An efficient approximation of the supercell approach to the calculation of the full phonon spectrum
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Duong, Thien C. (ORCID:000000018694814X)↗
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Results for “density functional approximations”
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SOPPA and CCSD vibrational corrections to NMR indirect spin-spin coupling constants of small hydrocarbons
We present zero-point vibrational corrections to the indirect nuclear spin-spin coupling constants in ethyne, ethene, cyclopropene and allene. The calculations have been carried out both at the level of the second order polarization propagator approximation (SOPPA) employing a new implementation in the DALTON program, at the density functional theory level with the B3LYP functional employing also the Dalton program and at the level of coupled cluster singles and doubles (CCSD) theory employing the implementation in the CFOUR program. Specialized coupling constant basis sets, aug-cc-pVTZ-J, have been employed in the calculations. We find that on average the SOPPA results for both the equilibrium geometry values and the zero-point vibrational corrections are in better agreement with the CCSD results than the corresponding B3LYP results. Furthermore we observed that the vibrational corrections are in the order of 5 Hz for the one-bond carbon-hydrogen couplings and about 1 Hz or smaller for the other couplings apart from the one-bond carbon-carbon coupling (11 Hz) and the two-bond carbon-hydrogen coupling (4 Hz) in ethyne. However, not for all couplings lead the inclusion of zero-point vibrational corrections to better agreement with experiment.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum chemical ab initio prediction of proton exchange barriers between CH{sub 4} and different H-zeolites
A hybrid MP2:DFT (second-order Møller–Plesset perturbation theory–density functional theory) method that combines MP2 calculations for cluster models with DFT calculations for the full periodic structure is used to localize minima and transition structures for proton jumps at different Brønsted sites in different frameworks (chabazite, faujasite, ferrierite, and ZSM-5) and at different crystallographic positions of a given framework. The MP2 limit for the periodic structures is obtained by extrapolating the results of a series of cluster models of increasing size. A coupled-cluster (CCSD(T)) correction to MP2 energies is calculated for cluster models consisting of three tetrahedra. For the adsorption energies, this difference is small, between 0.1 and 0.9 kJ/mol, but for the intrinsic proton exchange barriers, this difference makes a significant (10.85 ± 0.25 kJ/mol) and almost constant contribution across different systems. The total values of the adsorption energies vary between 22 and 34 kJ/mol, whereas the total proton exchange energy barriers fall in the narrow range of 152–156 kJ/mol. After adding nuclear motion contributions (harmonic approximation, 298 K), intrinsic enthalpy barriers between 134 and 141 kJ/mol and apparent energy barriers between 105 and 118 kJ/mol are predicted for the different sites examined for the different frameworks. These predictions are consistent with experimental results available for faujasite, ferrierite, and ZSM-5.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Selfsimilar and fractal analysis of n-type delta-doped quasiregular GaAs quantum wells
We study the electronic structure of n-type delta-doped quantum wells in GaAs in which the multiple well system is built according to the Fibonacci sequence. The building blocks A and B correspond to delta-doped wells with impurities densities n{sub 2DA} and n{sub 2DB}, and the same well width. The Thomas-Fermi approximation, the semi-empirical sp{sub 3}s* tight-binding model including spin, the Surface Green Function Matching method and the Transfer Matrix approach were implemented to obtain the confining potential, the electronic structure and the selfsimilarity of the spectrum. The fragmentation of the electronic spectra is observed whenever the building blocks A and B interact and it increases as the difference of impurities density between A and B increases as well. The wave function of the first sate of the fragmented bands presents critical characteristics, this is, it is not a localized state nor a extended one as well as it has selfsimilar features. So, the quasiregular characteristics are preserved irrespective of the complexity of the system and can affect the performance of devices based on these structures.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Calculation of nuclear spin-spin coupling constants using frozen density embedding
We present a method for a subsystem-based calculation of indirect nuclear spin-spin coupling tensors within the framework of current-spin-density-functional theory. Our approach is based on the frozen-density embedding scheme within density-functional theory and extends a previously reported subsystem-based approach for the calculation of nuclear magnetic resonance shielding tensors to magnetic fields which couple not only to orbital but also spin degrees of freedom. This leads to a formulation in which the electron density, the induced paramagnetic current, and the induced spin-magnetization density are calculated separately for the individual subsystems. This is particularly useful for the inclusion of environmental effects in the calculation of nuclear spin-spin coupling constants. Neglecting the induced paramagnetic current and spin-magnetization density in the environment due to the magnetic moments of the coupled nuclei leads to a very efficient method in which the computationally expensive response calculation has to be performed only for the subsystem of interest. We show that this approach leads to very good results for the calculation of solvent-induced shifts of nuclear spin-spin coupling constants in hydrogen-bonded systems. Also for systems with stronger interactions, frozen-density embedding performs remarkably well, given the approximate nature of currently available functionals for the non-additive kinetic energy. As an example we show results for methylmercury halides which exhibit an exceptionally large shift of the one-bond coupling constants between {sup 199}Hg and {sup 13}C upon coordination of dimethylsulfoxide solvent molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Curing the Divergence in Time-Dependent Density Functional Quadratic Response Theory
While time-dependent density functional theory has emerged as a method of choice for computing electronic spectra and response of molecules and materials, its reliability is hindered by the adiabatic approximation that is commonly made. In this work, we address one problematic aspect that arises from this approximation: an incorrect pole structure in the quadratic response function, leading to unphysical divergences in excited state-to-state transition probabilities and hyperpolarizabilties. We find the form of the exact quadratic response kernel and derive a practical and accurate approximation that cures the divergence. Here, we demonstrate our results on excited state-to-state transition probabilities of a model system and of the LiH molecule.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Geometric Analysis Based Double Closed-loop Iterative Learning Control of Output PDF Shaping of Fiber Length Distribution in Refining Process
In order to improve the pulp quality and to reduce the energy consumption, the fiber length distribution (FLD) is generally employed as one of the important technological indexes in the refining process. Considering that the traditional mean and variance of fiber length are unable to adequately characterize the non-Gaussian distribution properties, this paper proposes a novel geometric analysis based double closed-loop iterative learning control (ILC) method for probability density function (PDF) shaping of output FLD in the refining process. Primarily, a RBF neural network (NN) with Gaussian-type is utilized to approximate the square root PDF in the inner loop, where the RBF basis function parameters (center and width) are tuned between any two adjacent batches by using an ILC law, and the subspace identification method can be applied to establish the state-space model of weight vector. Then, for the sake of accelerating the convergence rate of the closed-loop sysyem, a geometric analysis based ILC method is adopted in the outer loop. Lastly, both simulation and experiments demonstrate the effectiveness and practicability of the proposed approach.
42 ENGINEERING↗
Modal density function and number of propagating modes in ducts
Often raised questions in duct sound propagation studies involve the total number of propagating modes, the number of propagating radial modes for a particular spinning lobe number, and the number of modes possible between two given values of cutoff ratio or eigenvalue. These questions can be answered approximately by using the modal distribution function which is the integral of the modal density function for ducts in a manner similar to that previously published for architectural acoustics. The modal density functions are derived for rectangular and circular ducts with a uniform steady flow. Results from this continuous theory are compared to the actual (discrete) modal distributions.
Rice, E. J.↗
Variational mixed quantum/semiclassical simulation of dihalogen guest and rare-gas solid host dynamics
A variational mixed quantum-semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested, and used to simulate the temporal evolution of nonstationary states of the internal molecular and surrounding medium degrees of freedom. In this theory, termed the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) method, the system is treated fully quantum mechanically while Gaussian wave packets are used for the bath degrees of freedom. An approximate time-dependent wave function of the entire model is obtained instead of just a reduced system density matrix, so the theory enables the analysis of the entangled system and bath dynamics that ensues following initial displacement of the internal-molecular (system) coordinate from its equilibrium position. The norm- and energy-conserving properties of the propagation of our trial wave function are natural consequences of the Dirac-Frenkel-McLachlan variational principle. The variational approach also stabilizes the time evolution in comparison to the same ansatz propagated under a previously employed locally quadratic approximation to the bath potential and system-bath interaction terms in the bath-parameter equations of motion. Dynamics calculations are carried out for molecular iodine in a 2D krypton lattice that reveal both the time-course of vibrational decoherence and the details of host-atom motion accompanying energy dissipation and dephasing. This work sets the stage for the comprehensive simulation of ultrafast time-resolved optical experiments on small molecules in low-temperature solids.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Spin and orbital magnetism of coinage metal trimers (Cu{sub 3}, Ag{sub 3}, Au{sub 3}): A relativistic density functional theory study
We have demonstrated electronic structure and magnetic properties of Cu{sub 3}, Ag{sub 3} and Au{sub 3} trimers using a full potential local orbital method in the framework of relativistic density functional theory. We have also shown that the non-relativistic generalized gradient approximation for the exchange-correlation energy functional gives reliable magnetic properties in coinage metal trimers compared to experiment. In addition we have indicated that the spin-orbit coupling changes the structure and magnetic properties of gold trimer while the structure and magnetic properties of copper and silver trimers are marginally affected. A significant orbital moment of 0.21μ{sub B} was found for most stable geometry of the gold trimer whereas orbital magnetism is almost quenched in the copper and silver trimers.
36 MATERIALS SCIENCE↗
A comparative density functional study on electrical properties of layered penta-graphene
We present a comparative study of the influence of the number of layers, the biaxial strain in the range of −3% to 3%, and the stacking misalignments on the electronic properties of a new 2D carbon allotrope, penta-graphene (PG), based on hybrid-functional method within the density functional theory (DFT). In comparison with local exchange-correlation approximation in the DFT, the hybrid-functional provides an accurate description on the degree of p{sub z} orbitals localization and bandgap. Importantly, the predicted bandgap of few-layer PG has a weak layer dependence. The bandgap of monolayer PG is 3.27 eV, approximately equal to those of GaN and ZnO; and the bandgap of few-layer PG decreases slowly with the number of layers (N) and converge to 2.57 eV when N ≥ 4. Our calculations using HSE06 functional on few-layer PG reveal that bandgap engineering by stacking misalignment can further tune the bandgap down to 1.37 eV. Importantly, there is no direct-to-indirect bandgap transition in PG by varying strain, layer number, and stacking misalignment. Owing to its tunable, robustly direct, and wide bandgap characteristics, few-layer PG is promising for optoelectronic and photovoltaic applications.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Turbulent shear-layer mixing: initial conditions, and direct-numerical and large-eddy simulations
Aspects of turbulent shear-layer mixing are investigated over a range of shear-layer Reynolds numbers, $Re_{\unicode[STIX]{x1D6FF}}=\unicode[STIX]{x0394}U\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D708}$ , based on the shear-layer free-stream velocity difference, $\unicode[STIX]{x0394}U$ , and mixing-zone thickness, $\unicode[STIX]{x1D6FF}$ , to probe the role of initial conditions in mixing stages and the evolution of the scalar-field probability density function (p.d.f.) and variance. Scalar transport is calculated for unity Schmidt numbers, approximating gas-phase diffusion. The study is based on direct-numerical simulation (DNS) and large-eddy simulation (LES), comparing different subgrid-scale (SGS) models for incompressible, uniform-density, temporally evolving forced shear-layer flows. Moderate-Reynolds-number DNS results help assess and validate LES SGS models in terms of scalar-spectrum and mixing estimates, as well as other metrics, to $Re_{\unicode[STIX]{x1D6FF}}\lesssim 3.3\times 10^{4}$ . High-Reynolds-number LES investigations to $Re_{\unicode[STIX]{x1D6FF}}\lesssim 5\times 10^{5}$ help identify flow parameters and conditions that influence the evolution of scalar variance and p.d.f., e.g. marching versus non-marching. Initial conditions that generate shear flows with different mixing behaviour elucidate flow characteristics in each flow regime and identify elements that induce p.d.f. transition and scalar-variance behaviour. P.d.f. transition is found to be largely insensitive to local flow parameters, such as $Re_{\unicode[STIX]{x1D6FF}}$ , or a previously proposed vortex-pairing parameter based on downstream distance, or other equivalent criteria. The present study also allows a quantitative comparison of LES SGS models in moderate- and high- $Re_{\unicode[STIX]{x1D6FF}}$ forced shear-layer flows.
Mechanics↗
Interacting boson model from energy density functionals: {gamma}-softness and the related topics
A comprehensive way of deriving the Hamiltonian of the interacting boson model (IBM) is described. Based on the fact that the multi-nucleon induced surface deformation in finite nucleus is simulated by effective boson degrees of freedom, the potential energy surface calculated with self-consistent mean-field method employing a given energy density functional (EDF) is mapped onto the IBM analog, and thereby the excitation spectra and transition rates with good symmetry quantum numbers are calculated. Recent applications of the proposed approach are reported: (i) an alternative robust interpretation of the {gamma}-soft nuclei and (ii) shape coexistence in lead isotopes.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Effect of hydrostatic pressure on the structural and electronic properties of Cd{sub 0.75}Cr{sub 0.25}S
In this paper we present the results obtained from first principle calculations of the effect of hydrostatic pressure on the structural and electronic properties of Cd{sub 1-x}Cr{sub x}S diluted magnetic semiconductor in Zinc Blende (B3) phase at x=0.25. High pressure behavior of Cd{sub 1-x}Cr{sub x}S has been investigated between 0 GPa to 100 GPa The calculations have been performed using Density functional theory as implemented in the Spanish Initiative for Electronic Simulations with Thousands of Atoms code using local density approximation as exchange-correlation (XC) potential. Calculated electronic band structures of Cd{sub 1-x}Cr{sub x}S are discussed in terms of contribution of Cr 3d{sup 5} 4s{sup 1}, Cd 4d{sup 10} 5s{sup 2}, S 3s{sup 2} 3p{sup 4} orbital’s. Study of band structures shows half-metallic ferromagnetic nature of Cd{sub 0.75}Cr{sub 0.25}S with 100% spin polarization. Under application of external pressure, the valence band and conduction band are shifted upward which leads to modification of electronic structure.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation
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charge transport↗
Brownian motion of a plasma crystal
The dynamics of a plasma crystal under the action of random external forces is considered. The pair correlation functions of the particle displacements are calculated in the harmonic approximation by using the Langevin equations. The case of a planar hexagonal lattice is analyzed in more detail. Analogues of the Van Hove singularities in the spectral densities are discovered.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Layer-dependent topological phase in a two-dimensional quasicrystal and approximant
The electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing “forbidden” symmetries via quasiperiodic ordering with low dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional (2D) chalcogenide quasicrystal and approximant, and investigate their electronic and topological properties. The 2D layers of the materials with a composition close to Ta 1.6 Te, derived from a layered transition metal dichalcogenide, are isolated with standard exfoliation techniques, and investigated with electron diffraction and atomic resolution scanning transmission electron microscopy. Density functional theory calculations and symmetry analysis of the large unit cell crystalline approximant of the quasicrystal, Ta 21 Te 13 , reveal the presence of symmetry-protected nodal crossings in the quasicrystalline and approximant phases, whose presence is tunable by layer number. Our study provides a platform for the exploration of physics in quasicrystalline, low-dimensional materials and the interconnected nature of topology, dimensionality, and symmetry in electronic systems.
36 MATERIALS SCIENCE↗
Approximating Photo- z PDFs for Large Surveys
Modern galaxy surveys produce redshift probability density functions (PDFs) in addition to traditional photometric redshift (photo-z) point estimates. However, the storage of photo-z PDFs may present a challenge with increasingly large catalogs, as we face a trade-off between the accuracy of subsequent science measurements and the limitation of finite storage resources. This work presents qp, a Python package for manipulating parameterizations of one-dimensional PDFs, as suitable for photo-z PDF compression. We use qp to investigate the performance of three simple PDF storage formats (quantiles, samples, and step functions) as a function of the number of stored parameters on two realistic mock data sets, representative of upcoming surveys with different data qualities. We propose some best practices for choosing a photo-z PDF approximation scheme and demonstrate the approach on a science case using performance metrics on both ensembles of individual photo-z PDFs and an estimator of the overall redshift distribution function. We show that both the properties of the set of PDFs we wish to approximate and the fidelity metric(s) chosen affect the optimal parameterization. Additionally, we find that quantiles and samples outperform step functions, and we encourage further consideration of these formats for PDF approximation.
79 ASTRONOMY AND ASTROPHYSICS↗