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DOE OSTI2016

Vibronic interactions proceeding from combined analytical and numerical considerations: Covalent functionalization of graphene by benzene, distortions, electronic transitions

Chemically bound states of benzene molecules with graphene are studied both analytically and numerically. The states are formed by switching off intrabonds of π-electrons in C{sub 6} rings to interbonds. A number of different undistorted and distorted structures are established both with aligned and with transversal mutual orientation of benzene and graphene. The vibronic interactions causing distortions of bound states are found, by using a combination of analytical and numerical considerations. This allows one to determine all electronic transitions of π-electrons without explicit numerical calculations of excited states, to find the conical intersections of potentials, and to show that the mechanism of distortions is the pseudo-Jahn-Teller effect. It is found that the aligned distorted benzene molecule placed between two graphene sheets makes a chemical bond with both of them, which may be used for fastening of graphene sheets together.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C{sub 10}H{sub 22}), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Analytical derivatives of the individual state energies in ensemble density functional theory. II. Implementation on graphical processing units (GPUs)

Conical intersections control excited state reactivity, and thus, elucidating and predicting their geometric and energetic characteristics are crucial for understanding photochemistry. Locating these intersections requires accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g., multireference perturbation theories such as XMS-CASPT2) are computationally challenging for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn–Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units. We demonstrate that our implementation gives the correct conical intersection topography and energetics for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient, with observed sub-quadratic scaling as a function of molecular size. This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Analytical capabilities for iodine detection: Review of possibilities for different applications

This Review summarizes a range of analytical techniques that can be used to detect, quantify, and/or distinguish between isotopes of iodine (e.g., long-lived 129 I, short-lived 131 I, stable 127 I). One reason this is of interest is that understanding potential radioiodine release from nuclear processes is crucial to prevent environmental contamination and to protect human health as it can incorporate into the thyroid leading to cancer. It is also of interest for evaluating iodine retention performances of next-generation iodine off-gas capture materials and long-term waste forms for immobilizing radioiodine for disposal in geologic repositories. Depending upon the form of iodine (e.g., molecules, elemental, and ionic) and the matter state (i.e., solid, liquid, and gaseous), the available options can vary. In addition, several other key parameters vary between the methods discussed herein, including the destructive vs nondestructive nature of the measurement process (including in situ vs ex situ measurement options), the analytical data collection times, and the amount of sample required for analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Analytical trial functions for modelling a two-dimensional Bose condensate

Approximate analytical solutions to the time-independent two-dimensional Gross–Pitaevsky equation are obtained by a variational method. The solutions found are compared with the results of direct numerical calculations. The accuracy of analytical solutions is determined under various conditions of the problem, primarily the degree of nonlinear interaction of atoms in a Bose condensate. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

A basis in an invariant subspace of analytic functions

The existence problem for a basis in a differentiation-invariant subspace of analytic functions defined in a bounded convex domain in the complex plane is investigated. Conditions are found for the solvability of a certain special interpolation problem in the space of entire functions of exponential type with conjugate diagrams lying in a fixed convex domain. These underlie sufficient conditions for the existence of a basis in the invariant subspace. This basis consists of linear combinations of eigenfunctions and associated functions of the differentiation operator, whose exponents are combined into relatively small clusters. Necessary conditions for the existence of a basis are also found. Under a natural constraint on the number of points in the groups, these coincide with the sufficient conditions. That is, a criterion is found under this constraint that a basis constructed from relatively small clusters exists in an invariant subspace of analytic functions in a bounded convex domain in the complex plane. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Nonvanishing quadrature derivatives in the analytical gradients of density functional energies in crystals and helices

It is shown that the quadrature derivatives in some analytical gradients of energies evaluated with a multi-centre radial-angular grid do not vanish even in the limit of an infinitely dense grid, causing severe errors when neglected. The gradients in question are those with respect to a lattice constant of a crystal or to the helical angle of a chain with screw axis symmetry. Furthermore, this is in contrast with the quadrature derivatives in atomic gradients, which can be made arbitrarily small by grid extension. The disparate behaviour is traced to whether the grid points depend on the coordinate with respect to which the derivative of energy is taken. Whereas the nonvanishing quadrature derivative in the lattice-constant gradient is identified as the surface integral arising from an expanding integration domain, the analytical origin of the nonvanishing quadrature derivative in the helical-angle gradient remains unknown.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

A critical review on additive manufacturing of refractory alloys from a data analytics perspective- beyond nickel-based superalloys

Refractory alloys (RAs) are promising materials due to their exceptional physicochemical properties, but most research remains at the laboratory scale. For broader adoption, advancements in manufacturing are essential. Because their high stability makes conventional methods like machining and casting difficult, additive manufacturing (AM) is emerging as an effective approach for fabricating refractory alloy components. However, AM's repeated non-equilibrium thermal cycles introduce undesired features (e.g. defects, anisotropic microstructures, and residual stresses), which are magnified due to RAs’ unique properties. This paper comprehensively reviews the state-of-the-art methods of AM for refractory alloys. It explores data analytics techniques to establish design rules based on multi-fidelity experimental and computational methods. Furthermore, it investigates integrated, collaborative efforts to harmonise standalone databases, information, knowledge, and predictive models at multi-physics, multi-stage, and multi-scale. Unlike the existing literature that focuses primarily on material systems or process fundamentals, this work provides an integrated perspective on AM of refractory alloys from a data analytics standpoint, highlighting the roles of integrated computational materials engineering (ICME), verification, validation, and uncertainty quantification (VV&UQ), and digital twin-driven qualification in overcoming data scarcity and accelerating rapid qualification.

Additive manufacturing↗

DOE OSTI2013

ANALYTICAL LIGHT CURVE MODELS OF SUPERLUMINOUS SUPERNOVAE: {chi}{sup 2}-MINIMIZATION OF PARAMETER FITS

We present fits of generalized semi-analytic supernova (SN) light curve (LC) models for a variety of power inputs including {sup 56}Ni and {sup 56}Co radioactive decay, magnetar spin-down, and forward and reverse shock heating due to supernova ejecta-circumstellar matter (CSM) interaction. We apply our models to the observed LCs of the H-rich superluminous supernovae (SLSN-II) SN 2006gy, SN 2006tf, SN 2008am, SN 2008es, CSS100217, the H-poor SLSN-I SN 2005ap, SCP06F6, SN 2007bi, SN 2010gx, and SN 2010kd, as well as to the interacting SN 2008iy and PTF 09uj. Our goal is to determine the dominant mechanism that powers the LCs of these extraordinary events and the physical conditions involved in each case. We also present a comparison of our semi-analytical results with recent results from numerical radiation hydrodynamics calculations in the particular case of SN 2006gy in order to explore the strengths and weaknesses of our models. We find that CS shock heating produced by ejecta-CSM interaction provides a better fit to the LCs of most of the events we examine. We discuss the possibility that collision of supernova ejecta with hydrogen-deficient CSM accounts for some of the hydrogen-deficient SLSNe (SLSN-I) and may be a plausible explanation for the explosion mechanism of SN 2007bi, the pair-instability supernova candidate. We characterize and discuss issues of parameter degeneracy.