c----------------------------------------------------------------------
      	program MULTI
c finds many different properties of 1 and 2 electron densities in 3 dimensions, either exponential 
c or gaussian, either analytic or from Hooke's atom or read in from Cyrus' exact densities
c
c author: Kieron Burke
c     in: mode(0=>out vs. r,1=>just engies,2=>do lambda scaling)
c         =Num, # of electrons
c         =next pot (1=Coulomb, 2=harmonic)
c         =np (if next=1, then np=smoothing; next=2, np=1=Kais)
c         =ncorr (0=uncorrelated, 1=correlated)
c         =n=num of grid points
c         =r0*alpha, r0=length scale for grid
c         =nmat = matrix size for Hooke's atom calc.
c         =nl,ngga = no. of lambda values, and gga to use
c         =methods for fake lambda
c         =nbeta = flag to indicate if beta is listed, or to be calcl
c 	  also need densities for two-electron ions, if called.
	include 'basics.inc'
	include 'con.inc'
	include 'dens.inc'
	include 'pot.inc'
	include 'sys.inc'
c	include 'res.d'
	include 'lam.inc'
c         mk= max number of calculations
c         vcgga=gga (or exact) correlation potential for a specific case
c               egga(j,k)
c               j : 1=>X, 2=>C
c               k : 1=LSD,2=PW91,3=PBE,4=BLYP
c               tcgga(j,k)
c               j : 1=> Tc, 2=>Uc
c               vgga(i,j,k)
c               i : r
c         ts,ex,ec,tc,uc 0=exact,1=LSD,...
c
c         m - max size of radial grid
c         n - actual size in calculations
c         r0 - length scale of grid
c         dy = 1/n

c         beta  - parameter determining external potential
c                 next=1=>beta=alpha=Z
c         omega=alpha^2
c         r0alph=r0*alpha
c         mode  - (0=>out vs. r,1=>just engies,2=>do lambda scaling)
c         nmat  - matrix size when doing Hooke's atom calc.
c         nl    - no. of lambda values for scaling calc.
c         ngga  - which gga to use, if only using one.

c         alpha - length scale of external potential
c                 next=1=>alpha=Z
c                 next=2=>alpha=sqrt(m*omega)
c         num   - number of electrons (1 or 2)
c         next  - type of external potential (1=Coulomb, 2=Harmonic)
c         np    - variations in next
c                 next=1, np=1=>smoothed
c                 next=2, np=1=>kais
c         ncorr - correlated (0=>uncorre, 1=>corr)
c
c         dens - density
c         grad - gradient of density
c         d2 = d^2 rho/ dr^2
c         dlap - laplacian of density
c         dl(i) - log(density) 
c
c         vs    - KS potential
c         vnuc  - external potential
c         vh    - hartree pot.
c         vx    - exchange pot.
c         vc    - correlation potential

c         ml    - max. no. of values of lambda
c         tslf  - Ts for different external potentials
c         exlf  - ex for different external potentials
c         Eclf  - Ec for different external potentials
c         Tclf  - Tc for different external potentials
c         Uclf   - Uc for different external potentials
c         vextlf - vextlf for different external potentials
c         xlf    - chosen value for lambda (by one of 4 different methods)
c         gamlf  - 1/xlf
c         nlf    - flag for which method to calculate xlf by.
        
	parameter(mk=200)
	dimension vcgga(0:m)
	dimension egga(2,4),tcgga(2,4)
	dimension ts(0:4),ex(0:4),ec(0:4),tc(0:4),uc(0:4)
	external fnorm,tstf,tsvw