10 Density Functionals -- User Interface

      subroutine dftfun_user (key,name,fderiv,open,igrad,npt,rhoc,rhoo,
     >                   sigmacc,sigmaco,sigmaoo,
     >                   tauc,tauo,upsilonc,upsilono,
     >                   zk,vrhoc,vrhoo,
     >                   vsigmacc,vsigmaco,vsigmaoo,
     >                   vtauc,vtauo,vupsilonc,vupsilono)
      implicit double precision (a-h,o-z)
      logical fderiv,open
      integer igrad,npt
      character*(*) key,name
      double precision rhoc(*),rhoo(*)
      double precision sigmacc(*),sigmaco(*),sigmaoo(*)
      double precision tauc(*),tauo(*)
      double precision upsilonc(*),upsilono(*)
      double precision zk(*),vrhoc(*),vrhoo(*)
      double precision vsigmacc(*),vsigmaco(*),vsigmaoo(*)
      double precision vtauc(*),vtauo(*)
      double precision vupsilonc(*),vupsilono(*)

evaluates density-functional integrand $K$ and pseudo functional derivative $v$ at integration points ${\bf r}_i, i=1,\ldots\verb*+npt+$. In the following, $\tilde\rho, \bar\rho$ are the $\alpha,\beta$ spin densities; the total and spin densities are

$$\rho=\tilde\rho+\bar\rho\; , \qquad \hat\rho=\tilde\rho-\bar\rho \; .$$ (1)

Input parameters:

key	specifies code-name of functional
fderiv	functional derivative required, else just $K$
npt	number of $\bf r$ points; if 0, run in test mode without doing any work.
rhoc	$\rho=\tilde\rho+\bar\rho$
rhoo	$\hat\rho=\tilde\rho-\bar\rho$
sigmacc	$\sigma = {\bf\nabla}\rho \cdot {\bf\nabla}\rho$
sigmaco	$\hat\sigma = {\bf\nabla}\rho \cdot {\bf\nabla}\hat\rho$
sigmaoo	$\hat{\hat\sigma} = {\bf\nabla}\hat\rho \cdot {\bf\nabla}\hat\rho$
tauc	$\tau=\left(\sum_i^\alpha+\sum_i^\beta\right) \left\vert{\bf\nabla}\phi_i\right\vert^2$
tauo	$\hat\tau=\left(\sum_i^\alpha-\sum_i^\beta\right) \left\vert{\bf\nabla}\phi_i\right\vert^2$
upsilonc	$\upsilon=\nabla^2\rho$
upsilono	$\hat\upsilon=\nabla^2\hat\rho$

Output parameters:

name	full descriptive name of functional
igrad	maximum order of density differentiation (0, 1 or 2)
zk	$K$
vrhoc	$v_{\rho} = \partial K / \partial \rho$
vrhoo	$v_{\hat\rho} = \partial K / \partial \hat\rho$
vsigmacc	$v_{\sigma} = \partial K / \partial \sigma$
vsigmaco	$v_{\hat\sigma} = \partial K / \partial \hat\sigma$
vsigmaoo	$v_{\hat{\hat\sigma}} = \partial K / \partial \hat{\hat\sigma}$
vtauc	$v_{\tau} = \partial K / \partial \tau$
vtauo	$v_{\hat\tau} = \partial K / \partial \hat\tau$
vupsilonc	$v_{\upsilon} = \partial K / \partial \upsilon$
vupsilono	$v_{\hat\upsilon} = \partial K / \partial \hat\upsilon$

All of the available functionals are of the general form

$$F\left[\rho,\hat\rho, \sigma,\hat\sigma,\hat{\hat\sigma}, \t... ...\hat{\hat\sigma}, \tau,\hat\tau, \upsilon,\hat\upsilon \right)$$ (2)

$K$ is always evaluated, and overwrites whatever was in zk. If fderiv, relevant functional derivatives $v_x$ computed, and are added in to the appropriate arrays. If .not.open, $\hat\rho$ and other open-shell entities are ignored. If igrad.lt.2, $\upsilon$ and similar are ignored; if igrad.lt.1, $\sigma, \tau$ and similar are ignored.

Additional functionals can go in like this:

      else if (key.eq.'MINE') then
        call dftfun_mine(name,fderiv,open,igrad,npt,rhoc,rhoo,
     >                   sigmacc,sigmaco,sigmaoo,tauc,tauo,
     >                   upsilonc,upsilono,
     >                   zk,vrhoc,vrhoo,
     >                   vsigmacc,vsigmaco,vsigmaoo,vtauc,vtauo,
     >                   vupsilonc,vupsilono)

Or simply inline as you like; see src/dft/dftfun.f for examples.