Chemical Solutions in a Quantum Solvent: Anionic Electrolytes in 4He Nanodroplets

Variational and diffusion Monte Carlo (VMC and DMC) calculations are presented for anionic electrolytes solvated in ⁴He. The electrolytes have the general structure X^?(He)_N, with X=F, Cl, Br and I, and N varying up to 40 (41 for I^?). The overall interaction potential is obtained from accurate ab initio data for the two‐body components and then using the sum‐of‐potentials approximation. Our computational scheme is a robust procedure, giving us accurate trial wavefunctions that can be used to perform high‐quality DMC calculations. The results indicate very marked delocalization and permanence of the liquid‐like quantum features of the solvent adatoms surrounding the anionic impurities. This finding stands in contrast to the more structured, solid‐like behavior of the quantum solutions with alkali metal cations embedded in He nanodroplets. While other negatively charged species such as H^? have shown an overall repulsive interaction with He, the present calculations clearly indicate that the halogen anions remain solvated within liquid‐like solvent “bubbles” of species‐dependent size.     

Quantum solvation dynamics of HCN in a helium-4 droplet

Ultracold nanodroplets of helium-4, containing several thousands of He atoms, offer considerable promise as microscopic cryogenic chambers. Potential applications include the creation of tailor-made chemical or biomolecular complexes and studies of superfluidity in nanoscale systems. Recent experiments have succeeded in interrogating droplets of quantum solvent which consist of as few as 1-20 helium-4 atoms and which contain a single solute molecule. This allows the transition from a floppy, but essentially molecular, complex to a dissolved molecule to be followed and, surprisingly, the transition is found to occur quite rapidly, in some cases for as few as N = 7-20 solvent atoms. For example, in experiments on helium-4 droplets seeded with CO molecules [Tang and McKellar, J. Chem. Phys. 119, 754 (2003)], two series of transitions are observed which correlate with the a-type (Delta K = 0) and b-type (Delta K = +/-1) lines of the binary complex, CO-He (K is the quantum number associated with the projection of the total angular momentum onto the vector connecting the atom and the molecular center of mass). The a-type series, which evolves from the end-over-end rotational motion of the CO-He binary complex, saturates to the nanodroplet limit for as few as 10-15 helium-4 atoms, i.e., the effective moment of inertia of the molecule converges to its asymptotic (solvated) value quite rapidly. In contrast, the b-type series, which evolves from the free-molecule rotational mode, disappears altogether for N approximately 7 atoms. Similar behavior is observed in recent computational studies of HCN(4He)N droplets [Paolini et al., J. Chem. Phys. 123, 114306 (2005)]. In this article the quantum solvation of HCN in small helium-4 droplets is studied using a new fixed-node diffusion Monte Carlo (DMC) procedure. In this approach a Born-Oppenheimer-type separation of radial and angular motions is introduced as a means of computing nodal surfaces of the many-body wave functions which are required in the fixed-node DMC method. Excited rotational energies are calculated for HCN(4He)N droplets with N = 1-20: the adiabatic node approach also allows concrete physical mechanisms to be proposed for the predicted disappearance of the b-type series as well as the rapid convergence of the a-type series to the nanodroplet limit with increasing N. The behavior of the a-type series is traced directly to the mechanics of angular momentum coupling-and decoupling-between identical bosons and the molecular rotor. For very small values of N there exists significant angular momentum coupling between the molecule and the helium atoms: at N approximately 10 solvation appears to be complete as evidenced by significant decoupling of the molecule and solvent angular momenta. The vanishing of the b-type series is predicted to be a result of increasing He-He repulsion as the number of solvent atoms increases.     

Ab initio quantum dynamics with very weak van der Waals interactions: Structure and stability of small Li2(1Sigmag+)-(He)n clusters

The potential energy surface (PES) for the interaction between Li2(1Sigmag+) and 4He has been computed using an accurate, post-Hartree-Fock quantum calculation for its ground electronic state. The orientational anisotropy of the forces and the interplay between repulsive and attractive effects within the PES are analyzed to extract information on the possible existence of bound states in the triatomic system. The structures of a few of the Li2(He)n small clusters are examined by comparing a classical approach with a full quantum one to generate bound configurations and to extract information on the possible spatial arrangements of the smaller clusters via à vis the location of the Li2 dopant. Some significant consequences on the Li2 behavior in larger clusters and droplets are drawn from the above findings.     

The shell structure of3He droplets

Liquid³He droplets and their shell structure are investigated in the framework of mean-field calculations using a recently developed effective energy functional which employs realistic finite range interactions throughout. The samples range fromN=20 up toN=1360. The shell closures found agree with the harmonic oscillator scheme up toN=168. Above that, magic droplets appear atN=198, 274, 300, 368, 398, 482, 516... The first and second differences of the free energy are computed as signals for the shell structure in future experiments. Shell closures are found to be still visible in these signals at comparatively high temperatures. The finite range character of the effective interaction generates oscillations in the density profile which are suppressed in comparable calculations with zero range interactions.     

NMR shielding in helium-3 atoms modified by gaseous nitrogen and oxygen

Helium-3 nuclear magnetic resonance (³He NMR) measurements were carried out for the gaseous mixtures of helium-3 with pure nitrogen and synthetic air as the solvents. It was found that ³He shielding is linearly dependent on solvent density up to approx. 6 mol/L. At higher density of the gaseous solvent, the change of ³He shielding is nonlinear and especially distinct when helium-3 atoms can interact with two O₂ molecules. The interaction with paramagnetic oxygen molecules can induce two kinds of ³He shielding changes: (1) due to the isotropic Fermi contact interaction and (2) from the dipolar magnetic interaction between unpaired O₂ electrons and ³He nuclear magnetic dipole moment. The two paramagnetic effects in helium-3 shielding cannot be experimentally separated, although for such small molecular objects, they could be presumably modeled by advanced theoretical calculations.     

Frozen density functional free energy simulations of redox proteins: computational studies of the reduction potential of plastocyanin and rusticyanin

The evaluation of reduction potentials of proteins by ab initio approaches presents a major challenge for computational chemistry. This is addressed in the present investigation by reporting detailed calculations of the reduction potentials of the blue copper proteins plastocyanin and rusticyanin using the QM/MM all-atom frozen density functional theory, FDFT, method. The relevant ab initio free energies are evaluated by using a classical reference potential. This approach appears to provide a general consistent and effective way for reproducing the configurational ensemble needed for consistent ab initio free energy calculations. The FDFT formulation allows us to treat a large part of the protein quantum mechanically by a consistently coupled QM/QM/MM embedding method while still retaining a proper configurational sampling. To establish the importance of proper configurational sampling and the need for a complete representation of the protein+solvent environment, we also consider several classical approaches. These include the semi-macroscopic PDLD/S-LRA method and classical all-atom simulations with and without a polarizable force field. The difference between the reduction potentials of the two blue copper proteins is reproduced in a reasonable way, and its origin is deduced from the different calculations. It is found that the protein permanent dipole tunes down the reduction potential for plastocyanin compared to the active site in regular water solvent, whereas in rusticyanin it is instead tuned up. This electrostatic environment, which is the major effect determining the reduction potential, is a property of the entire protein and solvent system and cannot be ascribed to any particular single interaction.     

Ion-molecule reactions in 4He droplets: flying nano-cryo-reactors

Ion-molecule reactions are studied inside large (approximately equal to 10(4) atoms) very cold (0.37 K) superfluid (4)He droplets by mass spectrometric detection of the product ions. He+ ions initially formed inside the droplets by electron impact ionization undergo charge transfer with either embedded D(2), N(2), or CH(4). For D(2) this charge transfer process was studied in detail by varying the pickup pressure. For either N(2) or CH(4) the reagent ions were formed by this charge transfer and the reaction pathways of the secondary reactions N(2) (+)+D(2), CH(4) (+)+D(2), and CH(3) (+)+D(2) each with an additionally embedded D(2) molecule were also determined from the pickup pressure dependencies. In several cases, notably He.N(2) (+) and CH(3)D(2) (+) reaction intermediates are observed. The analysis is facilitated by the tendency for molecular ion products to appear without (or with only very few) attached He atoms whereas the atomic ion products usually appear in the mass spectra with several attached He atoms, e.g., He(m).D+ ions with up to m=19.     

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.     

Semiclassical extension of the Landau-Teller theory of collisional energy transfer

A semiclassical version of the quantum coupled-states approximation for the vibrational relaxation of diatomic molecules in collisions with monatomic bath gases is presented. It is based on the effective mass approximation and a recovery of the semiclassical Landau exponent from the classical Landau-Teller collision time. For an interaction with small anisotropy, the Landau exponent includes first order corrections with respect to the orientational dependence of the collision time and the effective mass. The relaxation N(2)(v=1)-->N(2)(v=0) in He is discussed as an example. Employing the available vibrationally elastic potential, the semiclassical approach describes the temperature dependence of the rate constant k(10)(T) over seven orders of magnitude across the temperature range of 70-3000 K in agreement with experimental data and quantum coupled-states calculations. For this system, the hierarchy of corrections to the Landau-Teller conventional treatment in the order of importance is the following: quantum effects in the energy release, dynamical contributions of the rotation of N(2) to the vibrational transition, and deviations of the interaction potential from a purely repulsive form. The described treatment provides significant simplifications over complete coupled-states calculations such that applications to more complex situations appear promising.     

Microsolvation of an ionic dopant in small (4)He clusters: OH(+)((3)sigma)((4)He)(N) via genetic algorithm optimizations.

The optimized spatial structures of the small clusters (with N up to 33) formed by an increasing number of (4)He atoms, which act as a microsolvent surrounding the OH(+) ionic molecular dopant, are obtained using a sum-of-potentials scheme corrected by three-body (3B) effects. The most stable structures are generated using the type of genetic algorithm described herein, and the sequential formation of regular shell structures is analyzed in detail. Possible quantum corrections for both the solvent distributions and the stable energetics are analyzed and discussed.     

A full-configuration interaction "nuclear orbital" method to study doped 3HeN clusters (N< or =4)

An efficient full configuration interaction (FCI) treatment, based on the Jacobi-Davidson algorithm, is developed in order to study small doped (3)He(N) clusters. The state of each He atom in a given cluster is described by a set of wave-functions which by extention of the quantum-chemistry notation are caller here "nuclear orbitals". The FCI treatment is applied to the calculation of binding energies and helium natural orbitals of (3)He(N)...Br(2)(X) complexes. In agreement with our previous calculations using a Hartree-Fock approach [Phys. Rev. Lett. 93, 053401 (2004)], in which the He-He interaction is modified at small distances to account for short-range correlation effects, the lowest-energy states of each multiplet are found to be very close in energy. The natural orbital analysis, in turn, indicates the adequacy of the "nuclear orbital" approach in these systems.     

Water as a solute: competitive shell formation in (He,Ne) mixed microdroplets

Quantum Monte Carlo (QMC) stochastic calculations are carried out for a series of mixed rare gas clusters containing He and Ne which further include one H(2)O molecule as a single dopant. The ab initio potentials employed in the calculations, and the structural details provided by the QMC results, clearly reveal that the differences in the interaction forces which exist between the two solvent adatoms and the molecular solute are causing strongly competing environments that generate preferential shell structuring when surrounding the water molecule. The different behaviour of the two solvents, and the energetics of mixing, are analyzed in detail for small aggregates and for larger mixtures, revealing structural effects which originate from the different networking between solvent adatoms.     

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.     

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.     

Sizes of large He droplets

Helium droplets spanning a wide size range, N(He) = 10(3)-10(10), were formed in a continuous-nozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the droplet beam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N(He) = 10(5)-10(7). Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10(7)-10(10) atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the droplet beam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He(4) (+) signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N(He) = 10(4)-10(9) atoms.     

Spectroscopy of OCS-hydrogen clusters in He droplets

Clusters of para-hydrogen (pH2) and ortho-deuterium (oD2) have been assembled around an OCS chromophore molecule inside He droplets in a molecular beam and studied via IR diode laser depletion spectroscopy (nu approximately 2060 cm-1). The superfluid 4He droplets provide a gentle host ensuring a constant low temperature of either T = 0.38 K for 4He droplets or T = 0.15 K for both the pure 3He and mixed 4He-3He droplets. The spectra show well resolved rotational structure of the vibrational bands for each attached hydrogen molecule in the range n = 1-8. With only one (n = 1) attached pH2, HD or an oD2 molecule the best fit rotational constants were used to determine the structure of the complex, which was found to be in surprisingly good agreement with quantum chemical calculations for the free complex. With n = 5 and 6 the Q-branch disappears for the pH2 clusters but not for the oD2 clusters which is consistent with a donut model. The moments of inertia of the pH2 and the oD2 complexes are explained by a new model in which each of the 18 attached helium atoms in a shell surrounding the OCS molecule are assigned a mass of 0.55, while each attached H2 and D2 molecule has an effective mass of about 10 and 12 u, respectively.     

Quantum scattering and adiabatic channel treatment of the low-energy and low-temperature capture of a rotating quadrupolar molecule by an ion

The capture rate coefficients of homonuclear diatomic molecules (H(2) and N(2)) in the rotational state j=1 interacting with ions (Ar+ and He+) are calculated for low collision energies assuming a long-range anisotropic ion-induced dipole and ion-quadrupole interaction. A comparison of accurate quantum rates with quantum and state-specific classical adiabatic channel approximations shows that the former becomes inappropriate in the case when the cross section is dominated by few partial contributions, while the latter performs better. This unexpected result is related to the fact that the classical adiabatic channel approximation artificially simulates the quantum effects of tunneling and overbarrier reflection as well as the Coriolis coupling and it suppresses too high values of the centrifugal barriers predicted by a quantum adiabatic channel approach. For H2(j=1)+Ar+ and N(2)(j=1)+He+ capture, the rate constants at T-->0 K are about 3 and 6 times higher than the corresponding values for H2(j=0)+Ar+ and N(2)(j=0)+He+ capture.