutral water trimer.36,37

For a recent review on investigations of halide ion hydration, see .ref. 38

The halide–ammonia clusters have received relatively little attention compared to the analogous halide–water species.

Selected complexes have been probed via high pressure mass spectrometry,39 photoelectron spectroscopy,40,41 vibrational predissociation spectroscopy,42 and time resolved photoelectron spectroscopy.43

Castleman and co-workers performed high pressure mass spectrometry experiments on the chloride, bromide, and iodide–ammonia complexes and reported enthalpy changes for the association reactions of −8.2, −7.7, and −7.4 kcal mol−1, respectively.

The association reaction enthalpy change for the F–NH3 complex was estimated to be −11 kcal mol−1 from comparison of extrapolated and calculated values.39

Kaldor and co-workers applied photoelectron spectroscopy to the chloride–ammonia complex,41 and complemented this work with ab initio calculations at the CCSD level with a truncated ANO basis set for chloride and fluoride–ammonia.40

A binding energy of 0.36 eV (8.3 kcal mol−1) was reported for the chloride–ammonia complex in very good agreement with the work of Castleman and co-workers.

The complexes were predicted to have a Cs structure featuring a single hydrogen bond between the anion and ammonia.

Bieske and co-workers investigated the chloride–ammonia complex via vibrational predissociation spectroscopy.42

The infrared spectrum and supporting ab initio calculations at the MP2/aug-cc-pVTZ level of theory were consistent with the structure predicted by Kaldor.40

Three other stationary points were predicted; the Cs and C2v transition states, and the C3v second order stationary point.

The transition states correspond to tunnelling motion of the ammonia molecule between equivalent Cs minima.

The barrier to ‘turnstile’ tunnelling of the ammonia (via the Cs bifurcated transition state) was predicted to be 1.72 kcal mol−1, while the barrier to umbrella inversion of the ammonia molecule (via the planar C2v transition state) was estimated as 5.23 kcal mol−1.

Neumark and co-workers applied time resolved photoelectron spectroscopy to I–(NH3)n clusters (n = 4–15).43

They investigated the dynamics associated with the excitation of the charge-transfer-to-solvent (CTTS) precursor states.

The spectra implied that electron solvation, via solvent rearrangement, occurs on a timescale of 0.5–2 ps following photoexcitation.

To date, there have been no reported electronic structure calculations or infrared spectra of the larger halide–ammonia clusters which are essential for defining cluster structures.

The current work constitutes an investigation of smaller fluoride–ammonia clusters, with up to three ammonias bound to a fluoride anion.

We wish to determine whether symmetric or asymmetric solvation structures are preferred.

Furthermore, we aim to provide vibrational frequencies that might prove helpful for future experimental studies.

Our choice of computational methodology is guided by previous studies of the water–halide clusters.

It has been shown that the MP2/aug-cc-pVxZ (x = D, T) calculations are good choices for describing the halide–water systems.28,31,34,35,44–46

Furthermore, the same methodology has been used for the ammonia dimer, adequately describing the ammonia–ammonia hydrogen bond47.


The fluoride–ammonia clusters were investigated at the MP2 level of theory using Dunning’s augmented correlation consistent polarized valence sets.48–50

For the F–NH3 complex, calculations were performed with basis sets of double, triple, and quadruple-ζ quality (aug-cc-pVxZ where x = D, T, Q).

HF and MP4(SDQ) geometry optimisations were performed to consider the effect of electron correlation.

Only the valence electrons were correlated in the MP2 and MP4 calculations.

MP2/aug-cc-pVDZ and MP2/aug-cc-pVTZ calculations were undertaken for F–(NH3)2, while MP2/aug-cc-pVDZ calculations were performed for F–(NH3)3 clusters.

All optimisations were performed using ‘Very Tight’ convergence criteria, as it is expected that the potential energy surfaces will be quite flat especially for the n = 2 and 3 clusters.

Corrections to the intermolecular interaction energy arising from basis set superposition error (BSSE) were estimated using the method of Boys and Bernardi.51

Harmonic vibrational frequencies were computed analytically at the same level of theory used for the geometry optimisations.

It should be remembered that the calculated vibrational frequencies overestimate the actual frequencies, due to not taking anharmonicity into account.

NBO analyses were performed on the clusters to determine the extent of H-bonding.52

Enthalpy changes for the ligand association reactions at 298 K were estimated using the method described in .ref. 53

The geometry optimisations, energy and vibrational frequency calculations, and NBO analyses were performed with the GAUSSIAN-03 program suite.54

Diagrams of the cluster structures were produced using gOpenMol55,56.


A. F–NH3

Four stationary points were located for the fluoride–ammonia complex.

The points, shown in Fig. 1, correspond to the Cs minimum energy structure, Cs and C2v first order transition states, and the C3v second order stationary point.

Calculated data are provided in Tables 1 and 2, including internal coordinates, vibrational frequencies, energies, and for the Cs minimum the enthalpy change for the ligand association reaction at 298 K.

I. Cs minimum

The Cs minimum energy complex was investigated by HF and MP2 methods with basis sets of double, triple, and quadruple-ζ quality, and by the MP4(SDQ) method using basis sets of double and triple-ζ quality.

The results of these calculations are given in Table 1.

One can see that increasing the level of electron correlation from HF to MP2 to MP4 affects the predicted structure.

Using calculations with the aug-cc-pVTZ basis set as an example, the intermolecular bond length shortens on going from HF to MP2 theory (Δr = −0.132 Å), and increases slightly on going from MP2 to MP4 (Δr = +0.035 Å).

The F–Hb–N angle increases from HF to MP2 (Δθ(F–Hb–N) = +2.7°), and then decreases on going from MP2 to MP4 (Δθ(F–Hb–N) = −0.9°).

The differences between the MP2 and MP4 calculations are not so large, leading us to believe that MP2 method is adequate in describing the systems, and has the advantage of reduced computation times.

From the MP2 calculations it can be seen that increasing the basis set size above triple-ζ quality results in only slight changes to the structure (Δr = 0.002 Å and Δθ = 0.2°), therefore this basis set is considered to be a good choice to describe the system.

The following discussion of the 1 : 1 complex will concentrate on the MP2/aug-cc-pVTZ results.

In agreement with the previous theoretical study of Kaldor,40 the minimum energy structure for the fluoride–ammonia complex is one with the ammonia bound to the fluoride anion via a single, nearly linear hydrogen bond (θ(F–Hb–N) = 176.3°).

Compared to the CCSD calculations,40 the intermolecular bond length from our MP2/aug-cc-pVTZ calculations is contracted (1.586 vs.

1.626 Å), and closer to linearity (176.3 vs.


The calculated enthalpy change for the ligand association reaction (at 298 K) is −15.8 kcal mol−1.

This is somewhat higher than the value estimated by Castleman and co-workers of −11 kcal mol−1.39

Complex formation with F affects the ammonia in a number of ways, most noticeably by elongation of the H-bonded N–H bond (Δr = +0.055 Å from Table 2), and further distortion of the ammonia molecule from planarity (Δθ(H–N–H) = −1.7 and −2.3°).

The non-bonded N–H bond lengths are slightly elongated relative to bare ammonia (Δr = +0.003 Å).

II. Other stationary points

We turn our attention now to the three other stationary points of the 1 : 1 complex (Table 2, Fig. 1).

Firstly, the Cs structure involves a double hydrogen bond (confirmed by NBO analysis, vide infra) between the ammonia and fluoride, and corresponds to the ‘turnstile’ tunnelling transition state between equivalent singly bound Cs minima.

After BSSE and zpe corrections are made, the energy difference between this transition state and the Cs minimum, or effectively the barrier to tunnelling along this coordinate, is estimated to be 3.97 kcal mol−1 or 1600 cm−1.

The fluoride–ammonia complex is more rigid along this coordinate than Cl–NH3 which has a tunnelling barrier of 1.66 kcal mol−1, an effect of the stronger H-bond for the minimum.42

The planar C2v transition state involves a single H-bond between ammonia and fluoride (see NBO analysis), and corresponds to ‘umbrella’ inversion of the NH3 molecule.

The calculations predict a smaller barrier of 4.44 kcal mol−1 for the fluoride–ammonia complex compared to 5.23 kcal mol−1 for Cl–NH3.42

Finally, the C3v structure is a second order stationary point, with a doubly degenerate imaginary frequency (321i cm−1) corresponding to the rocking motion towards one of the three equivalent hydrogens.

This structure lies some 6.46 kcal mol−1 to higher energy from the Cs minimum, while for Cl–NH3 the energy difference is only 2.24 kcal mol−1.42

This difference may arise from the shorter intermolecular distance in the fluoride complex (2.530 vs.

3.053 Å),42 leading to a more repulsive interaction in this configuration compared with the chloride complex.

III. NBO analyses

NBO analyses were performed to assess the nature of the hydrogen bond in the predicted structures.

The results of the analysis constitute molecular orbital occupancies (in me) and second-order perturbation energies E(2) for electron density donor → acceptor interactions (in kcal mol−1).

The signature of H-bonding is electron density transfer from the lone pairs of the H-bond acceptor (F), to the anti-bonding orbitals of the H-bond donor (NH3).

The results of the NBO analysis for the Cs structure reveal significant electron density transfer from the lone pairs of the fluoride anion to anti-bonding orbital associated with the H-bonded N–H group.

In total, 52 me of electron density is transferred.

An NBO analysis was also performed on the ammonia molecule in the complex geometry with the fluoride anion replaced with a point charge to determine the change in orbital occupancies due to polarisation by the negative charge.

This analysis reveals that a very small portion, ca.

10 μe, is due to polarisation of the ammonia molecule by the anion.

The second-order perturbation energies E(2), or effectively the stabilisation energies resulting from the electron density transfer, reveal that the transfer from the lone pairs of the fluoride anion affords the greatest stabilisation.

The total value is 41.7 kcal mol−1 for transfer from the fluoride lone pairs to the antibonding orbital.

NBO analyses were also performed for the higher order stationary points shown in Fig. 1.

For the double H-bonded Cs structure, the analysis confirmed the double H-bond between anion and ammonia with electron density transfer from lone pairs of the fluoride anion to the two N–H antibonding orbitals.

The orbital occupancy and stabilisation energy E(2) (donor → acceptor) is ca.

2.5 me and 0.83 kcal mol−1, respectively, for each orbital.

The C3v structure features a triple H-bond from the anion to the ammonia, although in this instance the bond strengths are much weaker.

The orbital occupancy is predicted to be 0.38 me per orbital, while the stabilisation energy is 0.07 kcal mol−1.

Finally, the C2v planar structure exhibits the strongest H-bond of all the geometries.

The N–H antibonding orbital occupancy is predicted to be 66.25 me, while the stabilisation energy is 51.88 kcal mol−1.

The strength of this H-bond is not surprising if one considers that the F–Hb–N intermolecular angle is 180°, and hence the lone pair-antibonding orbital alignment is maximised.

The H-bond strength is seen to decrease in the order C2v > Cs min > Cs > C3v in proportion to the intermolecular angle θ(F–Hb–N) = 180, 176.3, 112.8, and 49.9°, respectively (Table 2).

IV. 1-D intermolecular potentials

To further characterise the fluoride–ammonia interaction, a relaxed scan along the association coordinate, r(F–N), was undertaken at the MP2/aug-cc-pVTZ level of theory.

The results of this scan in terms of internal coordinates and energies are presented in Fig. 2, with the intermolecular bonding angle now defined as θ(F–N–Hb).

Data from the scan can be found in the Electronic Supplementary Information. At large intermolecular separations, the fluoride ammonia interaction is dominated by the electrostatic interaction between the ion and the ammonia dipole moment, leading to an F–N–Hb angle of approximately 67°.

As the fragments move closer together, the complex adopts a single hydrogen bond, moving towards the Cs minimum energy structure shown in Fig. 1 (θ(F–N–Hb) = 2.2° at r(F–N) = 2.651 Å).

The change in the bond lengths and angles of the ammonia molecule are shown in Fig. 2.

The ammonia bond lengths elongate, while the H–N–H angles decrease.

Finally, at very short intermolecular separations, the ammonia twists into a strained geometry where the F–N–H angle increases again (θ(F–N–H) = 25° at r(F–N) = 2.1 Å) as the H-bonded hydrogen points away from the anion.

One-dimensional potential energy curves describing the interaction between the fluoride and ammonia along the association coordinate r(F–N) were also developed for the Cs and C3v stationary points.

The purely repulsive interaction where the fluoride approaches the nitrogen of the ammonia, in a C3v symmetry arrangement, was also considered.

The curves are provided in Fig. 3, and the data for these scans in terms of energy differences (ΔEe) and BSSE corrected energy differences (ΔEe/BSSE) are given in the Electronic Supplementary Information. These 1-D intermolecular potential energy curves, along with the corresponding curve for the minimum energy Cs structure, should prove useful for undertaking MD and Monte Carlo simulations in condensed phases involving fluoride anions and ammonia.

V. Predicted infrared spectrum

The effects of complex formation on the ammonia molecule manifest themselves strongly in the vibrational modes.

A stick spectrum produced from the calculated harmonic frequencies is presented in Fig. 4.

Starting from low wavenumber, three bands are introduced corresponding to the intermolecular stretching and two intermolecular bending modes.

To higher wavenumber are the bending modes of the ammonia molecule, in the 1000–2000 cm−1 range.

The two bending modes of the bare ammonia with a1 and e symmetry transform into three modes, two with a′ and one with a′′ symmetry.

The N–H stretching modes, in the 2500–3600 cm−1 range, are affected most by formation of the complex.

Similar to the bending modes, the a1 and e symmetry modes of bare ammonia transform into three modes, two with a′ symmetry and one with a″ symmetry.

One of these modes appears as the strong band located at 2685 cm−1, and is due predominantly to motion of the H-bonded hydrogen.

This band is shifted by 890 cm−1 to lower wavenumber from the centroid of the two calculated bare ammonia N–H stretches (Table 2), and has a marked increase in IR intensity (1615 km mol−1 in the complex vs.

8 and 3 km mol−1 for bare ammonia).

Both of these effects are characteristic of hydrogen bond formation.58

Two further vibrational modes, with very low IR intensity, are predicted to higher wavenumber and are due to the symmetric and antisymmetric vibrations of the non-bonded hydrogens.

It is hoped that this data will be helpful for future experimental studies, however due to the large predicted binding energy of the complex (−15.8 kcal mol−1 or ca.

5315 cm−1) vibrational predissociation spectroscopy is not applicable without resorting to the use of ‘spy’ atoms (recent examples can be found in refs. 38 and 59)

B. F–(NH3)2

The addition of a second ammonia to a fluoride anion results in ammonia–ammonia solvent interactions, which may lead to symmetric versus asymmetric solvation structures.

With this in mind, we move now to the discussion of the 1 : 2 cluster, F–(NH3)2.

Stationary points found from calculations at the MP2 level with aug-cc-pVDZ and aug-cc-pVTZ basis sets are shown in Fig. 5.

Two higher symmetry C2h and C2v structures (Fig. 5a) were predicted at both levels of theory.

The C1 symmetry structure, Fig. 5b, predicted from a MP2/aug-cc-pVDZ calculation converged to the C2 structure shown in Fig. 5c when used as input for a MP2/aug-cc-pVTZ calculation.

A fourth structure, with C1 symmetry, was found from MP2/aug-cc-pVTZ calculations (henceforth labelled C1′).

When this stationary point was used as input in a MP2/aug-cc-pVDZ optimisation, it converged to the C1 structure shown in Fig. 5b.

Optimised internal coordinates and calculated energies are provided in Table 3, highlighting the differences between the structures of the stationary points at the two levels of theory sampled.

For common structures between the two levels of theory, the results indicate that increasing the basis set size has only a small effect on the internal coordinates.

For the C2v isomer, increasing the size of the basis set has no discernible effect on the structure (Table 3).

For the C2h structure, increasing the basis set size reduces the H-bonded N–H bond length, (Δr ∼ −0.01 Å) and the intermolecular H-bonding angle (Δθ ∼ −0.2°).

The most striking difference however between the two levels of theory is that this C2h stationary point is predicted to be a minimum for aug-cc-pVDZ and a second order stationary point for aug-cc-pVTZ.

From the discussion of the 1 : 1 complex, the pVTZ level is considered to be a better choice to describe these systems, however the differences in bond lengths and angles between the two levels of theory are not so large.

I. Structure descriptions and NBO analyses

The C2h structure (Fig. 5a) has the two ammonias situated on opposite sides of a central fluoride anion, represents a symmetric type solvation structure.

As stated previously, this structure is a minimum for the pVDZ calculations and a second order stationary point when the larger pVTZ basis set is used.

The C1′ structure (Fig. 5c) predicted from calculations with the pVTZ basis set is similar to the C2h isomer, however the angle between the two ammonia molecules θ(Hb–F–Hb) is 156.4° compared to 180°.

The ammonias are no longer equivalent, and have different H-bond lengths and angles, with r(F–Hb) = 1.669 and 1.665 Å and θ(F–Hb–N) = 176.0 and 175.7°.

This stationary point is a minimum at the MP2/aug-cc-pVTZ level of theory, and resembles a symmetric solvation structure.

The C1 and C2 structures (Fig. 5b and c) are minima, and feature both ammonias to one side of the fluoride anion, corresponding to an asymmetric type solvation structure.

The difference between the two structures is that for C2 the ammonias are equivalent, whereas for the C1 structure the two ammonias have different H-bond lengths and angles (refer to Table 3).

To determine whether H-bonding occurs between the two ammonias, NBO analyses were performed.

The signature of an ammonia–ammonia H-bonding interaction is electron transfer from the nitrogen lone pairs of the proton acceptor to the σ*(N–H) antibonding orbital of the proton donor.

The NBO analyses reveal that there is no significant electron transfer, and hence the interactions cannot be considered true H-bonds.

This is reflected in the geometries of the clusters.

If there was a hydrogen bonding interact and transfer to the antibonding orbital, one should see an increased N–H bond length relative to the terminal N–H group.

This is not observed (Table 3).

The third stationary point, with C2v symmetry (Fig. 5a), is a first order transition state from calculations with both basis sets.

The imaginary frequency for this structure corresponds to a concerted twisting of the ammonia molecules about the F–Hb–N axes.

This isomer features both ammonias to one side of the anion, and hence can be thought of as an asymmetric type solvation structure.

As with the 1 : 1 complex, the geometry of the ammonia is perturbed from that of the bare molecule for both minima (refer to aug-cc-pVTZ calculations in Tables 2 and 3).

Relative to bare ammonia, the N–H bond lengths associated with the hydrogen bound to the anion are elongated by ca.

0.04 Å, while the N–H bond lengths associated with free hydrogens are also longer by ca.

0.01 Å.

The intramolecular H–N–H angles are smaller than in bare ammonia by roughly 1–2°.

Compared with the 1 : 1 complex (Table 2, aug-cc-pVTZ results), the angle of the hydrogen bonds for the minima C1′ and C2 are slightly further from linearity, with θ(F–Hb–N) = 176.0/175.7° and 173.2°, respectively, compared with 176.3° for the 1 : 1 complex.

The intermolecular F–Hb bond lengths are increased, for example Δr = +0.101 Å for the C2 isomer.

II. Cluster energies

One can see from the calculated energies at MP2/aug-cc-pVTZ presented in Table 3 that the energy differences between the stationary points are very small, and hence it is not possible to state conclusively which structure will be the preferred one.

This situation is further clouded as the calculations predict that after BSSE and zpe corrections are made, the second order stationary point (C2h symmetry) lies slightly lower in energy compared with the C1′ minimum.

Obviously, at this level of theory the energies are not accurate enough, furthermore the value of the zpe from the ab initio calculations is derived using harmonic frequencies, and hence will also be a source of error.

One can say, however, that at both levels of theory the symmetric type solvation structures are lower than the asymmetric ones, hinting that symmetric structures may be preferred.

The dominant structure should be found by comparison of the predicted vibrational frequencies with experimental spectra (vide infra).

We also calculated the enthalpy change for the ligand association reaction for both the C1′ and C2 minima (MP2/aug-cc-pVTZ) as −11.8 and −11.4 kcal mol−1, respectively.

These are conservative values due to the aforementioned errors associated with the calculated zpe.

III. Predicted infrared spectra

Harmonic vibrational frequencies are given in Table 4, and stick spectra derived from the calculated vibrational frequencies are presented in Fig. 6.

At low wavenumber (5–500 cm−1) the bands are due to motion of ammonia ligands with respect to the anion and each other.

These vibrations correspond to the intermolecular stretching, bending, rocking and wagging modes.

To higher wavenumber, 1200–1700 cm−1, lie the intramolecular bending vibrations of ammonia.

The most obvious difference between the two isomers is seen in the highest frequency vibrations, corresponding to the N–H stretching modes (2900–3600 cm−1).

The C1′ cluster features a very strong absorption around 2914 cm−1 (IR intensity = 2454 km mol−1) due predominantly to the concerted antisymmetric motion of the two H-bonded hydrogens.

The symmetric mode involving motion of these hydrogens is predicted to be considerably weaker (76 km mol−1).

In contrast for the C2 isomer, two bands with appreciable intensity are predicted at 2944 and 3033 cm−1 (IR intensity = 921 and 957 kJ mol−1, respectively) due to the antisymmetric and symmetric motion of the bound hydrogens, respectively.

It is hoped that these spectra will prove valuable for the interpretation of future experimental studies.

Unfortunately, as with the 1 : 1 F–NH3 complex, predissociation spectroscopy can not be applied to the 1 : 2 cluster as the predicted binding energy of the second ligand of ca.

4130 cm−1 exceeds the energy imparted to the molecule by an IR photon following vibrational excitation of the N–H stretching modes.

C. F–(NH3)3

The F–(NH3)3 clusters were studied at the MP2/aug-cc-pVDZ level of theory, as this level was shown to produce structures that were quite similar to the higher MP2/aug-cc-pVTZ level when used for F–(NH3)2.

To illustrate this point, the C3 symmetry isomer found for F–(NH3)3 was trialled at the MP2/aug-cc-pVTZ level.

The differences in bond lengths and angles are <0.008 Å and <0.9°, respectively (see Table 5).

I. Structure descriptions

Four stationary points, shown in Fig. 7, were found for the F–(NH3)3 cluster at the MP2/aug-cc-pVDZ level of theory.

Calculated data and harmonic vibrational frequencies are provided in Tables 5 and 6.

The four stationary points correspond to a highly symmetric C3h structure with three equivalent ammonia ligands (symmetric solvation), a C3 isomer featuring a pyramid of ammonia ligands that are bound to each other (asymmetric solvation), a C1 asymmetric structure with three non-equivalent ligands on one side of the anion (asymmetric solvation), and a Cs or ‘ring’ isomer which features two ammonias bound to the anion, and a third further out bound to these two (asymmetric solvation).

At the MP2/aug-cc-pVDZ level the four stationary points are minima with all real vibrational frequencies.

This is in contrast to the predictions for the analogous F–(H2O)3 clusters, where only three structures are observed and the symmetric C3h structure is a higher order stationary point.28,34

It is, of course, possible that at higher levels of theory some of the stationary points may no longer be minima as found for the F–(NH3)2 cluster.

Differences in the predicted infrared spectra should allow experimentalists to determine which structure is preferred (vide infra).

Distortions of the ammonia ligands are evident from association with the fluoride anion, however they are generally less perturbed than in the F–(NH3)2 clusters.

The N–H bond lengths are elongated relative to the calculated structure of bare ammonia, with r(N–Hb) = 1.05 Å compared with r(N–H) = 1.02 Å (aug-cc-pVDZ results, Table 2).

The intramolecular ammonia angles θ(H–N–H) are smaller than in bare ammonia, with θ(H–N–H) in the cluster generally in the 103–106° range, compared with θ(H–N–H) = 106.3°.

The linearity of the anion–ammonia hydrogen bonds differs between the isomers of F–(NH3)3 and F–(NH3)2.

II. Cluster energies

The energetic ordering of the isomers, after BSSE and zero point energy difference corrections are taken into account, is C3h < C1 < C3 < Cs.

Unlike the F–(NH3)2 clusters, the difference in the energies of the isomers is appreciable (greater than 1 kcal mol−1), which may hint at a basis set size effect.

Similar to the F–(NH3)2 clusters the accuracy of these energies is questionable as firstly the zero point energy used in the calculation is derived from the calculated harmonic frequencies, and secondly the use of the aug-cc-pVDZ basis set may not be adequate.

This said however, it appears that symmetric solvation structure with C3h symmetry is favoured.

The calculated enthalpy changes for association of a third ammonia ligand are −9.3, −9.0, −9.1, and −7.1 kcal mol−1 for the C3h, C3, C1, and Cs isomers, respectively.

These values are calculated with respect to the most stable isomer from MP2/aug-cc-pVDZ calculations of F–(NH3)2, which was the C2h structure.

III. NBO analyses

NBO analyses were performed for each stationary point to determine the extent, if any, of hydrogen bonding between the ammonia solvent molecules.

Obviously, there should be no significant H-bonding interaction in the C3h isomer as the ammonias are pointing away from one another.

This is revealed in the NBO analysis, with no evidence for lpN → σ*N–H electron density transfer.

There is, however, some evidence of H-bonding between the ammonia ligands for the remaining three isomers.

Firstly, for the C3 isomer, the NBO analysis reveals ca.

1.0 me of electron density transfer from a lone pair of each nitrogen into the σ*N–H orbital of the neighbouring ammonia.

The second-order perturbation energy, or stabilisation energy, for the density transfer is predicted to be E(2) = 0.35 kcal mol−1.

For the C1 isomer, ca.

0.5 me is transferred from a lone pair of the nitrogen of ammonia (2) to the σ*N–H of ammonia (1), with the second-order perturbation energy being E(2) = 0.12 kcal mol−1.

There is no evidence for an H-bonding interaction between ammonia (2) and ammonia (3).

Finally, for the Cs ‘ring’ isomer, the NBO analysis predicts that 9.4 me is transferred from a lone pair of the nitrogens of both B ammonias to the σ*N–Hba orbitals of the S ammonia.

In this case, the stabilisation energy is quite large E(2) = 6.2 kcal mol−1, which is understandable as it is the ammonia–ammonia H-bonds between the S and B ammonias which form the ‘ring’ structure.

The strengths of the H-bonds are reflected in the isomer structures.

The Cs isomer features the strongest ammonia–ammonia H-bond, and hence the N–H bond length of the proton donor is somewhat longer than the terminal N–H bonds (r(N–H) = 1.028 Å versus 1.022 Å).

The second strongest ammonia–ammonia H-bond is seen in the C3 isomer, and in this case the proton donor N–H bond lengths are 1.024 Å compared with 1.022 Å for the terminal N–H bonds.

Finally, the C1 isomer features the weakest H-bond, and the difference is 1.023 Å vs.

1.022 Å.

While the ammonia–ammonia interactions can be called H-bonds due to the predicted electron density transfer, they are certainly much weaker than the H-bond formed between the anion and the ammonia molecules.

For example, from the NBO analysis for the C3 isomer, the stabilisation energy provided from electron density transfer from the lone pairs of the fluoride anion to the ammonia ligand (Total lpF → σ*N–H) is approximately 20 kcal mol−1, and the occupancy of the σ*N–Hb orbital is on the order of 28 me.

IV. Predicted infrared spectra

The results of vibrational frequency calculations for the four isomers are provided in Table 6, and shown as stick spectra in Fig. 8.

As with the F–(NH3)2 cluster, the vibrations can be placed into three groups.

At low wavenumber are the intermolecular vibrations (15–530 cm−1), at intermediate wavenumber are the bending vibrations of the ammonia ligands (1190–1720 cm−1), and at higher wavenumber the N–H stretching modes (2895–3600 cm−1).

Looking to this N–H stretch region, there are distinct differences in the band positions and intensities which should prove useful for analysis of experimental spectra.

Firstly, for the most stable C3h symmetry isomer, only one N–H stretching mode has appreciable IR intensity.

This mode corresponds predominantly to the concerted antisymmetric motion of the H-bonded hydrogens.

For the C3 isomer, two bands are predicted at 3138 and 3215 cm−1, corresponding to the antisymmetric and symmetric motion of the H-bonded hydrogens, respectively.

For the C1 isomer, three bands are predicted at 3046, 3136, and 3222 cm−1.

The first two bands correspond to concerted antisymmetric motion of the bound hydrogens, while the third is due to their symmetric motion.

The Cs isomer is an interesting case, as two strong bands are predicted at 2895 and 2982 cm−1 corresponding to the antisymmetric and symmetric motion of the hydrogens bound to the anion (B).

Two weaker bands are predicted at 3389 and 3496 cm−1, corresponding to symmetric and antisymmetric motion of the hydrogens of the satellite ammonia forming the ammonia–ammonia hydrogen bonds to the two ammonias bound to the fluoride anion (see Fig. 7).

The calculations predict that the binding energies of the third ammonia ligands to the C3h, C3, and C1 isomers are around 3200–3400 cm−1 (Table 5).

While these binding energies are still higher than the predicted H-bonded N–H stretching frequencies, it may be possible to apply vibrational predissociation spectroscopy to complexes which have several low wavenumber intermolecular vibrational levels populated, i.e. vibrationally warm complexes.

Spectra obtained via argon predissociation spectroscopy would be preferable as the complexes would be locked into the minimum energy conformation.

The binding energy of the third ammonia to the Cs isomer is predicted to be lower, at ca.

2480 cm−1.

The predicted H-bonded N–H stretching modes are higher than this value, and hence this cluster should be amenable to vibrational predissociation spectroscopy, without resorting to argon predissociation.


The structures, binding energies, and vibrational spectra of small fluoride–ammonia clusters have been investigated via ab initio calculations.

The F–NH3 complex features a single hydrogen bond, and has Cs symmetry.

The predicted binding energy for this complex is 15.8 kcal mol−1 or 5525 cm−1.

Two minimum energy structures with C2 and C1 symmetry were found for the F–(NH3)2 cluster from MP2/aug-cc-pVTZ calculations.

While the predicted energy separations of the isomers are quite small, differences in the predicted infrared spectra should help experimentalists determine the preferred structure.

Finally, four isomers were predicted for the F–(NH3)3 cluster from MP2/aug-cc-pVDZ calculations.

The symmetric C3h isomer was found to be lowest in energy, indicating that symmetric solvation was more likely than asymmetric solvation.

The predicted binding energy of the third ammonia ligand was estimated to be ca.

9.6 kcal mol−1 or 3360 cm−1 for the most stable isomer.

Again, comparison with experimental spectra should help define the most probable structure.