Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

ABSTRACT

A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm^?1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.     

Nilpotent bases for distributions and control systems

Let V(M) be the Lie algebra (infinite dimensional) of real analytic vector fields on the n-dimensional manifold M. Necessary conditions that a real analytic k-dimensional distibution on M have a local basis which generates a nilpotent subalgebra of V(M) are derived. Two methods for sufficient conditions are given, the first depending on the existence of a solution to a system of partial differential equations, the second using Darboux's theorem to give a computable test for an (n ? 1)-dimensional distribution. A nonlinear control system in which the control variables appear linearly can be transformed into an orbit equivalent system whose describing vector fields generate a nilpotent algebra if the distribution generated by the original describing vector fields admits a nilpotent basis. When this is the case, local analysis of the control system is greatly simplified.     

The correlation of proton affinities with atomic charges and electronegativities for the group 14 to 17 hydrides

Proton affinities for hydrides of formula $\mathrm{AH}^{-}_{n-1}$ containing the elements A from the second to the fifth period of the periodic table and groups 14 to 17 are predicted at the Hartree–Fock, MP2 and B3LYP levels of theory employing both core potential basis sets and the 3‐21G basis set. The core potential methods perform well when compared with all electron calculations using the 3‐21++G** basis set. The proton affinities of the hydrides containing elements from groups 15 and 16 of the periodic table are more accurate than those with elements from groups 14 and 17. A cancellation of errors appears to occur more completely if the protonated and nonprotonated molecules contain both bond and lone pairs before and after the protonation reaction. Proton affinities correlate nearly linearly with the atomic charges on the hydrogen atoms when these charges are determined by the generalized atomic polar tensor (GAPT) method. This tendency can be associated, in principle, with the group electronegativities as introduced by Iczkowski and Margrave. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1119–1131, 2000     

Clustered and integrated fluorescence spectra from single atmospheric aerosol particles excited by a 263- and 351-nm laser at New Haven,CT, and Adelphi,MD

Fluorescence spectra from individual micron-sized atmospheric aerosol particles were measured by a Dual-wavelength-excitation Particle Fluorescence Spectrometer (DPFS). Particles were drawn into our laboratory at Adelphi, MD, an urban site in the Washington, DC, metroplex and within the Yale University campus at New Haven, CT. Two fluorescence spectra were obtained for every individual particle as it was moving through the DPFS system and excited sequentially by single laser pulses at 263 and 351 nm. There were around ten to a few hundred particles detected per second and up to a few million per day within the 1–10 μm particle size range. The majority of the particles have weak fluorescence, but 10–50% of the particles have fluorescence signals above the noise level at both sites at different time period. For the first time, these Ultra Violet laser-induced-fluorescence (UV-LIF) spectra from individual particles were integrated every 10 min, which forms a group of about a few thousand to a few tens of thousand particles, to provide the averaged background atmospheric fluorescence spectral profiles which may be helpful in the development of bioaerosol detection systems, particularly those systems based on integrated fluorescence from a group of aerosol particles, such as Light Detection And Rangeing (LIDAR) remotor biosensor and the point sensor based on collected particles on substrate. These integrated spectral profiles had small variations from time to time and were distinguishable from that of the bacterial simulant B. subtilis. Also for the first time, the individual spectra excited by a 351 nm laser were grouped using unstructured hierarchical cluster analysis, with parameters chosen so that spectra clustered into 8 main categories. They showed less spectral variations than that excited by a 263-nm laser. Over 98% of the spectra were able to be grouped into 8 clusters, and over 90% of the fluorescent particles were in clusters 3–5 with a fluorescence emission peak around 420–470 nm; these were mostly from biological and organic carbon-containing compounds. Integrated fluorescence spectral profiles and averaged spectra for each cluster show high similarity between New Haven, CT and Adelphi, MD.     

Membrane fluidity of tetramyristoyl cardiolipin (TMCL) liposomes studied by chronoamperometric monitoring of their adhesion and spreading at the surface of a mercury electrode

Giant unilamellar liposomes of the synthetic cardiolipin 1′,3′-bis[1,2-dimyristoyl-sn-glycero-3-phospho]-sn-glycerol give chronoamperometric current peaks at a stationary mercury electrode. The signals are due to the adhesion and spreading of the liposomes on the hydrophobic mercury surface. The potential dependence shows a minimum of the peak frequency at the point of zero charge, a large maximum of peak frequency at about ?0.2?V and a second, however, smaller maximum at ?0.8?V. The electrochemical behaviour of the liposomes indicates phase transitions of the cardiolipin which could be also observed in differential scanning calorimetry.     

Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: a comparison of simulation techniques

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Sch?tzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.     

Self-assembly of a colloidal interstitial solid with tunable sublattice doping

We determine the phase diagram of a binary mixture of small and large hard spheres with a size ratio of 0.3 using free-energy calculations in Monte Carlo simulations. We find a stable binary fluid phase, a pure face-centered-cubic (fcc) crystal phase of the small spheres, and binary crystal structures with LS and LS(6) stoichiometries. Surprisingly, we demonstrate theoretically and experimentally the stability of a novel interstitial solid solution in binary hard-sphere mixtures, which is constructed by filling the octahedral holes of an fcc crystal of large spheres with small spheres. We find that the fraction of octahedral holes filled with a small sphere can be completely tuned from 0 to 1. Additionally, we study the hopping of the small spheres between neighboring octahedral holes, and interestingly, we find that the diffusion increases upon increasing the density of small spheres.     

Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden

Ohne Zusammenfassung