Ground and excited states of the complex of CO with water: A diffusion Monte Carlo study

Molecular Oxygen Trimer: Multiplet Structures and Stability

We present a detailed theoretical study of the molecular oxygen trimer where the potential energy surfaces of the seven multiplet states have been calculated by means of a pair approximation with very accurate dimer ab initio potentials. In order to obtain all the states a matrix representation of the potential using the uncoupled spin representation has been applied. TheS = 0 ${S = 0}$ andS = 1 ${S = 1}$ states are nearly degenerate and low-lying isomers appear for most multiplicities. A crucial point in deciding the relative stabilities is the zero-point energy which represents a sizable fraction of the electronic well-depth. Therefore, we have performed accurate diffusion Monte Carlo studies of the lowest state in each multiplicity. Analysis of the wavefunction allows a deeper interpretation of the cluster structures, finding that they are significantly floppy in most cases.

Trihydrogen Cation Helium Clusters: A New Potential Energy Surface

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom,H 3 + - H e ${{H}_{3}^{+}-He}$ , in its electronic ground state. The proposed PES has been built as a sum of two contributions: a polarization energy term due to the electric field generated by the molecular cation at the position of the polarizable He atom, and an exchange-repulsion and dispersion interactions represented by a sum of "atom-bond" potentials between the three bonds ofH 3 + ${{H}_{3}^{+}}$ and the He atom. All parameters of this new PES have been chosen and fitted from data obtained from high-level ab-initio calculations. Using this new PES plus the Aziz-Slaman potential for the interaction between Helium atoms and assuming pair-wise interactions, we carry out classical Basin-Hopping (BH) global optimization, semiclassical BH with Zero Point Energy corrections, and quantum Diffusion Monte Carlo simulations. We have found the minimum energy configurations of small He clusters doped withH 3 + ${{H}_{3}^{+}}$ ,H 3 + H e N ${{H}_{3}^{+}{\left(He\right)}_{N}}$ , with N=1-16. The study of the energies of these clusters allows us to find a pronounced anomaly for N=12, in perfect agreement with previous experimental findings, which we relate to a greater relative stability of this aggregate.

Observation of Multiple Ordered Solvation Shells in Doped Helium Droplets: The Case of HeNCa2

In this Letter, we report the experimental detection of likely the largest ordered structure of helium atoms surrounding a monatomic impurity observed to date using a recently developed technique. The mass spectrometry investigation of He_NCa²⁺ clusters, formed in multiply charged helium nanodroplets, reveals magic numbers at N = 12, 32, 44, and 74. Classical optimization and path integral Monte Carlo calculations suggest the existence of up to four shells surrounding the calcium dication which are closed with well-ordered Mozartkugel-like structures: He₁₂Ca²⁺ with an icosahedron, the second at He₃₂Ca²⁺ with a dodecahedron, the third at He₄₄Ca²⁺ with a larger icosahedron, and finally for He₇₄Ca²⁺, we find that the outermost He atoms form an icosidodecahedron which contains the other inner shells. We analyze the reasons for the formation of such ordered shells in order to guide the selection of possible candidates to exhibit a similar behavior.

Isotope Effects on Ground and Excited States of Ethyl Cation, H+(C2H4)

The structure and spectra of ethyl cation, H⁺(C₂H₄), and its deuterated analogues are investigated using diffusion Monte Carlo (DMC). These calculations all show that the ground state wave function for H⁺(C₂H₄) is localized near the minimum energy configuration in which the excess proton is in a bridging configuration, although the amplitude of the vibrational motions of the bridging proton is large. Deuteration of the bridging proton reduces the amplitude of this motion, while deuteration of only the ethylenic hydrogen atoms in H⁺(C₂D₄) has little effect on the amplitude of the motion of the bridging proton. Excited states that are accessed by spectroscopically observed transitions in H⁺(C₂H₄) are calculated using fixed-node DMC. The calculated and measured frequencies for the states with one quantum of excitation in the ethylenic CH stretching vibrations show good agreement. We also explore the excited state with one quantum of excitation in the proton transfer vibration of the bridging proton and obtain a frequency of 616 cm^-1 for H⁺(C₂H₄). This frequency increases to 629 cm^-1 in H⁺(C₂D₄). Deuteration decreases this frequency to 491 and 495 cm^-1 in D⁺(C₂H₄) and D⁺(C₂D₄), respectively. The effects of partial deuteration on the frequencies of the CH stretching vibrations, and the corresponding probability amplitudes are also explored. Finally, we report the vibrationally averaged rotational constants for the four isotopologues of ethyl cation considered in this study.

Helium nanodroplets as an efficient tool to investigate hydrogen attachment to alkali cations

We report a novel method to reversibly attach and detach hydrogen molecules to positively charged sodium clusters formed inside a helium nanodroplet host matrix. It is based on the controlled production of multiply charged helium droplets which, after picking up sodium atoms and exposure to H2 vapor, lead to the formation of Nam+(H2)n clusters, whose population was accurately measured using a time-of-flight mass spectrometer. The mass spectra reveal particularly favorable Na+(H2)n and Na2+(H2)n clusters for specific "magic" numbers of attached hydrogen molecules. The energies and structures of these clusters have been investigated by means of quantum-mechanical calculations employing analytical interaction potentials based on ab initio electronic structure calculations. A good agreement is found between the experimental and the theoretical magic numbers.

Ca+ Ions Solvated in Helium Clusters

We present a combined experimental and theoretical investigation on Ca+ ions in helium droplets, HeNCa+. The clusters have been formed in the laboratory by means of electron-impact ionization of Ca-doped helium nanodroplets. Energies and structures of such complexes have been computed using various approaches such as path integral Monte Carlo, diffusion Monte Carlo and basin-hopping methods. The potential energy functions employed in these calculations consist of analytical expressions following an improved Lennard-Jones formula whose parameters are fine-tuned by exploiting ab initio estimations. Ion yields of HeNCa+ -obtained via high-resolution mass spectrometry- generally decrease with N with a more pronounced drop between N=17 and N=25, the computed quantum HeNCa+ evaporation energies resembling this behavior. The analysis of the energies and structures reveals that covering Ca+ with 17 He atoms leads to a cluster with one of the smallest energies per atom. As new atoms are added, they continue to fill the first shell at the expense of reducing its stability, until N=25, which corresponds to the maximum number of atoms in that shell. Behavior of the evaporation energies and radial densities suggests liquid-like cluster structures.

Investigation of the structure and spectroscopy of H5(+) using diffusion Monte Carlo

The results of diffusion Monte Carlo (DMC) calculations of the ground and selected excited states of H5(+) and its deuterated analogues are presented. Comparisons are made between the results obtained from two recently reported potential surfaces. Both of these surfaces are based on CCSD(T) electronic energies, but the fits display substantial differences in the energies of low-lying stationary points. Little sensitivity to these features is found in the DMC results, which yield zero-point energies based on the two surfaces that differ by between 20 and 30 cm(–1) for all twelve isotopologues of H5(+). Likewise, projections of the ground state probability amplitudes, evaluated for the two surfaces, are virtually identical. By using the ground state probability amplitudes, vibrationally averaged rotational constants and dipole moments were calculated. On the basis of these calculations, all isotopologues are shown to be near-prolate symmetric tops. Further, in cases where the ion had a nonzero dipole moment, the magnitude of the vibrationally averaged dipole moment was found to range from 0.33 to 1.15 D, which is comparable to the dipole moments of H2D+ and HD2(+). Excited states with up to three quanta in the shared proton stretch and one quantum in the in-phase stretch of the outer H2 groups were also investigated. Trends in the energies and the properties of these states are discussed.

Using fixed-node diffusion Monte Carlo to investigate the effects of rotation-vibration coupling in highly fluxional asymmetric top molecules: application to H2D+

A fixed-node diffusion Monte Carlo approach for obtaining the energies and wave functions of the rotationally excited states of asymmetric top molecules that undergo large amplitude, zero-point vibrational motions is reported. The nodal surfaces required to introduce rotational excitation into the diffusion Monte Carlo calculations are obtained from the roots of the asymmetric top rigid rotor wave functions calculated using the system's zero-point, vibrationally averaged rotational constants. Using H(2)D(+) as a model system, the overall accuracy of the methodology is tested by comparing to the results of converged variational calculations. The ability of the fixed-node diffusion Monte Carlo approach to provide insights into the nature and strength of the rotation-vibration coupling present in the rotationally excited states of highly fluxional asymmetric tops is discussed. Finally, the sensitivity of the methodology to the details of its implementation, such as the choice of embedding scheme, is explored.

Fixed node diffusion Monte Carlo using a genetic algorithm: a study of the CO-(4)He(N) complex, N = 1…10

The diffusion Monte Carlo (DMC) method is a widely used algorithm for computing both ground and excited states of many-particle systems; for states without nodes the algorithm is numerically exact. In the presence of nodes approximations must be introduced, for example, the fixed-node approximation. Recently we have developed a genetic algorithm (GA) based approach which allows the computation of nodal surfaces on-the-fly [Ramilowski and Farrelly, Phys. Chem. Chem. Phys., 2010, 12, 12450]. Here GA-DMC is applied to the computation of rovibrational states of CO-(4)He(N) complexes with N≤ 10. These complexes have been the subject of recent high resolution microwave and millimeter-wave studies which traced the onset of microscopic superfluidity in a doped (4)He droplet, one atom at a time, up to N = 10 [Surin et al., Phys. Rev. Lett., 2008, 101, 233401; Raston et al., Phys. Chem. Chem. Phys., 2010, 12, 8260]. The frequencies of the a-type (microwave) series, which correlate with end-over-end rotation in the CO-(4)He dimer, decrease from N = 1 to 3 and then smoothly increase. This signifies the transition from a molecular complex to a quantum solvated system. The frequencies of the b-type (millimeter-wave) series, which evolves from free rotation of the rigid CO molecule, initially increase from N = 0 to N∼ 6 before starting to decrease with increasing N. An interesting feature of the b-type series, originally observed in the high resolution infra-red (IR) experiments of Tang and McKellar [J. Chem. Phys., 2003, 119, 754] is that, for N = 7, two lines are observed. The GA-DMC algorithm is found to be in good agreement with experimental results and possibly detects the small (∼0.7 cm(-1)) splitting in the b-series line at N = 7. Advantages and disadvantages of GA-DMC are discussed.

Stereographic projection diffusion monte carlo (SPDMC) algorithms for molecular condensed matter

We develop and test three algorithms for diffusion Monte Carlo simulations in non-Euclidean manifolds. The methods are based on the construction of the "velocity" distribution by rejection techniques and are capable of functioning in a broad class of non-Euclidean spaces generated by holonomic constraints. The formulation of the propagator for non-Euclidean manifolds avoids the use of Lagrange multipliers; it is derived instead from the Feynman quantization in manifolds proposed by DeWitt. The manifolds are mapped onto Rd by using stereographic projection coordinates. Numerical tests are conducted for the particle in a ring of unit radius subjected to a sinusoidal potential, for the electron in the field of an infinitely massive proton, and for a water molecule modeled as an asymmetric top subjected to an external field.

Quantum studies of the vibrations in H3O2− and D3O2−

The vibrations of H3O2- and D3O2- are investigated using diffusion Monte Carlo (DMC) and vibrational configuration-interaction approaches, as implemented in the program MULTIMODE. These studies use the potential surface recently developed by Huang et al. [ J. Am. Chem. Soc. 126, 5042 (2004)]. The focus of this work is on the vibrational ground state and fundamentals which occur between 100 and 3700 cm(-1). In most cases, excellent agreement is obtained between the fundamental frequencies calculated by the two approaches. This serves to demonstrate the power of both methods for treating this very anharmonic system. Based on the results of the MULTIMODE and DMC treatments, the extent and nature of the couplings in H3O2- and D3O2- are investigated.

Full-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surface

We report quantum diffusion Monte Carlo (DMC) and variational calculations in full dimensionality for selected vibrational states of H(5)O(2) (+) using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calculations. OH-stretch fundamentals are also calculated using "fixed-node" DMC calculations and variationally using two versions of the code MULTIMODE. These results are compared with infrared multiphoton dissociation measurements of Yeh et al. [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)]. Some preliminary results for the energies of several modes of the shared hydrogen are also reported.

Quantum and classical studies of vibrational motion of CH5+ on a global potential energy surface obtained from a novel ab initio direct dynamics approach

We report a full dimensional, ab initio based potential energy surface for CH(5) (+). The ab initio electronic energies and gradients are obtained in direct-dynamics calculations using second-order Møller-Plesset perturbation theory with the correlation consistent polarized valence triple zeta basis. The potential energy and the dipole moment surfaces are fit using novel procedures that ensure the full permutational symmetry of the system. The fitted potential energy surface is tested by comparing it against additional electronic energy calculations and by comparing normal mode frequencies at the three lowest-lying stationary points obtained from the fit against ab initio ones. Well-converged diffusion Monte Carlo zero-point energies, rotational constants, and projections along the CH and HH bond lengths and the tunneling coordinates are presented and compared with the corresponding harmonic oscillator and standard classical molecular dynamics ones. The delocalization of the wave function is analyzed through comparison of the CH(5) (+) distributions with those obtained when all of the hydrogen atoms are replaced by (2)H and (3)H. The classical dipole correlation function is examined as a function of the total energy. This provides a further probe of the delocalization of CH(5) (+).