1,638 research outputs found
Perspective: Treating electron over-delocalization with the DFT+U method
No full textMany people in the materials science and solid-state community are familiar with the acronym “DFT+U.” For those less familiar, this technique uses ideas from model Hamiltonians that permit the description of both metals and insulators to address problems of electron over-delocalization in practical implementations of density functional theory (DFT). Exchange-correlation functionals in DFT are often described as belonging to a hierarchical “Jacob’s ladder” of increasing accuracy in moving from local to non-local descriptions of exchange and correlation. DFT+U is not on this “ladder” but rather acts as an “elevator” because it systematically tunes relative energetics, typically on a localized subshell (e.g., d or f electrons), regardless of the underlying functional employed. However, this tuning is based on a metric of the local electron density of the subshells being addressed, thus necessitating physical or chemical or intuition about the system of interest. I will provide a brief overview of the history of how DFT+U came to be starting from the origin of the Hubbard and Anderson model Hamiltonians. This history lesson is necessary because it permits us to make the connections between the “Hubbard U” and fundamental outstanding challenges in electronic structure theory, and it helps to explain why this method is so widely applied to transition-metal oxides and organometallic complexes alike.Burroughs Wellcome Fund (Career Award at the Scientific Interface)Massachusetts Institute of Technology. Research Support CorporationNational Science Foundation (U.S.) (ECCS-1449291)MIT Energy InitiativeMassachusetts Institute of Technology. Department of Chemical Engineering (Startup Funds
Physical understanding and modeling of chemical mechanical planarization in dielectric materials
No full textThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2007.Includes bibliographical references (p. 257-268).Chemical mechanical planarization (CMP) has become the enabling planarization technique of choice for current and emerging silicon integrated circuit (IC) fabrication processes. This work studies CMP in dielectric materials in particular, which is widely used in device formation for isolation and in interconnect formation for dielectric planarization. The physical understanding of the process is essential for CMP tool engineers to design optimal consumables, for circuit engineers to make the layout design manufacturing friendly and for process engineers to better control the process. The major contributions of this work are a framework to study the physics of CMP and physically-based particle-level and die-level models of polishing and planarization. A framework for studying the physics of CMP is established by analyzing the complex system and decoupling the interactions occurring at different scales. A particle- level CMP model is developed that bridges the microscopic polishing mechanisms to the macroscopic properties of the system. A physically-based die-level model is proposed by explicit modeling of the pad and pad surface asperities, with model parameters that are based on the physical properties of the pad rather than purely fitting parameters. A semi-empirical die-level CMP model, motivated by the new physically-based die-level model, is developed that improves upon previous pattern density step-height models by making realistic assumptions and approximations, and improving the ease of computation. The model is applied to simulate polishing of either single- material or dual-material structures with either conventional or non conventional slurries. The die-level models are then applied to engineering problems, including design for manufacturing, nanotopography impact, wafer edge roll-off effects, and motor current based endpoint detection.by Xiaolin Xie.Ph.D
Chemical reaction dynamics of Rydberg atoms with neutral molecules: A comparison of molecular-beam and classical trajectory results for the H(n)+D-2 -> HD+D(n ') reaction
No full textRecent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, H(n)+D-2 -> HD+D(n) at low collision energies. It was discovered that the rotationally resolved product distribution was remarkably similar to a much more limited data set obtained at a single scattering angle for the ion-molecule reaction H++D-2 -> D++HD. The equivalence of these two problems would be consistent with the Fermi-independent-collider model (electron acting as a spectator) and would provide an important new avenue for the study of ion-molecule reactions. In this work, we employ a classical trajectory calculation on the ion-molecule reaction to facilitate a more extensive comparison between the two systems. The trajectory simulations tend to confirm the equivalence of the ion+molecule dynamics to that for the Rydberg-atom+molecule system. The theory reproduces the close relationship of the two experimental observations made previously. However, some differences between the Rydberg-atom experiments and the trajectory simulations are seen when comparisons are made to a broader data set. In particular, the angular distribution of the differential cross section exhibits more asymmetry in the experiment than in the theory. The potential breakdown of the classical model is discussed. The role of the "spectator" Rydberg electron is addressed and several crucial issues for future theoretical work are brought out. (c) 2005 American Institute of Physics
Strongly interacting quantum mixtures of ultracold atoms
No full textThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 198-202).This thesis describes the construction of a new apparatus for ultracold quantum gases as well as the scientific results this machine has produced so far. This new apparatus is capable of simultaneously cooling and trapping lithium, sodium, and potassium. It therefore provides a platform to study a large variety of quantum mixtures. Three main experimental results are presented. Firstly, the direct cooling of "K to Bose-Einstein condensation is presented. Then the 41K atoms provide the coolant for 6Li and 40K, achieving a triply degenerate gas of 6Li -40K -41K. In particular, a broad interspecies Feshbach resonance between 40K -41K is observed, opening a new pathway to study a strongly interacting isotopic Bose-Fermi mixture of 40K -41K. Secondly, a new Bose-Fermi mixture of 23Na -40K is introduced. We show that 23Na is a very efficient coolant for 40K by sympathetically cooling 40K to quantum degeneracy with the help of a 23Na condensate. Moreover, over thirty interspecies Feshbach resonances are identified, paving the way to study strongly interacting Bose- Fermi problems, in particular the Bose polaron problem. Thirdly, we report on the first formation of ultracold fermionic Feshbach molecules of 23Na40K by radio-frequency association. The lifetime of the nearly degenerate molecular gas exceeds 100 ms in the vicinity of the Feshbach resonance. The NaK molecule features chemical stability in its ground state in contrast to the case of the KRb molecule. Therefore, our work opens up the prospect of creating chemically stable, fermionic ground state molecules of 23Na40K where strong, long-range dipolar interactions will set the dominant energy scale. Finally, the thesis concludes with an outlook on future topics in polaron physics and quantum dipolar gases, which can be studied using the new apparatus.by Cheng-Hsun Wu.Ph.D
Solving sign problems with meron cluster algorithms : simulating field theories at non-zero chemical potential
No full textThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, February 2001.Includes bibliographical references (p. 97-102) and index.Numerical simulation of quantum systems develop sign problems upon the introduction of a chemical potential. The sign problem thus makes many interesting physical systems very difficult to study numerically. In this thesis, two related systems which develop sign problems in this way are considered: a D-Theory representation of a 1+1 dimensional 0(3) quantum field theory with a chemical potential, and antiferromagnetic Heisenberg quantum spin ladders in a magnetic field. In both cases, meron cluster algorithms are used to completely solve the sign problem. Using these algorithms, numerical results were generated in the two models for, respectively, the particle number as a function of the chemical potential and magnetization as a function of the external field. These results are in agreement with corresponding analytic predictions.by Benjamin S. Scarlet.Ph.D
Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces
No full texturface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work [J. Comput.-Aided Mol. Des. 9, 149 (1995) ], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.National Institutes of Health (U.S.) (GM065418)National Institutes of Health (U.S.) (CA096504)Singapore-MIT AllianceNational Science Foundation (U.S.)Natural Sciences and Engineering Research Council of Canada (NSERC
Physics-informed neural networks and functional interpolation for stiff chemical kinetics
No full textThis work presents a recently developed approach based on physics-informed neural networks (PINNs) for the solution of initial value problems (IVPs), focusing on stiff chemical kinetic problems with governing equations of stiff ordinary differential equations (ODEs). The framework developed by the authors combines PINNs with the theory of functional connections and extreme learning machines in the so-called extreme theory of functional connections (X-TFC). While regular PINN methodologies appear to fail in solving stiff systems of ODEs easily, we show how our method, with a single-layer neural network (NN) is efficient and robust to solve such challenging problems without using artifacts to reduce the stiffness of problems. The accuracy of X-TFC is tested against several state-of-the-art methods, showing its performance both in terms of computational time and accuracy. A rigorous upper bound on the generalization error of X-TFC frameworks in learning the solutions of IVPs for ODEs is provided here for the first time. A significant advantage of this framework is its flexibility to adapt to various problems with minimal changes in coding. Also, once the NN is trained, it gives us an analytical representation of the solution at any desired instant in time outside the initial discretization. Learning stiff ODEs opens up possibilities of using X-TFC in applications with large time ranges, such as chemical dynamics in energy conversion, nuclear dynamics systems, life sciences, and environmental engineering. © 2022 Author(s).12 month embargo; published online: 01 June 2022This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]
Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics
No full textThe recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network such that the network not only conforms to the measurements and initial and boundary conditions but also satisfies the governing equations. This work first investigates the performance of the PINN in solving stiff chemical kinetic problems with governing equations of stiff ordinary differential equations (ODEs). The results elucidate the challenges of utilizing the PINN in stiff ODE systems. Consequently, we employ quasi-steady-state assumption (QSSA) to reduce the stiffness of the ODE systems, and the PINN then can be successfully applied to the converted non-/mild-stiff systems. Therefore, the results suggest that stiffness could be the major reason for the failure of the regular PINN in the studied stiff chemical kinetic systems. The developed stiff-PINN approach that utilizes QSSA to enable the PINN to solve stiff chemical kinetics shall open the possibility of applying the PINN to various reaction-diffusion systems involving stiff dynamics
Accurate schemes for calculation of thermodynamic properties of liquid mixtures from molecular dynamics simulations
No full textWe explore different schemes for improved accuracy of entropy calculations in aqueous liquid mixtures from molecular dynamics (MD) simulations. We build upon the two-phase thermodynamic (2PT) model of Lin et al. [J. Chem. Phys. 119, 11792 (2003)] and explore new ways to obtain the partition between the gas-like and solid-like parts of the density of states, as well as the effect of the chosen ideal “combinatorial” entropy of mixing, both of which have a large impact on the results. We also propose a first-order correction to the issue of kinetic energy transfer between degrees of freedom (DoF). This problem arises when the effective temperatures of translational, rotational, and vibrational DoF are not equal, either due to poor equilibration or reduced system size/time sampling, which are typical problems for ab initio MD. The new scheme enables improved convergence of the results with respect to configurational sampling, by up to one order of magnitude, for short MD runs. To ensure a meaningful assessment, we perform MD simulations of liquid mixtures of water with several other molecules of varying sizes: methanol, acetonitrile, N, N-dimethylformamide, and n-butanol. Our analysis shows that results in excellent agreement with experiment can be obtained with little computational effort for some systems. However, the ability of the 2PT method to succeed in these calculations is strongly influenced by the choice of force field, the fluidicity (hard-sphere) formalism employed to obtain the solid/gas partition, and the assumed combinatorial entropy of mixing. We tested two popular force fields, GAFF and OPLS with SPC/E water. For the mixtures studied, the GAFF force field seems to perform as a slightly better “all-around” force field when compared to OPLS+SPC/E.Peer reviewe
Calculation of state-to-state cross sections for triatomic reaction by the multi-configuration time-dependent Hartree method
No full textA framework for quantum state-to-state integral and differential cross sections of triatomic reactive scattering using the Multi-Configuration Time-Dependent Hartree (MCTDH) method is introduced, where a modified version of the Heidelberg MCTDH package is applied. Parity of the system is adopted using only non-negative helicity quantum numbers, which reduces the basis set size of the single particle functions in angular degree of freedom almost by half. The initial wave packet is constructed in the space-fixed frame, which can accurately account for the centrifugal potential. By using the reactant-coordinate-based method, the product state-resolved information can be accurately extracted. Test calculations are presented for the H + H-2 reactive scattering. This work demonstrates the capability of the MCTDH method for extracting accurate state-to-state integral and differential cross sections. As an efficient scheme for high-dimensional problems, the MCTDH method may be promising for the study of product state-resolved cross sections for polyatomic reactive systems. (C) 2014 AIP Publishing LLC
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