Electronic Density - Definition

Definition

The electronic density corresponding to a normalized N-electron wavefunction (with r and s denoting spatial and spin variables respectively) is defined as

\begin{align} \rho(\mathbf{r})&=N\sum_{{s}_{1}} \cdots \sum_{{s}_{N}} \int \ \mathrm{d}\mathbf{r}_2 \ \cdots \int\ \mathrm{d}\mathbf{r}_N \ |\Psi(\mathbf{r},s_{1},\mathbf{r}_{2},s_{2},...,\mathbf{r}_{N},s_{N})|^2, \\ &= \langle\Psi|\hat{\rho}(\mathbf{r})|\Psi\rangle, \end{align}

where the operator corresponding to the density observable is

In Hartree-Fock and density functional theories the wave function is typically represented as a single Slater determinant constructed from N orbitals, φk, with corresponding occupations nk. In these situations the density simplifies to

Read more about this topic:  Electronic Density

Famous quotes containing the word definition:

    “Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?”
    —Richard Eberhart (b. 1904)

    “The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
    —Jean Baudrillard (b. 1929)

    “The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
    —Samuel Taylor Coleridge (1772–1834)