Path integral ground state with a fourth-order propagator: application to condensed helium

Ground state properties of condensed helium are calculated using the path integral ground state (PIGS) method. A fourth-order approximation is used as short (imaginary) time propagator. We compare our results with those obtained with other quantum Monte Carlo (QMC) techniques and different propagators. For this particular application, we find that the fourth-order propagator performs comparably to the pair product approximation, and is far superior to the primitive approximation. Results obtained for the equation of state of condensed helium show that PIGS compares favorably to other QMC methods traditionally utilized for this type of calculation.     

Excitation levels and magic numbers of small parahydrogen clusters (N<or=40)

The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of 1 molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies, the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes of N=13, 31, and 36, which is in agreement with the experiment.     

Infrared spectra of N2O-(ortho-D2)N and N2O-(HD)N clusters trapped in bulk solid parahydrogen

High-resolution infrared spectra of the clusters N2O-(ortho-D2)N and N2O-(HD)N, N=1-4, isolated in bulk solid parahydrogen at liquid helium temperatures are studied in the 2225 cm-1 region of the nu3 antisymmetric stretch of N2O. The clusters form during vapor deposition of separate gas streams of a precooled hydrogen mixture (ortho-D2para-H2 or HDpara-H2) and N2O onto a BaF2 optical substrate held at approximately 2.5 K in a sample-in-vacuum liquid helium cryostat. The cluster spectra reveal the N2O nu3 vibrational frequency shifts to higher energy as a function of N, and the shifts are larger for ortho-D2 compared to HD. These vibrational shifts result from the reduced translational zero-point energy for N2O solvated by the heavier hydrogen isotopomers. These spectra allow the N=0 peak at 2221.634 cm-1, corresponding to the nu3 vibrational frequency of N2O isolated in pure solid parahydrogen, to be assigned. The intensity of the N=0 absorption feature displays a strong temperature dependence, suggesting that significant structural changes occur in the parahydrogen solvation environment of N2O in the 1.8-4.9 K temperature range studied.     

Experimental and computational study of small (N = 1-16) stoichiometric zinc and cadmium chalcogenide clusters

Zinc selenide, cadmium sulfide, and cadmium selenide clusters were produced by direct laser ablation and analyzed in a time-of-flight mass spectrometer. The positive-ion mass spectra indicated that clusters composed of six and thirteen monomer units were ultrastable in all cases. The geometries and energies of the neutral and positively charged M(n)X(n) clusters up to n = 16 were obtained computationally at the B3LYP level of theory using the SKBJ basis set for the metal atoms and the SKBJ(d,2df) basis set for the chalcogen atoms. Small neutral and positive clusters (n = 1-4) have planar geometries, neutral three-dimensional clusters have the geometry of closed-cage polyhedra, and cationic three-dimensional clusters have structures with a pair of two-coordinated atoms. Physical properties of the clusters as a function of size are reported. The relative stability of the positive stoichiometric clusters provides a thermodynamic explanation for the relative stability observed experimentally from the laser-ablation mass spectrometry.     

Quantum Monte Carlo simulations of selected ammonia clusters (n = 2-5): isotope effects on the ground state of typical hydrogen bonded systems

Variational Monte Carlo, diffusion Monte Carlo, and stereographic projection path integral simulations are performed on eight selected species from the (NH(3))(n), (ND(3))(n), (NH(2)D)(n), and (NH(3))(n-1)(ND(3)) clusters. Each monomer is treated as a rigid body with the rotation spaces mapped by the stereographic projection coordinates. We compare the energy obtained from path integral simulations at several low temperatures with those obtained by diffusion Monte Carlo, for two dimers, and we find that at 4 K, the fully deuterated dimer energy is in excellent agreement with the ground state energy of the same. The ground state wavefunction for the (NH(3))(2-5) clusters is predominantly localized in the global minimum of the potential energy. In all simulations of mixed isotopic substitutions, we find that the heavier isotope is almost exclusively the participant in the hydrogen bond.     

Infrared spectra of seeded hydrogen clusters: (paraH2)N - OCS, (orthoH2)N - OCS, and (HD)N - OCS, N = 2 - 7

Infrared spectra of hydrogen-carbonyl sulfide clusters containing paraH2, orthoH2, or HD have been studied in the 2060 cm(-1) region of the C-O stretching vibration. The clusters were formed in pulsed supersonic jet expansions and probed using a tunable infrared diode laser spectrometer. Simple symmetric rotor type spectra were observed and assigned for clusters containing up to N = 7 hydrogen molecules. There was no resolved K structure, and Q-branch features were present for orthoH2 and HD but absent for paraH2. These characteristics can be rationalized in terms of near symmetric rotor structures, very low effective rotational temperatures (0.15 to 0.6 K), and nuclear spin statistics. The observed vibrational shifts were compared with those from recent observations on the same clusters embedded in helium nanodroplets. The observed rotational constants for the paraH2 clusters are in good agreement with a recent quantum Monte Carlo simulation. Some mixed clusters were also observed, such as HD-HD-He-OCS and paraH2 - orthoH2 - OCS.     

A theoretical study of small copper oxide clusters: Cu2Ox (x = 1 - 4)

Density functional theory (DFT) calculations are performed to study Cu2Ox (x = 1 - 4) clusters in their neutral, anionic and cationic states. The ground state structures are obtained and found to exhibit linear or near linear structures, which are different from the two- or three-dimensional ones suggested by the previous theoretical calculations. The calculated electron affinities of the clusters are in good agreement with the experimental ones. The low-lying excited states for the clusters are calculated using time-dependent DFT and used to assign the features in the photoelectron spectra. Our results compare well with the available experimental data.     

Growth and structural properties of Mg(N) (N = 10-56) clusters: density functional theory study

Using the minima hopping global geometry optimization method on density functional potential energy surface, we have studied the structural and electronic properties of magnesium clusters for a size range of Mg(N) where N = 10-56. Our exhaustive search reveals that most of our global minima are nonsymmetric in the size range above N = 20. We elucidate the evolutionary trend of the entire series and present more details about the peculiar growth of the clusters. For N > 20, it is possible to divide the cluster into two regions: the core region and the surface region. It turns out that the growth follows a peculiar cyclic pattern where the core and surface grow alternatively. The surface energy, as a function of number of atoms shows a clear signature as the number of atoms in the core increases by one. We have also carried out stability analysis and the stable sizes(magic numbers) agree very well with the experimental magic numbers reported by Diederich [J. Chem. Phys. 2011, 134, 124302]. We point out the similarities and differences between our results and sodium clusters.     

A Gaussian-3 theoretical study of small silicon-lithium clusters: electronic structures and electron affinities of SinLi(-) (n = 2-8)

The molecular structures of neutral Si n Li ( n = 2-8) species and their anions have been studied by means of the higher level of the Gaussian-3 (G3) techniques. The lowest energy structures of these clusters have been reported. The ground-state structures of neutral clusters are "attaching structures", in which the Li atom is bound to Si n clusters. The ground-state geometries of anions, however, are "substitutional structures", which is derived from Si n+1 by replacing a Si atom with a Li (-). The electron affinities of Si n Li and Si n have been presented. The theoretical electron affinities of Si n are in good agreement with the experiment data. The reliable electron affinities of Si n Li are predicted to be 1.87 eV for Si 2Li, 2.06 eV for Si 3Li, 2.01 eV for Si 4Li, 2.61 eV for Si 5Li, 2.36 eV for Si 6Li, 2.21 eV for Si 7Li, and 3.18 eV for Si 8Li. The dissociation energies of Li atom from the lowest energy structures of Si n Li and Si atom from Si n clusters have also been estimated respectively to examine relative stabilities.     

Stereographic projection path integral simulations of (HCl)n clusters (n=2-5): evidence of quantum induced melting in small hydrogen bonded networks

We investigate the quantum thermodynamic properties of small (HCl)(n) clusters using stereographic projection path integral simulations. The HCl stretches are rigid, the orientations are mapped with stereographic projection coordinates, and we make use of the reweighted random series techniques to obtain cubic convergence with respect to the number of path coefficients. Path integral simulations are converged at and above 10 K for the pentamer and above 15 K for the dimer and the trimer. None of the systems display a melting feature in the classical limit. We find an evidence of quantum induced melting between 15 and 45 K.     

Spectroscopic characterization of N(2)O aggregates: from clusters to the particulate state

Collisional cooling is used to generate N(2)O particles with radii ranging from the subnanometer to the submicrometer region. The vibrational dynamics of the aggregates is studied by Fourier transform infrared spectroscopy. In the region of the stretching fundamentals and combination bands, the infrared spectra of the particles exhibit characteristic size-dependent features. For the very small particles, the results obtained from collisional cooling are compared for the first time with corresponding results from supersonic jet expansions. It turns out that with both methods very similar clusters are generated. A pronounced temperature dependence of a combination band maximum in the collisional cooling cell spectra is found. This correlation is exploited to estimate cluster temperatures in supersonic jet spectra.     

A topological method for global optimization of clusters: application to (TiO2)n (n = 1-6)

A new topological method is presented to generate the isomer structures of compound clusters with well defined covalent bonds. This method, combined with density functional theory, has been used to perform global optimization of (TiO(2))(n) (n = 1-6) clusters. Our comprehensive search not only reproduces all of the known lowest-energy structures reported in previous works but also reveals some new low-energy structures. Some energetically unfavorable motifs that induce energy penalties are obtained and discussed. Based on the ground state structures of the anionic (TiO(2))(n). clusters, the electron affinities and photoelectron spectra are simulated and compared with available experimental data.     

Structure and electric properties of Sn(N) clusters (N = 6-20) from combined electric deflection experiments and quantum theoretical studies

Electric deflection experiments have been performed on neutral Sn(N) clusters (N = 6-20) at different nozzle temperatures in combination with a systematic search for the global minimum structures and the calculation of the dielectric properties based on density functional theory. For smaller tin clusters (N = 6-11), a good agreement between theory and experiment is found. Taking theoretically predicted moments of inertia and the body fixed dipole moment into account permits a quantitative simulation of the deflected molecular beam profiles. For larger Sn(N) clusters (N = 12-20), distinct differences between theory and experiment are observed; i.e., the predicted dipole moments from the quantum chemical calculations are significantly larger than the experimental values. The investigation of the electric susceptibilities at different nozzle temperatures indicates that this is due to the dynamical nature of the tin clusters, which increases with cluster size. As a result, even at the smallest nozzle temperature of 40 K, the dipole moments of Sn(12-20) are partially quenched. This clearly demonstrates the limits of current electric deflection experiments for structural determination and demonstrates the need for stronger cooling of the clusters in future experiments.     

An ab initio study of the formation and structure of NO+-(N2)n (n = 1 and 2) clusters

The geometries and clustering energies of the NO⁺ (N₂)_n (n = 1 and 2) clusters have been determined by ab initio calculations at different levels. At the MP4SDQ/6-31G^* level, plus zero-point vibrational corrections making use of the HF/4-31G-optimized geometries, the energy differences between clusters and their relative fragments have been calculated to be −5.3 and −4.1 kcal/mol for n = 1 and n = 2, respectively. These values can be compared to the experimental enthalpies of clustering of −4.4 and −3.9 kcal/mol. The interaction between NO⁺ and N₂ and the structures of two stable cluster ions have also been examined.     

Density-functional study of small neutral and cationic bismuth clusters Bi(n) and Bi(n) (+)(n=2-24)

Density-functional theory with scalar-relativistic pseudopotential and a generalized gradient correction is used to calculate the neutral and cationic Bi(n) clusters (2< or =n< or =24), with the aim to elucidate their structural evolution, relative stability, and magnetic property. The structures of neutral Bi clusters are found to be similar to that of other group-V elemental clusters, with the extensively studied sizes of n=4 and 8 having a tetrahedron and wedgelike structure, respectively. Generally, larger Bi clusters consist of a combination of several stable units of Bi(4), Bi(6), and Bi(8), and they have a tendency to form an amorphous structure with the increase of cluster sizes. The curves of second order energy difference exhibit strong odd-even alternations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizes are relatively stable in neutral clusters (cationic clusters). The calculated magnetic moments are 1micro (B) for odd-atom clusters and zero for even-atom clusters. We propose that the difference in magnetism between experiment and theory can be greatly improved by considering the orbital contribution. The calculated fragmentation behavior agrees well with the experiment, and for each cationic cluster the dissociation into Bi(4) or Bi(7) (+) subclusters confirms the special stability of Bi(4) and Bi(7) (+). Moreover, the bond orders and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital show that small Bi clusters would prefer semiconductor characters to metallicity.     

Global optimization study of small (10 < or = N < or = 120) Pd clusters supported on MgO(100)

Experimental evidence suggests that Pd clusters on MgO, known to be good reaction catalysts, have face centered cubic (fcc) epitaxial structures. The structure of such clusters is the result of the interplay of Pd-Pd and Pd-substrate bonds, the former inclined to favor icosahedral (Ih) and decahedral (Dh)-like structures, the latter leading to place Pd atoms on top of oxygen sites, according to an epitaxial stacking. This paper shows the results of a basin-hopping global optimization procedure applied to free and MgO-supported Pd clusters in the size range 10 < or = N < or = 120. Pd-MgO interactions are modeled by an analytical function fitted to ab initio results, while Pd-Pd interactions are modeled by a semiempirical potential. Besides the tight-binding Rosato-Guillopé-Legrand (RGL) potential, we have adopted a modified version of RGL that better reproduces the experimental surface energy of palladium, modifying the attractive part of Pd atoms potential energy. We have compared the two potential models, and as a result, the RGL potential favors clusters with epitaxial arrangements, so that cluster structures are epitaxial fcc in almost all the size ranges considered. On the contrary, the alternative potential model preserves some Ih-like characteristics typical of the free Pd clusters, and it suggests that a transition size from Ih-like to epitaxial structures can take place at about 100 atoms.     

Path integral Monte Carlo study of CO2 solvation in 4He clusters

We present a finite temperature quantum mechanical study of the dynamical and structural properties of small (4)He(N)-CO(2) clusters (N< or =17) using a path integral Monte Carlo (PIMC) method. The simulations were based on a He-CO(2) interaction potential with explicit dependence on the asymmetric stretch of the CO(2) molecule obtained at the CCSD(T) level. The shift of the CO(2) antisymmetric stretching (nu(3)) band origin and effective rotational constant were calculated as a function of the cluster size. In excellent agreement with experimental observations, the CO(2) vibrational band origin shifts and rotational constant show a turnaround near N=5, corresponding to a donut structure with the He atoms in equatorial positions of the linear dopant molecule.     

Structures and stabilities of small lead oxide clusters PbmOn (m=1-4,n=1-2m)

The structures and stabilities of small lead oxide clusters PbmOn with m=1-4, n=1-2m are systematically studied using density functional theory. It is found that the lowest-energy structures of all these clusters can be obtained by the sequential oxidation of small "core" lead clusters. For Pb-rich clusters (oxygen-to-lead ratio<1), oxygen atoms favor bridge sites for Pb2On and Pb3On and surface sites for Pb4On. The lead-monoxide-like clusters (PbO)i (i=1-4) have great stability because of their significant dissociation energies and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps. This suggests that they could be adopted as the building blocks of cluster-assembled materials. For O-rich clusters (oxygen-to-lead ratio>1), the grouping of oxygen atoms usually appears. It is found that the structures with a grouping of more than two oxygen atoms are unstable.     

Computational studies of small (AlP)N clusters

We have carried out extensive LDA calculations to investigate the structures of small (AlP)_N clusters.We find that the polarity of the Al-P bond has a significant effect on the cluster geometries and that the need to minimize electrostatic repulsion between relatively diffuse lone pair electrons on phosphorous atoms is a dominant energetic consideration in the structural arrangement.     

Solvent configuration-interaction calculations of intermolecular states in molecule-(atom)N clusters: application to Br2-4HeN

We describe variational calculations of J=0 intermolecular states in Br(2)-(4)He(N) clusters. The method employed is analogous to configuration-interaction calculations in electronic-structure work and relies on the ability to express the intermolecular Hamiltonian H(v) as a sum of one- and two-body terms. A basis set is built up from solutions to the Schr?dinger equation in which only the one-body terms of H(v) are included. These configurations are products of N=1 eigenstates. The matrix of H(v) in a symmetry-adapted configuration basis is then computed, the two-body terms of H(v) serving to couple different configurations. This computation involves integrals of dimension five or less. Filter diagonalization is then used to obtain energies and eigenfunctions within a selected energy range. Results on clusters having N=2-5 are reported.