Chapter Two Ionization Energy Measurements

Total Page:16

File Type:pdf, Size:1020Kb

Chapter Two Ionization Energy Measurements Chapter Two Ionization Energy Measurements Abstract The photorefractive effect depends strongly on the magnitude and rate of formation of the space-charge field. The space-charge field is created by the photogeneration, transport and trapping of charges. In polymers these processes are performed by specific molecules which are added to the material. Since these processes involve electron transfer from one molecule to another it is important to have information about the energy levels of the molecular orbitals of origin and destination. A technique is described which allows the determination of the HOMO energy levels of organic molecules. This technique, ultraviolet photoelectron spectroscopy (UPS), can be employed on molecules either in the gas or the solid phase. In this first attempt, the molecules were investigated in the gas phase, since only in this case can their properties be directly compared with each other. By doing so it was possible to obtain values for the HOMO levels of most of the molecules which are used in photorefractive polymers as described in the forthcoming chapters. Some preliminary understanding of the effect that certain molecules have upon the space-charge field formation and the photorefractive behaviour was obtained. 22 Chapter Two 2.1. Introduction The photorefractive mechanism can roughly be divided into two different regimes, the process of the space-charge field formation and the conversion of this space-charge field into a refractive index grating1. The latter process, although very important, will not be dealt with in this chapter but is thoroughly described in the next chapters. The process of the space-charge field formation is dependent on a number of parameters and can be described by: charge generation, charge transport and charge trapping, as was shown in chapter 1 (figure 1.2). There is one feature that all the processes involved in the space-charge field formation have in common, the transfer of an electron from one molecule to another. This can only be done if the electron overcomes the barrier between the two states2. The barrier that must be overcome depends on geometrical factors, the distance between the two molecules and the positioning of the molecules with respect to one another, but also on the energies of the state of origin and destination3. The total energies of the different states involved in the space-charge field formation are schematically presented in figure 2.1. Fig. 2.1: Schematic representation of the total energy of the states involved in the creation of a space-charge field. CG* and CG- represent the excited and the negatively charged charge generator molecule, CT*, CT and CT+ represent the excited, the neutral and the positively charged charge transport molecule and Tr+ represents the positively charged trapping site. It is possible to determine the energies of the different states if information about the ionization energy and electron affinity of the different molecules is available. The main molecular orbitals that are involved in the space-charge field formation are Ionization Energy Measurements 23 the highest occupied molecular orbitals (HOMO’s) of the charge generator, transport and trapping molecule and the lowest unoccupied molecular orbital (LUMO) of the charge generator molecule. One technique that gives information on the energy levels of occupied molecular orbitals is Photoelectron Spectroscopy (PES)4,5,6. In PES a molecule (M) is exited by a monochromatic beam of photons with energy hv, in which process M loses an electron. M + hv ® M+ + e (3.1) M+ is the resulting ion formed and e is the product photoelectron. In order for this process to occur, the incident photons should have an energy higher than the lowest ionization energy (EI) of the sample. It follows that the energy available after ionization, hv - Ip, must appear as translational energy of the electron. Thus, if mono-chromatic photons are used for ionization and the photon energy is known, a simple determination of the kinetic energy of the photoelectrons provides the ionization energy of the molecules. Depending on the energy of the photons employed, PES is sensitive to different energy ranges of molecular orbitals. For instance when x-ray sources are used to provide the photons, information about the core orbitals of the molecules and atoms under investigation is obtained. In this case the technique is referred to as XPS. When detailed information about the highest occupied molecular orbitals is needed, a source that provides photons with energies comparable to the first ionization energies of the sample is required. Usually a helium gas discharge lamp is used, which provides light in the vacuum-ultraviolet (VUV) region of the electromagnetic spectrum consequently the technique is referred to as Ultraviolet Photoelectron Spectroscopy (UPS). A schematic representation of this process is shown in figure 2.2. Here a molecule with five filled molecular orbitals is depicted, of which only three are accessible by the photons used in this experiment. Electrons can be ejected from these orbitals if photons are absorbed. This results in a molecular ion with three different final states, M+(1), M+(2) and M+(3), and three electrons with different kinetic energies. Usually the features are broadened by various vibrational relaxations. This is schematically depicted as the broadening of the lines in the photoelectron spectrum. 24 Chapter Two Fig. 2.2: Schematic representation of the processes involved in a UPS experiment. On the left, a molecule with five filled levels, three of which are accessible to the photons. In the middle: the molecular ions M+(1), M+(2) and M+(3) resulting from the ionization of the three highest occupied orbitals. On the right, the corresponding photoelectron spectrum reflecting molecular orbital levels is displayed. The peaks observed in this spectrum mimic the kinetic energy of the electrons. The energies of the originating molecular orbitals can now be reconstructed by subtracting the kinetic energy of the electrons from the known photon energy. For example, electrons ejected from the highest occupied molecular orbital (which will result in the creation of molecular ion M+(1)) will have the largest kinetic energy and will be observed as the first peak in the photoelectron spectrum. UPS can be performed both on molecules in the solid and in the gas phase6. The main difference between the UPS spectra of molecules measured in the solid and those measured in the gas phase is that in the solid phase interactions between neighbouring molecules play a significant role whereas they do not in the gas phase. These interactions between neighbouring molecules are mainly caused by their polarizabilities. When a molecule is photoionized it can be stabilized by interaction with induced dipoles on surrounding molecules. These interactions decrease the ionization energy and increase the electron affinity resulting in a decrease of the conductivity gap. From the above- described considerations it is not clear in which phase the molecules used in photorefractive polymers should be measured. If the investigated molecules would be used in the pure solid phase, it is obvious that the ionization energy should be measured in the solid phase. However, due to the fact that the molecules will be used in Ionization Energy Measurements 25 combination with an inactive polymer binder and, more importantly, with large concentrations of very polar NLO molecules, the values obtained from the pure solid phase will be inaccurate. This is caused by the difference in polarity of the actual surroundings and that of the investigated molecules, which will shift the energy levels of the investigated molecules, due to a change in dipolar interaction. For this reason the experiments were performed in the gas phase, as the effect of the surroundings is avoided and a more direct comparison of the energy levels can be made. The so obtained energy levels can only be used as an approximation to the actual situation if the highly polar environment has approximately the same effect on all the different molecules investigated. This assumption is a crucial one for the interpretation of the values obtained. 2.2. Experimental section 2.2.1. The ultraviolet photoelectron spectrometer The essential components of an ultraviolet photoelectron spectrometer are a lamp that produces suitable radiation, an ionization chamber, an electron energy analyser, an electron detector and a recorder5. These components are shown schematically in figure 2.3, and will be briefly discussed. Fig. 2.3: Essentials of an ultraviolet photoelectron spectrometer. All the electron optics must be contained within a vessel evacuated to 10-6 mbar or less. The lamp provides the photons which are used to ionize the sample. In order to reach the highest occupied orbitals, which generally have ionization energies between 26 Chapter Two five and fifteen electron volts, photons from a helium discharge lamp are used; more precisely the photons from the He I resonance line at 58.4 nm, equivalent to a photon energy of 21.22 eV. A hemispherical analyser, in combination with a lens system, was used as the electron energy analyser. This system was chosen because it provides a high resolution of the photoelectron spectrum5. Since the molecules are (large) organic molecules and solids at room temperature, some kind of heating device must be constructed to evaporate these molecules. In order to create a sufficiently high density for an acceptable signal-to-noise ratio, large amounts of molecules should be evaporated. Due to the organic nature of these molecules, however, they contaminate the apparatus, which prohibits accurate measurements due to charging effects. Therefore, a source was constructed which provides a collimated beam of gas molecules on which the helium lamp and the analyser are focused. In figure 2.4 a detailed drawing of the employed oven is shown. Fig. 2.4: A schematic representation of the source used to create a collimated beam of organic gas molecules.
Recommended publications
  • Density Functional Theory
    Density Functional Theory Fundamentals Video V.i Density Functional Theory: New Developments Donald G. Truhlar Department of Chemistry, University of Minnesota Support: AFOSR, NSF, EMSL Why is electronic structure theory important? Most of the information we want to know about chemistry is in the electron density and electronic energy. dipole moment, Born-Oppenheimer charge distribution, approximation 1927 ... potential energy surface molecular geometry barrier heights bond energies spectra How do we calculate the electronic structure? Example: electronic structure of benzene (42 electrons) Erwin Schrödinger 1925 — wave function theory All the information is contained in the wave function, an antisymmetric function of 126 coordinates and 42 electronic spin components. Theoretical Musings! ● Ψ is complicated. ● Difficult to interpret. ● Can we simplify things? 1/2 ● Ψ has strange units: (prob. density) , ● Can we not use a physical observable? ● What particular physical observable is useful? ● Physical observable that allows us to construct the Hamiltonian a priori. How do we calculate the electronic structure? Example: electronic structure of benzene (42 electrons) Erwin Schrödinger 1925 — wave function theory All the information is contained in the wave function, an antisymmetric function of 126 coordinates and 42 electronic spin components. Pierre Hohenberg and Walter Kohn 1964 — density functional theory All the information is contained in the density, a simple function of 3 coordinates. Electronic structure (continued) Erwin Schrödinger
    [Show full text]
  • Electron Density Functions for Simple Molecules (Chemical Bonding/Excited States) RALPH G
    Proc. Natl. Acad. Sci. USA Vol. 77, No. 4, pp. 1725-1727, April 1980 Chemistry Electron density functions for simple molecules (chemical bonding/excited states) RALPH G. PEARSON AND WILLIAM E. PALKE Department of Chemistry, University of California, Santa Barbara, California 93106 Contributed by Ralph G. Pearson, January 8, 1980 ABSTRACT Trial electron density functions have some If each component of the charge density is centered on a conceptual and computational advantages over wave functions. single point, the calculation of the potential energy is made The properties of some simple density functions for H+2 and H2 are examined. It appears that for a diatomic molecule a good much easier. However, the kinetic energy is often difficult to density function would be given by p = N(A2 + B2), in which calculate for densities containing several one-center terms. For A and B are short sums of s, p, d, etc. orbitals centered on each a wave function that is composed of one orbital, the kinetic nucleus. Some examples are also given for electron densities that energy can be written in terms of the electron density as are appropriate for excited states. T = 1/8 (VP)2dr [5] Primarily because of the work of Hohenberg, Kohn, and Sham p (1, 2), there has been great interest in studying quantum me- and in most cases this integral was evaluated numerically in chanical problems by using the electron density function rather cylindrical coordinates. The X integral was trivial in every case, than the wave function as a means of approach. Examples of and the z and r integrations were carried out via two-dimen- the use of the electron density include studies of chemical sional Gaussian bonding in molecules (3, 4), solid state properties (5), inter- quadrature.
    [Show full text]
  • Chemistry 1000 Lecture 8: Multielectron Atoms
    Chemistry 1000 Lecture 8: Multielectron atoms Marc R. Roussel September 14, 2018 Marc R. Roussel Multielectron atoms September 14, 2018 1 / 23 Spin Spin Spin (with associated quantum number s) is a type of angular momentum attached to a particle. Every particle of the same kind (e.g. every electron) has the same value of s. Two types of particles: Fermions: s is a half integer 1 Examples: electrons, protons, neutrons (s = 2 ) Bosons: s is an integer Example: photons (s = 1) Marc R. Roussel Multielectron atoms September 14, 2018 2 / 23 Spin Spin magnetic quantum number All types of angular momentum obey similar rules. There is a spin magnetic quantum number ms which gives the z component of the spin angular momentum vector: Sz = ms ~ The value of ms can be −s; −s + 1;:::; s. 1 1 1 For electrons, s = 2 so ms can only take the values − 2 or 2 . Marc R. Roussel Multielectron atoms September 14, 2018 3 / 23 Spin Stern-Gerlach experiment How do we know that electrons (e.g.) have spin? Source: Theresa Knott, Wikimedia Commons, http://en.wikipedia.org/wiki/File:Stern-Gerlach_experiment.PNG Marc R. Roussel Multielectron atoms September 14, 2018 4 / 23 Spin Pauli exclusion principle No two fermions can share a set of quantum numbers. Marc R. Roussel Multielectron atoms September 14, 2018 5 / 23 Multielectron atoms Multielectron atoms Electrons occupy orbitals similar (in shape and angular momentum) to those of hydrogen. Same orbital names used, e.g. 1s, 2px , etc. The number of orbitals of each type is still set by the number of possible values of m`, so e.g.
    [Show full text]
  • Electron Charge Density: a Clue from Quantum Chemistry for Quantum Foundations
    Electron Charge Density: A Clue from Quantum Chemistry for Quantum Foundations Charles T. Sebens California Institute of Technology arXiv v.2 June 24, 2021 Forthcoming in Foundations of Physics Abstract Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schr¨odingerand Born, are in tension with one another but are not incompatible. Schr¨odinger'sidea that the nucleus of an atom is surrounded by a spread-out electron charge density is supported by a variety of evidence from quantum chemistry, including two methods that are used to determine atomic and molecular structure: the Hartree-Fock method and density functional theory. Taking this evidence as a clue to the foundations of quantum physics, Schr¨odinger'selectron charge density can be incorporated into many different interpretations of quantum mechanics (and extensions of such interpretations to quantum field theory). Contents 1 Introduction2 2 Probability Density and Charge Density3 3 Charge Density in Quantum Chemistry9 3.1 The Hartree-Fock Method . 10 arXiv:2105.11988v2 [quant-ph] 24 Jun 2021 3.2 Density Functional Theory . 20 3.3 Further Evidence . 25 4 Charge Density in Quantum Foundations 26 4.1 GRW Theory . 26 4.2 The Many-Worlds Interpretation . 29 4.3 Bohmian Mechanics and Other Particle Interpretations . 31 4.4 Quantum Field Theory . 33 5 Conclusion 35 1 1 Introduction Despite the massive progress that has been made in physics, the composition of the atom remains unsettled. J. J. Thomson [1] famously advocated a \plum pudding" model where electrons are seen as tiny negative charges inside a sphere of uniformly distributed positive charge (like the raisins|once called \plums"|suspended in a plum pudding).
    [Show full text]
  • Nature of Noncovalent Carbon-Bonding Interactions Derived from Experimental Charge-Density Analysis
    Nature of Noncovalent Carbon-Bonding Interactions Derived from Experimental Charge-Density Analysis Eduardo C. Escudero-Adán, Antonio Bauzffl, Antonio Frontera, and Pablo Ballester E. C. Escudero-Adán,+ Prof. P. Ballester X-Ray Diffraction Unit Institute of Chemical Research of Catalonia (ICIQ) Avgda. Països Catalans 16, 43007 Tarragona (Spain) E-mail : [email protected] A. Bauzffl,+ Prof. A. Frontera Department of Chemistry Universitat de les Illes Balears Crta. de Valldemossa km 7.5, 07122 Palma de Mallorca (Spain) E-mail : [email protected] Prof. P. Ballester Catalan Institution for Research and Advanced Studies (ICREA) Passeig Lluïs Companys 23, 08010 Barcelona (Spain) In an effort to better understand the nature of noncovalent carbon-bonding interactions, we undertook accurate high-res- olution X-ray diffraction analysis of single crystals of 1,1,2,2-tet- racyanocyclopropane. We selected this compound to study the fundamental characteristics of carbon-bonding interactions, because it provides accessible s holes. The study required ex- tremely accurate experimental diffraction data, because the in- teraction of interest is weak. The electron-density distribution around the carbon nuclei, as shown by the experimental maps of the electrophilic bowl defined by a (CN)2C-C(CN)2 unit, was assigned as the origin of the interaction. This fact was also evidenced by plotting the D21(r) distribution. Taken together, the obtained results clearly indicate that noncovalent carbon bonding can be explained as an interaction between confront- ed oppositely polarized regions. The interaction is, thus elec- trophilic–nucleophilic (electrostatic) in nature and unambigu- ously considered as attractive. Attractive intermolecular electrostatic interactions encompass electron-rich and electron-poor regions of two molecules that complement each other.[1] Electron-rich entities are typically anions or lone-pair electrons and the most well-known elec- tron-poor entity is the hydrogen atom.
    [Show full text]
  • 10 Mar 2015 Density Functional Theory for Field Theorists I
    RUNHETC-2015-07 SCIPP 15/11 Density Functional Theory for Field Theorists I Tom Banks NHETC and Department of Physics Rutgers University, Piscataway, NJ 08854-8019 and Department of Physics and SCIPP University of California, Santa Cruz, CA 95064 E-mail: [email protected] Abstract I summarize Density Functional Theory (DFT) in a language familiar to quantum field theorists, and introduce several apparently novel ideas for constructing systematic approximations for the density functional. I also note that, at least within the large K approximation (K is the number of electron spin components), it is easier to compute the quantum effective action of the Coulomb photon field, which is related to the density functional by algebraic manipulations in momentum space. arXiv:1503.02925v1 [cond-mat.mtrl-sci] 10 Mar 2015 0 Contents 1 Density Functional Theory for Quantum Field Theorists 1 2 Expansions in the Number of Spin Components 5 2.1 The Large K Expansion ............................. 5 2.2 SmallKExpansion ................................ 8 2.3 TheKSEquations ................................ 9 3 Expansions of the Functional Determinant 10 4 1/K expansion of the HEG 11 5 Conclusions 12 6 Acknowledgments 13 1 Density Functional Theory for Quantum Field The- orists Much of atomic, molecular and (quantum) condensed matter physics, reduces, in the non- relativistic limit, to the problem of solving the Schr¨odinger equation for point-like nuclei and electrons, interacting via the Coulomb potential. The electrons are fermions, and are best treated by introducing an electron field ik x ψi(x)= ai(k)e · , (1.1) Xk where i is a spin label. If we introduce dimensionless space-time coordinates, by using the Bohr radius to measure length, and the Rydberg to measure energy, the only parameters in me the problem are the nuclear charges Za and the mass ratios ma .
    [Show full text]
  • Density Functional Theory
    NEA/NSC/R(2015)5 Chapter 12. Density functional theory M. Freyss CEA, DEN, DEC, Centre de Cadarache, France Abstract This chapter gives an introduction to first-principles electronic structure calculations based on the density functional theory (DFT). Electronic structure calculations have a crucial importance in the multi-scale modelling scheme of materials: not only do they enable one to accurately determine physical and chemical properties of materials, they also provide data for the adjustment of parameters (or potentials) in higher-scale methods such as classical molecular dynamics, kinetic Monte Carlo, cluster dynamics, etc. Most of the properties of a solid depend on the behaviour of its electrons, and in order to model or predict them it is necessary to have an accurate method to compute the electronic structure. DFT is based on quantum theory and does not make use of any adjustable or empirical parameter: the only input data are the atomic number of the constituent atoms and some initial structural information. The complicated many-body problem of interacting electrons is replaced by an equivalent single electron problem, in which each electron is moving in an effective potential. DFT has been successfully applied to the determination of structural or dynamical properties (lattice structure, charge density, magnetisation, phonon spectra, etc.) of a wide variety of solids. Its efficiency was acknowledged by the attribution of the Nobel Prize in Chemistry in 1998 to one of its authors, Walter Kohn. A particular attention is given in this chapter to the ability of DFT to model the physical properties of nuclear materials such as actinide compounds.
    [Show full text]
  • Electronic Structure and Physical Properties of 13C Carbon Composite
    Electronic structure and physical properties of 13C carbon composite ABSTRACT: This review is devoted to the application of graphite and graphite composites in science and technology. Structure and electrical properties, as so technological aspects of producing of high-strength artificial graphite and dynamics of its destruction are considered. These type of graphite are traditionally used in the nuclear industry. Author was focused on the properties of graphite composites based on carbon isotope 13C. Generally, the review relies on the original results and concentrates on actual problems of application and testing of graphite materials in modern nuclear physics and science and its technology applications. Translated by author from chapters 5 of the Russian monograph by Zhmurikov E.I., Bubnenkov I.A., Pokrovsky A.S. et al. Graphite in Science and Nuclear Technique// eprint arXiv:1307.1869, 07/2013 (BC 2013arXiv1307.1869Z Author: Evgenij I. Zhmurikov Address: 68600 Pietarsaari, Finland E-mail: [email protected] KEYWORDS: Structure and properties of carbon; Isotope 13C; Radioactive ion beams 2 1. Introduction In order to explore ever-more exotic regions of the nuclear chart, towards the limits of stability of nuclei, European nuclear physicists have built several large-scale facilities in various countries of the European Union. Today they are collaborating in planning of a new radioactive ion beam (RIB) facility which will permit them to investigate hitherto unreachable parts of the nuclear chart. This European ISOL (isotope-separation-on-line) facility is called EURISOL [1]. At the present moment experiments with RIB of the first generation have yielded important results. But the first generation RIB facilities are often limited by the low intensity of the beams.
    [Show full text]
  • Theoretical Basis of Quantum-Mechanical Modeling of Functional Nanostructures
    S S symmetry Review Theoretical Basis of Quantum-Mechanical Modeling of Functional Nanostructures Aleksey Fedotov 1,2 , Alexander Vakhrushev 1,2,*, Olesya Severyukhina 1,2, Anatolie Sidorenko 2 , Yuri Savva 2, Nikolay Klenov 3,4 and Igor Soloviev 3 1 Department Simulation and Synthesis Technology Structures, Institute of Mechanics, Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences, 426067 Izhevsk, Russia; [email protected] (A.F.); [email protected] (O.S.) 2 Laboratory of Functional Nanostructures, Orel State University named after I.S. Turgenev, 302026 Orel, Russia; [email protected] (A.S.); su_fi[email protected] (Y.S.) 3 Laboratory of Nanostructure Physics, Department of Microelectronics, Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia; [email protected] (N.K.); [email protected] (I.S.) 4 Science and Research Department, Moscow Technical University of Communication and Informatics, 111024 Moscow, Russia * Correspondence: [email protected] Abstract: The paper presents an analytical review of theoretical methods for modeling functional nanostructures. The main evolutionary changes in the approaches of quantum-mechanical modeling are described. The foundations of the first-principal theory are considered, including the stationery and time-dependent Schrödinger equations, wave functions, the form of writing energy operators, and the principles of solving equations. The idea and specifics of describing the motion and inter- action of nuclei and electrons in the framework of the theory of the electron density functional are Citation: Fedotov, A.; Vakhrushev, A.; Severyukhina, O.; Sidorenko, A.; presented. Common approximations and approaches in the methods of quantum mechanics are Savva, Y.; Klenov, N.; Soloviev, I.
    [Show full text]
  • The Radial Electron Density in the Hydrogen Atom and the Model of Oscillations in a Chain System
    July, 2012 PROGRESS IN PHYSICS Volume 3 The Radial Electron Density in the Hydrogen Atom and the Model of Oscillations in a Chain System Andreas Ries Universidade Federal de Pernambuco, Centro de Tecnologia e Geociencias,ˆ Laboratorio´ de Dispositivos e Nanoestruturas, Rua Academicoˆ Helio´ Ramos s/n, 50740-330 Recife – PE, Brazil E-mail: [email protected] The radial electron distribution in the Hydrogen atom was analyzed for the ground state and low-lying excited states by means of a fractal scaling model originally published by Muller¨ in this journal. It is shown that Muller’s¨ standard model is not fully adequate to fit these data and an additional phase shift must be introduced into its mathematical apparatus. With this extension, the radial expectation values could be expressed on the logarithmic number line by very short continued fractions where all numerators are Euler’s number. Within the rounding accuracy, no numerical differences between the expectation values (calculated from the wavefunctions)and the corresponding modeled values exist, so the model matches these quantum mechanical data exactly. Besides that, Muller’s¨ concept of proton resonance states can be transferred to electron resonances and the radial expectation values can be interpreted as both, proton resonance lengths and electron resonance lengths. The analyzed data point to the fact that Muller’s¨ model of oscillations in a chain system is compatible with quantum mechanics. 1 Introduction partial denominators are positive or negative integer values: The radial electron probability density in the Hydrogen atom 1 S = n + . (2) was analyzed by a new fractal scaling model, originally pub- 0 1 n + lished by Muller¨ [1–3] in this journal.
    [Show full text]
  • Introduction to First-Principles Method
    Joint ICTP/CAS/IAEA School & Workshop on Plasma-Materials Interaction in Fusion Devices, July 18-22, 2016, Hefei Introduction to First-Principles Method by Guang-Hong LU (吕广宏) Beihang University Computer Modeling & Simulation Theory ComputerComputer modeling & simulation” has Modeling emerged as an indespensableExperiment method for & scientificSimulation research of materials in parallel to experiment and theory. Outline Introduction (first principles) Introduction (history of first principles) Basic principles • calculation of total energy • electron-electron interaction (DFT-LDA) • Bloch’s theorem – periodic system • electron-ion interaction (pseudopotential) Supercell technique Computational procedure Future 3 Multiscale Modeling & Simulation: Conceptual framework First-principles method First-principles method Solve quantum mechanic Schrodinger equation to obtain Eigen value and Eigen function, and thus the electronic structure. • The charm: only atomic number and crystal structure as input, which can determine precisely the structure and the properties of the real materials. • first principles - physics, materials Density functional theory • ab initio -quantum chemistry Hartree-Fork self-consistent field A connection between atomic and macroscopic levels (不同尺度之间的联系) First-principles method Elastic constants Binding energy Energy barrier mechanics thermodynamics kinetics 7 Outline Introduction (first principles) Introduction (history of first principles) Basic principles • calculation of total energy • electron-electron interaction
    [Show full text]
  • Quantum Mechanics
    Quantum Mechanics • No real understanding of the chemical bond is possible in terms of classical mechanics because very small particles such as electrons do not obey the laws of classical mechanics. • Their behavior is determined by quantum mechanics, which was developed in the second half of the 1920s culminating in a mathematical formalism that we still use today. • Quantum mechanics is used by chemists as a tool to obtain the wave function and corresppgonding energy and ggyeometry of a molecule by solving the fundamental equation of quantum mechanics, called the Schrödinger equation. • The Schrödinger equation can only be completely solved for the hydrogen atom, or isoelectronic ions, with just one electron. Approximation methods must be used for multi‐ electron atoms and polyatomic molecules. • The most characteristic feature of quantum mechanics which differentiates it from classical mechanics is its probalistic character. Classical statistical Quantum probabilistic Dual Wave‐Particle Nature of Light • Light is not just emitted or absorbed in light quanta but that it travels through space as small bundles of energy called photons. • Although photons are regarded as mass‐less particles, their energy is remarkably expressed in terms of the frequency of a wave. • Although light has no mass it has momentum, which depends on the wavelength of the light. E = h . = c/ E = h . c / h / pde Broglie wavelength E = p.c (E = m.c2) Ephoton photon 1 / photon pphoton • In summary, the energy of light is transmitted in the form of particle‐like photons, which have an energy that depends of the frequency and momentum of the photon.
    [Show full text]