A gold cyano complex in nitromethane: MD simulation and X-ray diffraction.

The solvation structure around the dicyanoaurate(I) anion (Au(CN)2-) in a dilute nitromethane (CH3NO2) solution is presented from X-ray diffraction measurements and molecular dynamics simulation (NVT ensemble, 460 nitromethane molecules at room temperature). The simulations are based on a new solute-solvent force-field fitted to a training set of quantum-chemically derived interaction energies. Radial distribution functions from experiment and simulation are in good agreement. The solvation structure has been further elucidated from MD data. Several shells can be identified. We obtain a solvation number of 13-17 nitromethane molecules with a strong preference to be oriented with their methyl groups towards the solute.

Introduction

Gold ions in non-aqueous solution appear in old and new applications and technologies [1]. Examples are the processing of electronic scrap [2], the decoration of nanomaterials [3] and processes for the synthesis of functional nanostructures [4], wires [5] and clusters [6], often involving self-assembly of ligands around gold ions. New applications for gold solutions in nanotechnology and cluster science also involve the catalytic properties of gold nanoclusters utilizing the ability of gold to easily toggle between the oxidation states 0, 1 and 3 [7].

Due to the high complexation tendency of gold ions, normally the bare Au(I) or Au(III) ions are not present in solution. Dicyanoaurate(I) anion (Au(CN)2−) is an especially stable and well-known gold complex. It can, for example, be prepared as an alkaline salt (NaAu(CN)2 or KAu(CN)2) by cyanidation of gold clusters [8]. In general, little is known about the microscopic details of gold complexes in solution and the aim of the present work is to elucidate the solvation structure around the Au(CN)2− ion in nitromethane (NM), a prototypical gold complex in a solvent that is widely used for gold solutions. Compared to small cations, large monovalent negative ions in solution usually show only a rather weak ability to organize the solvent molecules around it. Here we will find out if this is also true for the Au(CN)2− ion in nitromethane.

The methods we use are X-ray diffraction and molecular dynamics (MD) simulations, the latter performed with a solute–solvent force-field that we construct from ab initio calculations. This is done in a way consistent with our earlier nitromethane force-field [9]. In the results section, we compare the total radial distribution functions (rdf functions) from the X-ray diffraction experiments and the MD simulation and then proceed to analysing the detailed structural information that MD simulations can provide. We first decompose the total simulated rdf into atom–atom contributions and then go on to discussing the possible existence of solvation shells around the negative solute, and the organizing ability of the anion in terms of the solvent orientation. Finally, we will compare the solvation structure in the solution with that found in smaller Au(CN)2− • n NM clusters (n = 1–10) (published earlier by some of us in Ref. [10]). There it was found that two types of solvation structures were stable: either the nitromethane molecules tended to form head-to-tail chains among each other and surround the solute in that way, or they tended to populate the cyano ends of the solute orienting themselves predominantly with their methyl group towards the solute (see Fig. 4 in Ref. [9]). We will find out if these arrangements persist in the solution.

Figure 4

Au(CN)2−⋯NM radial distribution functions and running integration numbers from the MD simulation. The distance scale is the same in the three bottom panels and is different from that in the top panel.

Methods

Quantum chemical calculations

In a previous study [9] on the Au(I)–nitromethane interaction, we found that the Hartree–Fock (HF) method with the LANL2DZ basis set [11] for Au(I) and the D95V [12] basis set for N, O, C and H is suitable for describing these systems to a good degree of accuracy. We use the same method and basis sets in this work on the Au(CN)2− anion⋯nitromethane interaction. Normally, anions require more diffuse basis sets, but the negative charge of dicyanoaurate(I) anion is rather evenly distributed over all atoms. This makes it possible to use a more compact basis set, at least as far as the energetics is concerned, which is the only way we will make use of the ab initio calculations in the present work.

Au(CN)2− itself is a linear molecule with D∞h symmetry. In many respects, calculations on the interaction of the Au(CN)2− anion with solvent molecules are less problematic than with the bare Au(I) ion, because the 6s orbital of gold in Au(CN)2− is nearly fully occupied and therefore does not change its hybridization when interacting with ligands. Here a large number of quantum-chemical calculations were performed, where the NM molecule was placed in different orientations along specified directions with respect to the solute ion, and the energies were collected and used in the force-field fitting; details are given in Section 3. All these calculations were carried out with the Gaussian 03 code [13].

Molecular dynamics simulations

The molecular dynamics simulations of Au(CN)2− in liquid NM were performed by using our published NM⋯NM intermolecular potential energy function [9] together with our new Au(CN)2−⋯NM potential function, constructed as described below. The cubic MD box (35.561 Å boxlength) contained one Au(CN)2− anion, one K+ ion and 460 rigid NM molecules. The interaction potentials involving K were derived in the same way as the Au(CN)2−⋯NM potentials but will not be further discussed in this Letter since the potassium ion hydration will not be discussed at all (the K+⋯NM potential and fitting data are available from the authors upon request). Periodic boundary conditions were employed, together with the minimal image convention for the short-range forces. For the electrostatic forces, the Ewald summation was used. The simulation was performed in the NVT ensemble at 300 K. A timestep of 0.5 fs was chosen. The simulation time was 1 ns, divided such that the production run was performed for 980 ps after equilibrating the system for 22.5 ps. Before that, several equilibration cycles at high temperature with crude temperature scaling were performed to relax the system. The molecular dynamics code used was DL_POLY 2.19 [14].

X-ray diffraction measurements

The X-ray diffraction measurement was carried out for a solution of 0.036 M KAu(CN)2 in nitromethane (anhydrous, special grade, produced by Aldrich). The physical properties of the solution were as follows: density ρ = 1.125 g cm−3, linear X-ray absorption coefficient μ = 2.0876 cm−1, atomic number density ρ0 = 0.0771·10−24 cm−3.

The measurements were performed at room temperature (24 ± 1 °C), with a Philips X’Pert goniometer in a vertical Bragg–Brentano geometry with a pyrographite monochromator placed in the scattered beam and a proportional detector using MoKα radiation (λ = 0.7107 Å). Quartz capillaries (1.5 mm diameter, 0.01 mm wall thickness) were used as the liquid sample holder. The scattering angle range of the measurement spanned over 1.28 ⩽ 2Θ ⩽ 130.2°, corresponding to a k = (4π/λ)·sinΘ range of 0.2 Å−1 ⩽ k ⩽ 16.06 Å−1. Over 100,000 counts were collected at each angle in Δk ≈ 0.05 Å−1 steps. Data reduction procedures were performed using our own software and were described previously [15].

Results and discussion

Potential energy functions

In Ref. [10], quantum-chemical results for the electronic structure and the electrostatic potential of the isolated Au(CN)2− ion were presented, and, as mentioned, small Au(CN)2− • n NM clusters were also explored. In the present study, we develop a Au(CN)2−⋯NM intermolecular potential function with the aim of exploring the solvation structure of Au(CN)2− in a dilute NM solution. The analytical pair potential functions were constructed by fitting parameters of functions of the interatomic distances to energies derived from the quantum-chemical calculations.

To construct the analytical potential function for Au(CN)2−⋯NM, 22 geometrical cases were explored, namely different ‘rays’ originating on the NM molecules with different orientations of the ion along these rays, as shown in Figure 1. Both the linear Au(CN)2− anion and the NM molecule were kept rigid and the ion was stepwise moved out from the NM molecule (cf. Figure 2a) The atomic partial charges (Mulliken) of Au(CN)2− were calculated (Table 1), while the partial charges of NM were taken from Ref. [9]. The fitting of the free parameters was performed by minimizing the least-square deviation between the energies from the analytical formula and their quantum chemically calculated counterparts.

Figure 1

Structures of the Au(CN)2− ion and the nitromethane (NM) molecule used in the quantum-mechanical calculations. The lines in (b) and (c) indicate the directions of approach of the Au(CN)2− ion towards the NM molecule for the exploration of the potential energy curves. In (b), the NC–Au–CN axis is oriented along the directions shown. In (c), the NC–Au–CN axis is oriented perpendicular to the directions shown, with X = Au, C or N, yielding the triplet of numbers listed for each direction. For the cases (11, 12, 13) and (17, 18, 19), the NC-Au-CN axis is perpendicular to the NO2 plane. For the cases (14, 15, 16), (20, 21, 22), (5, 6, 7) and (8, 9, 10), the NC–Au–CN axis is parallel to the NO2 plane.

Figure 2

(a) NM–Au(CN)2− potential energy curves from the QC calculations (x) and from the fitted force-field expression (solid lines). (b) Fitting accuracy of the NM–Au(CN)2− potential energy function.

Table 1

Atomic partial charges in Au(CN)2− and NM used in Eq. (1).

NM	qk	Au(CN)2−	qj
C	−0.305	Au	0.411
H	0.146	C	−0.433
N	0.821	N	−0.272
O	−0.477

An analytical pair potential for the Au(CN)2−⋯NM, interaction was fitted to the ab initio interaction energies according to

The values of the parameters A to C for each pair-potential are given in Table 2. The direct physical meaning of these functions is limited but the powers of the polynomials were selected to reproduce perfectly the attractive and repulsive energies obtained from quantum-chemical calculations.

Table 2

Values of the fitted parameters (kcal/mol and Å) for the Au(CN)2−⋯NM pair potential.

j	k	A	B	C
Au	C	576.3645	−5411.1	10 557.0
Au	H	−163.8395	391.271	131.2832
Au	N	−1331.2	1890.3	0.0
Au	O	1864.3	−6534.9	8405.5
C1	C	625.6538	−5240.7	8500.7
C1	H	233.4933	−176.6096	89.4191
C1	N	692.8688	317.4628	0.0
C1	O	−1194.8	1877.8	339.4626
N1	C	−1142.0	2439.6	104.5295
N1	H	−65.3314	168.5723	0.0
N1	N	546.0669	−4127.1	5480.0
N1	O	561.9225	−1716.3	2847.2

The fitted energy together with the ab initio data of each pair-potential is plotted as shown in Figure 2b. The analytical formulas are seen to reproduce the quantum-chemical data nearly perfectly.

X-ray diffraction experiment and comparison with the simulation

The total radial distribution function obtained from this X-ray diffraction experiment is compared with the one obtained from the MD simulation in Figure 3. The agreement between the experimental and calculated total radial distribution functions is very satisfactory and lends credibility to the quality of our ab initio based potential functions. We therefore conclude that it is useful and worthwhile to analyze the MD simulation data in depth to derive structural information that our X-ray diffraction analysis is not able to give.

Figure 3

Comparison of the total radial distribution functions obtained from the X-ray diffraction experiment and from the MD simulation.

Molecular dynamics simulation – results and discussion

From the MD trajectory we calculated the radial distribution functions g(r) between the atoms in the Au(CN)2− ion and the NM molecules according towhere N is the number of centers, ρ is the macroscopic density of center x and n is the number of xy pairs. The g curves are shown in Figure 4 with characteristic values listed in Table 3. In this table also the running integration numbers n, defined asare given.

Table 3

Characteristic values of selected radial distribution functions for the Au(CN)2−⋯NM system studied in this Letter. Distances are in Å.

Atom-pair	1st Shell					2nd Shell
	rmax	g(rma)	rmin	g(rmin)	n(rmin)	rmax	g(rmax)	rmin	g(rmin)	n(rmin)
Au–O	6.17	1.15	∼8.0	0.9	∼26
Au–N	5.22	1.40	7.77	0.88	18.44	9.41	1.10	11.16	0.93	58.32
Au–C	3.97	1.97	6.97	0.56	15.25	9.46	1.20	11.56	0.88	66.41
Au–H	4.82	1.54	6.97	0.76	46.27	9.36	1.12	11.71	0.93	207.95

Table 3 and Figure 4 suggest that the CH3 groups of the NM molecules on average lie closer to the Au atom than the NO2 groups. A closer look at the rdf for Au⋯C in Figure 4 reveals a double peak in the region 4 Å < r < 7 Å. Also the other rdfs in Figure 4 suggest that there are (at least) two overlapping rdf peaks below, say, 7 Å.

To acquire better insight into the solvation shell structure of the dicyano aurate(I) anion, we calculated a two-dimensional cylindrical distribution function (Figure 5). The upper half of the figure refers to the nitromethane C atom distribution. Here, the value in a certain 2D bin represents the probability to find the nitromethane C atom anywhere in the corresponding ring around the ionic axis (regardless of the azimuthal angle with respect to the axis). The value for each bin has been normalized according to the respective volume of the ring. The upper half of Figure 5 thus displays any deviations of the NM solvation structure from an isotropic solvent distribution.

Figure 5

Two dimensional projection of the distribution of nitromethane molecules around the central dicyanoaurate(I) ion resulting from the MD simulation The upper half of the plot shows the distribution of the CH3 groups of the NM molecules, the lower part shows the distribution of the NO2 groups of the same NM molecules. The plot has been normalized as explained in the text, i.e. each area element (x, r) represents the average population in the corresponding ring around the dicyanoaurate(I) iońs axis.

The lower half of Figure 5 shows the corresponding distribution for the N atoms of the nitromethane molecules.

The first shell of the CH3 groups is seen to lie closer to the solute than the first-shell NO2 groups, in agreement with the rdf results. This is so everywhere around the solute, possibly with the exception of the region close to x ≈ 0 in the lower panel of the figure, where the N population is seen to bulge slightly inwards. This solution result is consistent with the electrostatic potential for the (free) Au(CN)2− ion [10], which indicates that the positive gold atom dominates the electrostatic map in a narrow belt around the middle of this long negative ion.

Both the C and N distributions indicate a pronounced shell structure around the anion, but this is particularly evident for the C atoms (CH3 groups), where two shells are clearly visible in Figure 5. We have added some auxiliary rings in the figure to help explain the origin of the double peaks found in all of the rdfs for r < 7 Å. It is clear from Figure 4 that this feature is a consequence of the elongated shape of the solute. For Au⋯C, for example, the peak centered at around 5.5 Å originates from the solvent molecules residing at the ends of the solute, while the first peak, at ∼4 Å, is seen to originate from solvent molecules closer to the Au atom.

The sphere drawn around the Au atom with a radius of ∼7 Å is seen to encompass most, but perhaps not all, of the first-shell solvent molecules at the ends of the solute, while the sphere appears to include more than the first-shell solvent molecules along the middle of the ion (i.e. at x ≈ 0). The Au⋯C rdf integrated out to the first minimum at 7 Å gives a solvation number of about 15 (Table 3), and the Au⋯N rdf integrated out to the first minimum at 7.8 Å gives a coordination number of about 18. Comparison with Figure 5, suggests that such a large sphere (7.8 Å radius) contains more than the first solvation shell in certain directions. We constructed an alternative ‘first-shell region’ that adheres better to the elongated shape of the solute, namely the region consisting of the union of three spheres with equal radii, centered at the solute’s Au atom, and at its two terminal N atoms, respectively. This first-shell shape is shown in the inset in Figure 6. For each of the snapshots analyzed, all NM molecules which had either their C or N atoms residing within this volume were counted. When the radii were set to 5 Å, the average number of NM molecules in the volume was 13.6, with instantaneous values in the range 12–15. If instead a radius of 6 Å is used for the three spheres, the resulting volume extends somewhat beyond the region that can justifiably be called the first solvation shell (judging from a comparison with Figure 5). The average number of NM molecules then becomes 17.1, with instantaneous solvation numbers almost always falling in the range 15–20. In summary, the coordination number of NM molecules around the gold cyano complex is on average about 15.

Figure 6

Angular distribution function of NM molecules in the first shell around the Au(CN)2− ion. The first shell is here defined as all NM molecules whose N atom or C atom (or both) reside within 5 Å from at least one of the Au, N1 and N2 atoms in the Au(CN)2− ion. This region is outlined in the inset. Θ Is the angle between the dipole moment vector of the center of NM and the Au(I) atom.

Figure 6 also displays the orientation of the NM molecules around Au(CN)2−. It is found that an NM orientation with CH3 pointing towards the anion is strongly preferred in the first hydration shell.

Finally, we will compare our liquid solution results with the solvation structure found for smaller Au(CN)2− • n NM clusters (n = 1–10) (published earlier by some of us in Ref. [10].). The cluster calculations in Ref. [10] were performed with the same quantum-mechanical method as we used in the present work to generate the force-fields. Bearing in mind that calculations with well-fitted ab initio-based force-fields can be viewed as equivalent to performing the actual ab initio calculations themselves (in a cost-efficient manner), it is thus adequate to compare the optimized cluster results with our simulation results from the NM solution. For the smallest quantum-chemically optimized clusters, the NM molecules tend to populate the cyano ends of the solute and orient themselves with the methyl group towards it (see Fig. 4 in Ref. [10]). For larger clusters, an almost equally stable solvation structure was found for a head-to-tail arrangement of the NM molecules forming a small chain around the Au(CN)2− ion, again with a preference for the CH3 groups to be located closer than the NO2 group to the solute. The tendency for the CH3 ends of the first-shell NM molecules to be oriented towards the gold complex persists in the solution, as already discussed above. Moreover, in the solution structure at room temperature we find dynamically distorted fragments of head-to-tail NM chains which often change partners. Also anti-parallel arrangements of two or more nearest-neighbor NM molecules are found. Several of these structural features can be discerned in the three sample snapshots of the Au(CN)2−⋯NM system shown in Figure 7.

Figure 7

Three selected snapshots from the MD simulation showing the NM coordination around the Au(CN)2− anion. All solvent molecules within the first solvation shell, defined as the union of the three spheres with radii 5 Å, defined in Figure 6 are displayed. All C⋯N inter- and intra-molecular distances are drawn in the same style.

Conclusions

An ab initio pair energy function for Au(CN)2−⋯NM was derived by fitting analytical terms to quantum chemically calculated energies. This potential was then employed in a molecular dynamics simulation using a box containing one K+ ion, one Au(CN)2− ion and 460 NM molecules in the NVT ensemble at room temperature. It was found that the first solvation shell around Au(CN)2− typically consists of 13–17 nitromethane molecules in a rather ordered shell. The solvation shell preserves some structural features of the zero-K structures of small Au(CN)2−⋯NM clusters. An X-ray diffraction experiment with a diluted solution of KAu(CN)2 in nitromethane was performed as well. The total radial distribution function agrees well with the corresponding curve from the molecular dynamics simulation.