Microsolvation of the sodium and iodide ions and their ion pair in acetonitrile clusters: a theoretical study

The structural and thermodynamic properties of Na+(CH3CN)n, I-(CH3CN)n, and NaI(CH3CN)n clusters have been investigated by means of room-temperature Monte Carlo simulations with model potentials developed to reproduce the properties of small clusters predicted by quantum chemistry. Ions are found to adopt an interior solvation shell structure, with a first solvation shell containing approximately 6 and approximately 8 acetonitrile molecules for large Na+(CH3CN)n and I-(CH3CN)n clusters, respectively. Structural features of Na+(CH3CN)n are found to be similar to those of Na+(H2O)n clusters, but those of I-(CH3CN)n contrast with those of I-(H2O)n, for which "surface" solvation structures were observed. The potential of mean force calculations demonstrates that the NaI ion pair is thermodynamically stable with respect to ground-state ionic dissociation in acetonitrile clusters. The properties of NaI(CH3CN)n clusters exhibit some similarities with NaI(H2O)n clusters, with the existence of contact ion pair and solvent-separated ion pair structures, but, in contrast to water clusters, both types of ion pairs adopt a well-defined interior ionic solvation shell structure in acetonitrile clusters. Whereas contact ion pair species are thermodynamically favored in small clusters, solvent-separated ion pairs tend to become thermodynamically more stable above a cluster size of approximately 26. Hence, ground-state charge separation appears to occur at larger cluster sizes for acetonitrile clusters than for water clusters. We propose that the lack of a large Na+(CH3CN)n product signal in NaI(CH3CN)n multiphoton ionization experiments could arise from extensive stabilization of the ground ionic state by the solvent and possible inhibition of the photoexcitation mechanism, which may be less pronounced for NaI(H2O)n clusters because of surface solvation structures. Alternatively, increased solvent evaporation resulting from larger excess energies upon photoexcitation or major solvent reorganization on the ionized state could account for the observed solvent-selectivity in NaI cluster multiphoton ionization.     

Predicting atomic dopant solvation in helium clusters: the MgHe(n) case

We present a quantum Monte Carlo study of the solvation and spectroscopic properties of the Mg-doped helium clusters MgHe(n) with n=2-50. Three high-level [MP4, CCSD(T), and CCSDT] MgHe interaction potentials have been used to study the sensitivity of the dopant location on the shape of the pair interaction. Despite the similar MgHe well depth, the pair distribution functions obtained in the diffusion Monte Carlo simulations markedly differ for the three pair potentials, therefore indicating different solubility properties for Mg in He(n). Moreover, we found interesting size effects for the behavior of the Mg impurity. As a sensitive probe of the solvation properties, the Mg excitation spectra have been simulated for various cluster sizes and compared with the available experimental results. The interaction between the excited 1P Mg atom and the He moiety has been approximated using the diatomics-in-molecules method and the two excited 1pi and 1sigma MgHe potentials. The shape of the simulated MgHe50 spectra shows a substantial dependency on the location of the Mg impurity, and hence on the MgHe pair interaction employed. To unravel the dependency of the solvation behavior on the shape of the computed potentials, exact density-functional theory has been adapted to the case of doped He(n) and various energy distributions have been computed. The results indicate the shape of the repulsive part of the MgHe potential as an important cause of the different behaviors.     

Experimental and theoretical study of the microsolvation of sodium atoms in methanol clusters: differences and similarities to sodium-water and sodium-ammonia

Methanol clusters are generated in a continuous He-seeded supersonic expansion and doped with sodium atoms in a pick-up cell. By this method, clusters of the type Na(CH(3)OH)(n) are formed and subsequently photoionized by applying a tunable dye-laser system. The microsolvation process of the Na 3s electron is studied by determining the ionization potentials (IPs) of these clusters size-selectively for n = 2-40. A decrease is found from n = 2 to 6 and a constant value of 3.19 +/- 0.07 eV for n = 6-40. The experimentally-determined ionization potentials are compared with ionization potentials derived from quantum-chemical calculations, assuming limiting vertical and adiabatic processes. In the first case, energy differences are calculated between the neutral and the ionized cationic clusters of the same geometry. In the second case, the ionized clusters are used in their optimized relaxed geometry. These energy differences and relative stabilities of isomeric clusters vary significantly with the applied quantum-chemical method (B3LYP or MP2). The comparison with the experiment for n = 2-7 reveals strong variations of the ionization potential with the cluster structure indicating that structural diversity and non-vertical pathways give significant signal contributions at the threshold. Based on these findings, a possible explanation for the remarkable difference in IP evolutions of methanol or water and ammonia is presented: for methanol and water a rather localized surface or semi-internal Na 3s electron is excited to either high Rydberg or more localized states below the vertical ionization threshold. This excitation is followed by a local structural relaxation that couples to an autoionization process. For small clusters with n < 6 for methanol and n < 4 for water the addition of solvent molecules leads to larger solvent-metal-ion interaction energies, which consequently lead to lower ionization thresholds. For n = 6 (methanol) and n = 4 (water) this effect comes to a halt, which may be connected with the completion of the first cationic solvation shell limiting the release of local relaxation energy. For Na(NH(3))(n), a largely delocalized and internal electron is excited to autoionizing electronic states, a process that is no longer local and consequently may depend on cluster size up to very large n.     

Rotational excitations of N2O in small helium clusters and the role of Bose permutation symmetry

We present a detailed study of the energetics, structures, and Bose properties of small clusters of (4)He containing a single nitrous oxide (N(2)O) molecule, from N=1 (4)He up to sizes corresponding to completion of the first solvation shell around N(2)O (N=16 (4)He). Ground state properties are calculated using the importance-sampled rigid-body diffusion Monte Carlo method, rotational excited state calculations are made with the projection operator imaginary time spectral evolution method, and Bose permutation exchange and associated superfluid properties are calculated with the finite temperature path integral method. For N< or =5 the helium atoms are seen to form an equatorial ring around the molecular axis, at N=6 helium density starts to occupy the second (local) minimum of the N(2)O-He interaction at the oxygen side of the molecule, and N=9 is the critical size at which there is onset of helium solvation all along the molecular axis. For N> or =8 six (4)He atoms are distributed in a symmetric, quasirigid ring around N(2)O. Path integral calculations show essentially complete superfluid response to rotation about the molecular axis for N> or =5, and a rise of the perpendicular superfluid response from zero to appreciable values for N> or =8. Rotational excited states are computed for three values of the total angular momentum, J=1-3, and the energy levels fitted to obtain effective spectroscopic constants that show excellent agreement with the experimentally observed N dependence of the effective rotational constant B(eff). The non-monotonic behavior of the rotational constant is seen to be due to the onset of long (4)He permutation exchanges and associated perpendicular superfluid response of the clusters for N> or =8. We provide a detailed analysis of the role of the helium solvation structure and superfluid properties in determining the effective rotational constants.     

Structure and photoabsorption properties of cationic alkali dimers solvated in neon clusters

We present a theoretical investigation of the structure and optical absorption of M(2)(+) alkali dimers (M=Li,Na,K) solvated in Ne(n) clusters for n=1 to a few tens Ne atoms. For all these alkali, the lowest-energy isomers are obtained by aggregation of the first Ne atoms at the extremity of the alkali molecule. This particular geometry, common to other M(2)(+)-rare gas clusters, is intimately related to the shape of the electronic density of the X (2)Σ(g)(+) ground state of the bare M(2)(+) molecules. The structure of the first solvation shell presents equilateral Ne(3) and capped pentagonal Ne(6) motifs, which are characteristic of pure rare gas clusters. The size and geometry of the complete solvation shell depend on the alkali and were obtained at n=22 with a D(4h) symmetry for Li and at n=27 with a D(5h) symmetry for Na. For K, our study suggests that the closure of the first solvation shell occurs well beyond n=36. We show that the atomic arrangement of these clusters has a profound influence on their optical absorption spectrum. In particular, the XΣ transition from the X (2)Σ(g)(+) ground state to the first excited (2)Σ(u)(+) state is strongly blueshifted in the Frank-Condon area.     

Geometrical and electronic structures of Au(m)Ag(n) (2 < or = m + n < or = 8)

The structural and electronic properties of Au(m)Ag(n) binary clusters (2 < or = m + n < or = 8) have been investigated by density functional theory with relativistic effective core potentials. The results indicate that Au atoms tend to occupy the surface of Au(m)Ag(n) clusters (n > or = 2 and m > or = 2). As a result, segregation of small or big bimetallic clusters can be explained according to the atomic mass. The binding energies of the most stable Au(m)Ag(n) clusters increase with increasing m+n. The vertical ionization potentials of the most stable Au(m)Ag(n) clusters show odd-even oscillations with changing m+n. The possible dissociation channels of the clusters considered are also discussed.     

Vibrational shifts of OCS in mixed clusters of parahydrogen and helium

We present a detailed theoretical study of the solvation structure and solvent induced vibrational shifts for an OCS molecule embedded in pure parahydrogen clusters and in mixed parahydrogen/helium clusters. The use of two recent OCS-(parahydrogen) and OCS-helium ab initio potential energy surfaces having explicit dependence on the asymmetric stretch of the OCS molecule allows calculation of the frequency shift of the OCS nu(3) vibration as a function of the cluster size and composition. We present results for clusters containing up to a full first solvation shell of parahydrogen (N=17 molecules), and up to M=128-N helium atoms. Due to the greater interaction strength of parahydrogen than helium with OCS, in the mixed clusters the parahydrogen molecules always displace He atoms in the first solvation shell around OCS and form multiple axial rings as in the pure parahydrogen clusters. In the pure clusters, the chemical potential of parahydrogen shows several magic numbers (N=8,11,14) that reflect an enhanced stability of axial rings containing one less molecule than required for complete filling at N=17. Only the N=14 magic number survives in the mixed clusters, as a result of different filling orders of the rings and greater delocalization of both components. The OCS vibration shows a redshift in both pure and mixed clusters, with N-dependent values that are in good agreement with the available experimental data. The dependence of the frequency shift on the cluster size and its composition is analyzed in terms of the parahydrogen and helium density distributions around the OCS molecule as a function of N and M. The frequency shift is found to be strongly dependent on the detailed distribution of the parahydrogen molecules in the pure parahydrogen clusters, and to be larger but show a smoother dependence on N in the presence of additional helium, consistent with the more delocalized nature of the mixed clusters.     

A first-principles study of the influence of helium atoms on the optical response of small silver clusters

Optical excitation spectra of Ag(n) and Ag(n)@He(60) (n = 2, 8) clusters are investigated in the framework of the time-dependent density functional theory (TDDFT) within the linear response regime. We have performed the ab initio calculations for two different exact exchange functionals (GGA-exact and LDA-exact). The computed spectra of Ag(n)@He(60) clusters with the GGA-exact functional accounting for exchange-correlation effects are found to be generally in a relatively good agreement with the experiment. A strategy is proposed to obtain the ground-state structures of the Ag(n)@He(60) clusters and in the initial process of the geometry optimization, the He environment is simulated with buckyballs. A redshift of the silver clusters spectra is observed in the He environment with respect to the ones of bare silver clusters. This observation is discussed and explained in terms of a contraction of the Ag-He bonding length and a consequent confinement of the s valence electrons in silver clusters. Likewise, the Mie-Gans predictions combined with our TDDFT calculations also show that the dielectric effect produced by the He matrix is considerably less important in explaining the redshifting observed in the optical spectra of Ag(n)@He(60) clusters.     

Infrared spectroscopy of Cu+(H2O)(n) and Ag+(H2O)(n): coordination and solvation of noble-metal ions

M(+)(H(2)O)(n) and M(+)(H(2)O)(n)Ar ions (M=Cu and Ag) are studied for exploring coordination and solvation structures of noble-metal ions. These species are produced in a laser-vaporization cluster source and probed with infrared (IR) photodissociation spectroscopy in the OH-stretch region using a triple quadrupole mass spectrometer. Density functional theory calculations are also carried out for analyzing the experimental IR spectra. Partially resolved rotational structure observed in the spectrum of Ag(+)(H(2)O)(1) x Ar indicates that the complex is quasilinear in an Ar-Ag(+)-O configuration with the H atoms symmetrically displaced off axis. The spectra of the Ar-tagged M(+)(H(2)O)(2) are consistent with twofold coordination with a linear O-M(+)-O arrangement for these ions, which is stabilized by the s-d hybridization in M(+). Hydrogen bonding between H(2)O molecules is absent in Ag(+)(H(2)O)(3) x Ar but detected in Cu(+)(H(2)O)(3) x Ar through characteristic changes in the position and intensity of the OH-stretch transitions. The third H(2)O attaches directly to Ag(+) in a tricoordinated form, while it occupies a hydrogen-bonding site in the second shell of the dicoordinated Cu(+). The preference of the tricoordination is attributable to the inefficient 5s-4d hybridization in Ag(+), in contrast to the extensive 4s-3d hybridization in Cu(+) which retains the dicoordination. This is most likely because the s-d energy gap of Ag(+) is much larger than that of Cu(+). The fourth H(2)O occupies the second shells of the tricoordinated Ag(+) and the dicoordinated Cu(+), as extensive hydrogen bonding is observed in M(+)(H(2)O)(4) x Ar. Interestingly, the Ag(+)(H(2)O)(4) x Ar ions adopt not only the tricoordinated form but also the dicoordinated forms, which are absent in Ag(+)(H(2)O)(3) x Ar but revived at n=4. Size dependent variations in the spectra of Cu(+)(H(2)O)(n) for n=5-7 provide evidence for the completion of the second shell at n=6, where the dicoordinated Cu(+)(H(2)O)(2) subunit is surrounded by four H(2)O molecules. The gas-phase coordination number of Cu(+) is 2 and the resulting linearly coordinated structure acts as the core of further solvation processes.     

Computational spectroscopy of carbon monoxide isotopomers in helium clusters

The rotational excitation spectrum, including the vibrational shift of the rotational band, of several CO isotopomers solvated in He clusters has been calculated. Reptation quantum Monte Carlo simulations are used in conjunction with an accurate He-CO potential energy surface, which quantitatively describes the rovibrational spectrum of the binary complex. Our simulations, when compared with number-selective infrared spectra taken for different isotopomers, help discriminate among the alternative assignments proposed for cluster sizes around 15 He atoms. The origin of the vibrational band has a red shift that is nearly linear with the cluster size within the first solvation shell and is almost constant up to the largest cluster studied, well beyond completion of the second solvation shell. A blue upturn at even larger sizes would be needed to attain the nanodroplet limit, as recently estimated from the isotopic dependence of the measured R(0) transitions.     

HF in clusters of molecular hydrogen. I. Size evolution of quantum solvation by parahydrogen molecules

We present a theoretical study of the quantum solvation of the HF molecule by a small number of parahydrogen molecules, having n = 1-13 solvent particles. The minimum-energy cluster structures determined for n = 1-12 have all of the H(2) molecules in the first solvent shell. The first solvent shell closes at n = 12 and its geometry is icosahedral, with the HF molecule at the center. The quantum-mechanical ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. The zero-point energy of (p-H(2))(n)HF clusters is unusually large, amounting to 86% of the potential well depth for n > 7. The radial probability distribution functions (PDFs) confirm that the first solvent shell is complete for n = 12, and that the 13th p-H(2) molecule begins to fill the second solvent shell. The p-H(2) molecules execute large-amplitude motions and are highly mobile, making the solvent cage exceptionally fluxional. The anisotropy of the solvent, very pronounced for small clusters, decreases rapidly with increasing n, so that for n approximately 8-9 the solvent environment is practically isotropic. The analysis of the pair angular PDF reveals that for a given n, the parahydrogen solvent density around the HF is modulated in a pattern which clearly reflects the lowest-energy cluster configuration. The rigidity of the solvent clusters displays an interesting size dependence, increasing from n = 6 to 9, becoming floppier for n = 10, and increasing again up to n = 12, as the solvent shell is filled. The rigidity of the solvent cage appears to reach its maximum for n = 12, the point at which the first solvent shell is closed.     

Theoretical studies for structures and energetics of Rgn-N2O (Rg=He, Ne, Ar) clusters

Minimum-energy structures of the Rg(2)-N(2)O (Rg=He, Ne, Ar) clusters have been determined with ab initio MP2 optimization, whereas the minimum-energy structures of the Rg(n)-N(2)O clusters with n = 3-7 have been obtained with the pairwise additive potentials. Interaction energies and nonadditive three-body effects of the Rg(2)-N(2)O ternary complex have been calculated using supermolecule method at MP4 and CCSD(T) levels. It was found from the calculations that there are two minima corresponding to one distorted tetrahedral structure and one planar structure for the ternary complex. The nonadditive three-body effects were found to be small for Rg(2)-N(2)O complexes. Our calculations also indicated that, for He(n)-N(2)O and Ne(n)-N(2)O clusters, the first six He and Ne atoms form the first solvation ring around the middle nitrogen of the N(2)O monomer, while for Ar(n)-N(2)O, the first five Ar atoms form the first solvation ring.     

Rotational spectrum of cyanoacetylene solvated with helium atoms

The high resolution microwave spectra of He(N)-HCCCN clusters were studied in the size ranges of 1-18 and 25-31. In the absence of an accompanying infrared study, rotational excitation energies were computed by the reptation quantum Monte Carlo method and used to facilitate the search and assignment of R(0) transitions from N > 6, as well as R(1) transitions with N > 1. The assignments in the range of 25-31 are accurate to +/-2 cluster size units, with an essentially certain relative ordering. The rotational transition frequencies decrease with N = 1-6 and then show oscillatory behavior for larger cluster sizes, which is now recognized to be a manifestation of the onset and microscopic evolution of superfluidity. For cluster sizes beyond completion of the first solvation shell the rotational frequencies increase significantly above the large-droplet limit. This behavior, common to other linear molecules whose interaction with He features a strong nearly equatorial minimum, is analyzed using path integral Monte Carlo simulations. The He density in the incipient second solvation shell is shown to open a new channel for long permutation cycles, thus increasing the decoupling of the quantum solvent from the rotation of the dopant molecule.     

Calculation of solvation free energies of charged solutes using mixed cluster/continuum models

We derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. We find that some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the standard state corrections for water molecules or water clusters present in the thermodynamic cycle. This problem can be avoided by using the same standard state for each species involved in the reaction under consideration. We analyze two different thermodynamic cycles for calculating the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water molecules as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the experimental values obtained from studies of ion-water clusters. The mean absolute errors are 0.8 kcal/mol for H(+) and 2.0 kcal/mol for Cu(2+). Conversely, calculations using the monomer cycle lead to mean absolute errors that are >10 kcal/mol for H(+) and >30 kcal/mol for Cu(2+). The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancellation of the systematic errors in the calculated free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H(+) (6 waters) and 27 kcal/mol for Cu(2+) (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu(2+) (18 waters) and 1 kcal/mol for H(+) (10 waters).     

Structure, bonding, and linear optical properties of a series of silver and gold nanorod clusters: DFT/TDDFT studies

DFT/TDDFT calculations have been carried out for a series of silver and gold nanorod clusters (Ag(n), Au(n), n = 12-120) whose structures are of cigar-type. Pentagonal Ag(n) clusters with n = 49-121 and hexagonal Au(n) clusters with n = 14-74 were also calculated for comparison. Metal-metal distances, binding energies per atom, ionization potentials, and electron affinities were determined, and their trends with cluster size were examined. The TDDFT calculated excitation energies and oscillator strengths were fit by a Lorentz line shape modification, which gives rise to the simulated absorption spectra. The significant features of the experimental spectra for actual silver and gold nanorod particles are well reproduced by the calculations on the clusters. The calculated spectral patterns are also in agreement with previous theoretical results on different-type Ag(n) clusters. Many differences in the calculated properties are found between the Ag(n) and Au(n) clusters, which can be explained by relativistic effects.     

Coordination structures of the silver ion: infrared photodissociation spectroscopy of Ag(+)(NH(3))(n) (n = 3-8)

Infrared (IR) spectra are measured for Ag(+)(NH(3))(n) with n = 3-8 in the NH-stretch region using photodissociation spectroscopy. The spectra of n = 3 and 4 exhibit absorption features only near the frequencies of the isolated NH(3), indicating that every NH(3) molecule is coordinated individually to Ag(+). For n >or= 5, the occupation of the second shell is evidenced by lower-frequency features characteristic of hydrogen bonding between NH(3) molecules. Density functional theory and MP2 calculations are carried out in support of the experiments. A detailed comparison of the experimental and theoretical IR spectra reveals the preference for a tetrahedral coordination in the n = 5 and 6 ions. Likewise, most of the features observed in the spectra of n = 7 and 8 can be assigned to isomers containing a tetrahedrally coordinated inner shell as the basic structural motif. These results signify that the ammonia-solvated Ag(+) ion has a propensity toward a coordination number of four and the resulting tetrahedral Ag(+)(NH(3))(4) complex forms the central core of further solvation process.     

Photoelectron spectroscopy of silicon doped gold and silver cluster anions

Photoelectron spectra of low temperature silicon doped gold cluster anions Au(n)Si(-) with n = 2-56 and silver cluster anions Ag(n)Si(-) with n = 5-82 have been measured. Comparing the spectra as well as the general size dependence of the electron detachment energies to the results on undoped clusters shows that the silicon atom changes the apparent free electron count in the clusters. In the case of larger gold clusters (with more than about 30 gold atoms) the silicon atom seems to consistently delocalize all of its four valence electrons, while in the case of the silver clusters a less uniform behavior is observed. Here the silicon atoms act partly as electron donors, partly as electron acceptors, without following an obvious simple principle. Additionally some structural information can be obtained from the measured spectra: while Ag(54)Si(-) seems to adopt an icosahedral structural motif, Au(54)Si(-) seems to take on a low symmetry structure, much like the corresponding pure 55 atom clusters. This indicates that for such larger clusters the incorporation of a single silicon atom does not change the ground state geometry significantly.     

Electron solvation dynamics in I-(NH3)n clusters

Femtosecond photoelectron spectroscopy (FPES) is used to monitor the dynamics associated with the excitation of the charge-transfer-to-solvent (CTTS) precursor states in I-(NH3)n = 4-15 clusters. The FPE spectra imply that the weakly bound excess electron in the excited state undergoes partial solvation via solvent rearrangement on a time scale of 0.5-2 ps, and this partially solvated state decays by electron emission on a 10-50 ps time scale. Both the extent of solvation and the lifetimes increase gradually with cluster size, in contrast to the more abrupt size-dependent effects previously observed in I-(H2O)n clusters.     

Infrared photodissociation spectroscopy of Na(NH3)n clusters: probing the solvent coordination

The first mass-selective vibrational spectra have been recorded for Na(NH3)n clusters. Infrared spectra have been obtained for n = 3-8 in the N-H stretching region. The spectroscopic work has been supported by ab initio calculations carried out at both the DFT(B3LYP) and MP2 levels, using a 6-311++G(d,p) basis set. The calculations reveal that the lowest energy isomer for n or= 7 is indicative of molecules entering a second solvation shell, i.e., the inner solvation shell around the sodium atom can accommodate a maximum of six NH3 molecules.