/*! \page OBDMDoc one-body density matrix Keyword: OBDM \section description Description Spherically averaged one-body density matrix for up-spin electrons \f$ \rho_{1\uparrow}^{sph}(|{\bf r}|) \f$, \f[ \rho_{1\uparrow}({\bf r}_1,{\bf r}_1') =\int d^3r_2\ldots d^3r_N\, \Psi^*({\bf r}_1,{\bf r}_2,\ldots,{\bf r}_N) \Psi({\bf r}_1',{\bf r}_2,\ldots,{\bf r}_N)\,, \f] \f[ \rho_{1\uparrow}^{sph}(|{\bf r}|) = \frac1{4\pi}\int d\Omega_{\bf r}\, \int d^3r_1 \rho_{1\uparrow}({\bf r}_1+{\bf r},{\bf r}_1)\,, \f] calculated on a one-dimensional grid. The many-body wave function \f$ \Psi \f$ in the above definition is assumed normalized to unity. Normalization of the density matrix is chosen so that \f$ \rho_{1\uparrow}^{sph}(0)=1 \f$. In homogeneous and isotropic systems, such as homogeneous electron gas, the one-body density matrix is a spherically symmetric function of only one distance, and therefore \f$ \rho_{1\uparrow}^{sph} \equiv \rho_{1\uparrow} \f$. In polarized cases, \f$ N_{\uparrow}\not = N_{\downarrow} \f$, the density matrix for down-electrons differs from the matrix for up-electrons. Quantity \f$ \rho_{1\downarrow}^{sph} \f$ is not (yet) implemented. \section options Options \subsection reqopt Required None. \subsection optopt Optional
Option | Type | Default | Description |
---|---|---|---|
CUTOFF | Float | half of the smallest distance in the simulation cell | Largest distance at which the density matrix is calculated. Values much larger than the default value have little physical meaning. |
NGRID | Integer | 5 | Number of points in the interval [0;CUTOFF] where the density matrix is calculated. The first point is CUTOFF/NGRID, the last point is CUTOFF. |
AIP | Integer | 1 | Number of directions for spherical averaging using a Gaussian quadrature rule. Available are Gaussian rules with 4, 6, 12, 18, 26 and 32 points. Value AIP=1 disables spherical averaging and the vector \f$ \bf r \f$ then points in the x-direction. |