!-------------------------------------------------------------------
    ! function  : Qfunc
    !
    ! package   : Li3 Potential
    !
    ! Language  : Fortran 77 - freeform
    !
    ! author    : F. Colavecchia (flavioc@lanl.gov)
    !
    ! date      : 03/10/03       version:
    ! revision  :                version:
    !
    ! purpose   :  Compute the Q function eq. (19) of the paper JCP 118 5484 (2003).
    !
    ! input     :  t  -> (dim=3) integrity basis eq. (16)
    !              x  -> (dim=n) vector of coefficients of the expansion (20).
    !              n  -> number of coefficients 
    !
    ! output    :  qfunc -> Q function eq. (19) 
    !
    !-------------------------------------------------------------------
      real*8 function Qfunc(t,x,n)
      implicit none
      integer n
      real*8 t(3),x(n)


      logical debug
      integer i,j,k,l
      integer i1,i2,i3,i4      
      real*8 tmp1
      data debug /.false./
!     0th order
      tmp1 = 1d0 
!     1st order
      tmp1 = tmp1 + t(1)*x(3)
!     2nd order
      tmp1 = tmp1 + x(4)*t(1)**2+x(5)*t(2)
!     3rd order
      tmp1 = tmp1 + x(6)*t(1)**3+x(7)*t(2)*t(1)+x(8)*t(3)
!     4th order
      tmp1 = tmp1 + x(9)*t(1)**4+x(10)*t(2)*t(1)**2+x(11)*t(1)*t(3)
     >            + x(12)*t(2)**2
!     5th order
      tmp1 = tmp1 + x(13)*t(1)**5+x(14)*t(2)*t(1)**3+x(15)*t(1)**2*t(3)
     >            + x(16)*t(1)*t(2)**2+x(17)*t(2)*t(3)
      
      Qfunc = tmp1
      
      return
      end

    !-------------------------------------------------------------------
    ! subroutine: dQfunc
    !
    ! package   : Li3 Potential
    !
    ! Language  : Fortran 77 - freeform
    !
    ! author    : F. Colavecchia (flavioc@lanl.gov)
    !
    ! date      : 03/10/03       version:
    ! revision  :                version:
    !
    ! purpose   :  Compute the gradient respect to
    !              the parameters of Q function eq. (19) of the paper JCP 118 5484 (2003)
    !
    ! input     :  t  -> (dim=3) integrity basis eq. (16)
    !              x  -> (dim=n) vector of coefficients of the expansion (20).
    !              n  -> number of coefficients 
    !
    ! output    :  grad -> gradient of Q function eq. (19)
    !
    !-------------------------------------------------------------------



      subroutine  dQfunc(t,x,grad,n)
      implicit none
      integer n
      real*8 t(3),x(n),grad(n)

      
      integer i,j,k,l
      integer i1,i2,i3,i4
!
!     x(2-4) = C(1-3)
!     x(5-10) = C11,C21,C22,C31,C32,C33
!     x(11-20) = C111,....
!
!     Unfold x
!
      grad(3) = t(1)
      grad(4) = t(1)**2
      grad(5) = t(2)
      grad(6) = t(1)**3
      grad(7) = t(2)*t(1)
      grad(8) = t(3)
      grad(9) = t(1)**4
      grad(10)= t(2)*t(1)**2
      grad(11)= t(1)*t(3)
      grad(12)= t(2)**2         
      grad(13)= t(1)**5         
      grad(14)= t(2)*t(1)**3         
      grad(15)= t(1)**2*t(3)       
      grad(16)= t(1)*t(2)**2         
      grad(17)= t(2)*t(3)
      
      return
      end