Ab initio calculation of temperature effects in the optical response of open-shell sodium clusters

Many properties of atomic clusters have been found to be size dependent, e.g., the optical response. There are, however, factors other than size that can also play an important role in determining the properties of nanoscale systems. Temperature, in particular, has been shown to have a strong effect on the optical response of open-shell sodium clusters. We incorporate the temperature effect on the optical absorption spectra by combining pseudopotentials, Langevin molecular dynamics, and time-dependent density functional theory. We have done calculations for several open-shell sodium clusters, Na(4) (+), Na(7) (+), and Na(11) (+), for which experimental data are available for comparison. We find that the positions of the lower energy peaks of the calculated spectra correspond very well to the peaks in the experimental spectra, although the local density approximation tends to overestimate the gap of the smaller clusters by up to 0.2 eV and underestimate the gap of the largest cluster by 0.4 eV. We fit the width of the peaks in the lower-temperature calculations to the corresponding experimental result to obtain the instrumental linewidth. We then use this same width for the high-temperature calculations and find very good agreement with experiment. Finally, we analyze the transitions that contribute to the observed peaks in the absorption spectra and we plot the effective valence charge density for specific transitions for each cluster. We find that for the two smaller clusters the absorption spectra are dominated by transitions from the occupied levels to a few (three for Na(4) (+) and five for Na(7) (+)) empty levels, although the contribution from transitions to other empty levels can still be significant. In contrast, the absorption spectra for Na(11) (+) come from a greater mixture of transitions as evidenced in the analysis as well as in the plot of the effective valence charge density.     

Computational studies of nonstoichiometric sodium auride clusters

The molecular structures of low-lying isomers of anionic and neutral sodium auride clusters have been studied computationally at the second-order M?ller-Plesset perturbation theory level using quadruple-ζ basis sets augmented with a double set of polarization functions. The first vertical detachment energies were calculated at the M?ller-Plesset level as the energy difference between the cluster anion and the corresponding neutral cluster. The photodetachment energies of higher-lying ionization channels were calculated by adding electronic excitation energies of the neutral clusters to the first vertical detachment energy. The excitation energies were calculated at the linear response approximate coupled-cluster singles and doubles level using the anionic cluster structures. The obtained ionization energies for NaAu(-), NaAu(2)(-), NaAu(3)(-), NaAu(4)(-), Na(2)Au(2)(-), Na(2)Au(3)(-), Na(3)Au(3)(-), and Na(2)Au(4)(-) were compared to values deduced from experimental photoelectron spectra. Comparison of the calculated photoelectron spectra for a few energetically low-lying isomers shows that the energetically lowest cluster structures obtained in the calculations do not always correspond to the clusters produced experimentally. Spin-component-scaled second-order M?ller-Plesset perturbation theory calculations shift the order of the isomers such that the observed clusters more often correspond to the energetically lowest structure, whereas the spin-component-scaled approach does not improve the photodetachment energies of the sodium aurides. The potential energy surface of the sodium aurides is very soft, with several low-lying isomers requiring an accurate electron correlation treatment. The calculations show that merely the energetic criterion is not a reliable means to identify the structures of the observed sodium auride clusters; other experimental information is needed to ensure a correct assignment of the cluster structures. The cluster structures of nonstoichiometric anionic sodium aurides have been determined by comparing calculated ionization energies for low-lying structures of the anionic clusters with experimental data.     

Infrared multiple photon dissociation spectroscopy of cationized histidine: effects of metal cation size on gas-phase conformation

The gas phase structures of cationized histidine (His), including complexes with Li(+), Na(+), K(+), Rb(+), and Cs(+), are examined by infrared multiple photon dissociation (IRMPD) action spectroscopy utilizing light generated by a free electron laser, in conjunction with quantum chemical calculations. To identify the structures present in the experimental studies, measured IRMPD spectra are compared to spectra calculated at B3LYP/6-311+G(d,p) (Li(+), Na(+), and K(+) complexes) and B3LYP/HW*/6-311+G(d,p) (Rb(+) and Cs(+) complexes) levels of theory, where HW* indicates that the Hay-Wadt effective core potential with additional polarization functions was used on the metals. Single point energy calculations were carried out at the B3LYP, B3P86, and MP2(full) levels using the 6-311+G(2d,2p) basis set. On the basis of these experiments and calculations, the only conformation that reproduces the IRMPD action spectra for the complexes of the smaller alkali metal cations, Li(+)(His) and Na(+)(His), is a charge-solvated, tridentate structure where the metal cation binds to the backbone carbonyl oxygen, backbone amino nitrogen, and nitrogen atom of the imidazole side chain, [CO,N(α),N(1)], in agreement with the predicted ground states of these complexes. Spectra of the larger alkali metal cation complexes, K(+)(His), Rb(+)(His), and Cs(+)(His), have very similar spectral features that are considerably more complex than the IRMPD spectra of Li(+)(His) and Na(+)(His). For these complexes, the bidentate [CO,N(1)] conformer in which the metal cation binds to the backbone carbonyl oxygen and nitrogen atom of the imidazole side chain is a dominant contributor, although features associated with the tridentate [CO,N(α),N(1)] conformer remain, and those for the [COOH] conformer are also clearly present. Theoretical results for Rb(+)(His) and Cs(+)(His) indicate that both [CO,N(1)] and [COOH] conformers are low-energy structures, with different levels of theory predicting different ground conformers.     

Anharmonicity of weakly bound M(+)-H2 complexes

The anharmonicity of weakly bound complexes is studied using the vibrational self-consistent field (VSCF) approach for a series of metal cation dihydrogen (M(+)-H(2)) complexes. The H-H stretching frequency shifts of M(+)-H(2) (M(+) = Li(+), Na(+), B(+), and Al(+)) complexes are calculated with the coupled-cluster method including all single and double excitations with perturbative triples (CCSD(T)) level of theory with the cc-pVTZ basis set. The calculated H-H stretching frequency of Li(+)-H(2), B(+)-H(2), Na(+)-H(2), and Al(+)-H(2) is red-shifted by 121, 202, 74, and 62 cm(-1), respectively, relative to that of unbound H(2). The calculated red shifts and their trends are in good agreement with the available experimental and previously calculated data. Insight into the observed trends is provided by symmetry adapted perturbation theory (SAPT).     

Electrospray ionization tandem mass spectrometric study of salt cluster ions. Part 1--investigations of alkali metal chloride and sodium salt cluster ions

Salt cluster ions of alkali metal chlorides ACl (A = Li(+), Na(+), K(+), Rb(+) and Cs(+)) and sodium salts NaB (B = I(-), HCOO(-), CH(3)COO(-), NO(2)(-), and NO(3)(-)), formed by electrospray ionization, were studied systematically by mass spectrometry. The influences on the total positive ion and negative ion currents of variation of solvent, solution concentration, desolvation temperature, solution flow-rate, capillary voltage and cone voltage were investigated. Only cone voltage was found to influence dramatically the distribution of salt cluster ions in the mass spectra observed. Under conditions of normal cone voltage of approximately 70 V, cluster ions having magic numbers of molecules are detected with high relative signal intensity. Under conditions of low cone voltage of approximately 10 V, the distribution of cluster ions detected is characterized by a relatively low average mass/charge ratio due to the presence of multiply charged cluster ions; in addition, there is a marked reduction in cluster ions having a magic number of molecules. Product ion mass spectra obtained by tandem mass spectrometry of cluster ions are characterized by a base peak having a magic number of molecules that is less than and closest to the number of molecules in the precursor ion. Structures have been proposed for some dications and some quadruply charged ions. At pH 3 and 11, the mass spectra of NaCl clusters show the presence of mixed clusters of NaCl with HCl and NaOH, respectively. The effects of ionic radius on 20 distributions of cluster ions for 10 salts were investigated; however, the fine structure of these effects is not readily discerned.     

Cations-modified cluster model for density-functional theory simulation of potential dependent Raman scattering from surface complex/electrode systems

Aiming to solve the problem of simulation of the potential dependent surface Raman spectra of anion containing surface complexes on electrodes, we developed a new simulation model by adding different cations (Li(+), Na(+), K(+), Rb(+) or Cs(+)) attached to the bottom layer of a large metallic cluster while the surface complex sits on the top layer.     

Energetics of the Preyssler anion's molecular orbitals: quantifying the effect of the encapsulated-cation's charge

The ground state electronic properties of metal-exchanged Preyssler heteropolyoxoanions [M(n+)P(5)W(30)O(110)](n-15), in which the encapsulated M(n+) ions are the spherical, diamagnetic ions Na(+), Ca(2+), Sr(2+), Y(3+), La(3+) and Th(4+), are studied using a combination of electrochemical, optical, and NMR experiments. We have designed experiments that focus on the influence of the charge (n) of the encapsulated cations, which themselves have no redox response, and its effect upon the W-O framework MOs. As n increases, the cluster anions accept electrons into their LUMOs with increasing ease, and their lowest-energy LMCT bands reveal a corresponding blue shift, which is indicative of an increase of the LUMO-HOMO energy splitting with increasing n. (183)W NMR spectra are used to identify the atomic origin of the LUMO states, which are shown to be composed primarily of orbitals from the ring of 5 W atoms near M(n+). The cation charge correlates directly and linearly with the half-wave potentials of the first redox couples, the LMCT band energies, and the W chemical shifts. We have combined this suite of experimental results to construct an energy level diagram of the frontier MOs for the Preyssler cluster anions. In so doing, we provide a fundamental perspective that is not otherwise available on the cation's role with specific regard to the electronic behavior of the W-O orbitals. These results are expected to provide benchmarking information as theorists begin to study these large POM systems.     

Isomer population analysis of gaseous ions from infrared multiple photon dissociation kinetics

Infrared multiple photon dissociation (IRMPD) kinetics measured with tunable laser radiation from a free electron laser (FEL) are used to probe the relative populations of and interconversions between energetically competitive isomers of gas-phase ions at 298 K. On-resonance IRMPD kinetics of monoisomeric benzoate anion and anilinium (protonated aniline) are measured to determine the extent of overlap of the laser beam with the precursor ion population (～93%). IRMPD kinetics indicating different photodissociation behavior for different isomers obtained at isomer-specific resonances are used to determine relative populations of salt bridge and charge-solvated isomers for ArgGly·Na(+), Ser·Cs(+), and Arg·Na(+). These values and Gibbs free energy differences obtained from them for thermal precursor populations are compared to values reported using other, less direct population probes. Rapid interconversion of two charge-solvated isomers occurs for ArgGly·Li(+), precluding population analysis for this ion. ArgGly·Na(+), ArgGly·Li(+), and Arg·Na(+) exhibit IRMPD induction periods lasting many seconds for some isomers at the laser photon energies and power used, indicating that IRMPD relative spectral intensities are time-dependent for these ions and that the relative band intensities in IRMPD spectra measured with short irradiation times may not provide meaningful information about relative isomer populations. These results constitute the first direct probe of ion isomer populations using IRMPD kinetics obtained with a FEL and illustrate a number of caveats in interpreting IRMPD spectra measured with just a single irradiation time. These results also indicate that more complete overlap of the laser beam with the ions will be highly advantageous in future instrument designs for IRMPD kinetics and spectroscopy experiments.     

On the dissolution processes of Na2I+ and Na3I2+ with the association of water molecules: mechanistic and energetic details

The sequential association energies for one through six water molecules clustering to Na(2)I(+), as well as one and two water molecules clustering to Na(3)I(2)(+), are measured. The association energies show a pairwise behavior, indicating a symmetric association of water molecules to the linear Na(2)I(+) and Na(3)I(2)(+) ions. This pairwise behavior is well reproduced by Density Functional Theory (DFT) calculations. DFT calculations also suggest that a significant separation of charge for the Na-I ion pair occurs when four or more water molecules cluster to a single sodium center. Two different solvent-separated ion pairs have been identified with the DFT calculations. Experiments also show that the dissolution processes, loss of a neutral NaI unit, occurs when six or more water molecules have been added to Na(2)I(+) cluster. However, one or two water molecules are able to detach an NaI unit from the Na(3)I(2)(+) cluster. The difference in solubility of the Na(2)I(+) and Na(3)I(2)(+) ions is due to the difference in the energies required to lose an NaI unit from these two species. The experiment also confirms that the loss of a neutral NaI unit, instead of an Na(+) ion, occurs during the dissolution processes of Na(3)I(2)(+). The microsolvation schemes proposed to explain our experimental observations are supported by DFT and phase space theory (PST) calculations.     

UV and IR spectroscopic studies of cold alkali metal ion-crown ether complexes in the gas phase

We report UV photodissociation (UVPD) and IR-UV double-resonance spectra of dibenzo-18-crown-6 (DB18C6) complexes with alkali metal ions (Li(+), Na(+), K(+), Rb(+), and Cs(+)) in a cold, 22-pole ion trap. All the complexes show a number of vibronically resolved UV bands in the 36,000-38,000 cm(-1) region. The Li(+) and Na(+) complexes each exhibit two stable conformations in the cold ion trap (as verified by IR-UV double resonance), whereas the K(+), Rb(+), and Cs(+) complexes exist in a single conformation. We analyze the structure of the conformers with the aid of density functional theory (DFT) calculations. In the Li(+) and Na(+) complexes, DB18C6 distorts the ether ring to fit the cavity size to the small diameter of Li(+) and Na(+). In the complexes with K(+), Rb(+), and Cs(+), DB18C6 adopts a boat-type (C(2v)) open conformation. The K(+) ion is captured in the cavity of the open conformer thanks to the optimum matching between the cavity size and the ion diameter. The Rb(+) and Cs(+) ions sit on top of the ether ring because they are too large to enter the cavity of the open conformer. According to time-dependent DFT calculations, complexes that are highly distorted to hold metal ions open the ether ring upon S(1)-S(0) excitation, and this is confirmed by extensive low-frequency progressions in the UVPD spectra.     

Copper doping of small gold cluster cations: influence on geometric and electronic structure

The effect of Cu doping on the properties of small gold cluster cations is investigated in a joint experimental and theoretical study. Temperature-dependent Ar tagging of the clusters serves as a structural probe and indicates no significant alteration of the geometry of Au(n) (+) (n = 1-16) upon Cu doping. Experimental cluster-argon bond dissociation energies are derived as a function of cluster size from equilibrium mass spectra and are in the 0.10-0.25 eV range. Near-UV and visible light photodissociation spectroscopy is employed in conjunction with time-dependent density functional theory calculations to study the electronic absorption spectra of Au(4-m)Cu(m) (+) (m = 0, 1, 2) and their Ar complexes in the 2.00-3.30 eV range and to assign their fragmentation pathways. The tetramers Au(4) (+), Au(4) (+)[middle dot]Ar, Au(3)Cu(+), and Au(3)Cu(+)[middle dot]Ar exhibit distinct optical absorption features revealing a pronounced shift of electronic excitations to larger photon energies upon substitution of Au by Cu atoms. The calculated electronic excitation spectra and an analysis of the character of the optical transitions provide detailed insight into the composition-dependent evolution of the electronic structure of the clusters.     

Ions in solutions: Determining their polarizabilities from first-principles

Dipole polarizabilities of a series of ions in aqueous solutions are computed from first-principles. The procedure is based on the study of the linear response of the maximally localized Wannier functions to an applied external field, within density functional theory. For most monoatomic cations (Li(+), Na(+), K(+), Rb(+), Mg(2+), Ca(2+) and Sr(2+)) the computed polarizabilities are the same as in the gas phase. For Cs(+) and a series of anions (F(-), Cl(-), Br(-) and I(-)), environmental effects are observed, which reduce the polarizabilities in aqueous solutions with respect to their gas phase values. The polarizabilities of H((aq)) (+), OH((aq)) (-) have also been determined along an ab initio molecular dynamics simulation. We observe that the polarizability of a molecule instantaneously switches upon proton transfer events. Finally, we also computed the polarizability tensor in the case of a strongly anisotropic molecular ion, UO(2) (2+). The results of these calculations will be useful in building interaction potentials that include polarization effects.     

Potentials of mean force between ionizable amino acid side chains in water

Potentials of mean force (PMF) between all possible ionizable amino acid side chain pairs in various protonation states were calculated using explicit solvent molecular dynamics simulations with umbrella sampling and the weighted histogram analysis method. The side chains were constrained in various orientations inside a spherical cluster of 200 water molecules. Beglov and Roux's Spherical Solvent Boundary Potential was used to account for the solvent outside this sphere. This approach was first validated by calculating PMFs between monatomic ions (K(+), Na(+), Cl(-)) and comparing them to results from the literature and results obtained using Ewald summation. The strongest interaction (-4.5 kcal/mol) was found for the coaxial Arg(+).Glu(-) pair. Many like-charged side chains display a remarkable lack of repulsion, and occasionally a weak attraction. The PMFs are compared to effective energy curves obtained with common implicit solvation models, namely Generalized Born (GB), EEF1, and uniform dielectric of 80. Overall, the EEF1 curves are too attractive, whereas the GB curves in most cases match the minima of the PMF curves quite well. The uniform dielectric model, despite some fortuitous successes, is grossly inadequate.     

UV and IR spectroscopy of cold 1,2-dimethoxybenzene complexes with alkali metal ions

We report UV photodissociation (UVPD) and IR-UV double-resonance spectra of 1,2-dimethoxybenzene (DMB) complexes with alkali metal ions, M(+)·DMB (M = Li, Na, K, Rb, and Cs), in a cold, 22-pole ion trap. The UVPD spectrum of the Li(+) complex shows a strong origin band. For the K(+)·DMB, Rb(+)·DMB, and Cs(+)·DMB complexes, the origin band is very weak and low-frequency progressions are much more extensive than that of the Li(+) ion. In the case of the Na(+)·DMB complex, spectral features are similar to those of the K(+), Rb(+), and Cs(+) complexes, but vibronic bands are not resolved. Geometry optimization with density functional theory indicates that the metal ions are bonded to the oxygen atoms in all the M(+)·DMB complexes. For the Li(+) complex in the S(0) state, the Li(+) ion is located in the same plane as the benzene ring, while the Na(+), K(+), Rb(+), and Cs(+) ions are located off the plane. In the S(1) state, the Li(+) complex has a structure similar to that in the S(0) state, providing the strong origin band in the UV spectrum. In contrast, the other complexes show a large structural change in the out-of-plane direction upon S(1)-S(0) excitation, which results in the extensive low-frequency progressions in the UVPD spectra. For the Na(+)·DMB complex, fast charge transfer occurs from Na(+) to DMB after the UV excitation, making the bandwidth of the UVPD spectrum much broader than that of the other complexes and producing the photofragment DMB(+) ion.     

Two-step melting of Na(41)(+)

The heat capacity of the mass selected Na(41) (+) cluster has been measured using a differential nanocalorimetry method. A two-peak structure appears in the heat capacity curve of Na(41) (+), whereas Schmidt and co-workers [M. Schmidt, J. Donges, Th. Hippler, and H. Haberland, Phys. Rev. Lett. 90, 103401 (2003)] observed, within their experimental accuracy, a smooth caloric curve. They concluded from the absence of any structure that there is a second order melting transition in Na(41) (+) with no particular feature such as premelting. The observed difference with the latter results is attributed to the better accuracy of our method owing to its differential character. The two structures in the heat capacity are ascribed to melting and premelting of Na(41) (+). The peak at lower temperature is likely due to an anti-Mackay to Mackay solid-solid transition.     

Calculations of nonlinear response properties using the intermediate state representation and the algebraic-diagrammatic construction polarization propagator approach: two-photon absorption spectra

An earlier proposed approach to molecular response functions based on the intermediate state representation (ISR) of polarization propagator and algebraic-diagrammatic construction (ADC) approximations is for the first time employed for calculations of nonlinear response properties. The two-photon absorption (TPA) spectra are considered. The hierarchy of the first- and second-order ADC∕ISR computational schemes, ADC(1), ADC(2), ADC(2)-x, and ADC(3/2), is tested in applications to H(2)O, HF, and C(2)H(4) (ethylene). The calculated TPA spectra are compared with the results of coupled cluster (CC) models and time-dependent density-functional theory (TDDFT) calculations, using the results of the CC3 model as benchmarks. As a more realistic example, the TPA spectrum of C(8)H(10) (octatetraene) is calculated using the ADC(2)-x and ADC(2) methods. The results are compared with the results of TDDFT method and earlier calculations, as well as to the available experimental data. A prominent feature of octatetraene and other polyene molecules is the existence of low-lying excited states with increased double excitation character. We demonstrate that the two-photon absorption involving such states can be adequately studied using the ADC(2)-x scheme, explicitly accounting for interaction of doubly excited configurations. Observed peaks in the experimental TPA spectrum of octatetraene are assigned based on our calculations.     

Many-body potentials for aqueous Li(+), Na(+), Mg(2+), and Al(3+): comparison of effective three-body potentials and polarizable models

Many-body potentials for the aqueous Li(+), Na(+), Mg(2+), and Al(3+) ions have been constructed from ab initio cluster calculations. Pure pair, effective pair, effective three-body, and effective polarizable models were created and used in subsequent molecular dynamics simulations. The structures of the first and second solvation shells were studied using radial distribution functions and angular-radial distribution functions. The effective three-body and polarizable potentials yield similar first-shell structures, while the contraction of the O-O distances between the first and second solvation shells is more pronounced with the polarizable potentials. The definition of the tilt angle of the water molecules around the ions is discussed. When a proper definition is used, it is found that for Li(+), Mg(2+), and Al(3+) the water molecules prefer a trigonal orientation, but for Na(+) a tetrahedral orientation (ion in lone-pair direction) is preferred. The self-diffusion coefficients for the water molecules and the ions were calculated; the ionic values follow the order obtained from experiment, although the simulated absolute values are smaller than experiment for Mg(2+) and Al(3+).     

Structural and electric field effects of ions in aqueous nanodrops

Ensemble infrared photodissociation (IRPD) spectra in the hydrogen stretch region (～2950-3800 cm(-1)) are reported for M(H(2)O)(35-37), with M = I(-), Cl(-), HCO(3)(-), OH(-), tetrabutyl-, tetrapropyl-, and tetramethylammonium, Cs(+), Na(+), Li(+), H(+), Ba(2+), Ca(2+), Co(2+), Mg(2+), La(3+), and Tm(3+), at 133 K. A single, broad feature is observed in the bonded-OH region of the spectra that indicates that the water network in these clusters is bulk-like and likely resembles liquid water more strongly than ice. The free-OH region for all of these clusters is dominated by peaks corresponding to water molecules that accept two and donate one hydrogen bond (AAD water molecules), indicating that AAD water molecules are more abundant at the surface of these ions than AD water molecules. A-only water molecules are present in significant abundance only for the trivalent metal cations. The frequency of the AAD free-OH stretch band shifts nearly linearly with the charge state of the ion, consistent with a Stark shift attributable to the ion's electric field. From these data, a frequency range of 3704.9-3709.7 cm(-1) is extrapolated for the free-OH of AAD water molecules at the (uncharged) bulk liquid water surface, consistent with sum-frequency generation spectroscopy experiments. Differences in both the bonded- and the free-OH regions of the spectra for these ions are attributable to ion-induced patterning of the water network that extends to the surface of the clusters, which includes water molecules in the third and fourth solvation shells; that is, these ions pattern water molecules at long distance to various extents. These spectra are simulated using two different electrostatic models previously used to calculate OH-stretch spectra of bulk water and aqueous solutions and parametrized for bonded-OH frequencies. These models qualitatively reproduce a number of features in the experimental spectra, although it is evident that more sophisticated treatment of water molecule and ion polarizability and vibrational coupling is necessary for more quantitative comparisons.     

Photoabsorption in sodium clusters on the basis of time-dependent density-functional theory

The photoabsorption spectra of a continuous series of Na(n) clusters (n相似文献