Rotation of real spherical harmonics

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. II. The Fourier transform method

The Fourier transform method for analytical determination of the two-center Coulomb integrals needed for evaluation of the electrostatic interaction energies between pseudoatom-based charge distributions is presented, and its Fortran-based implementation using the 128-bit floating-point arithmetic in the XDPROP module of the XD software is described. In combination with mathematical libraries included in the Lahey/Fujitsu LF64 Linux compiler, the new implementation outperforms the previously reported Löwdin α-function technique [Nguyen et al. (2018). Acta Cryst. A74, 524-536] in terms of precision of the determined individual Coulomb integrals regardless of whether the latter uses the 64-, 80- or 128-bit precision floating-point format, all the while being only marginally slower. When the Löwdin α-function or Fourier transform method is combined with a multipole moment approximation for large interatomic separations (such a hybrid scheme is called the analytical exact potential and multipole moment method, aEP/MM) the resulting electrostatic interaction energies are evaluated with a precision of ≤5 × 10^-5 kJ mol^-1 for the current set of benchmark systems composed of H, C, N and O atoms and ranging in size from water-water to dodecapeptide-dodecapeptide dimers. Using a 2012 4.0 GHz AMD FX-8350 computer processor, the two recommended aEP/MM implementations, the 80-bit precision Löwdin α-function and 128-bit precision Fourier transform methods, evaluate the total electrostatic interaction energy between two 225-atom monomers of the benchmark dodecapeptide molecule in 6.0 and 7.9 s, respectively, versus 3.1 s for the previously reported 64-bit Löwdin α-function approach.

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. I. The Löwdin α-function method

The previously reported [Volkov et al. (2004). Chem. Phys. Lett. 391, 170-175] exact potential and multipole moment (EP/MM) method for evaluation of intermolecular electrostatic interaction energies using the nuclei-centered pseudoatom representation of electron densities is significantly improved in terms of both speed and accuracy by replacing the numerical quadrature integration of the exact potential with a fully analytical technique. The resulting approach, incorporated in the XDPROP module of the software package XD, has been tested on several molecular systems ranging in size from water-water to dodecapeptide-dodecapeptide dimers using electron densities constructed via the University at Buffalo Aspherical Atom Databank. The improved hybrid method provides electrostatic interaction energies within the uncertainty of ≤0.2 kJ mol^-1 for all benchmark systems. The running time for a dimer of a sizable, 225-atom dodecapeptide is under 4 s on a 2012 central processing unit (2.8 GHz AMD Opteron 6348) and under 3 s on a relatively modern processor (2.8 GHz Intel Xeon E3-1505M v5).

Toward amino acid typing for proteins in FFLUX

Continuing the development of the FFLUX, a multipolar polarizable force field driven by machine learning, we present a modern approach to atom-typing and building transferable models for predicting atomic properties in proteins. Amino acid atomic charges in a peptide chain respond to the substitution of a neighboring residue and this response can be categorized in a manner similar to atom-typing. Using a machine learning method called kriging, we are able to build predictive models for an atom that is defined, not only by its local environment, but also by its neighboring residues, for a minimal additional computational cost. We found that prediction errors were up to 11 times lower when using a model specific to the correct group of neighboring residues, with a mean prediction of ∼0.0015 au. This finding suggests that atoms in a force field should be defined by more than just their immediate atomic neighbors. When comparing an atom in a single alanine to an analogous atom in a deca-alanine helix, the mean difference in charge is 0.026 au. Meanwhile, the same difference between a trialanine and a deca-alanine helix is only 0.012 au. When compared to deca-alanine models, the transferable models are up to 20 times faster to train, and require significantly less ab initio calculation, providing a practical route to modeling large biological systems. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

A preferred orientation correction to describe a fiber texture under glancing incidence

Much work is nowadays being devoted to the characterization of the structure and the microstructure of thin films and mesoporous materials. Different physical and chemical processes used to elaborate these thin films often induce a fiber texture in these materials. The X-ray glancing-incidence technique appears to be a useful tool for collecting diffraction patterns of thin films while avoiding the peaks of the substrate. However, the scattering vector in this asymmetric scattering geometry is not perpendicular to the surface of the sample. This point implies that the correction developed to model the effects of a fiber texture in Bragg–Brentano geometry, where the scattering vector is always normal to the surface of the sample, cannot be applied in glancing incidence. This work presents a procedure to correct the preferred orientation due to this fiber texture in asymmetric scattering geometry and then in glancing incidence. By an example, it is proved that this correction of the fiber texture is efficient. The main point of interest regarding this correction is that only a few parameters are needed to handle the effect of the fiber texture on the diffraction patterns collected in asymmetric scattering geometry and then under glancing incidence.

On the acoustic radiation modes of compact regular polyhedral arrays of independent loudspeakers

Compact spherical loudspeaker arrays can be used to provide control over their directivity pattern. Usually, this is made by adjusting the gains of preprogrammed spatial filters corresponding to a finite set of spherical harmonics, or to the acoustic radiation modes of the loudspeaker array. Unlike the former, the latter are closely related to the radiation efficiency of the source and span the subspace of the directivities it can produce. However, the radiation modes depend on frequency for arbitrary distributions of transducers on the sphere, which yields complex directivity filters. This work focuses on the most common loudspeaker array configurations, those following the regular shape of the Platonic solids. It is shown that the radiation modes of these sources are frequency independent, and simple algebraic expressions are derived for their radiation efficiencies. In addition, since such modes are vibration patterns driven by electrical signals, the transduction mechanism of compact multichannel sources is also investigated, which is an important issue, especially if the transducers interact inside a shared cabinet. For Platonic solid loudspeakers, it is shown that the common enclosure does not lead to directivity filters that depend on frequency.

General DFT++ method implemented with projector augmented waves: electronic structure of SrVO3 and the Mott transition in Ca(2-x)Sr(x)RuO4

The realistic description of correlated electron systems took an important step forward a few years ago as the combination of density functional methods and dynamical mean-field theory was conceived. This framework allows access to both high and low energy physics and is capable of the description of the specific physics of strongly correlated materials, like the Mott metal-insulator transition. A very important step in the procedure is the interface between the band structure method and the dynamical mean-field theory and its impurity solver. We present a general interface between a projector augmented-wave-based density functional code and many-body methods based on Wannier functions obtained from a projection on local orbitals. The implementation is very flexible and allows for various applications. Quantities like the momentum-resolved spectral function are accessible. We present applications to SrVO(3) and the metal-insulator transition in Ca(2-x)Sr(x)RuO(4).