The infrared spectrum of the Ne-C2D2 complex.

Infrared spectra of Ne-C2D2 are observed in the region of the ν3 fundamental band (asymmetric C-D stretch, ≈2440 cm(-1)) using a tunable optical parametric oscillator to probe a pulsed supersonic slit jet expansion from a cooled nozzle. Like helium-acetylene, this system lies close to the free rotor limit, making analysis tricky because stronger transitions tend to pile up close to monomer (C2D2) rotation-vibration transitions. Assignments are aided by predicted rotational energies calculated from a published ab initio intermolecular potential energy surface. The analysis extends up to the j = 3←2 band, where j labels C2D2 rotation within the dimer, and is much more complete than the limited infrared assignments previously reported for Ne-C2H2 and Ne-C2HD. Two previous microwave transitions within the j = 1 state of Ne-C2D2 are reassigned. Coriolis model fits to the theoretical levels and to the spectrum are compared. Since the variations observed as a function of C2D2 vibrational excitation are comparable to those noted between theory and experiment, it is evident that more detailed testing of theory will require vibrational averaging over the acetylene intramolecular modes.

The infrared spectrum of the He-C2D2 complex.

Spectra of the helium-acetylene complex are elusive because this weakly bound system lies close to the free rotor limit. Previously, limited assignments of He-C2D2 transitions in the R(0) region of the ν3 fundamental band (≈2440 cm(-1)) were published. Here, new He-C2D2 infrared spectra of this band are obtained using a tunable optical parametric oscillator laser source to probe a pulsed supersonic slit jet expansion from a cooled nozzle, and the analysis is extended to the weaker and more difficult P(1) and R(1) regions. A term value approach is used to obtain a consistent set of "experimental" energy levels. These are compared directly with calculations using two recently reported ab initio intermolecular potential energy surfaces, which exhibit small but significant differences. Rovibrational energies for the He-C2H2 complex are also calculated using both surfaces. A Coriolis model, useful for predicting spectral intensities, is used to interpret the energy level patterns, and a comparison with the isoelectronic complex He-CO is made.

Microscopic superfluidity in 4He clusters stirred by a rotating impurity molecule.

The effective moment of inertia of a CO impurity molecule in 4HeN and p-(H2)N solvent clusters initially increases with N but then commences a nonclassical decrease at N=4 (4He) or N=6 (p-H2). This suggests molecule-solvent decoupling and a transition to microscopic superfluidity. However, the quantum decoupling mechanism has not been elucidated. To understand the decoupling mechanism, a one-dimensional model is introduced in which the 4He atoms are confined to a ring. This model captures the physics and shows that decoupling happens primarily because of bosonic solvent-solvent repulsion. Quantum Monte Carlo and basis set calculations suggest that the system can be modeled as a stirred Tonks-Girardeau gas. This allows the N-particle time-dependent Schrödinger equation to be solved directly. Computations of the integrated particle current reveal a threshold for stirring and current generation, indicative of superfluidity.

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.

Computation of nodal surfaces in fixed-node diffusion Monte Carlo calculations using a genetic algorithm.

The fixed-node diffusion Monte Carlo (DMC) algorithm is a powerful way of computing excited state energies in a remarkably diverse number of contexts in quantum chemistry and physics. The main difficulty in implementing the procedure lies in obtaining a good estimate of the nodal surface of the excited state in question. Although the nodal surface can sometimes be obtained from symmetry or by making approximations this is not always the case. In any event, nodal surfaces are usually obtained in an ad hoc way. In fact, the search for nodal surfaces can be formulated as an optimization problem within the DMC procedure itself. Here we investigate the use of a genetic algorithm to systematically and automatically compute nodal surfaces. Application is made to the computation of excited states of the HCN-(4)He complex and to the computation of tunneling splittings in the hydrogen bonded HCl-HCl complex.

Chaos in the classical mechanics of bound and quasi-bound HX-4He complexes with X = F, Cl, Br, CN.

The classical dynamics of weakly bound floppy van der Waals complexes have been extensively studied in the past except for the weakest of all, i.e., those involving He atoms. These complexes are of considerable current interest in light of recent experimental work focussed on the study of molecules trapped in small droplets of the quantum solvent (4)He. Despite a number of quantum investigations, details on the dynamics of how quantum solvation occurs remain unclear. In this paper, the classical rotational dynamics of a series of van der Waals complexes, HX-(4)He with X = F, Cl, Br, CN, are studied. In all cases, the ground state dynamics are found to be almost entirely chaotic, in sharp contrast to other floppy complexes, such as HCl-Ar, for which chaos sets in only at relatively high energies. The consequences of this result for quantum solvation are discussed. We also investigate rotationally excited states with J = 1 which, except for HCN-(4)He, are actually resonances that decay by rotational pre-dissociation.

Controlling feature selection in random forests of decision trees using a genetic algorithm: classification of class I MHC peptides.

Feature selection is an important challenge in many classification problems, especially if the number of features greatly exceeds the number of examples available. We have developed a procedure--GenForest--which controls feature selection in random forests of decision trees by using a genetic algorithm. This approach was tested through our entry into the Comparative Evaluation of Prediction Algorithms 2006 (CoEPrA) competition (accessible online at: http://www.coepra.org). CoEPrA was a modeling competition organized to provide an objective testing for various classification and regression algorithms via the process of blind prediction. In the competition GenForest ranked 10/23, 5/16 and 9/16 on CoEPrA classification problems 1, 3 and 4, respectively, which involved the classification of type I MHC nonapeptides i.e. peptides containing nine amino acids. These problems each involved the classification of different sets of nonapeptides. Associated with each amino acid was a set of 643 features for a total of 5787 features per peptide. The method, its application to the CoEPrA datasets, and its performance in the competition are described.

Fractal Weyl law behavior in an open Hamiltonian system.

We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relatively far away from the classical limit. The complex resonance wave functions are found to be localized on the fractal classical repeller.

Rotational structure of small 4He clusters seeded with HF, HCl, and HBr molecules.

Diffusion Monte Carlo calculations are performed for ground and excited rotational states of HX(4He)N, complexes with N

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.

Nondispersive two-electron wave packets in a helium atom.

We demonstrate the existence of stable nondispersing two-electron wave packets in the helium atom in combined magnetic and circularly polarized microwave fields. These packets follow circular orbits and we show that they can also exist in quantum dots. Classically the two electrons follow trajectories which resemble orbits discovered by Langmuir and which were used in attempts at a Bohr-like quantization of the helium atom. Eigenvalues of a generalized Hessian matrix are computed to investigate the classical stability of these states. Diffusion Monte Carlo simulations demonstrate the quantum stability of these two-electron wave packets in the helium atom and quantum-dot helium with an impurity center.

Chaos-assisted capture of irregular moons.

It has been thought that the capture of irregular moons--with non-circular orbits--by giant planets occurs by a process in which they are first temporarily trapped by gravity inside the planet's Hill sphere (the region where planetary gravity dominates over solar tides). The capture of the moons is then made permanent by dissipative energy loss (for example, gas drag) or planetary growth. But the observed distributions of orbital inclinations, which now include numerous newly discovered moons, cannot be explained using current models. Here we show that irregular satellites are captured in a thin spatial region where orbits are chaotic, and that the resulting orbit is either prograde or retrograde depending on the initial energy. Dissipation then switches these long-lived chaotic orbits into nearby regular (non-chaotic) zones from which escape is impossible. The chaotic layer therefore dictates the final inclinations of the captured moons. We confirm this with three-dimensional Monte Carlo simulations that include nebular drag, and find good agreement with the observed inclination distributions of irregular moons at Jupiter and Saturn. In particular, Saturn has more prograde irregular moons than Jupiter, which we can explain as a result of the chaotic prograde progenitors being more efficiently swept away from Jupiter by its galilean moons.

Statistical theory of asteroid escape rates.

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations.