Electron density

<p>Electron density or electronic density is the measure of the <a href="/facts/Probability/fgYvMhwb">probability</a> of an <a href="/facts/Electron/L0KBo5cW">electron</a> 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 
  
    
      
        ρ
        (
        
          
            r
          
        
        )
      
    
    {\displaystyle \rho ({\textbf {r}})}
  
 or 
  
    
      
        n
        (
        
          
            r
          
        
        )
      
    
    {\displaystyle n({\textbf {r}})}
  
. The density is determined, through definition, by the normalised 
  
    
      
        N
      
    
    {\displaystyle N}
  
-electron <a href="/facts/Wavefunction/KgM5ykjY">wavefunction</a> which itself depends upon 
  
    
      
        4
        N
      
    
    {\displaystyle 4N}
  
 variables (
  
    
      
        3
        N
      
    
    {\textstyle 3N}
  
 spatial and 
  
    
      
        N
      
    
    {\displaystyle N}
  
 <a href="/facts/Spin_(physics)/4Jvp7e8P">spin</a> coordinates). Conversely, the density determines the wave function modulo up to a phase factor, providing the formal foundation of <a href="/facts/Density_functional_theory/wwz4Gqdg">density functional theory</a>.
</p><p>According to <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, due to the <a href="/facts/Uncertainty_principle/UUSoSp4T">uncertainty principle</a> 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.
</p>

Electron density open-in-new

Electron density