Dft Definition and 112 Threads

I saw in a reference "For a system consisting just of one electron, DFT predicts an non-physical self-interaction energy." (Theor Chem Acc (2009) 123:171–182), and thus wrong single electron energy. Does this mean I can quickly conclude whether a specific exchange-correlation functional has been...

Hello All! I was wondering if anyone can tell me if or if not the wavefunctions used to construct the electron density in density functional theory contains hybridizied orbitals. I have been working with a planewave pseudopotential code and in the input file of a pseudopotential, say...

Hi, I have the following problem: Let x,y be finite real valued sequences defined on 0...N-1 and let g be a non negative integer . define also on 0..N-1. In addition, the DFT of y is known in closed form. Is there a way to write z as some cyclic convolution, so that with the...

Let x,y be finite real valued sequences defined on 0...N-1 and let g be a non negative integer . define also on 0..N-1. In addition, the DFT of y is known in closed form. Is there a way to write z as some cyclic convolution, so that with the help of the convolution theorem z can be calculated...

Hello. I started studying DFT and using it for a bit of work I needed to do in College. I found it a bit interesting, because of the possibility of getting in touch with more "applied" science. However, after a time reading papers related to it I got a little disappointed. It seems to me that...

From what I have read, FFT seems to simply be faster than DFT, thus making DFT redundant. However, if computational speed is not an issue, are there any advantages of using DFT over FFT (such as increased precision, for example)?

Problem: The first six values of the 10-point DFT of a real-valued sequence x(n) are given by {10, −2 + j3, 3 + j4, 2 − j3, 4 + j5, 12} Determine the DFT of x[n] = x[n+5] (10 point sequence) Relevant Equations: DFT(x[n-m]) = exp(-j*(2pi/N)*k*m) * X(k) where N = 10 ; m = -5...

Hi All, I'm finishing up my PhD in Computational Condensed Matter. I've worked almost exclusively in spin systems using things like Monte Carlo and Exact Diagonalization. However, my specialty is in producing high-quality, high-performance, often parallel research codes (i.e. none of my...

so this is from math lab x is a 2 kHz sinewave >> n = 0:1023; >> t = n/8000; >> x = sin(2000*2*pi*t); >> X = fft(x); >> plot(n,abs(X)); I have uploaded the picture of the graph ... but is it wrong 2000 is the only one that should have a real value right ?

ok this is the best example i could find of DFT http://faculty.ksu.edu.sa/ghulam/Documents/CEN352/DSP_CEN352_ch4_DFT.pdf example 1) this is what I am trying to do... however it did not work for the guy... f[1] should be the only one with an value but it was a j0.5 and he got that for...

I took f(t) = SIN(10*t) +SIN(5*t) and got this f(0) = 0 f(1) = -1.5 f(2) = 0.4 f(3) = -0.3 now I tried to do the DFT Fs = 4Hz N = 4 samples 3 f[r] = Ʃ x[k]ε^(-j(2πkr/4) k=0 f[r] = 0 -1.5ε^(-j(2πr/4) + 0.4ε^(-j(2π(2)r/4) -0.3ε^(-j(2π(3)r/4) f[0] = 0 - 1.5 +...

I realize this is something I should probably know intuitively, but why are core states (generally) treated relativistically in density functional calculations? What exactly makes these relativistic bound states rather than non-relativistic? I think this is some basic physics I'm forgetting.

Homework Statement Calculate, by hand, the DFT of cos(2*pi(fx*m + fy*n)). It should simplify to something simple. It should NOT be left as a summation. Homework Equations 2D DFT Formula: \tilde{s(k,l)} = \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} s(m,n) e^{-j 2 \pi (\frac{1}{M}mk +...

Homework Statement Compute the M sample DFT of: f(m) = cos(2*pi*(f*m)) for 0 <= m <= M-1 where M = 128, f = 1/16 This should be done by hand, and the solution will reduce to a very simple form. Homework Equations The Attempt at a Solution I slaved through this problem...

I am reading the following paper: Soft-decision decoding of polar codes with Reed-Solomon kernels On the last line of the page 319 (page 3 of the pdf) the author says "and G is a Reed-Solomon kernel, which is in fact a DFT matrix". G is defined on the page 321 (page 5 of the pdf) with...

The problem: What is the discrete Fourier transform of a constant value? Example DFT{2} This is not my homework problem but will help me immensly in solving the actual problem. DFT formula: X_{k} =\sumx[n] * e^{\frac{-2\pi kn}{N}} from n = 0 to N-1 where N is the number of...

A somewhat strange request. I have come across this paper: http://jcp.aip.org/resource/1/jcpsa6/v98/i7/p5648_s1 It lists hybrid DFT results for dissociation calculations. I am looking for DFT calculations that are not as phenomenological, but can't seem to find any in the literature. Are...

In Kohn-Sham DFT, the Coulomb potential, which is a component of the Kohn-Sham potential, is given by: v_H(\mathbf{r}) = \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'} where \rho(\mathbf{r'}) is the electron density. For molecular systems with exponential densities...

Hello I am trying to calculate the n-point DFT of a signal using fft where n=512 and plot it in matlab. The signal is a separate file that I have read into matlab. I am able read and plot the first 512 values of the signal but when I try to get the dft of the signal and plot it the outcome does...

greetings, i have typed some code in MATLAB to find the 5 point fft of cos function of frequency 100hz but in answer i am not geting the answer at 100 hz.may i know where the things going wrong. the code is as this one clc; t=0:1/4:1; x=cos(2*pi*100*t); xm=abs(fft(x)); disp(xm)...

why does the DFT of sin(2∏nKo/N) give two value at k=K0 and k=-K0 though sin has only one frequency component and the DFT is complex , what does it mean? frequency can't have any phase the why it is complex? thanks

Homework Statement Consider the finite length x[n]= 2δ[n]+δ[n-1]+δ[n-3] We perform the following operation on this sequence: (i) We compute the 5-point DFT X[k] (ii) We compute a 5-point inverse DFT of Y[k]=X[k]2 a) Determine the sequence y[n] for n= 0, 1, 2, 3, 4 b) If N-point...

This question is not directly related to QM although my reason for asking it is I'm trying to compute wavefunctions on my PC -- please excuse me if this is the wrong place to ask. I am having trouble using the DFT in Mathematica although I don't think my problem is directly Mathematica related...

I am a freshman in DFT calculation. I don't understand the DFT method clearly,but I want to use DFT to do some calculations. My question is that how how can I get the potential energy of each atom in a structure using DFT package ,which I have done by using classical MD method in Lammps(the...

I have a f(n*t) vs t data areay how to find out its (DFT) Fourier transform in c. I find every time that every program needs its real and imaginarry part. but i have only magnitude. please help me out to find DFT of these data .

Homework Statement As an example, if we find a DFT of x[n]={1,1,0,1} the result will be X(m)={3,1,-1,1} Homework Equations My Question is that as we know DFT holds symmetry property, why this answer does not void for that property?

Continious FT of a rectangle is real valued but DFT of it is not!? Continious Fourier Transform of a rectangle with amplitude of 1 between [-u,u] is a real valued function (u is a positive number). Actually it is a sinc function. However when I use discrete Fourier Transform (fft) I obtain...

Thanks for any help! I'm trying to understand the coefficients of a 2d DFT. say we've got this matrix, f(a,b) \left( \begin{array}{ccc} 9 & 1 & 9 \\ 9 & 1 & 9 \\ 9 & 1 & 9 \end{array} \right) I used wolfram alpha's function, Fourier{f(a,b)} and the transform comes back as \left(...

How does one edit the input sequence and the results so as to be able to calculate the inverse dft with the dft algorthm?

Hi Everyone, I am a PhD student working on different collector molecules used in flotation process (an important mineral separation process). One of the important part of my project will be to study the reactivity of different types of collectors towards some particular mineral(s) by using...

Hi, could someone explain the following quote to me, please? It explains, why the Kohn-Sham-Scheme of DFT fails to describe transition states. My questions: If N_i ist the occupation number and the wavefunction may be given by \Psi = \sum_I{c_I \Phi_I} where \Phi_I are...

The band gap discontinuity in DFT? Hi everybody... I've read about the band gap problem of Density functional theory, there is a discontinuity of the band gap when an electron add to the Kohn-Sham system I have two questions could anybody answer me? please 1- why this discontinuity happens...

Maybe someone else had this problem. Lets say we have a sampled Gaussian pulse in time domain and transform it into frequency domain. For that I use the discrete Fourier transform. Now the resulting set of transformed values is made up of complex numbers. I want to extract two things from that...

Hello, I was trawling through some MATLAB work, and came across a question that bugged me, and I hope that someone might be able to give a suitable explanation. The question was explain why the 21 point DFT has so many values equal to zero. Both DFT's are sinc functions where: sinc(L)=...

Hello All, I am little confused with the Fourier family of transforms. I would really appreciate it if someone could have a look at them My understanding is as follows: Fourier Series: Only used for Peiodic continuous signals. Fourier Transform: Can be used for periodic or...

Dear all, I trying to get a better understanding of the DFT method, but the more I read the more I'm confused. Well, for crystal states it seems that the use of the plane wave with pseudo potentials is the "best" choice. But yet we have to choice between soft pseudo potentials or projector...

Hello to everyone :) Since I did not notice a presentation section I put some info about myself before the question,. My name is Enrico, I am Italian (form Modena) and I am 18. I am studying Electronics&Telecommunications in High School and I have applied for UCSD/UCLA/Berkeley (I hope they...

I'm curious to know why chemists like to use Gaussian basis set in case of an ab-initio (ex.DFT) calculation. I understand that the molecules that are of interest to chemists are non-periodic and hence plane wave basis is not useful, but can't they use other real space basis like a grid? What...

DFT used electron density instead wavefunction, and in same time DFT use Schrodinger equation that use wavefunction. !?? so it still depend on wavefunction of Kohn-Sham and not depend on density only non interaction system wavefunction of still stand please I have many Paradox to...

Hi there! I need to calculate the Fourier transform of a continuous function in C++. To do this I need to use the Dft, but what is the relation between the Dft and the continuous Fourier transform? I mean, how can I get the continuous Fourier transform from the Dft?

Dear all, In Density Functional Theory (DFT) the Kohn-Sham eigenvalues are used to construct the band structure and the density of states (DOS). For a 3D extended system the eigenvalues are determined up to a constant since there is no absolute energy reference, while for a 2D extended...

hi everyone, I need help in a project.I have a signal x(n)=(0.5^n)*u(n). i want to find the DFT of the signal for N1=50,N2=20,N3=11 and then the reconstruction of the signal. I don't know anything about MATLAB and i don't have any idea how i'll do this. My problem is the code so if someone can...

Hey. I got a locked configuration of atoms, that is there positions are fixed. I would like to calculate the energy of this configuration and also the electron density. I've looked around on the internet and in some books and found that maybe Density Functional Theory (DFT) is the answer. If...

When I take the fft of a set of data and plot it, there is a reflection around the nyquist. Everybody knows this, but I would like to know what the physical meaning of the second half (the reflected half) is. The real component is the same as the first half, and the imaginary component has...

Hello, Does anybody know commercial codes in which you can implement semi-infinite boundary conditions for surface calculations. I know for modeling metallic adhesion semi-infinite BC's have been used in the past along with a Jellium potential approximation. Unfortunately, I've been searching...

-- i know there were threads about reduced density matrix in this forum, but I am reading "Density-functional theory of atoms and molecules" by Parr R., Yang W., their notation is quite confusing to me... their notation is the same as shown in this page...

Dear all: I need to calculate the density of states of electrons from metallic clusters. I ran a DFT program and output the mulliken population analysis datas, such as the following: (I show only part of the data) ATOM # 1 ORBITAL ALPHA OCCUPATION 5s...

Hello all, I have read a few papers lately that have used DFT based techniques to investigate metallic adatom adsorption on top of graphene (see for instance PRB 77, 235430 2008). I was under the impression that electrons in graphene are described by the Dirac equation and not the...

"Sliding DFT" discrete Fourier transform... I was wondering if any of you had had experience with the sliding DFT algorithm. It is somewhat similar to the Goertzel algorithm. I am having some trouble understanding the mathematics of the algorithm, and I also cannot seem to identify a useful...

Hi everybody, Can you tell me, in general, why Density Functional Theory does not describe the Van de Waals interaction? Many thanks,