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At least 631 records · Page 35

Perspective: Ab initio force field methods derived from quantum mechanics

It is often desirable to accurately and efficiently model the behavior of large molecular systems in the condensed phase (thousands to tens of thousands of atoms) over long time scales (from nanoseconds to milliseconds). In these cases, ab initio methods are difficult due to the increasing computational cost with the number of electrons. A more computationally attractive alternative is to perform the simulations at the atomic level using a parameterized function to model the electronic energy. Many empirical force fields have been developed for this purpose. However, the functions that are used to model interatomic and intermolecular interactions contain many fitted parameters obtained from selected model systems, and such classical force fields cannot properly simulate important electronic effects. Furthermore, while such force fields are computationally affordable, they are not reliable when applied to systems that differ significantly from those used in their parameterization. They also cannot provide the information necessary to analyze the interactions that occur in the system, making the systematic improvement of the functional forms that are used difficult. Ab initio force field methods aim to combine the merits of both types of methods. The ideal ab initio force fields are built on first principles and require no fitted parameters. Ab initio force field methods surveyed in this perspective are based on fragmentation approaches and intermolecular perturbation theory. This perspective summarizes their theoretical foundation, key components in their formulation, and discusses key aspects of these methods such as accuracy and formal computational cost. The ab initio force fields considered here were developed for different targets, and this perspective also aims to provide a balanced presentation of their strengths and shortcomings. Finally, this perspective suggests some future directions for this actively developing area.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elements require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spin-flip, tensor equation-of-motion configuration interaction with a density-functional correction: A spin-complete method for exploring excited-state potential energy surfaces

We revisit the formalism of the spin-adapted, spin-flip (SA-SF) configuration-interaction singles (CIS) method based on a tensor equation-of-motion formalism that affords proper spin eigenstates without sacrificing single-reference simplicity. Matrix elements for SA-SF-CIS are then modified in a manner similar to collinear spin-flip time-dependent density functional theory (SF-TDDFT), to include a DFT exchange-correlation correction. The performance of this method, which we call SA-SF-DFT, is evaluated numerically and we find that it systematically improves the energies of electronic states that exhibit significant spin contamination within the conventional SF-TDDFT approach. The new method cures the state assignment problem that plagues geometry optimizations and ab initio molecular dynamics simulations using traditional SF-TDDFT, without sacrificing computational efficiency, and furthermore provides correct topology at conical intersections, including those that involve the ground state, unlike conventional TDDFT. As such, SA-SF-DFT appears to be a promising method for generating excited-state potential energy surfaces at DFT cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Adding ($\mathcal{α}$,n) Emission to an Existing Subcritical Benchmark Statistical Uncertainty Method

Subcritical measurements often use radiation detectors to infer parameters related to the physics of a measured system. One type of subcritical measurements typically performed are called neutron noise measurements. These types of measurements utilize the fact that prompt neutrons are produced from fission immediately after a fission event and are therefore correlated in time. Subcritical benchmarks require evaluation of the statistical and systematic uncertainties of a measurement. Previous work established methods for determining statistical and systematic uncertainties in subcritical benchmarks. The data were analyzed using the Hage-Cifarelli formalism of the Feynman Variance-to-Mean method. The previous work made an assumption that the ($\mathcal{α}$,n) emission rate was negligible. This assumption was used because the previous work focused on systems with metal Plutonium. This work extends the existing statistical uncertainty method to include ($\mathcal{α}$,n) emissions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Supersymmetric symplectic quantum mechanics

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space H{sub Γ} to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville–von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theoretical structural and vibrational study of 5-trifluoromethyluracil. A comparison with uracil

In the present work, a comparative study on the structural and vibrational properties of the 5-trifluoromethyluracil (TFMU) derivative with those corresponding to uracil in gas and aqueous solution phases was performed combining the available H{sup 1}-NMR, C{sup 13}-NMR, F{sup 19}-NMR and FTIR spectra with Density Functional Theory (DFT) calculations. Three stable conformers were theoretically determined in both media by using the hybrid B3LYP/6-31G* method. The solvent effects were simulated by means of the self-consistent reaction field (SCRF) method employing the integral equation formalism variant (IEFPCM). Complete assignments of the vibrational spectra in both phases were performed combining the internal coordinates analysis and the DFT calculations with the Scaled Quantum Mechanics Force Field (SQMFF) methodology. The atomic charges, bond orders, solvation energies, dipole moments, molecular electrostatic potentials and force constants parameters were calculated for the three conformers of TFMU in gas phase and aqueous solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Carpenter, Mark H.↗

New tools for the systematic analysis and visualization of electronic excitations. I. Formalism

A variety of density matrix based methods for the analysis and visualization of electronic excitations are discussed and their implementation within the framework of the algebraic diagrammatic construction of the polarization propagator is reported. Their mathematical expressions are given and an extensive phenomenological discussion is provided to aid the interpretation of the results. Starting from several standard procedures, e.g., population analysis, natural orbital decomposition, and density plotting, we proceed to more advanced concepts of natural transition orbitals and attachment/detachment densities. In addition, special focus is laid on information coded in the transition density matrix and its phenomenological analysis in terms of an electron-hole picture. Taking advantage of both the orbital and real space representations of the density matrices, the physical information in these analysis methods is outlined, and similarities and differences between the approaches are highlighted. Moreover, new analysis tools for excited states are introduced including state averaged natural transition orbitals, which give a compact description of a number of states simultaneously, and natural difference orbitals (defined as the eigenvectors of the difference density matrix), which reveal details about orbital relaxation effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct calculation of the reactive transition matrix by L-squared quantum mechanical variational methods with complex boundary conditions

A new formalism of the generalized Newton variational principle for the calculation of quantum mechanical state-to-state reaction probabilities is presented. The reformulation involves solving directly for the transition matrix rather than the reactance mtrix so that calculations may be carried out for individual columns of the transition matrix without obtaining solutions for all possible initial channels. The convergence of calculations with real and complex boundary conditions are compared for H + H2 - H2 + H, O + H2 - OH + H, and O + HD - OH + D and OD + H.

Sun, Yan↗

A unified neural-network framework for nucleon imaging from numerical simulations of QCD

Parton distributions encode the momentum-space structure and, in their generalizations, the spatial tomography of quarks and gluons inside hadrons, the building blocks of visible matter. We present a unified neural-network approach that learns these distributions directly from matrix elements calculated via numerical simulations of quantum chromodynamics (QCD) on the lattice by fitting two complementary inputs simultaneously: data matched to physical quantities via known momentum-space and coordinate-space formalisms. Utilizing data from both methods stabilizes the extraction and mitigates biases that can arise when either is used alone. We validate the method on controlled mock data and apply it to lattice-QCD matrix elements to extract parton distribution functions (PDFs). We show benefits of such an approach for determining the physical quantities. We further extend the framework to zero-skewness generalized parton distributions and demonstrate nucleon tomography within the same neural-network parameterization. Our results provide an adaptable and systematically improvable approach for extracting partonic distributions from Euclidean correlators. It can incorporate polarization, additional channels, and future experimental constraints from current and future facilities, such as the Electron-Ion Collider.

Hadronic Spectroscopy↗

Anyonic entanglement and topological entanglement entropy

We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy. - Highlights: • Entanglement of anyonic systems is studied using standard notions of entropy. • The algebraic theory of anyon models for higher genus surfaces is developed. • A general method for calculating topological entanglement entropy is presented. • Topological entanglement entropy originates from conservation of topological charge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A kinetic model for simulating non-equilibrium mass transport in oxides applied to hematite growth under irradiation

We propose an approach to simulating the dynamic evolution and transport of charged point defects within and through the oxide scales that form during corrosion. The method follows the cluster dynamics formalism widely adopted for radiation damage in solids, which can apply in both quasi-static and far from equilibrium conditions, such as in radiation environments. By treating each charged defect as a cluster of an atomic defect and associated unit charges, the proposed model flexibly allows charge state transitions and shifts in the Fermi level by absorption and emission of charge carriers from point defects in a reaction network with rates constrained by local equilibrium. Applying this model to hematite predicts changes in self-diffusion and oxidation kinetics in irradiation environments, surprisingly showing reduced oxidation rates in many conditions, despite enhanced self-diffusion. In conclusion, the origin of this effect lies in a change in Fermi level induced by excess vacancies formed under irradiation, which in turn suppresses the transport of cation interstitials which facilitate hematite growth.

36 MATERIALS SCIENCE↗

Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. Here, this present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

36 MATERIALS SCIENCE↗

Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis

A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux surfaces in the vicinity of the axis. This framework can provide meaningful analytical insight into the character of high-aspect-ratio stellarator shapes, such as the dependence of the rotational transform and the plasma beta limit on geometrical properties of the resulting flux surfaces. The approach developed here is based on an asymptotic expansion on the inverse aspect ratio of the ideal magnetohydrodynamics equation. The analysis is simplified by using an orthogonal coordinate system relative to the Frenet–Serret frame at the magnetic axis. The magnetic field vector, the toroidal magnetic flux, the current density, the field line label and the rotational transform are derived at arbitrary order in the expansion parameter. Moreover, a comparison with a near-axis expansion formalism employing an inverse coordinate method based on Boozer coordinates (the so-called Garren–Boozer construction) is made, where both methods are shown to agree at lowest order. Finally, as a practical example, a numerical solution using a W7-X equilibrium is presented, and a comparison between the lowest-order solution and the W7-X magnetic field is performed.

Physics↗

From the Ternary Phase Ca 14 Zn 1+δ Sb 11 (δ ≈ 0.4) to the Quaternary Solid Solutions Ca 14– x RE x ZnSb 11 (RE = La–Nd, Sm, Gd, x ≈ 0.9). A Tale of Electron Doping via Rare-Earth Metal Substitutions and the Concomitant Structural Transformations

In this work, the ternary compound Ca 14 Zn 1.37(1) Sb 11 and its six rare-earth metal substituted derivatives Ca 14–x RE x ZnSb 11 (RE = La–Nd, Sm, Gd; x ≈ 0.90±0.06) have been synthesized and structurally characterized by single-crystal X-ray diffraction methods. All com-pounds formally crystallize in the tetragonal Ca 14 AlSb 11 structure type (space group $I$4 1 $/ acd$, No. 142, $Z$ = 8). The crystal structure of Ca 14 Zn 1.37(1) Sb 11 subtly differs from the structure of the remaining six, as well as from the structure of the archetype, due to the presence of a partially occupied interstitial Zn position. The extra zinc atom is needed in this structure to alleviate the unfavorable number of valence electrons in the imaginary Ca 14 ZnSb 11 . Electron doping, via substitution of RE 3+ ions on Ca 2+ sites is shown as an alternative route to achieve electron balance in these Zn-based analogs of the Ca 14 AlSb 11 structure, which does not require the in-corporation of interstitial atoms. Electrical resistivity measurements done on single-crystalline samples are in agreement with the notion that Ca 14–x RE x ZnSb 11 behave as either bad metals or heavily-doped semi-conductors. Magnetization measurements show Curie-Weiss paramagnetic behavior related to the local-moment magnetism of the RE 3+ ions.

36 MATERIALS SCIENCE↗

Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics

Extended Lagrangian Born–Oppenheimer molecular dynamics [ Phys. Rev. Lett. 2008, 100, 123004] is presented for Hartree–Fock theory, where the extended electronic degrees of freedom are represented by a density matrix, including fractional occupation numbers at elevated electronic temperatures. In contrast to regular direct Born–Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. To sample regions of the potential energy landscape where the gap is small or vanishing, which leads to particular convergence problems in regular direct Born–Oppenheimer molecular dynamics simulations, an adaptive integration scheme for the extended electronic degrees of freedom is presented. The integration scheme is based on a tunable, low-rank approximation of a fourth-order kernel, K, that determines the metric tensor, T ≡ K T K, used in the extended harmonic oscillator of the Lagrangian that generates the dynamics of the electronic degrees of freedom. Here, the formulation and algorithms provide a general guide to implement extended Lagrangian Born–Oppenheimer molecular dynamics for quantum chemistry, density functional theory, and semiempirical methods using a density matrix formalism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transition metal dimer on Au(111) surface: A first principle study

The adsorption behaviour of transition metal dimers M{sub 2} (M= Cu, Ag, Au) on the Au(111) surface have been studied using the density functional theory formalism. The projector augmented wave method under the spin polarized version of generalized gradient approximation scheme was employed to calculate the total energy. The results suggest that all dimers prefer to orient in parallel to the surface plane, where two M atoms are adsorbed on two nearby threefold fcc sites. We have investigated the chemical interaction between M atoms and Au surface through electronic density of state analysis. It is found that on deposition, the electronic density of states (EDOS) of M{sub 2} dimer becomes broader in comparison to their gas phase spectrum.

36 MATERIALS SCIENCE↗