Virtual Synthesis of Nanosystems by Design (eBook)

From First Principles to Applications

Liudmila Pozhar (Autor)

eBook Download: PDF | EPUB

2015 | 1. Auflage
382 Seiten
Elsevier Science (Verlag)
978-0-12-397289-7 (ISBN)

Infos

This is the only book on a novel fundamental method that uses quantum many body theoretical approach to synthesis of nanomaterials by design. This approach allows the first-principle prediction of transport properties of strongly spatially non-uniform systems, such as small QDs and molecules, where currently used DFT-based methods either fail, or have to use empirical parameters. The book discusses modified algorithms that allow mimicking experimental synthesis of novel nanomaterials---to compare the results with the theoretical predictions--and provides already developed electronic templates of sub-nanoscale systems and molecules that can be used as components of larger materials/fluidic systems. - The only publication on quantum many body theoretical approach to synthesis of nano- and sub-nanoscale systems by design. - Novel and existing many-body field theoretical, computational methods are developed and used to realize the theoretical predictions for materials for IR sensors, light sources, information storage and processing, electronics, light harvesting, etc. Novel algorithms for EMD and NEMD molecular simulations of the materials' synthesis processes and charge-spin transport in synthesized systems are developed and described. - Includes the first ever models of Ni-O quantum wires supported by existing experimental data. - All-inclusive analysis of existing experimental data versus the obtained theoretical predictions and nanomaterials templates.

Dr. Liudmila A. Pozhar is the Chief Scientist with PermaNature, LLC, a company that develops and manages research projects in sciences, engineering and education, and provides professional help and advice to undergraduate and graduate students seeking professional degrees in sciences and engineering. Since 1995 she has also served as Associate Scientific Editor, Series in Contemporary Chemical Physics, for World Scientific (Singapore). She received her Master Degree in Physics from the Department of Physics (currently School of Physics) at Kharkov State University (currently Kharkov National University) in Kharkov, USSR/Ukraine, and her PhD in Physics and Mathematics from B. I. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences, Kharkov, USSR/Ukraine. Dr. Pozhar is an expert in fundamental theoretical approaches to and modeling of physical and chemical processes in and properties of quantum and classical systems. She pioneered several first-principle theoretical methods in non-equilibrium and equilibrium statistical mechanics, condensed matter, quantum, theoretical, statistical, mathematical, computational and chemical physics, and quantum chemistry. Her major achievements include Pozhar-Gubbins projection operator method, a fundamental transport theory of strongly inhomogeneous fluids, and Pozhar's theory of charge and spin transport in strongly spatially non-uniform quantum systems. Currently, Dr. Pozhar works on a generalization of this latter method to a generalized projection operator approach with Sarry's closure applicable to any quantum or classical system with arbitrary spatial inhomogeneities. Applying her theoretical methods to practical engineering problems, Dr. Pozhar has developed a concept and computational tools of a first-principle theory-based, computational method (called virtual synthesis method) and synthesized virtually about 40 quantum dot and wire systems, and 20 nanofluidic systems, with pre-designed structural, electronic, optical, magnetic and dynamic properties. She is an author of 3 books, and several book chapters, and published about 160 peer-reviewed papers in refereed journals. Prior to her appointment as the Chief Scientist with PermaNature, Dr. Pozhar worked as a professor for the University of Idaho, Western Kentucky University, University of Tennessee/ORNL, and the University of Surrey (UK). She served as a Senior National Research Council Research Associate, Senior Scientist, Visiting Scholar, Deputy Director for Research, and Research Group Head with world-class Government Labs and academic institutions, including the Air Force Research Laboratory (AFRL, Dayton, OH), Cornell University, UNESCO International Center for Theoretical Physics (ICTP, Trieste, Italy), Institute of Electromagnetic Research (Kharkov, Ukraine), and B.I. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Scientist (ILTPE, Kharkov, USSR/Ukraine).

Textauszug

1

Transport Properties of Spatially Inhomogeneous Quantum Systems From the First Principles

Summary

First-principle theoretical tools of statistical mechanics include perturbation theory, projection operator methods and density functional theory (DFT) that form a fundamental basis of modern description of thermodynamic and transport properties in systems composed of three or more real or virtual quantum or classical particles. Among other technical advantages, the first two of these methods allow self-consistent prediction of the properties of such systems in terms of correlation functions and two-time temperature Green’s functions calculated analytically or numerically. Since its introduction in physics, perturbation theory remains the only rigorous and self-consistent method of those three available, although it encounters technical difficulties when applied to strongly spatially inhomogeneous systems, such as fluid flows at interfaces, or non-equilibrium processes in small and low-dimensional systems, such as molecules, quantum dots and wires, and thin films. Density functional theory experiences fundamental difficulties due to its non-variational nature already in the equilibrium system case, and its applications to non-equilibrium systems have not been rigorously justified. This chapter overviews a recent Green’s function (GF) - based fundamental theory of strongly spatially inhomogeneous quantum systems, and a self-consistent and explicit projection operator method to calculate GFs developed by Yu. A. Tserkovnikov in collaboration with D. N. Zubarev. This method of GF calculations is the only first-principle approach applicable to systems of any nature and dimensionality without fundamental restrictions. At the same time, as any projection operator method, this method is not closed in a sense discussed below, and thus currently undergoes further development.

Keywords

quantum statistical mechanics

projection operator method

two-time temperature Green’s functions

linear response theory

transport properties

1.1. Introduction

Since Gibbs and Boltzmann, statistical mechanics has been focused on the first-principle prediction of thermodynamic and transport properties of many particle systems. The majority of models and mathematical methods of statistical mechanics are designed to work in so-called thermodynamic limit where the number of particles (N) and the system volume (V) simultaneously tend to infinity, while their ratio remains finite. Another important concept concerns the initial state of a many-particle system that is assumed to be the thermodynamic equilibrium corresponding to the minimum minimorum of the total energy of the system. These two concepts validate rigorously the use of theory of stochastic processes and mathematical statistics methods to reduce a system of 6N coupled equations of motion (in the simplest case) for the system particles to one equation of motion of the entire system formulated with respect to the N-particle distribution function of the system (classical Liouville equation) or the N-particle density matrix (the von Neumann, or quantum Liouville equation), respectively. At the next step, perturbation theory, DFT or projection operator methods are used to reduce the Liouville, or von Neumann (in the quantum case) equations to the so-called master equation for collective dynamical variables or observables, respectively, that can be further reduced to a manageable system of coupled equations for correlation functions or Green’s functions (GFs). Further on, the equations for conserved collective dynamical variables (observables) are derived, and the thermodynamic and/or transport properties are identified in terms of the correlation functions and/or GFs. Thus, once the correlation functions or GFs are determined, the thermodynamic and transport properties of the N-particle system can be calculated directly.

With advent of novel technologies of materials and media synthesis there is a growing demand for updating the fundamental basis of statistical mechanics to account for small and/or strongly spatially inhomogeneous systems. Such first-principle statistical mechanical foundation is especially important to design novel materials for quantum electronics, spinstronics, quantum computing, communication, information processing and storage technologies. In particular, fundamental understanding of coherent, polarized, and entangled charge and spin states of quantum particles, their dynamics, and their contributions to quantum spin/charge transport properties at realistic materials synthesis conditions, such as quantum confinement, is paramount [1–5] to establish novel electronic materials technologies. In other words, relations between the structure, and thermodynamic and transport properties of materials and media, must be established using first principle quantum statistical mechanical methods.

At present, solid state electronic structure theory [6–10] largely employs somewhat modified statistical mechanical foundation specific to bulk solid lattices and various half-heuristic methods [11] to identify systems exhibiting new electronic properties, such as quantum wells, large quantum wires [12] and quantum dots (QDs) [13]. In the case of small structures, such as small QDs, where statistical mechanical approaches so modified do not work, computational methods, such as DFT- and Hartree-Fock-based (HF) methods, self-consistent field (SCF) approximations, configuration interaction (CI) methods, complete active space SCF (CASSCF), multi configuration SCF (MCSCF), Møller-Plesset - and coupled-clusters approximations are used to calculate the electronic energy level structure directly solving the Schrödinger equation numerically. [These methods will be briefly discussed in Chapter 2.] At present, the corresponding software packages, such as GAMESS, NWChem [14], GAUSSIAN or Molpro, allow the electronic structure calculations for systems in equilibrium at zero temperature. In addition, equilibrium and non-equilibrium molecular dynamics (MD) simulations are widely used to study structure-property relations at non-zero temperature. In particular, the spin/charge transport processes are simulated using MD or Monte-Carlo means in the Born-Oppenheimer approximation. In the case of numerical calculations and MD simulations, correlations between the electronic structure and the transport properties are introduced heuristically, adjusting the statistical mechanical and semi-phenomenological approaches developed for large systems. Such computations, on their own, do not permit first-principle predictions of the spin/charge transport properties of small QDs and molecules. Yet accurate first-principle predictions are crucial to manipulate with electron spins and quantum states of energy and information carriers in small QD/QW systems.

In their turn, existing semi-heuristic modifications [15–23] of various theoretical models developed originally for much larger systems at low temperature conditions and applied to characterize charge and spin transport in small systems often lead to physically incorrect predictions even for mesoscopic tunneling junctions [24]. Even the best of such models do not include adequate description of system-to-confinement coupling, such as quantum confinement effects. At the same time, such coupling is one of the major sources of both decoherence and coherence [25,26] of states of quantum particles, such as the electron charge and spin states [27–29]. Thus, the nature of such models does not allow, in principle, first-principle predictions of electronic and spin/charge transport properties of small and strongly spatially inhomogeneous systems.

As already mentioned in the beginning of this section, first-principle predictions of electronic transport properties imply the use of specifically tailored quantum statistical mechanical methods to derive self-consistently the spin/charge transport theory from the quantum Liouville (von Neumann) equation. Thus far, this formidable task has been properly addressed only for mesoscale systems where non-equilibrium GF (NGF)-based methods [such as Keldysh’s two-time NGF [30–32] and more recent DFT-NGF approaches [33]] are among the most adequate statistical mechanical techniques used. Unfortunately, these methods have several major disadvantages. In particular, the field-theoretical NGFs used in the majority of these approaches are not directly related to the transport coefficients. Thus, despite the availability of a system of coupled equations for NGFs that can be reduced by controlled approximations to a manageable master equation (such as the Kadanoff-Dyson equation, etc.), these methods require further approximations to link NGFs to the transport coefficients. This is done using the major uncontrolled approximation - introducing the (Wigner’s) distribution functions (DFs) [34,35], and deriving and solving the corresponding kinetic equations for DFs with (semi-heuristic) boundary and initial conditions. Using these solutions, one can establish semi-heuristic structure-property relations for the transport coefficients in terms of DFs that are related to NGFs.

Some of the NGF-based approaches correctly use thermodynamic NGFs that can be related to the transport properties directly [36] in the case of large systems, but still have to make use of semi-heuristic considerations...

Produkt-Details

• Erscheint lt. Verlag: 20.2.2015
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Archäologie
• Themenwelt: Geschichte ► Allgemeine Geschichte ► Vor- und Frühgeschichte
• Themenwelt: Naturwissenschaften ► Chemie ► Anorganische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-12-397289-2 / 0123972892
• ISBN-13: 978-0-12-397289-7 / 9780123972897