qp2/src/becke_numerical_grid/integration_radial.irp.f

! ---

double precision function knowles_function(alpha, m, x)

  BEGIN_DOC
  ! Function proposed by Knowles (JCP, 104, 1996) for distributing the radial points :
  ! the Log "m" function ( equation (7) in the paper )
  END_DOC
 
  implicit none
  double precision, intent(in) :: alpha, x
  integer,          intent(in) :: m

  !print*, x
  knowles_function = -alpha * dlog(1.d0-x**m)

  return
end

! ---

double precision function derivative_knowles_function(alpha, m, x)

  BEGIN_DOC
  ! Derivative of the function proposed by Knowles (JCP, 104, 1996) for distributing the radial points
  END_DOC

  implicit none
  double precision, intent(in) :: alpha, x
  integer,          intent(in) :: m
  double precision             :: f

  f = x**(m-1)
  derivative_knowles_function = alpha * dble(m) * f / (1.d0 - x*f)

  return
end

! ---

BEGIN_PROVIDER [double precision, alpha_knowles, (100)]

  BEGIN_DOC
  ! Recommended values for the alpha parameters according to the paper of Knowles (JCP, 104, 1996)
  ! as a function of the nuclear charge
  END_DOC

  implicit none
  integer :: i

  ! H-He
  alpha_knowles(1) = 5.d0
  alpha_knowles(2) = 5.d0
 
  ! Li-Be
  alpha_knowles(3) = 7.d0
  alpha_knowles(4) = 7.d0
 
  ! B-Ne
  do i = 5, 10
   alpha_knowles(i) = 5.d0
  enddo
 
  ! Na-Mg
  do i = 11, 12
   alpha_knowles(i) = 7.d0
  enddo
 
  ! Al-Ar
  do i = 13, 18
   alpha_knowles(i) = 5.d0
  enddo
 
  ! K-Ca
  do i = 19, 20
   alpha_knowles(i) = 7.d0
  enddo
 
  ! Sc-Zn
  do i = 21, 30
   alpha_knowles(i) = 5.d0
  enddo
 
  ! Ga-Kr
  do i = 31, 100
   alpha_knowles(i) = 7.d0
  enddo

END_PROVIDER

! ---