Solvation of HF by Molecular Hydrogen: Helium Nanodroplet Vibrational Spectroscopy

Hydrogen bond types which do not fit accepted definitions

There are various interactions that either partially fit or do not fit the currently accepted definitions of the hydrogen bond. However, they possess characteristics of this interaction. It seems that it is partly connected to the fact that these definitions are not precise. The typical 3c-4e (three centres - four electrons) A-H⋯B hydrogen bond is characterized by the single-atom A and B centres that are highly electronegative. On the other hand, non-typical interactions that do not fit the hydrogen bond definitions well are characterised by uncommon proton donors and/or proton acceptors. The cases of multi-centre proton acceptors, π-electron or σ-electron systems are well known - such interactions are designated as A-H⋯π and A-H⋯σ hydrogen bonds, respectively. However, the cases of interactions with the multi-centre proton donors and proton acceptors do not fit the majority of definitions of hydrogen bond. The π⋯H+⋯π system in the proton-bound homodimer of acetylene is an example. This system can be classified as a hydrogen bond according to the two-sites hydrogen bond, 2sHB, definition. There are various types of interactions discussed in this review; among them, those that are undoubtedly unclassified as hydrogen bonds, i.e., hydride bonds, and charge inverted hydrogen bonds, CIHBs. Special emphasis is also put here on the proton sponges and other systems such as the [FHF]- anion or [NgHNg]+ cation (Ng is the noble gas centre).

Molecular Hydrogen as a Lewis Base in Hydrogen Bonds and Other Interactions

The second-order Møller–Plesset perturbation theory calculations with the aug-cc-pVTZ basis set were performed for complexes of molecular hydrogen. These complexes are connected by various types of interactions, the hydrogen bonds and halogen bonds are most often represented in the sample of species analysed; most interactions can be classified as σ-hole and π-hole bonds. Different theoretical approaches were applied to describe these interactions: Quantum Theory of ‘Atoms in Molecules’, Natural Bond Orbital method, or the decomposition of the energy of interaction. The energetic, geometrical, and topological parameters are analysed and spectroscopic properties are discussed. The stretching frequency of the H-H bond of molecular hydrogen involved in intermolecular interactions is considered as a parameter expressing the strength of interaction.

A-H…σ Hydrogen Bonds: Dihydrogen and Cycloalkanes as Proton Acceptors

ωB97XD/aug-cc-pVTZ calculations were performed for complexes of dihydrogen, cyclopropane, cyclobutane and cyclopentane, with simple proton donating species such as hydrogen fluoride, hydrogen chloride, water, hydrogen cyanide and acetylene. Numerous dependencies between geometrical, energetic and topological parameters of complexes considered were found, since various theoretical approaches were applied: Quantum Theory of 'Atoms in Molecules' (QTAIM), Natural Bond Orbital (NBO) method and energy decomposition analysis (EDA). It was confirmed that complexes of dihydrogen and cyclopropane are linked through the A-H…σ interactions that may be classified as hydrogen bonds. In the case of complexes of cyclobutane such hydrogen bonds are rather weak. Other type and also weak A-H…C hydrogen bonds are formed for complexes with cyclopentane.

Microscopic molecular superfluid response: theory and simulations

Since its discovery in 1938, superfluidity has been the subject of much investigation because it provides a unique example of a macroscopic manifestation of quantum mechanics. About 60 years later, scientists successfully observed this phenomenon in the microscopic world though the spectroscopic Andronikashvili experiment in helium nano-droplets. This reduction of scale suggests that not only helium but also para-H2 (pH2) can be a candidate for superfluidity. This expectation is based on the fact that the smaller number of neighbours and surface effects of a finite-size cluster may hinder solidification and promote a liquid-like phase. The first prediction of superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo simulations. The possible superfluidity of pH2 was later indirectly observed in a spectroscopic Andronikashvili experiment in 2000. Since then, a growing number of studies have appeared, and theoretical simulations have been playing a special role because they help guide and interpret experiments. In this review, we go over the theoretical studies of pH2 superfluid clusters since the experiment of 2000. We provide a historical perspective and introduce the basic theoretical formalism along with key experimental advances. We then present illustrative results of the theoretical studies and comment on the possible future developments in the field. We include sufficient theoretical details such that the review can serve as a guide for newcomers to the field.

Simulating Asymmetric Top Impurities in Superfluid Clusters: A para-Water Dopant in para-Hydrogen

We present the first simulation study of bosonic clusters doped with an asymmetric top molecule. The path-integral Monte Carlo method with the latest methodological advance in treating rigid-body rotation [Noya, E. G.; Vega, C.; McBride, C. J. Chem. Phys.2011, 134, 054117] is employed to study a para-water impurity in para-hydrogen clusters with up to 20 para-hydrogen molecules. The growth pattern of the doped clusters is similar in nature to that of pure clusters. The para-water molecule appears to rotate freely in the cluster. The presence of para-water substantially quenches the superfluid response of para-hydrogen with respect to the space-fixed frame.

Molecular superfluid: nonclassical rotations in doped para-hydrogen clusters

Clusters of para-hydrogen (pH₂) have been predicted to exhibit superfluid behavior, but direct observation of this phenomenon has been elusive. Combining experiments and theoretical simulations, we have determined the size evolution of the superfluid response of pH₂ clusters doped with carbon dioxide (CO₂). Reduction of the effective inertia is observed when the dopant is surrounded by the pH₂ solvent. This marks the onset of molecular superfluidity in pH₂. The fractional occupation of solvation rings around CO₂ correlates with enhanced superfluid response for certain cluster sizes.

N(2)O in small para-hydrogen clusters: Structures and energetics

We present the minimum-energy structures and energetics of clusters of the linear N(2)O molecule with small numbers of para-hydrogen molecules with pairwise additive potentials. Interaction energies of (p-H(2))-N(2)O and (p-H(2))-(p-H(2)) complexes were calculated by averaging the corresponding full-dimensional potentials over the H(2) angular coordinates. The averaged (p-H(2))-N(2)O potential has three minima corresponding to the T-shaped and the linear (p-H(2))-ONN and (p-H(2))-NNO structures. Optimization of the minimum-energy structures was performed using a Genetic Algorithm. It was found that p-H(2) molecules fill three solvation rings around the N(2)O axis, each of them containing up to five p-H(2) molecules, followed by accumulation of two p-H(2) molecules at the oxygen and nitrogen ends. The first solvation shell is completed at N = 17. The calculated chemical potential oscillates with cluster size up to the completed first solvation shell. These results are consistent with the available experimental measurements.

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.

HF in clusters of molecular hydrogen: II. Quantum solvation by H2 isotopomers, cluster rigidity, and comparison with CO-doped parahydrogen clusters

We present a comprehensive theoretical study of the quantum solvation of the HF molecule by small clusters of the H2 isotopomers, p-H2, HD, and o-D2, with up to 13 hydrogen solvent molecules. This complements our earlier work on the HF-doped parahydrogen clusters [H. Jiang and Z. Bacic, J. Chem. Phys. 122, 244306 (2005)]. The ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. Detailed information is obtained regarding the size and isotopomer dependences of the energetics, vibrationally averaged structures, and their rigidity. The rigidity of these clusters is investigated further by analyzing the distributions of their principal moments of inertia from the diffusion Monte Carlo simulations. The clusters are found to be rather rigid, especially when compared with the pure parahydrogen clusters of the same size. Extensive comparison is made with the quantum Monte Carlo results for the CO-doped parahydrogen clusters and significant differences are observed in the size evolution of certain properties, notably the chemical potential.

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.

OCS in para-hydrogen clusters: Rotational dynamics and superfluidity

We present a detailed analysis of the rotational excitations of the linear OCS molecule solvated by a variable number of para-hydrogen molecules (9 < or = N < or = 17). The effective rotational constant extracted from the fit of the rotational energy levels decreases up to N = 13, indicating near-rigid coupling between OCS rotations and para-hydrogen motion. Departure from rigidity is instead seen for larger clusters with 14 < or = N < or = 17. Path-integral Monte Carlo calculations show that the N dependence of the effective rotational constant can be explained in terms of a partial superfluid response of para-hydrogen to rotations about an axis perpendicular to the OCS axis. Complete para-hydrogen superfluid response to rotations about the OCS axis is found for N > or = 10.