... Reiner Dreizler and E. K. U. Gross, “Density Functional Theory” (Springer 1990)
In addition to these, journal articles will be recommended as we go along.
There will be about 5 long problem sets, due about every two weeks.
Seminar Presentation: 50%
During the last few weeks, y ...
Systematic improvement of the correlation energy of solids
... Quantum mechanics provides a comprehensive description of the properties of
matter at the atomic scale. Accordingly, the Schrödinger equation could be used as
a powerful tool to predict and interpret the properties of materials of technological
interest or biological systems, for example. However, t ...
Exercises in Statistical Mechanics
... problems are original, while other were assembled from various undocumented sources. In particular some problems originate from exams that were written by B. Horovitz (BGU), S. Fishman
(Technion), and D. Cohen (BGU).
FINAL REVIEW 1st SEMESTER 2014-2015
... Balance the following equation.
aluminum acetate + sodium hydroxide → aluminum hydroxide + sodium acetate
... Calculate the location at which the radial probability density is a maximum for the
2-s state of the hydrogen atom. Then calculate the expectation value of the radial
coordinate in this state. Which answer if either is consistent with the Bohr model
Chemistry 2000 Review: quantum mechanics of
... This equation was know to belong to a special class known as an eigenvector equation: an
operator acts on a function (ψ) and generates a scalar times the same function
Ψ is known as the wavefunction of the electron: there are an infinite number of such
wavefunctions, each of which is characterized b ...
QuantumChem - II
... functionals used are approximate
• DFT calculations scale as N3
• More rapid basis-set convergence
• Much better for transition metal complexes
• Known problems with DFT
– Not good at dispersion (van der Waals)
– H-bonds are somewhat too short
Radiation Equilibrium (in Everything Including Direct Semiconductors)
... But how about hν = Eg/2 or any other energy inside the band gap? After all, photons with these energies can not
be created in the semiconductor, while they have a certain density according to Plancks formula.
Well, as in the free electron gas model (which does not have band gaps after all) we have m ...
Materials Computation Center R.M. Martin and J.P. Leburton
... Approach: We concentrate on material and
design parameters that influence the exchange
interaction between conduction electrons in realistic
double QDs. For this purpose, we use a combined
approach based on density functional theory (DFT)
to model the QD potential, and diffusion quantum
Monte Carlo ...
... Given that red light has a wavelength of 700 x 10-9 meters, what is the frequency
and how much energy does it have?
To find frequency, use first formula, c=lambda x frequency
Frequency = 3x 108 m/s / 700 x 10-9 meters = 4.29 x 1014 Hz
To find Energy, plug it into the second formula:
E = hf = (6.6 x ...
3 — Blackbody Radiation [Revision : 1.5]
... – In the UV, visible and IR parts of spectrum of many stars, Fλ is crudely approximated
as a blackbody
• Blackbody radiation
– Blackbody (BB) is an object that absorbs all radiation falling on it
– In thermal equilibrium at temperature T , radiation re-emitted by BB has a unique Fλ
that depends only ...
homework 2, due October 3rd
... Consider a particle described at some particular instant of time by the wave function ψ(x) = Ae−ax .
1. Determine A so ψ is normalized.
2. Compute hxi, hx2 i and σx2 = h(x − hxi)2 i.
3. Compute hpi, hp2 i and σp2 = h(p − hpi)2 i.
4. Show that by changing a one can make either σx2 or σp2 small, but n ...
Electronic Structure Theory
... § Full account of electronic correlations
§ Allows model and calculations beyond
i.e., potential energy surface (PES)
§ Accepting the challenge of
Lecture 2 Hamiltonian operators for molecules CHEM6085: Density
... 1) Use summation symbols to generalise the example of the water molecule from the lectures to an expression for
the electronic Hamiltonian operator of any molecule, with any number of nuclei and electrons.
2) Write down an expression for the expectation value of each of the terms of the above Hamilt ...
Chapter 4 Test Question Topics
... 1- Know the definitions of the ground state and the excited states of
2- What must occur for an atom to move from the ground to the
excited state or from the excited to the ground state?
3- Know the definitions of an electron cloud and an atomic nucleus.
4- What determines the size and shap ...
Final Exam Review
... 44. Write the orbital diagram & electron
configurations for the following elements: K, Ar,
H, He, Br
45. Define precision and accuracy.
46. What determines an element’s order on the
47. What happens to the temperature of a
substance as it is changing states?
48. What is kinetic energ ...
Density functional theory
Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function, which in this case is the spatially dependent electron density. Hence the name density functional theory comes from the use of functionals of the electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry.DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. In many cases the results of DFT calculations for solid-state systems agree quite satisfactorily with experimental data. Computational costs are relatively low when compared to traditional methods, such as Hartree–Fock theory and its descendants based on the complex many-electron wavefunction.Despite recent improvements, there are still difficulties in using density functional theory to properly describe intermolecular interactions (of critical importance to understanding chemical reactions), especially van der Waals forces (dispersion); charge transfer excitations; transition states, global potential energy surfaces, dopant interactions and some other strongly correlated systems; and in calculations of the band gap and ferromagnetism in semiconductors. Its incomplete treatment of dispersion can adversely affect the accuracy of DFT (at least when used alone and uncorrected) in the treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms) or where dispersion competes significantly with other effects (e.g. in biomolecules). The development of new DFT methods designed to overcome this problem, by alterations to the functional and inclusion of additional terms to account for both core and valence electrons or by the inclusion of additive terms, is a current research topic.