What is Electron density: Definition and 38 Discussions

In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either




{\displaystyle \rho ({\textbf {r}})}




{\displaystyle n({\textbf {r}})}
. The density is determined, through definition, by the normalized


{\displaystyle N}
-electron wavefunction which itself depends upon


{\displaystyle 4N}
variables (


{\textstyle 3N}
spatial and


{\displaystyle N}
spin coordinates). Conversely, the density determines the wave function modulo up to a phase factor, providing the formal foundation of density functional theory.
According to quantum mechanics, due to the uncertainty principle on an atomic scale the exact location of an electron cannot be predicted, only the probability of its being at a given position; therefore electrons in atoms and molecules act as if they are "smeared out" in space. For one-electron systems, the electron density at any point is proportional to the square magnitude of the wavefunction.

View More On Wikipedia.org
  1. Vick

    A Peebles Equation for fractional electron density

    I am trying to compute the Peebles equation as found here: I am doing so in Python and the following is my attempt: However, I'm unable to solve it. Either my solver is not enough, or I have wrongly done the function for calculating the Equation. # imports from scipy.optimize import fsolve...
  2. Dario56

    I Potential Energy of an Electron-Nuclei Interaction in DFT

    In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional on electron density. If we know how potential energy varies across space, we can calculate this functional with plugging particular...
  3. shahbaznihal

    Electron density Saha Ionization Equation

    Saha-Boltzmann equation describes the ratio of number densities between any two consecutive ionization states and its product with the number electron density i.e. $$n_e\frac{n_{i+1}}{n_{i}}$$ Here, ##n_e## is the electron number density, ##n_{i+1}## is the number density in ##i+1## ionization...
  4. GiovanniNunziante

    A Derivation of the Heisenberg equation for electron density

    I'm studying plasmons from "Haken-Quantum Field Theory of Solids", and i need some help in the calculation of the equation of motion of eletrons' density \begin{equation} \hat{\rho}_{\overrightarrow{q}} = \frac{1}{\sqrt{V}} \sum_{\overrightarrow{k}}...
  5. Kara386

    Free electron density conduction band

    Homework Statement How many free electrons are there in the CB? Diamond has a bandgap of ##5.5##eV.Assume the material is at room temperature and that there are ##2 \times 10^{22}## cm##^{-3}## electrons in the material. What does this mean for their use in semiconductor devices? Homework...
  6. harini07

    General organic chemistry -- finding maximum electron density

    Homework Statement In pyrrole the electron density is maximum on which carbon atom? so if the numbering starts from nitrogen, the carbon on the right side of nitrogen let it be numbered as 2 and the next one as 3 and so on... which of the following options will have the carbons of maximum...
  7. Eric Walker

    B Non-equilibrium variation in electron density in a metal

    Consider two atoms of platinum, A and B, in a sample of platinum. Atom A lives deep within the sample, and atom B lives at the tip of a sharp protuberance at the surface. My understanding is that electrons in the sample will accumulate within a surface defect such as the tip of a sharp needle...
  8. Karan Punjabi

    Oxygen Charge & Electron Density in Simple Carboxylic Acids

    In any simple carboxylic acid there are two oxygen atoms then i have a confusion that which oxygen has more negative charge on it or which one has the most electron density on it?
  9. E

    I Number of electrons in conduction band

    Hello! In order to obtain the number of actual electrons in the conduction band or in a range of energies, two functions are needed: 1) the density of states for electrons in conduction band, that is the function g_c(E); 2) the Fermi probability distribution f(E) for the material at its...
  10. T

    I How is a top gate used to change electron density?

    How is a top gate used to change electron density in 2D semi conductors? I get the principle, you are just shifting the chemical potential by some voltage so that there are more or less electrons in the specific bands. But how is it physically done? Thanks.
  11. I

    How do I solve an electron density continuity equation for Earth's atmosphere?

    Homework Statement Hi! I need to solve a continuity equation for electron density as a function of time in the E-region of Earth's atmosphere. I shall neglect vertical transport and that the ion production rate completely shuts off dusk. Homework Equations See below The Attempt at a...
  12. I

    Electron density as a function of time

    Homework Statement Hi! I really need help with finding time- dependent continuity equation for electron densities in the atmosphere. I've tried to solve it without any success. My question is if someone can give me a good link/link or equations that I can start with. Homework Equations See...
  13. P

    Determine electron density with impurites

    Homework Statement Let’s introduce an imaginary atom which can replace the silicon atom and generate one mobile electron. What is electron density when all silicon atoms are replaced by this imaginary atom Homework EquationsThe Attempt at a Solution I have tried looking for a formula to...
  14. P

    Electron Density when Introducing Impurites

    How do you go about calculating electron densities, especially when impurities are involved?
  15. Jan Wo

    Getting electron density from probability density function

    Hello Lastly I was thinking a lot about electron density definition. It is not intuitive for me and I'm looking for any mathematical tool that could explain it to me more. My friend told me about idea to derivate it from propability density function using Dirac delta distribution. I'd like to...
  16. Jan Wo

    Interpreting Electron Density Definition

    Hi I'd like to ask you about interpretation of electron density definition. According to the "Handbook of Molecular Physics and Quantum Chemistry" it goes like: ##\rho (\textbf{r})=N \sum_{\sigma_1}^{\sigma_N} \idotsint_{\mathbb{R^3}} |\psi_V (\textbf{r}_1, \sigma_1;\dots...
  17. Tone L

    Calculating Electron Density: Ionospheric Research

    Homework Statement I am conducting some research and have come across a problem, it could very well be misunderstanding. I am trying to calculate electron density N.Homework Equations There was given a simple formula F = 9√N ... where F = critical frequency and N = electron density... But...
  18. R

    Slab Beam of electrons through Neutralising Ions

    Homework Statement A slab beam of electrons of thickness a, width w >> a, charge density (-ρb ), (Take ρb to be positive.) and velocity vbez passes through a channel of neutralizing ions with charge density f*ρb where f is some number between zero and one (all parameters given above apply in...
  19. C

    Free electron concentration range between semiconductors and metals

    A structure with free electron density around 10^26 m^-3 is considered as a highly doped semiconductor or a metal? Or in other words, what is the lowest possible free electron concentration for a metal and what is the highest possible free electron concentration for a doped semiconductor?
  20. A

    How can the electron density expression be simplified using momenta?

    Suppose we have a system with M nuclei and N electrons the electron density is defined as: \rho(\mathbf{r}) = \sum\limits_{\sigma = \uparrow, \downarrow} \sum\limits_{i}^N \psi^{*}_{i}(\mathbf{r\sigma})\psi_{i}(\mathbf{r\sigma}) i would like to know if it is valid...
  21. W

    Interpretation of deformation electron density maps (for Al alloys)

    I am posting this from a friend's account since I've been unable to register for a while. Brace yourselves for this is going to be a long post. ----------------------- TLDR: I am trying to figure out the reason for AlSi's lower than expected from atomic misfit solid solution hardening...
  22. P

    Electron density in terms of squares of wavefunctions

    Dear all, I have a quantum system made up of two layers. An electric field is applied with two voltages applied at both layers. I want to calculate the electronic densities that reside at the two laters in terms of the wavefunctions obtained from solving the HamiltoniaN..Anyone knows of an...
  23. H

    How were electron density clouds established?

    Suppose I plan an experiment to sample the position of an electron in an atom. I pick an arbitrary position that's close to the nucleus. Isn't the probability that I will find an electron at that exact chosen position at anyone moment in time equal to 0, since an electron is thought of being...
  24. M

    Free Electron Density of States question

    I have seen thee following relation in regards to free electron waves with wavevector k : < k | k' > = (2.pi)^3 . d( k - k') where d() is a Dirac delta function. Why the 2.pi factor?? I can't seem to motivate it. Also, from this, it is stated that the density of states is then 1 /...
  25. U

    Electrostatic charge vs. Electric current: Effect on electron density of states

    I am having difficulty ascertaining the difference between an electrostatic charge present on the surface of a conductor and the flow of an electron current (or holes, if you prefer) along the surface of a conductor with respect to their effects on the electron density of states (and, more...
  26. M

    Electron Density of Silver: Calculate With Formula

    Given: density of silver = 10.5 g/cm3, atomic weight = 108, assume 1 electron per atom. Question: Find the electron density in the metallic state of silver. i have the formula 2V/h3 for the density of states in momentum space. I'm not sure if this is the correct formula to use and if so, how...
  27. L

    Electron Density in a 2s Orbital

    Why does a 2s orbital have some electron density near the nucleus rather than have all of it outside the node?
  28. L

    Electron Density: Probability of Finding Electrons?

    In an orbital with 2 electrons is electron density the probability of finding a particular electron in that region or the probability of finding either of the 2 electrons (the probability of finding electron 1 plus the probability of finding electron 2)?
  29. A

    What is the electron density of stars in their atmospheres?

    Hi, Does anybody know a place where i can find a list of electron densities of stars?
  30. C

    Electron Density: Do They Become More Dense When Cold?

    In my physics class today my teacher was wondering when electrons get colder do they become more dense . So do electron become more dense if the get colder.
  31. N

    Trichloroacetic acid: electron density and stability

    "The rather strong acidity of trichloroacetic acid is usually ascribed to the inductive effect of the three chlorine atoms attached to the end of the molecle opposite the acidic proton. Electron density is withdrawn away from the carboxylate group so that the trichloroacetate anion that is...
  32. I

    Valence/conduction electron density of a classical gas

    sorry if this is in the wrong section. the forum rules say a textbook related issue goes here. i'm reading the ashcroft and mermin solid state physics book and referring to page 4. in the context of drude theory, the book states that the valence/conduction electron densities for metals are...
  33. H

    Quantum Mechanics: Expression for electron density

    I'm a little confused about the expression for the electron density. For example in Marder's Condensed Matter Physics, he writes this \rho(\vec{r}) = N \int \Psi^{*} \delta( \vec{r} - \vec{r}_1) \Psi d\vec{r}_1 \ldots d\vec{r}_N \delta what's going on?
  34. H

    Electron Density vs Electron Density Difference

    From articles reporting DFT calculations in atomic systems (eg. unit cells of metallic systems), I have seen charts that display contours of the "Electron Density" and "Electron Density Difference". Would appreciate it if someone could give a brief explanation of (1) what the difference between...
  35. A

    IO3− - 5 Regions of Electron Density, 6 Bonded Electrons

    [SOLVED] electron density I think this is the topic if not then I apologize. IO3− Has how many regions of high electron density and how many bonded electrons? I got 5 regions of electron density and 6 bonded electrons. Is this correct? I could use some help or any advice for this question.
  36. S

    Calculating Electron Density in F2 Layer Using Ionosonde Pulse

    The electron densities, ne, at any height h < 300 km on the lower side of an F2 layer can be described by a scale height relationship: n_{e}(h) = n_{e}(300) \exp\left(\frac{0.75(h-300)}{H_{O}}\right) where HO is the neutral atomic oxygen scale height. If the ionosphere has an isothermal...
  37. Mk

    Free Electron Density Explained: What Is It?

    Is free electron denisty how many electrons per volume unit, flowing through? Do the electrons actually flow through? How do you find the free electron density with only known the diameter of a wire, and the drift velocity? I found out how to get it with the atomic mass, and density of the...
  38. N

    Calculating Free Electron Density in a Metal Wire

    A length of metal wire has a radius of 0:002 m and a resistance of 0.1. When the potential difference across the wire is 14 V, the electron drift speed is found to be 0:000229 m/s. Based on these data, calculate the density of free electron in the wire. Answer in units of m^-3. r=.002m R=.1...