!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright (C) 2000 - 2018  CP2K developers group                                               !
!--------------------------------------------------------------------------------------------------!

! **************************************************************************************************
!> \brief Routines to optimize the RI-MP2 basis. Only exponents of
!>        non-contracted auxiliary basis basis are optimized. The derivative
!>        of the MP2 energy with respect to the exponents of the basis
!>        are calculated numerically.
!> \par History
!>      08.2013 created [Mauro Del Ben]
!> \author Mauro Del Ben
! **************************************************************************************************
MODULE mp2_optimize_ri_basis
   USE atomic_kind_types,               ONLY: atomic_kind_type
   USE basis_set_container_types,       ONLY: add_basis_set_to_container,&
                                              remove_basis_from_container
   USE basis_set_types,                 ONLY: allocate_gto_basis_set,&
                                              gto_basis_set_type
   USE cp_log_handling,                 ONLY: cp_add_default_logger,&
                                              cp_get_default_logger,&
                                              cp_logger_create,&
                                              cp_logger_get_default_unit_nr,&
                                              cp_logger_release,&
                                              cp_logger_set,&
                                              cp_logger_type,&
                                              cp_rm_default_logger
   USE cp_para_env,                     ONLY: cp_para_env_create,&
                                              cp_para_env_release
   USE cp_para_types,                   ONLY: cp_para_env_type
!
   USE hfx_libint_wrapper_types,        ONLY: build_eri_size
   USE hfx_types,                       ONLY: hfx_basis_info_type,&
                                              hfx_basis_type
   USE kinds,                           ONLY: dp
   USE machine,                         ONLY: default_output_unit
   USE memory_utilities,                ONLY: reallocate
   USE message_passing,                 ONLY: mp_comm_split_direct,&
                                              mp_sum
   USE mp2_direct_method,               ONLY: mp2_canonical_direct_single_batch
   USE mp2_ri_libint,                   ONLY: libint_ri_mp2,&
                                              read_RI_basis_set,&
                                              release_RI_basis_set
   USE mp2_types,                       ONLY: mp2_biel_type,&
                                              mp2_type
   USE orbital_pointers,                ONLY: indco,&
                                              init_orbital_pointers,&
                                              nco,&
                                              ncoset,&
                                              nso
   USE orbital_symbols,                 ONLY: cgf_symbol,&
                                              sgf_symbol
   USE qs_environment_types,            ONLY: get_qs_env,&
                                              qs_environment_type
   USE qs_kind_types,                   ONLY: get_qs_kind,&
                                              qs_kind_type
   USE qs_rho_types,                    ONLY: qs_rho_type
   USE util,                            ONLY: sort
#include "./base/base_uses.f90"

   IMPLICIT NONE

   PRIVATE

   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'mp2_optimize_ri_basis'

   PUBLIC :: optimize_ri_basis_main

CONTAINS

! **************************************************************************************************
!> \brief optimize RI-MP2 basis set
!> \param Emp2 ...
!> \param Emp2_Cou ...
!> \param Emp2_ex ...
!> \param Emp2_S ...
!> \param Emp2_T ...
!> \param dimen ...
!> \param natom ...
!> \param homo ...
!> \param mp2_biel ...
!> \param mp2_env ...
!> \param C ...
!> \param Auto ...
!> \param kind_of ...
!> \param qs_env ...
!> \param rho ...
!> \param para_env ...
!> \param unit_nr ...
!> \param homo_beta ...
!> \param C_beta ...
!> \param Auto_beta ...
!> \author Mauro Del Ben
! **************************************************************************************************
   SUBROUTINE optimize_ri_basis_main(Emp2, Emp2_Cou, Emp2_ex, Emp2_S, Emp2_T, dimen, natom, homo, &
                                     mp2_biel, mp2_env, C, Auto, kind_of, &
                                     qs_env, rho, para_env, &
                                     unit_nr, homo_beta, C_beta, Auto_beta)

      REAL(KIND=dp)                                      :: Emp2, Emp2_Cou, Emp2_ex, Emp2_S, Emp2_T
      INTEGER                                            :: dimen, natom, homo
      TYPE(mp2_biel_type)                                :: mp2_biel
      TYPE(mp2_type), POINTER                            :: mp2_env
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: C
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: Auto
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: kind_of
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(qs_rho_type), POINTER                         :: rho
      TYPE(cp_para_env_type), POINTER                    :: para_env
      INTEGER                                            :: unit_nr
      INTEGER, OPTIONAL                                  :: homo_beta
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :), &
         OPTIONAL                                        :: C_beta
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), OPTIONAL :: Auto_beta

      CHARACTER(len=*), PARAMETER :: routineN = 'optimize_ri_basis_main', &
         routineP = moduleN//':'//routineN

      INTEGER :: color_sub, comm_sub, dimen_RI, elements_ij_proc, handle, i, iiter, ikind, ipgf, &
         iset, ishell, j, local_unit_nr, max_l_am, max_num_iter, ndof, nkind, number_groups, &
         virtual, virtual_beta
      INTEGER, ALLOCATABLE, DIMENSION(:, :)              :: ij_list_proc, index_table_RI
      LOGICAL                                            :: hess_up, open_shell_case, reset_boundary
      LOGICAL, ALLOCATABLE, DIMENSION(:)                 :: basis_was_assoc
      REAL(KIND=dp) :: DI, DI_new, DRI, DRI_new, Emp2_AA, Emp2_AA_Cou, Emp2_AA_ex, Emp2_AB, &
         Emp2_AB_Cou, Emp2_AB_ex, Emp2_BB, Emp2_BB_Cou, Emp2_BB_ex, Emp2_RI, Emp2_RI_new, &
         eps_DI_rel, eps_DRI, eps_step, expon, fac, fad, fae, reset_edge, sumdg, sumxi
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: deriv, dg, g, hdg, lower_B, max_dev, &
                                                            max_rel_dev, p, pnew, xi
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: exp_limits, hessin
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :)  :: Integ_MP2, Integ_MP2_AA, Integ_MP2_AB, &
                                                            Integ_MP2_BB
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(cp_logger_type), POINTER                      :: logger, logger_sub
      TYPE(cp_para_env_type), POINTER                    :: para_env_sub
      TYPE(gto_basis_set_type), POINTER                  :: ri_aux_basis
      TYPE(hfx_basis_info_type)                          :: RI_basis_info
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: basis_S0, RI_basis_parameter
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set

      CALL timeset(routineN, handle)
      logger => cp_get_default_logger()

      open_shell_case = .FALSE.
      IF (PRESENT(homo_beta) .AND. PRESENT(C_beta) .AND. PRESENT(Auto_beta)) open_shell_case = .TRUE.

      virtual = dimen-homo

      eps_DRI = mp2_env%ri_opt_param%DRI
      eps_DI_rel = mp2_env%ri_opt_param%DI_rel
      eps_step = mp2_env%ri_opt_param%eps_step
      max_num_iter = mp2_env%ri_opt_param%max_num_iter

      ! calculate the ERI's over molecular integrals
      Emp2 = 0.0_dp
      Emp2_Cou = 0.0_dp
      Emp2_ex = 0.0_dp
      Emp2_S = 0.0_dp
      Emp2_T = 0.0_dp
      IF (open_shell_case) THEN
         ! open shell case
         virtual_beta = dimen-homo_beta

         ! alpha-aplha case
         Emp2_AA = 0.0_dp
         Emp2_AA_Cou = 0.0_dp
         Emp2_AA_ex = 0.0_dp
         CALL calc_elem_ij_proc(homo, homo, para_env, elements_ij_proc, ij_list_proc)
         CALL mp2_canonical_direct_single_batch(Emp2_AA, Emp2_AA_Cou, Emp2_AA_ex, mp2_env, qs_env, rho, para_env, &
                                                mp2_biel, dimen, C, Auto, 0, homo, homo, &
                                                elements_ij_proc, ij_list_proc, homo, 0, &
                                                Integ_MP2=Integ_MP2_AA)
         CALL mp_sum(Emp2_AA_Cou, para_env%group)
         CALL mp_sum(Emp2_AA_Ex, para_env%group)
         CALL mp_sum(Emp2_AA, para_env%group)
         DEALLOCATE (ij_list_proc)

         ! beta-beta case
         Emp2_BB = 0.0_dp
         Emp2_BB_Cou = 0.0_dp
         Emp2_BB_ex = 0.0_dp
         CALL calc_elem_ij_proc(homo_beta, homo_beta, para_env, elements_ij_proc, ij_list_proc)
         CALL mp2_canonical_direct_single_batch(Emp2_BB, Emp2_BB_Cou, Emp2_BB_ex, mp2_env, qs_env, rho, para_env, &
                                                mp2_biel, dimen, C_beta, Auto_beta, 0, homo_beta, homo_beta, &
                                                elements_ij_proc, ij_list_proc, homo_beta, 0, &
                                                Integ_MP2=Integ_MP2_BB)
         CALL mp_sum(Emp2_BB_Cou, para_env%group)
         CALL mp_sum(Emp2_BB_Ex, para_env%group)
         CALL mp_sum(Emp2_BB, para_env%group)
         DEALLOCATE (ij_list_proc)

         ! aplha-beta case
         Emp2_AB = 0.0_dp
         Emp2_AB_Cou = 0.0_dp
         Emp2_AB_ex = 0.0_dp
         CALL calc_elem_ij_proc(homo, homo_beta, para_env, elements_ij_proc, ij_list_proc)
         CALL mp2_canonical_direct_single_batch(Emp2_AB, Emp2_AB_Cou, Emp2_AB_ex, mp2_env, qs_env, rho, para_env, &
                                                mp2_biel, dimen, C, Auto, 0, homo, homo, &
                                                elements_ij_proc, ij_list_proc, homo_beta, 0, &
                                                homo_beta, C_beta, Auto_beta, Integ_MP2=Integ_MP2_AB)
         CALL mp_sum(Emp2_AB_Cou, para_env%group)
         CALL mp_sum(Emp2_AB_Ex, para_env%group)
         CALL mp_sum(Emp2_AB, para_env%group)
         DEALLOCATE (ij_list_proc)

         ! IF (unit_nr>0) WRITE(unit_nr,'(T3,A,T56,F25.14)') 'MP2 Energy Alpha-Alpha = ', Emp2_AA
         ! IF (unit_nr>0) WRITE(unit_nr,'(T3,A,T56,F25.14)') 'MP2 Energy Beta-Beta   = ', Emp2_BB
         ! IF (unit_nr>0) WRITE(unit_nr,'(T3,A,T56,F25.14)') 'MP2 Energy Alpha-Beta  = ', Emp2_AB

         Emp2 = Emp2_AA+Emp2_BB+Emp2_AB*2.0_dp !+Emp2_BA
         Emp2_Cou = Emp2_AA_Cou+Emp2_BB_Cou+Emp2_AB_Cou*2.0_dp !+Emp2_BA
         Emp2_ex = Emp2_AA_ex+Emp2_BB_ex+Emp2_AB_ex*2.0_dp !+Emp2_BA

         Emp2_S = Emp2_AB*2.0_dp
         Emp2_T = Emp2_AA+Emp2_BB

         ! Replicate the MO-ERI's over all processes
         CALL mp_sum(Integ_MP2_AA, para_env%group)
         CALL mp_sum(Integ_MP2_BB, para_env%group)
         CALL mp_sum(Integ_MP2_AB, para_env%group)

      ELSE
         ! close shell case
         CALL calc_elem_ij_proc(homo, homo, para_env, elements_ij_proc, ij_list_proc)
         CALL mp2_canonical_direct_single_batch(Emp2, Emp2_Cou, Emp2_ex, mp2_env, qs_env, rho, para_env, &
                                                mp2_biel, dimen, C, Auto, 0, homo, homo, &
                                                elements_ij_proc, ij_list_proc, homo, 0, &
                                                Integ_MP2=Integ_MP2)
         CALL mp_sum(Emp2_Cou, para_env%group)
         CALL mp_sum(Emp2_Ex, para_env%group)
         CALL mp_sum(Emp2, para_env%group)
         DEALLOCATE (ij_list_proc)

         ! Replicate the MO-ERI's over all processes
         CALL mp_sum(Integ_MP2, para_env%group)

      END IF

      ! create the para_env_sub
      number_groups = para_env%num_pe/mp2_env%mp2_num_proc
      color_sub = para_env%mepos/mp2_env%mp2_num_proc
      CALL mp_comm_split_direct(para_env%group, comm_sub, color_sub)
      NULLIFY (para_env_sub)
      CALL cp_para_env_create(para_env_sub, comm_sub)

      IF (para_env%mepos == para_env%source) THEN
         local_unit_nr = cp_logger_get_default_unit_nr(logger, local=.FALSE.)
      ELSE
         local_unit_nr = default_output_unit
      ENDIF
      NULLIFY (logger_sub)
      CALL cp_logger_create(logger_sub, para_env=para_env_sub, &
                            default_global_unit_nr=local_unit_nr, close_global_unit_on_dealloc=.FALSE.)
      CALL cp_logger_set(logger_sub, local_filename="opt_RI_basis_localLog")
      CALL cp_add_default_logger(logger_sub)

      CALL generate_RI_init_basis(qs_env, mp2_env, nkind, max_rel_dev, basis_was_assoc)

      CALL read_RI_basis_set(qs_env, RI_basis_parameter, RI_basis_info, &
                             natom, nkind, kind_of, index_table_RI, dimen_RI, &
                             basis_S0)

      ndof = 0
      max_l_am = 0
      DO ikind = 1, nkind
         DO iset = 1, RI_basis_parameter(ikind)%nset
            ndof = ndof+1
            max_l_am = MAX(max_l_am, MAXVAL(RI_basis_parameter(ikind)%lmax))
         END DO
      END DO

      ALLOCATE (exp_limits(2, nkind))
      exp_limits(1, :) = HUGE(0)
      exp_limits(2, :) = -HUGE(0)
      DO ikind = 1, nkind
         DO iset = 1, RI_basis_parameter(ikind)%nset
            expon = RI_basis_parameter(ikind)%zet(1, iset)
            IF (expon <= exp_limits(1, ikind)) exp_limits(1, ikind) = expon
            IF (expon >= exp_limits(2, ikind)) exp_limits(2, ikind) = expon
         END DO
         IF (basis_was_assoc(ikind)) THEN
            exp_limits(1, ikind) = exp_limits(1, ikind)*0.5_dp
            exp_limits(2, ikind) = exp_limits(2, ikind)*1.5_dp
         ELSE
            exp_limits(1, ikind) = exp_limits(1, ikind)*0.8_dp*0.5_dp
            exp_limits(2, ikind) = exp_limits(2, ikind)*1.2_dp*1.5_dp
         END IF
      END DO
      DEALLOCATE (basis_was_assoc)

      ! check if the max angular momentum exceed the libint one
      IF (max_l_am > build_eri_size) THEN
         CPABORT("The angular momentum needed exceeds the value assumed when configuring libint.")
      END IF

      ! Allocate stuff
      ALLOCATE (p(ndof))
      p = 0.0_dp
      ALLOCATE (xi(ndof))
      xi = 0.0_dp
      ALLOCATE (g(ndof))
      g = 0.0_dp
      ALLOCATE (dg(ndof))
      dg = 0.0_dp
      ALLOCATE (hdg(ndof))
      hdg = 0.0_dp
      ALLOCATE (pnew(ndof))
      pnew = 0.0_dp
      ALLOCATE (deriv(ndof))
      deriv = 0.0_dp
      ALLOCATE (hessin(ndof, ndof))
      hessin = 0.0_dp
      DO i = 1, ndof
         hessin(i, i) = 1.0_dp
      END DO

      ! initialize trasformation function
      ALLOCATE (lower_B(ndof))
      lower_B = 0.0_dp
      ALLOCATE (max_dev(ndof))
      max_dev = 0.0_dp

      ! Initialize the transformation function
      CALL init_transf(nkind, RI_basis_parameter, lower_B, max_dev, max_rel_dev)

      ! get the atomic kind set for writing the basis
      CALL get_qs_env(qs_env=qs_env, atomic_kind_set=atomic_kind_set, qs_kind_set=qs_kind_set)

      ! Calculate RI-MO-ERI's
      CALL calc_energy_func(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, Emp2_RI, DRI, DI, &
                            Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, &
                            qs_env, natom, dimen, dimen_RI, homo, virtual, &
                            kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                            RI_basis_parameter, RI_basis_info, basis_S0, &
                            open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, para_env, unit_nr, &
                            .TRUE.)

      ! ! Calculate function (DI) derivatives with respect to the RI basis exponent
      CALL calc_energy_func_der(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, DI, &
                                Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, eps_step, &
                                qs_env, nkind, natom, dimen, dimen_RI, homo, virtual, &
                                kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                                RI_basis_parameter, RI_basis_info, basis_S0, &
                                open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, &
                                para_env, para_env_sub, number_groups, color_sub, unit_nr, &
                                p, lower_B, max_dev, &
                                deriv)

      g(:) = deriv
      xi(:) = -g

      reset_edge = 1.5_dp
      DO iiter = 1, max_num_iter
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,I5)') 'OPTIMIZATION STEP NUMBER', iiter

         ! perform step
         pnew(:) = p+xi
         CALL p2basis(nkind, RI_basis_parameter, lower_B, max_dev, pnew)

         ! check if we have to reset boundaries
         reset_boundary = .FALSE.
         ! nreset=0
         i = 0
         DO ikind = 1, nkind
            DO iset = 1, RI_basis_parameter(ikind)%nset
               i = i+1
               CALL transf_val(lower_B(i), max_dev(i), pnew(i), expon)
               IF (ABS(pnew(i)) > reset_edge .OR. expon < exp_limits(1, ikind) .OR. expon > exp_limits(2, ikind)) THEN
                  reset_boundary = .TRUE.
                  EXIT
               END IF
            END DO
         END DO
         ! IF(nreset>1) reset_boundary=.TRUE.

         IF (reset_boundary) THEN
            IF (unit_nr > 0) WRITE (unit_nr, '(T3,A)') 'RESET BASIS: one of the exponent hits the boundary'
            CALL reset_basis(nkind, ndof, RI_basis_parameter, reset_edge, &
                             pnew, lower_B, max_dev, max_rel_dev, exp_limits)
            p(:) = pnew
            xi = 0.0_dp
            g = 0.0_dp
            dg = 0.0_dp
            hdg = 0.0_dp
            pnew = 0.0_dp
            hessin = 0.0_dp
            DO i = 1, ndof
               hessin(i, i) = 1.0_dp
            END DO
            deriv = 0.0_dp
            ! Calculate RI-MO-ERI's
            CALL calc_energy_func(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, Emp2_RI, DRI, DI, &
                                  Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, &
                                  qs_env, natom, dimen, dimen_RI, homo, virtual, &
                                  kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                                  RI_basis_parameter, RI_basis_info, basis_S0, &
                                  open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, para_env, unit_nr, &
                                  .FALSE.)
            ! ! Calculate function (DI) derivatives with respect to the RI basis exponent
            CALL calc_energy_func_der(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, DI, &
                                      Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, eps_step, &
                                      qs_env, nkind, natom, dimen, dimen_RI, homo, virtual, &
                                      kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                                      RI_basis_parameter, RI_basis_info, basis_S0, &
                                      open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, &
                                      para_env, para_env_sub, number_groups, color_sub, unit_nr, &
                                      p, lower_B, max_dev, &
                                      deriv)

            g(:) = deriv
            xi(:) = -g
            pnew(:) = p+xi
            CALL p2basis(nkind, RI_basis_parameter, lower_B, max_dev, pnew)
         END IF

         ! calculate energy at the new point
         CALL calc_energy_func(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, Emp2_RI_new, DRI_new, DI_new, &
                               Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, &
                               qs_env, natom, dimen, dimen_RI, homo, virtual, &
                               kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                               RI_basis_parameter, RI_basis_info, basis_S0, &
                               open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, para_env, unit_nr, &
                               .FALSE.)

         ! update energy and direction
         DI = DI_new
         xi(:) = pnew-p
         p(:) = pnew

         ! check for convergence
         IF (unit_nr > 0) THEN
            WRITE (unit_nr, *)
            DO ikind = 1, nkind
               CALL get_qs_kind(qs_kind=qs_kind_set(ikind), basis_set=ri_aux_basis, &
                                basis_type="RI_AUX")
               WRITE (unit_nr, '(T3,A,A)') atomic_kind_set(ikind)%element_symbol, '   RI_opt_basis'
               WRITE (unit_nr, '(T3,I3)') RI_basis_parameter(ikind)%nset
               DO iset = 1, RI_basis_parameter(ikind)%nset
                  WRITE (unit_nr, '(T3,10I4)') iset, &
                     RI_basis_parameter(ikind)%lmin(iset), &
                     RI_basis_parameter(ikind)%lmax(iset), &
                     RI_basis_parameter(ikind)%npgf(iset), &
                     (1, ishell=1, RI_basis_parameter(ikind)%nshell(iset))
                  DO ipgf = 1, RI_basis_parameter(ikind)%npgf(iset)
                     WRITE (unit_nr, '(T3,10F16.10)') RI_basis_parameter(ikind)%zet(ipgf, iset), &
                        (ri_aux_basis%gcc(ipgf, ishell, iset), &
                         ishell=1, ri_aux_basis%nshell(iset))
                  END DO
               END DO
               WRITE (unit_nr, *)
            END DO
            WRITE (unit_nr, *)
         END IF
         IF (DI/ABS(Emp2) <= eps_DI_rel .AND. ABS(DRI_new) <= eps_DRI) THEN
            IF (unit_nr > 0) WRITE (unit_nr, '(T3,A)') 'OPTIMIZATION CONVERGED'
            IF (unit_nr > 0) WRITE (unit_nr, *)
            EXIT
         END IF

         ! calculate gradients
         CALL calc_energy_func_der(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, DI, &
                                   Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, eps_step, &
                                   qs_env, nkind, natom, dimen, dimen_RI, homo, virtual, &
                                   kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                                   RI_basis_parameter, RI_basis_info, basis_S0, &
                                   open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, &
                                   para_env, para_env_sub, number_groups, color_sub, unit_nr, &
                                   p, lower_B, max_dev, &
                                   deriv)

         ! g is the vector containing the old gradient
         dg(:) = deriv-g
         g(:) = deriv
         hdg(:) = MATMUL(hessin, dg)

         fac = SUM(dg*xi)
         fae = SUM(dg*hdg)
         sumdg = SUM(dg*dg)
         sumxi = SUM(xi*xi)

         hess_up = .TRUE.
         IF (fac**2 > sumdg*sumxi*3.0E-8_dp) THEN
            fac = 1.0_dp/fac
            fad = 1.0_dp/fae
            dg(:) = fac*xi-fad*hdg
            DO i = 1, ndof
               DO j = 1, ndof
                  hessin(i, j) = hessin(i, j)+fac*xi(i)*xi(j) &
                                 -fad*hdg(i)*hdg(j) &
                                 +fae*dg(i)*dg(j)
               END DO
            END DO
         ELSE
            IF (unit_nr > 0) WRITE (unit_nr, '(T3,A)') 'Skip Hessian Update'
            hess_up = .FALSE.
         END IF

         !XXXXXXXXXXXXX
         ! DO i=1, ndof
         !   IF(g(i)<0.0D+00) THEN
         !     xi(i)=MAX(0.05,ABS(g(i)))
         !   ELSE
         !     xi(i)=-MAX(0.05,ABS(g(i)))
         !   END IF
         ! END DO
         !XXXXXXXXXXXXX

         ! new direction
         xi(:) = -MATMUL(hessin, g)

      END DO

      IF (.NOT. (DI/ABS(Emp2) <= eps_DI_rel .AND. ABS(DRI_new) <= eps_DRI)) THEN
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,I5,A)') 'OPTIMIZATION NOT CONVERGED IN', max_num_iter, ' STEPS.'
         IF (unit_nr > 0) WRITE (unit_nr, *)
      END IF

      DEALLOCATE (max_rel_dev)

      DEALLOCATE (p)
      DEALLOCATE (xi)
      DEALLOCATE (g)
      DEALLOCATE (pnew)
      DEALLOCATE (dg)
      DEALLOCATE (hdg)
      DEALLOCATE (deriv)
      DEALLOCATE (Hessin)
      DEALLOCATE (lower_B)
      DEALLOCATE (max_dev)
      DEALLOCATE (exp_limits)

      IF (open_shell_case) THEN
         DEALLOCATE (Integ_MP2_AA)
         DEALLOCATE (Integ_MP2_BB)
         DEALLOCATE (Integ_MP2_AB)
      ELSE
         DEALLOCATE (Integ_MP2)
      END IF
      DEALLOCATE (index_table_RI)

      ! Release RI basis set
      CALL release_RI_basis_set(RI_basis_parameter, basis_S0)

      CALL cp_para_env_release(para_env_sub)
      CALL cp_rm_default_logger()
      CALL cp_logger_release(logger_sub)

      CALL timestop(handle)

   END SUBROUTINE optimize_ri_basis_main

! **************************************************************************************************
!> \brief ...
!> \param Emp2 ...
!> \param Emp2_AA ...
!> \param Emp2_BB ...
!> \param Emp2_AB ...
!> \param DI_ref ...
!> \param Integ_MP2 ...
!> \param Integ_MP2_AA ...
!> \param Integ_MP2_BB ...
!> \param Integ_MP2_AB ...
!> \param eps ...
!> \param qs_env ...
!> \param nkind ...
!> \param natom ...
!> \param dimen ...
!> \param dimen_RI ...
!> \param homo ...
!> \param virtual ...
!> \param kind_of ...
!> \param index_table_RI ...
!> \param mp2_biel ...
!> \param mp2_env ...
!> \param Auto ...
!> \param C ...
!> \param RI_basis_parameter ...
!> \param RI_basis_info ...
!> \param basis_S0 ...
!> \param open_shell_case ...
!> \param homo_beta ...
!> \param virtual_beta ...
!> \param Auto_beta ...
!> \param C_beta ...
!> \param para_env ...
!> \param para_env_sub ...
!> \param number_groups ...
!> \param color_sub ...
!> \param unit_nr ...
!> \param p ...
!> \param lower_B ...
!> \param max_dev ...
!> \param deriv ...
! **************************************************************************************************
   SUBROUTINE calc_energy_func_der(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, DI_ref, &
                                   Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, eps, &
                                   qs_env, nkind, natom, dimen, dimen_RI, homo, virtual, &
                                   kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                                   RI_basis_parameter, RI_basis_info, basis_S0, &
                                   open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, &
                                   para_env, para_env_sub, number_groups, color_sub, unit_nr, &
                                   p, lower_B, max_dev, &
                                   deriv)
      REAL(KIND=dp)                                      :: Emp2, Emp2_AA, Emp2_BB, Emp2_AB, DI_ref
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :)  :: Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, &
                                                            Integ_MP2_AB
      REAL(KIND=dp)                                      :: eps
      TYPE(qs_environment_type), POINTER                 :: qs_env
      INTEGER                                            :: nkind, natom, dimen, dimen_RI, homo, &
                                                            virtual
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: kind_of
      INTEGER, ALLOCATABLE, DIMENSION(:, :)              :: index_table_RI
      TYPE(mp2_biel_type)                                :: mp2_biel
      TYPE(mp2_type), POINTER                            :: mp2_env
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: Auto
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: C
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: RI_basis_parameter
      TYPE(hfx_basis_info_type)                          :: RI_basis_info
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: basis_S0
      LOGICAL                                            :: open_shell_case
      INTEGER                                            :: homo_beta, virtual_beta
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: Auto_beta
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: C_beta
      TYPE(cp_para_env_type), POINTER                    :: para_env, para_env_sub
      INTEGER                                            :: number_groups, color_sub, unit_nr
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: p, lower_B, max_dev, deriv

      CHARACTER(LEN=*), PARAMETER :: routineN = 'calc_energy_func_der', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, ideriv, ikind, iset, nseta
      REAL(KIND=dp)                                      :: DI, DRI, Emp2_RI, new_basis_val, &
                                                            orig_basis_val
      REAL(KIND=dp), VOLATILE                            :: step, temp

      CALL timeset(routineN, handle)

      step = eps

      ! cycle over the RI basis set exponent
      deriv = 0.0_dp
      ideriv = 0
      DO ikind = 1, nkind
         nseta = RI_basis_parameter(ikind)%nset
         DO iset = 1, nseta
            ! for now only uncontracted aux basis set
            ideriv = ideriv+1
            IF (MOD(ideriv, number_groups) /= color_sub) CYCLE

            ! ! calculate the numerical derivative
            ! ! The eps is the relative change of the exponent for the
            ! ! calculation of the numerical derivative
            ! CPPostcondition(RI_basis_parameter(ikind)%npgf(iset)==1,cp_failure_level,routineP,failure)
            ! step=eps*RI_basis_parameter(ikind)%zet(1,iset)
            ! temp=RI_basis_parameter(ikind)%zet(1,iset)+step
            ! step=temp-RI_basis_parameter(ikind)%zet(1,iset)
            ! RI_basis_parameter(ikind)%zet(1,iset)=RI_basis_parameter(ikind)%zet(1,iset)+step

            ! in the new case eps is just the step length for calculating the numerical derivative

            CPASSERT(RI_basis_parameter(ikind)%npgf(iset) == 1)
            orig_basis_val = RI_basis_parameter(ikind)%zet(1, iset)
            temp = p(ideriv)+step
            CALL transf_val(lower_B(ideriv), max_dev(ideriv), temp, new_basis_val)
            RI_basis_parameter(ikind)%zet(1, iset) = new_basis_val

            CALL calc_energy_func(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, Emp2_RI, DRI, DI, &
                                  Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, &
                                  qs_env, natom, dimen, dimen_RI, homo, virtual, &
                                  kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                                  RI_basis_parameter, RI_basis_info, basis_S0, &
                                  open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, &
                                  para_env_sub, unit_nr, .TRUE.)

            RI_basis_parameter(ikind)%zet(1, iset) = orig_basis_val

            IF (para_env_sub%mepos == 0) THEN
               temp = EXP(DI)
               temp = temp/EXP(DI_ref)
               deriv(ideriv) = LOG(temp)/step
            END IF

         END DO
      END DO

      CALL mp_sum(deriv, para_env%group)

      CALL timestop(handle)

   END SUBROUTINE

! **************************************************************************************************
!> \brief ...
!> \param Emp2 ...
!> \param Emp2_AA ...
!> \param Emp2_BB ...
!> \param Emp2_AB ...
!> \param Emp2_RI ...
!> \param DRI ...
!> \param DI ...
!> \param Integ_MP2 ...
!> \param Integ_MP2_AA ...
!> \param Integ_MP2_BB ...
!> \param Integ_MP2_AB ...
!> \param qs_env ...
!> \param natom ...
!> \param dimen ...
!> \param dimen_RI ...
!> \param homo ...
!> \param virtual ...
!> \param kind_of ...
!> \param index_table_RI ...
!> \param mp2_biel ...
!> \param mp2_env ...
!> \param Auto ...
!> \param C ...
!> \param RI_basis_parameter ...
!> \param RI_basis_info ...
!> \param basis_S0 ...
!> \param open_shell_case ...
!> \param homo_beta ...
!> \param virtual_beta ...
!> \param Auto_beta ...
!> \param C_beta ...
!> \param para_env ...
!> \param unit_nr ...
!> \param no_write ...
! **************************************************************************************************
   SUBROUTINE calc_energy_func(Emp2, Emp2_AA, Emp2_BB, Emp2_AB, Emp2_RI, DRI, DI, &
                               Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, Integ_MP2_AB, &
                               qs_env, natom, dimen, dimen_RI, homo, virtual, &
                               kind_of, index_table_RI, mp2_biel, mp2_env, Auto, C, &
                               RI_basis_parameter, RI_basis_info, basis_S0, &
                               open_shell_case, homo_beta, virtual_beta, Auto_beta, C_beta, para_env, unit_nr, &
                               no_write)
      REAL(KIND=dp)                                      :: Emp2, Emp2_AA, Emp2_BB, Emp2_AB, &
                                                            Emp2_RI, DRI, DI
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :)  :: Integ_MP2, Integ_MP2_AA, Integ_MP2_BB, &
                                                            Integ_MP2_AB
      TYPE(qs_environment_type), POINTER                 :: qs_env
      INTEGER                                            :: natom, dimen, dimen_RI, homo, virtual
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: kind_of
      INTEGER, ALLOCATABLE, DIMENSION(:, :)              :: index_table_RI
      TYPE(mp2_biel_type)                                :: mp2_biel
      TYPE(mp2_type), POINTER                            :: mp2_env
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: Auto
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: C
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: RI_basis_parameter
      TYPE(hfx_basis_info_type)                          :: RI_basis_info
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: basis_S0
      LOGICAL                                            :: open_shell_case
      INTEGER                                            :: homo_beta, virtual_beta
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: Auto_beta
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: C_beta
      TYPE(cp_para_env_type), POINTER                    :: para_env
      INTEGER                                            :: unit_nr
      LOGICAL                                            :: no_write

      CHARACTER(LEN=*), PARAMETER :: routineN = 'calc_energy_func', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle
      REAL(KIND=dp)                                      :: DI_AA, DI_AB, DI_BB, DRI_AA, DRI_AB, &
                                                            DRI_BB, Emp2_RI_AA, Emp2_RI_AB, &
                                                            Emp2_RI_BB
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :)     :: Lai, Lai_beta

      CALL timeset(routineN, handle)

      CALL libint_ri_mp2(dimen, dimen_RI, homo, natom, mp2_biel, mp2_env, C, &
                         kind_of, RI_basis_parameter, RI_basis_info, basis_S0, index_table_RI, &
                         qs_env, para_env, Lai)
      IF (open_shell_case) THEN
         CALL libint_ri_mp2(dimen, dimen_RI, homo_beta, natom, mp2_biel, mp2_env, C_beta, &
                            kind_of, RI_basis_parameter, RI_basis_info, basis_S0, index_table_RI, &
                            qs_env, para_env, Lai_beta)
      END IF

      ! Contract integrals into energy
      IF (open_shell_case) THEN
         ! alpha-alpha
         CALL contract_integrals(DI_AA, Emp2_RI_AA, DRI_AA, Emp2_AA, homo, homo, virtual, virtual, &
                                 1.0_dp, 0.5_dp, .TRUE., &
                                 Auto, Auto, Integ_MP2_AA, &
                                 Lai, Lai, para_env)

         ! beta-beta
         CALL contract_integrals(DI_BB, Emp2_RI_BB, DRI_BB, Emp2_BB, homo_beta, homo_beta, virtual_beta, virtual_beta, &
                                 1.0_dp, 0.5_dp, .TRUE., &
                                 Auto_beta, Auto_beta, Integ_MP2_BB, &
                                 Lai_beta, Lai_beta, para_env)

         ! alpha-beta
         CALL contract_integrals(DI_AB, Emp2_RI_AB, DRI_AB, Emp2_AB*2.0_dp, homo, homo_beta, virtual, virtual_beta, &
                                 1.0_dp, 1.0_dp, .FALSE., &
                                 Auto, Auto_beta, Integ_MP2_AB, &
                                 Lai, Lai_beta, para_env)

         Emp2_RI = Emp2_RI_AA+Emp2_RI_BB+Emp2_RI_AB
         DRI = DRI_AA+DRI_BB+DRI_AB
         DI = DI_AA+DI_BB+DI_AB
      ELSE
         CALL contract_integrals(DI, Emp2_RI, DRI, Emp2, homo, homo, virtual, virtual, &
                                 2.0_dp, 1.0_dp, .TRUE., &
                                 Auto, Auto, Integ_MP2, &
                                 Lai, Lai, para_env)
      END IF

      IF (.NOT. no_write) THEN
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,T56,F25.14)')
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,T56,F25.14)') 'Emp2 =   ', Emp2
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,T56,F25.14)') 'Emp2-RI =', Emp2_RI
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,T56,ES25.10)') 'DRI =    ', DRI
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,T56,ES25.10)') 'DI =     ', DI
         IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,T56,ES25.10)') 'DI/|Emp2| =     ', DI/ABS(Emp2)
      END IF

      DEALLOCATE (Lai)
      IF (open_shell_case) DEALLOCATE (Lai_beta)

      CALL timestop(handle)

   END SUBROUTINE

! **************************************************************************************************
!> \brief ...
!> \param nkind ...
!> \param RI_basis_parameter ...
!> \param lower_B ...
!> \param max_dev ...
!> \param max_rel_dev ...
! **************************************************************************************************
   SUBROUTINE init_transf(nkind, RI_basis_parameter, lower_B, max_dev, max_rel_dev)
      INTEGER                                            :: nkind
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: RI_basis_parameter
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: lower_B, max_dev, max_rel_dev

      INTEGER                                            :: ikind, ipos, iset

      ipos = 0
      DO ikind = 1, nkind
         DO iset = 1, RI_basis_parameter(ikind)%nset
            ipos = ipos+1
            lower_B(ipos) = RI_basis_parameter(ikind)%zet(1, iset)*(1.0_dp-max_rel_dev(ipos))
            max_dev(ipos) = RI_basis_parameter(ikind)%zet(1, iset)*2.0_dp*max_rel_dev(ipos)
         END DO
      END DO

   END SUBROUTINE

! **************************************************************************************************
!> \brief ...
!> \param nkind ...
!> \param RI_basis_parameter ...
!> \param Lower_B ...
!> \param max_dev ...
!> \param p ...
! **************************************************************************************************
   SUBROUTINE p2basis(nkind, RI_basis_parameter, Lower_B, max_dev, p)
      INTEGER                                            :: nkind
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: RI_basis_parameter
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: Lower_B, max_dev, p

      INTEGER                                            :: ikind, ipos, iset
      REAL(KIND=dp)                                      :: valout

      ipos = 0
      DO ikind = 1, nkind
         DO iset = 1, RI_basis_parameter(ikind)%nset
            ipos = ipos+1
            CALL transf_val(lower_B(ipos), max_dev(ipos), p(ipos), valout)
            RI_basis_parameter(ikind)%zet(1, iset) = valout
         END DO
      END DO

   END SUBROUTINE

! **************************************************************************************************
!> \brief ...
!> \param nkind ...
!> \param ndof ...
!> \param RI_basis_parameter ...
!> \param reset_edge ...
!> \param pnew ...
!> \param lower_B ...
!> \param max_dev ...
!> \param max_rel_dev ...
!> \param exp_limits ...
! **************************************************************************************************
   SUBROUTINE reset_basis(nkind, ndof, RI_basis_parameter, reset_edge, &
                          pnew, lower_B, max_dev, max_rel_dev, exp_limits)
      INTEGER                                            :: nkind, ndof
      TYPE(hfx_basis_type), DIMENSION(:), POINTER        :: RI_basis_parameter
      REAL(KIND=dp)                                      :: reset_edge
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: pnew, Lower_B, max_dev, max_rel_dev
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: exp_limits

      CHARACTER(LEN=*), PARAMETER :: routineN = 'reset_basis', routineP = moduleN//':'//routineN

      INTEGER                                            :: am_max, iexpo, ikind, ipos, ipos_p, &
                                                            iset, la
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: nf_per_l
      INTEGER, DIMENSION(ndof)                           :: change_expo
      LOGICAL, ALLOCATABLE, DIMENSION(:)                 :: has_to_be_changed
      REAL(KIND=dp)                                      :: expo, geom_fact, pmax
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: max_min_exp_per_l
      REAL(KIND=dp), DIMENSION(ndof)                     :: new_expo, old_expo, old_lower_B, &
                                                            old_max_dev, old_max_rel_dev, old_pnew

! make a copy of the original parameters

      old_pnew = pnew
      old_lower_B = lower_B
      old_max_dev = max_dev
      old_max_rel_dev = max_rel_dev
      old_expo = 0.0_dp
      ipos = 0
      DO ikind = 1, nkind
         DO iset = 1, RI_basis_parameter(ikind)%nset
            ipos = ipos+1
            old_expo(ipos) = RI_basis_parameter(ikind)%zet(1, iset)
         END DO
      END DO

      pnew = 0.0_dp
      lower_B = 0.0_dp
      max_dev = 0.0_dp
      max_rel_dev = 0.0_dp

      change_expo = 0

      new_expo = 0.0_dp
      ipos = 0
      ipos_p = 0
      DO ikind = 1, nkind
         am_max = MAXVAL(RI_basis_parameter(ikind)%lmax(:))
         ALLOCATE (nf_per_l(0:am_max))
         nf_per_l = 0
         ALLOCATE (max_min_exp_per_l(2, 0:am_max))
         max_min_exp_per_l(1, :) = HUGE(0)
         max_min_exp_per_l(2, :) = -HUGE(0)

         DO iset = 1, RI_basis_parameter(ikind)%nset
            la = RI_basis_parameter(ikind)%lmax(iset)
            expo = RI_basis_parameter(ikind)%zet(1, iset)
            nf_per_l(la) = nf_per_l(la)+1
            IF (expo <= max_min_exp_per_l(1, la)) max_min_exp_per_l(1, la) = expo
            IF (expo >= max_min_exp_per_l(2, la)) max_min_exp_per_l(2, la) = expo
         END DO

         max_min_exp_per_l(1, la) = MAX(max_min_exp_per_l(1, la), exp_limits(1, ikind))
         max_min_exp_per_l(2, la) = MIN(max_min_exp_per_l(2, la), exp_limits(2, ikind))

         ! always s exponents as maximum and minimu
         ! expo=MAXVAL(max_min_exp_per_l(2,:))
         ! max_min_exp_per_l(2,0)=expo
         ! expo=MINVAL(max_min_exp_per_l(1,:))
         ! max_min_exp_per_l(1,0)=expo

         ALLOCATE (has_to_be_changed(0:am_max))
         has_to_be_changed = .FALSE.
         DO la = 0, am_max
            pmax = -HUGE(0)
            DO iexpo = 1, nf_per_l(la)
               ipos_p = ipos_p+1
               IF (ABS(old_pnew(ipos_p)) >= pmax) pmax = ABS(old_pnew(ipos_p))
               ! check if any of the exponents go out of range
               CALL transf_val(old_lower_B(ipos_p), old_max_dev(ipos_p), old_pnew(ipos_p), expo)
               IF (expo < exp_limits(1, ikind) .OR. expo > exp_limits(2, ikind)) has_to_be_changed(la) = .TRUE.
            END DO
            IF (pmax > reset_edge) has_to_be_changed(la) = .TRUE.
         END DO

         DO la = 0, am_max
            IF (nf_per_l(la) == 1) THEN
               ipos = ipos+1
               new_expo(ipos) = max_min_exp_per_l(1, la)
               IF (new_expo(ipos) >= exp_limits(1, ikind) .AND. new_expo(ipos) <= exp_limits(2, ikind)) THEN
                  max_rel_dev(ipos) = (new_expo(ipos)-old_lower_B(ipos))/new_expo(ipos)
                  IF (max_rel_dev(ipos) <= 0.1_dp) max_rel_dev(ipos) = 0.8_dp
               ELSE
                  new_expo(ipos) = (exp_limits(2, ikind)+exp_limits(1, ikind))/2.0_dp
                  max_rel_dev(ipos) = (new_expo(ipos)-exp_limits(1, ikind))/new_expo(ipos)
               END IF
               IF (has_to_be_changed(la)) change_expo(ipos) = 1
            ELSE
               IF (max_min_exp_per_l(2, la)/max_min_exp_per_l(1, la) < 2.0_dp) THEN
                  max_min_exp_per_l(1, la) = max_min_exp_per_l(1, la)*0.5
                  max_min_exp_per_l(2, la) = max_min_exp_per_l(2, la)*1.5
               END IF
               geom_fact = (max_min_exp_per_l(2, la)/max_min_exp_per_l(1, la))**(1.0_dp/REAL(nf_per_l(la)-1, dp))
               DO iexpo = 1, nf_per_l(la)
                  ipos = ipos+1
                  new_expo(ipos) = max_min_exp_per_l(1, la)*(geom_fact**(iexpo-1))
                  max_rel_dev(ipos) = (geom_fact-1.0_dp)/(geom_fact+1.0_dp)*0.9_dp
                  IF (has_to_be_changed(la)) change_expo(ipos) = 1
               END DO
            END IF
         END DO

         DEALLOCATE (has_to_be_changed)

         DEALLOCATE (nf_per_l)
         DEALLOCATE (max_min_exp_per_l)
      END DO

      ipos = 0
      DO ikind = 1, nkind
         DO iset = 1, RI_basis_parameter(ikind)%nset
            ipos = ipos+1
            RI_basis_parameter(ikind)%zet(1, iset) = new_expo(ipos)
         END DO
      END DO

      CALL init_transf(nkind, RI_basis_parameter, lower_B, max_dev, max_rel_dev)

      ipos = 0
      DO ikind = 1, nkind
         DO iset = 1, RI_basis_parameter(ikind)%nset
            ipos = ipos+1
            IF (change_expo(ipos) == 0) THEN
               ! restore original
               pnew(ipos) = old_pnew(ipos)
               lower_B(ipos) = old_lower_B(ipos)
               max_dev(ipos) = old_max_dev(ipos)
               max_rel_dev(ipos) = old_max_rel_dev(ipos)
               RI_basis_parameter(ikind)%zet(1, iset) = old_expo(ipos)
            END IF
         END DO
      END DO

   END SUBROUTINE

! **************************************************************************************************
!> \brief ...
!> \param DI ...
!> \param Emp2_RI ...
!> \param DRI ...
!> \param Emp2 ...
!> \param homo ...
!> \param homo_beta ...
!> \param virtual ...
!> \param virtual_beta ...
!> \param fact ...
!> \param fact2 ...
!> \param calc_ex ...
!> \param MOenerg ...
!> \param MOenerg_beta ...
!> \param abij ...
!> \param Lai ...
!> \param Lai_beta ...
!> \param para_env ...
! **************************************************************************************************
   SUBROUTINE contract_integrals(DI, Emp2_RI, DRI, Emp2, homo, homo_beta, virtual, virtual_beta, &
                                 fact, fact2, calc_ex, &
                                 MOenerg, MOenerg_beta, abij, &
                                 Lai, Lai_beta, para_env)
      REAL(KIND=dp)                                      :: DI, Emp2_RI, DRI, Emp2
      INTEGER                                            :: homo, homo_beta, virtual, virtual_beta
      REAL(KIND=dp)                                      :: fact, fact2
      LOGICAL                                            :: calc_ex
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: MOenerg, MOenerg_beta
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :)  :: abij
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :)     :: Lai, Lai_beta
      TYPE(cp_para_env_type), POINTER                    :: para_env

      CHARACTER(LEN=*), PARAMETER :: routineN = 'contract_integrals', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: a, b, i, ij_counter, j
      REAL(KIND=dp)                                      :: t_iajb, t_iajb_RI
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: mat_ab

      ALLOCATE (mat_ab(virtual, virtual_beta))

      DI = 0.0_dp
      Emp2_RI = 0.0_dp
      ij_counter = 0
      DO j = 1, homo_beta
         DO i = 1, homo
            ij_counter = ij_counter+1
            IF (MOD(ij_counter, para_env%num_pe) /= para_env%mepos) CYCLE
            mat_ab = 0.0_dp
            mat_ab(:, :) = MATMUL(TRANSPOSE(Lai(:, :, i)), Lai_beta(:, :, j))
            DO b = 1, virtual_beta
               DO a = 1, virtual
                  IF (calc_ex) THEN
                     t_iajb = fact*abij(a, b, i, j)-abij(b, a, i, j)
                     t_iajb_RI = fact*mat_ab(a, b)-mat_ab(b, a)
                  ELSE
                     t_iajb = fact*abij(a, b, i, j)
                     t_iajb_RI = fact*mat_ab(a, b)
                  END IF
                  t_iajb = t_iajb/(MOenerg(a+homo)+MOenerg_beta(b+homo_beta)-MOenerg(i)-MOenerg_beta(j))
                  t_iajb_RI = t_iajb_RI/(MOenerg(a+homo)+MOenerg_beta(b+homo_beta)-MOenerg(i)-MOenerg_beta(j))

                  Emp2_RI = Emp2_RI-t_iajb_RI*mat_ab(a, b)*fact2

                  DI = DI-t_iajb*mat_ab(a, b)*fact2

               END DO
            END DO
         END DO
      END DO
      CALL mp_sum(DI, para_env%group)
      CALL mp_sum(Emp2_RI, para_env%group)

      DRI = Emp2-Emp2_RI
      DI = 2.0D+00*DI-Emp2-Emp2_RI

      DEALLOCATE (mat_ab)

   END SUBROUTINE

! **************************************************************************************************
!> \brief ...
!> \param homo ...
!> \param homo_beta ...
!> \param para_env ...
!> \param elements_ij_proc ...
!> \param ij_list_proc ...
! **************************************************************************************************
   SUBROUTINE calc_elem_ij_proc(homo, homo_beta, para_env, elements_ij_proc, ij_list_proc)
      INTEGER                                            :: homo, homo_beta
      TYPE(cp_para_env_type), POINTER                    :: para_env
      INTEGER                                            :: elements_ij_proc
      INTEGER, ALLOCATABLE, DIMENSION(:, :)              :: ij_list_proc

      CHARACTER(LEN=*), PARAMETER :: routineN = 'calc_elem_ij_proc', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: i, ij_counter, j

      elements_ij_proc = 0
      ij_counter = -1
      DO i = 1, homo
         DO j = 1, homo_beta
            ij_counter = ij_counter+1
            IF (MOD(ij_counter, para_env%num_pe) == para_env%mepos) elements_ij_proc = elements_ij_proc+1
         END DO
      END DO

      ALLOCATE (ij_list_proc(elements_ij_proc, 2))
      ij_list_proc = 0
      ij_counter = -1
      elements_ij_proc = 0
      DO i = 1, homo
         DO j = 1, homo_beta
            ij_counter = ij_counter+1
            IF (MOD(ij_counter, para_env%num_pe) == para_env%mepos) THEN
               elements_ij_proc = elements_ij_proc+1
               ij_list_proc(elements_ij_proc, 1) = i
               ij_list_proc(elements_ij_proc, 2) = j
            END IF
         END DO
      END DO

   END SUBROUTINE calc_elem_ij_proc

! **************************************************************************************************
!> \brief ...
!> \param lower_B ...
!> \param max_dev ...
!> \param valin ...
!> \param valout ...
! **************************************************************************************************
   SUBROUTINE transf_val(lower_B, max_dev, valin, valout)
      REAL(KIND=dp)                                      :: lower_B, max_dev, valin, valout

      REAL(KIND=dp), PARAMETER                           :: alpha = 2.633915794_dp

      valout = 0.0_dp
      valout = lower_B+max_dev/(1.0_dp+EXP(-alpha*valin))

   END SUBROUTINE

! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param mp2_env ...
!> \param nkind ...
!> \param max_rel_dev_output ...
!> \param basis_was_assoc ...
! **************************************************************************************************
   SUBROUTINE generate_RI_init_basis(qs_env, mp2_env, nkind, max_rel_dev_output, basis_was_assoc)
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(mp2_type), POINTER                            :: mp2_env
      INTEGER                                            :: nkind
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: max_rel_dev_output
      LOGICAL, ALLOCATABLE, DIMENSION(:)                 :: basis_was_assoc

      CHARACTER(LEN=*), PARAMETER :: routineN = 'generate_RI_init_basis', &
         routineP = moduleN//':'//routineN

      INTEGER :: basis_quality, handle, iexpo, iii, ikind, ipgf, iset, ishell, jexpo, jjj, la, &
         max_am, nexpo_shell, nseta, nsgfa, nsgfa_RI, prog_func, prog_l, RI_max_am, RI_nset, &
         RI_prev_size
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: l_expo, num_sgf_per_l, ordered_pos, &
                                                            RI_l_expo, RI_num_sgf_per_l, &
                                                            tot_num_exp_per_l
      INTEGER, ALLOCATABLE, DIMENSION(:, :)              :: l_tab
      INTEGER, DIMENSION(:), POINTER                     :: la_max, la_min, npgfa, nshell
      INTEGER, DIMENSION(:, :), POINTER                  :: first_sgfa, nl
      LOGICAL                                            :: external_num_of_func
      REAL(dp)                                           :: geom_fact
      REAL(dp), ALLOCATABLE, DIMENSION(:)                :: exponents, RI_exponents
      REAL(dp), ALLOCATABLE, DIMENSION(:, :)             :: exp_tab, max_min_exp_l
      REAL(dp), DIMENSION(:, :), POINTER                 :: sphi_a, zet
      REAL(dp), DIMENSION(:, :, :), POINTER              :: gcc
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: max_rel_dev, max_rel_dev_prev
      TYPE(gto_basis_set_type), POINTER                  :: orb_basis_a, tmp_basis
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(qs_kind_type), POINTER                        :: atom_kind

      CALL timeset(routineN, handle)

      basis_quality = mp2_env%ri_opt_param%basis_quality
      external_num_of_func = .FALSE.
      IF (ALLOCATED(mp2_env%ri_opt_param%RI_nset_per_l)) external_num_of_func = .TRUE.

      NULLIFY (qs_kind_set)
      CALL get_qs_env(qs_env=qs_env, qs_kind_set=qs_kind_set)
      nkind = SIZE(qs_kind_set, 1)

      ALLOCATE (basis_was_assoc(nkind))
      basis_was_assoc = .FALSE.

      IF (external_num_of_func .AND. nkind > 1) THEN
         CALL cp_warn(__LOCATION__, &
                      "There are more than one kind of atom. The same pattern of functions, "// &
                      "as specified by NUM_FUNC, will be used for all kinds.")
      END IF

      DO ikind = 1, nkind
         NULLIFY (atom_kind)
         atom_kind => qs_kind_set(ikind)

         CALL get_qs_kind(qs_kind=atom_kind, basis_set=orb_basis_a, basis_type="RI_AUX")
         ! save info if the basis was or not associated
         basis_was_assoc(ikind) = ASSOCIATED(orb_basis_a)

         ! skip the generation of the initial guess if the RI basis is
         ! provided in input
         IF (basis_was_assoc(ikind)) THEN
            nseta = orb_basis_a%nset
            la_max => orb_basis_a%lmax
            la_min => orb_basis_a%lmin
            npgfa => orb_basis_a%npgf
            nshell => orb_basis_a%nshell
            zet => orb_basis_a%zet
            nl => orb_basis_a%l

            max_am = MAXVAL(la_max)

            RI_max_am = max_am
            ALLOCATE (RI_num_sgf_per_l(0:RI_max_am))
            RI_num_sgf_per_l = 0
            RI_nset = 0
            DO iset = 1, nseta
               DO la = la_min(iset), la_max(iset)
                  RI_nset = RI_nset+1
                  RI_num_sgf_per_l(la) = RI_num_sgf_per_l(la)+1
                  IF (npgfa(iset) > 1) THEN
                     CALL cp_warn(__LOCATION__, &
                                  "The RI basis set optimizer can not handle contracted Gaussian. "// &
                                  "Calculation continue with only uncontracted functions.")
                  END IF
               END DO
            END DO

            ALLOCATE (exp_tab(MAXVAL(RI_num_sgf_per_l), 0:RI_max_am))
            exp_tab = 0.0_dp
            DO iii = 0, RI_max_am
               iexpo = 0
               DO iset = 1, nseta
                  DO la = la_min(iset), la_max(iset)
                     IF (la /= iii) CYCLE
                     iexpo = iexpo+1
                     exp_tab(iexpo, iii) = zet(1, iset)
                  END DO
               END DO
            END DO

            ! sort exponents
            DO iii = 0, RI_max_am
               ALLOCATE (ordered_pos(RI_num_sgf_per_l(iii)))
               ordered_pos = 0
               CALL sort(exp_tab(1:RI_num_sgf_per_l(iii), iii), RI_num_sgf_per_l(iii), ordered_pos)
               DEALLOCATE (ordered_pos)
            END DO

            ALLOCATE (RI_l_expo(RI_nset))
            RI_l_expo = 0
            ALLOCATE (RI_exponents(RI_nset))
            RI_exponents = 0.0_dp

            iset = 0
            DO iii = 0, RI_max_am
               DO iexpo = 1, RI_num_sgf_per_l(iii)
                  iset = iset+1
                  RI_l_expo(iset) = iii
                  RI_exponents(iset) = exp_tab(iexpo, iii)
               END DO
            END DO
            DEALLOCATE (exp_tab)

            ALLOCATE (max_rel_dev(RI_nset))
            max_rel_dev = 1.0_dp
            iset = 0
            DO iii = 0, RI_max_am
               IF (RI_num_sgf_per_l(iii) == 1) THEN
                  iset = iset+1
                  max_rel_dev(iset) = 0.35_dp
               ELSE
                  iset = iset+1
                  max_rel_dev(iset) = (RI_exponents(iset+1)+RI_exponents(iset))/2.0_dp
                  max_rel_dev(iset) = max_rel_dev(iset)/RI_exponents(iset)-1.0_dp
                  DO iexpo = 2, RI_num_sgf_per_l(iii)
                     iset = iset+1
                     max_rel_dev(iset) = (RI_exponents(iset)+RI_exponents(iset-1))/2.0_dp
                     max_rel_dev(iset) = 1.0_dp-max_rel_dev(iset)/RI_exponents(iset)
                  END DO
               END IF
            END DO
            max_rel_dev(:) = max_rel_dev(:)*0.9_dp
            DEALLOCATE (RI_num_sgf_per_l)

            ! deallocate the old basis before moving on
            CALL remove_basis_from_container(qs_kind_set(ikind)%basis_sets, basis_type="RI_AUX")

         ELSE

            CALL get_qs_kind(qs_kind=atom_kind, basis_set=orb_basis_a)

            sphi_a => orb_basis_a%sphi
            nseta = orb_basis_a%nset
            la_max => orb_basis_a%lmax
            la_min => orb_basis_a%lmin
            npgfa => orb_basis_a%npgf
            first_sgfa => orb_basis_a%first_sgf
            nshell => orb_basis_a%nshell
            zet => orb_basis_a%zet
            gcc => orb_basis_a%gcc
            nl => orb_basis_a%l
            nsgfa = orb_basis_a%nsgf

            max_am = MAXVAL(la_max)

            nexpo_shell = 0
            DO iset = 1, nseta
               DO ishell = 1, nshell(iset)
                  DO la = la_min(iset), la_max(iset)
                     IF (ishell > 1) THEN
                        IF (nl(ishell, iset) == nl(ishell-1, iset)) CYCLE
                     END IF
                     IF (la /= nl(ishell, iset)) CYCLE
                     nexpo_shell = nexpo_shell+npgfa(iset)
                  END DO
               END DO
            END DO

            ALLOCATE (exponents(nexpo_shell))
            exponents = 0.0_dp
            ALLOCATE (l_expo(nexpo_shell))
            l_expo = 0
            ALLOCATE (num_sgf_per_l(0:max_am))
            num_sgf_per_l = 0
            iexpo = 0
            DO iset = 1, nseta
               DO ishell = 1, nshell(iset)
                  DO la = la_min(iset), la_max(iset)
                     IF (ishell > 1) THEN
                        IF (nl(ishell, iset) == nl(ishell-1, iset)) CYCLE
                     END IF
                     IF (la /= nl(ishell, iset)) CYCLE
                     DO ipgf = 1, npgfa(iset)
                        iexpo = iexpo+1
                        exponents(iexpo) = zet(ipgf, iset)
                        l_expo(iexpo) = la
                     END DO
                     num_sgf_per_l(la) = num_sgf_per_l(la)+1
                  END DO
               END DO
            END DO

            ALLOCATE (exp_tab(nexpo_shell, nexpo_shell))
            exp_tab = 0.0_dp
            ALLOCATE (l_tab(nexpo_shell, nexpo_shell))
            l_tab = 0
            ALLOCATE (tot_num_exp_per_l(0:max_am*2))
            tot_num_exp_per_l = 0
            DO iexpo = 1, nexpo_shell
               DO jexpo = iexpo, nexpo_shell
                  exp_tab(jexpo, iexpo) = exponents(jexpo)+exponents(iexpo)
                  exp_tab(iexpo, jexpo) = exp_tab(jexpo, iexpo)
                  l_tab(jexpo, iexpo) = l_expo(jexpo)+l_expo(iexpo)
                  l_tab(iexpo, jexpo) = l_tab(jexpo, iexpo)
                  tot_num_exp_per_l(l_tab(jexpo, iexpo)) = tot_num_exp_per_l(l_tab(jexpo, iexpo))+1
               END DO
            END DO
            DEALLOCATE (l_expo)
            DEALLOCATE (exponents)

            ALLOCATE (max_min_exp_l(2, 0:max_am*2))
            max_min_exp_l(1, :) = HUGE(0)
            max_min_exp_l(2, :) = -HUGE(0)

            DO la = 0, max_am*2
               DO iexpo = 1, nexpo_shell
                  DO jexpo = iexpo, nexpo_shell
                     IF (la /= l_tab(jexpo, iexpo)) CYCLE
                     IF (exp_tab(jexpo, iexpo) <= max_min_exp_l(1, la)) max_min_exp_l(1, la) = exp_tab(jexpo, iexpo)
                     IF (exp_tab(jexpo, iexpo) >= max_min_exp_l(2, la)) max_min_exp_l(2, la) = exp_tab(jexpo, iexpo)
                  END DO
               END DO
            END DO
            DEALLOCATE (exp_tab)
            DEALLOCATE (l_tab)

            ! ! scale the limits of the exponents to avoid the optimizer to go out-of-range
            ! ! (0.2 just empirical parameter)
            max_min_exp_l(1, :) = max_min_exp_l(1, :)/0.80_dp
            max_min_exp_l(2, :) = max_min_exp_l(2, :)/1.20_dp

            ALLOCATE (RI_num_sgf_per_l(0:max_am*2))
            RI_num_sgf_per_l = 0

            SELECT CASE (basis_quality)
            CASE (0)
               ! normal
               prog_func = 0
               prog_l = 2
            CASE (1)
               ! large
               prog_func = 1
               prog_l = 2
            CASE (2)
               prog_func = 2
               prog_l = 2
            CASE DEFAULT
               prog_func = 0
               prog_l = 2
            END SELECT

            IF (external_num_of_func) THEN
               ! cp2k can not exceed angular momentum 7
               RI_max_am = MIN(SIZE(mp2_env%ri_opt_param%RI_nset_per_l)-1, 7)
               IF (RI_max_am > max_am*2) THEN
                  DEALLOCATE (RI_num_sgf_per_l)
                  ALLOCATE (RI_num_sgf_per_l(0:RI_max_am))
                  RI_num_sgf_per_l = 0
               END IF
               DO la = 0, RI_max_am
                  RI_num_sgf_per_l(la) = mp2_env%ri_opt_param%RI_nset_per_l(la)
               END DO
            ELSE
               RI_num_sgf_per_l(0) = num_sgf_per_l(0)*2+prog_func
               DO la = 1, max_am
                  RI_num_sgf_per_l(la) = RI_num_sgf_per_l(la-1)-1
                  IF (RI_num_sgf_per_l(la) == 0) THEN
                     RI_num_sgf_per_l(la) = 1
                     EXIT
                  END IF
               END DO
               DO la = max_am+1, max_am*2
                  RI_num_sgf_per_l(la) = RI_num_sgf_per_l(la-1)-prog_l
                  IF (RI_num_sgf_per_l(la) == 0) THEN
                     RI_num_sgf_per_l(la) = 1
                  END IF
                  IF (RI_num_sgf_per_l(la) == 1) EXIT
               END DO
               RI_max_am = MIN(max_am*2, 7)
               DO la = 0, MIN(max_am*2, 7)
                  IF (RI_num_sgf_per_l(la) == 0) THEN
                     RI_max_am = la-1
                     EXIT
                  END IF
               END DO

               iii = 0
               jjj = 0
               nsgfa_RI = 0
               DO la = 1, max_am*2
                  IF (tot_num_exp_per_l(la) >= iii) THEN
                     iii = tot_num_exp_per_l(la)
                     jjj = la
                  END IF
                  nsgfa_RI = nsgfa_RI+RI_num_sgf_per_l(la)*(la*2+1)
               END DO
               DEALLOCATE (tot_num_exp_per_l)
               IF (REAL(nsgfa_RI, KIND=dp)/REAL(nsgfa, KIND=dp) <= 2.5_dp) THEN
                  RI_num_sgf_per_l(jjj) = RI_num_sgf_per_l(jjj)+1
               END IF
            END IF

            RI_nset = SUM(RI_num_sgf_per_l)

            ALLOCATE (RI_exponents(RI_nset))
            RI_exponents = 0.0_dp

            ALLOCATE (RI_l_expo(RI_nset))
            RI_l_expo = 0

            ALLOCATE (max_rel_dev(RI_nset))
            max_rel_dev = 1.0_dp

            iset = 0
            DO la = 0, RI_max_am
               IF (RI_num_sgf_per_l(la) == 1) THEN
                  iset = iset+1
                  RI_exponents(iset) = (max_min_exp_l(2, la)+max_min_exp_l(1, la))/2.0_dp
                  RI_l_expo(iset) = la
                  geom_fact = max_min_exp_l(2, la)/max_min_exp_l(1, la)

                  max_rel_dev(iset) = (geom_fact-1.0_dp)/(geom_fact+1.0_dp)*0.9_dp
               ELSE
                  geom_fact = (max_min_exp_l(2, la)/max_min_exp_l(1, la))**(1.0_dp/REAL(RI_num_sgf_per_l(la)-1, dp))
                  DO iexpo = 1, RI_num_sgf_per_l(la)
                     iset = iset+1
                     RI_exponents(iset) = max_min_exp_l(1, la)*(geom_fact**(iexpo-1))
                     RI_l_expo(iset) = la
                     max_rel_dev(iset) = (geom_fact-1.0_dp)/(geom_fact+1.0_dp)*0.9_dp
                  END DO
               END IF
            END DO
            DEALLOCATE (num_sgf_per_l)
            DEALLOCATE (max_min_exp_l)
            DEALLOCATE (RI_num_sgf_per_l)

            ! IF(qs_env%para_env%mepos==0) THEN
            !   WRITE(*,*) RI_nset, RI_max_am, geom_fact
            !   iset=0
            !   DO la=0, RI_max_am
            !     DO iexpo=1, RI_num_sgf_per_l(la)
            !       iset=iset+1
            !       WRITE(*,*) RI_l_expo(iset), RI_exponents(iset)
            !     END DO
            !   END DO
            !   WRITE(*,*) nsgfa, nsgfa_RI
            ! END IF

         END IF ! RI basis not associated

         ! create the new basis
         NULLIFY (tmp_basis)
         CALL create_ri_basis(tmp_basis, RI_nset, RI_l_expo, RI_exponents)
         CALL add_basis_set_to_container(qs_kind_set(ikind)%basis_sets, tmp_basis, "RI_AUX")
!d    CALL copy_gto_basis_set(tmp_basis,qs_kind_set(ikind)%ri_aux_basis_set)

         DEALLOCATE (RI_exponents)
         DEALLOCATE (RI_l_expo)

         IF (.NOT. ALLOCATED(max_rel_dev_output)) THEN
            ALLOCATE (max_rel_dev_output(RI_nset))
            max_rel_dev_output(:) = max_rel_dev
         ELSE
            ! make a copy
            RI_prev_size = SIZE(max_rel_dev_output)
            ALLOCATE (max_rel_dev_prev(RI_prev_size))
            max_rel_dev_prev(:) = max_rel_dev_output
            DEALLOCATE (max_rel_dev_output)
            ! reallocate and copy
            ALLOCATE (max_rel_dev_output(RI_prev_size+RI_nset))
            max_rel_dev_output(1:RI_prev_size) = max_rel_dev_prev
            max_rel_dev_output(RI_prev_size+1:RI_prev_size+RI_nset) = max_rel_dev
            DEALLOCATE (max_rel_dev_prev)
         END IF
         DEALLOCATE (max_rel_dev)

      END DO ! ikind

      IF (external_num_of_func) DEALLOCATE (mp2_env%ri_opt_param%RI_nset_per_l)

      CALL timestop(handle)

   END SUBROUTINE generate_RI_init_basis

! **************************************************************************************************
!> \brief ...
!> \param gto_basis_set ...
!> \param RI_nset ...
!> \param RI_l_expo ...
!> \param RI_exponents ...
! **************************************************************************************************
   SUBROUTINE create_ri_basis(gto_basis_set, RI_nset, RI_l_expo, RI_exponents)
      TYPE(gto_basis_set_type), POINTER                  :: gto_basis_set
      INTEGER                                            :: RI_nset
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: RI_l_expo
      REAL(dp), ALLOCATABLE, DIMENSION(:)                :: RI_exponents

      CHARACTER(LEN=*), PARAMETER :: routineN = 'create_ri_basis', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, i, ico, ipgf, iset, ishell, &
                                                            lshell, m, maxco, maxl, maxpgf, &
                                                            maxshell, ncgf, nmin, nset, nsgf
      INTEGER, DIMENSION(:), POINTER                     :: lmax, lmin, npgf, nshell
      INTEGER, DIMENSION(:, :), POINTER                  :: l, n
      REAL(KIND=dp), DIMENSION(:, :), POINTER            :: zet
      REAL(KIND=dp), DIMENSION(:, :, :), POINTER         :: gcc

      CALL timeset(routineN, handle)
      NULLIFY (lmax, lmin, npgf, nshell, l, n, zet, gcc)

      ! allocate the basis
      CALL allocate_gto_basis_set(gto_basis_set)

      ! brute force
      nset = 0
      maxshell = 0
      maxpgf = 0
      maxco = 0
      ncgf = 0
      nsgf = 0
      gto_basis_set%nset = nset
      gto_basis_set%ncgf = ncgf
      gto_basis_set%nsgf = nsgf
      CALL reallocate(gto_basis_set%lmax, 1, nset)
      CALL reallocate(gto_basis_set%lmin, 1, nset)
      CALL reallocate(gto_basis_set%npgf, 1, nset)
      CALL reallocate(gto_basis_set%nshell, 1, nset)
      CALL reallocate(gto_basis_set%n, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%l, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%zet, 1, maxpgf, 1, nset)
      CALL reallocate(gto_basis_set%gcc, 1, maxpgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%set_radius, 1, nset)
      CALL reallocate(gto_basis_set%pgf_radius, 1, maxpgf, 1, nset)
      CALL reallocate(gto_basis_set%first_cgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%first_sgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%last_cgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%last_sgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%ncgf_set, 1, nset)
      CALL reallocate(gto_basis_set%nsgf_set, 1, nset)
      CALL reallocate(gto_basis_set%cphi, 1, maxco, 1, ncgf)
      CALL reallocate(gto_basis_set%sphi, 1, maxco, 1, nsgf)
      CALL reallocate(gto_basis_set%scon, 1, maxco, 1, nsgf)
      CALL reallocate(gto_basis_set%lx, 1, ncgf)
      CALL reallocate(gto_basis_set%ly, 1, ncgf)
      CALL reallocate(gto_basis_set%lz, 1, ncgf)
      CALL reallocate(gto_basis_set%m, 1, nsgf)
      CALL reallocate(gto_basis_set%norm_cgf, 1, ncgf)

      nset = RI_nset

      ! locals
      CALL reallocate(npgf, 1, nset)
      CALL reallocate(nshell, 1, nset)
      CALL reallocate(lmax, 1, nset)
      CALL reallocate(lmin, 1, nset)
      CALL reallocate(n, 1, 1, 1, nset)

      maxl = 0
      maxpgf = 0
      maxshell = 0
      DO iset = 1, nset
         n(1, iset) = iset
         lmin(iset) = RI_l_expo(iset)
         lmax(iset) = RI_l_expo(iset)
         npgf(iset) = 1

         maxl = MAX(maxl, lmax(iset))

         IF (npgf(iset) > maxpgf) THEN
            maxpgf = npgf(iset)
            CALL reallocate(zet, 1, maxpgf, 1, nset)
            CALL reallocate(gcc, 1, maxpgf, 1, maxshell, 1, nset)
         END IF
         nshell(iset) = 0
         DO lshell = lmin(iset), lmax(iset)
            nmin = n(1, iset)+lshell-lmin(iset)
            ishell = 1
            nshell(iset) = nshell(iset)+ishell
            IF (nshell(iset) > maxshell) THEN
               maxshell = nshell(iset)
               CALL reallocate(n, 1, maxshell, 1, nset)
               CALL reallocate(l, 1, maxshell, 1, nset)
               CALL reallocate(gcc, 1, maxpgf, 1, maxshell, 1, nset)
            END IF
            DO i = 1, ishell
               n(nshell(iset)-ishell+i, iset) = nmin+i-1
               l(nshell(iset)-ishell+i, iset) = lshell
            END DO
         END DO

         DO ipgf = 1, npgf(iset)
            zet(ipgf, iset) = RI_exponents(iset)
            DO ishell = 1, nshell(iset)
               gcc(ipgf, ishell, iset) = 1.0_dp
            END DO
         END DO
      END DO

      CALL init_orbital_pointers(maxl)

      gto_basis_set%nset = nset
      CALL reallocate(gto_basis_set%lmax, 1, nset)
      CALL reallocate(gto_basis_set%lmin, 1, nset)
      CALL reallocate(gto_basis_set%npgf, 1, nset)
      CALL reallocate(gto_basis_set%nshell, 1, nset)
      CALL reallocate(gto_basis_set%n, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%l, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%zet, 1, maxpgf, 1, nset)
      CALL reallocate(gto_basis_set%gcc, 1, maxpgf, 1, maxshell, 1, nset)

      ! Copy the basis set information into the data structure

      DO iset = 1, nset
         gto_basis_set%lmax(iset) = lmax(iset)
         gto_basis_set%lmin(iset) = lmin(iset)
         gto_basis_set%npgf(iset) = npgf(iset)
         gto_basis_set%nshell(iset) = nshell(iset)
         DO ishell = 1, nshell(iset)
            gto_basis_set%n(ishell, iset) = n(ishell, iset)
            gto_basis_set%l(ishell, iset) = l(ishell, iset)
            DO ipgf = 1, npgf(iset)
               gto_basis_set%gcc(ipgf, ishell, iset) = gcc(ipgf, ishell, iset)
            END DO
         END DO
         DO ipgf = 1, npgf(iset)
            gto_basis_set%zet(ipgf, iset) = zet(ipgf, iset)
         END DO
      END DO

      ! Initialise the depending atomic kind information

      CALL reallocate(gto_basis_set%set_radius, 1, nset)
      CALL reallocate(gto_basis_set%pgf_radius, 1, maxpgf, 1, nset)
      CALL reallocate(gto_basis_set%first_cgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%first_sgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%last_cgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%last_sgf, 1, maxshell, 1, nset)
      CALL reallocate(gto_basis_set%ncgf_set, 1, nset)
      CALL reallocate(gto_basis_set%nsgf_set, 1, nset)

      maxco = 0
      ncgf = 0
      nsgf = 0

      DO iset = 1, nset
         gto_basis_set%ncgf_set(iset) = 0
         gto_basis_set%nsgf_set(iset) = 0
         DO ishell = 1, nshell(iset)
            lshell = gto_basis_set%l(ishell, iset)
            gto_basis_set%first_cgf(ishell, iset) = ncgf+1
            ncgf = ncgf+nco(lshell)
            gto_basis_set%last_cgf(ishell, iset) = ncgf
            gto_basis_set%ncgf_set(iset) = &
               gto_basis_set%ncgf_set(iset)+nco(lshell)
            gto_basis_set%first_sgf(ishell, iset) = nsgf+1
            nsgf = nsgf+nso(lshell)
            gto_basis_set%last_sgf(ishell, iset) = nsgf
            gto_basis_set%nsgf_set(iset) = &
               gto_basis_set%nsgf_set(iset)+nso(lshell)
         END DO
         maxco = MAX(maxco, npgf(iset)*ncoset(lmax(iset)))
      END DO

      gto_basis_set%ncgf = ncgf
      gto_basis_set%nsgf = nsgf

      CALL reallocate(gto_basis_set%cphi, 1, maxco, 1, ncgf)
      CALL reallocate(gto_basis_set%sphi, 1, maxco, 1, nsgf)
      CALL reallocate(gto_basis_set%scon, 1, maxco, 1, nsgf)
      CALL reallocate(gto_basis_set%lx, 1, ncgf)
      CALL reallocate(gto_basis_set%ly, 1, ncgf)
      CALL reallocate(gto_basis_set%lz, 1, ncgf)
      CALL reallocate(gto_basis_set%m, 1, nsgf)
      CALL reallocate(gto_basis_set%norm_cgf, 1, ncgf)
      ALLOCATE (gto_basis_set%cgf_symbol(ncgf))

      ALLOCATE (gto_basis_set%sgf_symbol(nsgf))

      ncgf = 0
      nsgf = 0

      DO iset = 1, nset
         DO ishell = 1, nshell(iset)
            lshell = gto_basis_set%l(ishell, iset)
            DO ico = ncoset(lshell-1)+1, ncoset(lshell)
               ncgf = ncgf+1
               gto_basis_set%lx(ncgf) = indco(1, ico)
               gto_basis_set%ly(ncgf) = indco(2, ico)
               gto_basis_set%lz(ncgf) = indco(3, ico)
               gto_basis_set%cgf_symbol(ncgf) = &
                  cgf_symbol(n(ishell, iset), (/gto_basis_set%lx(ncgf), &
                                                gto_basis_set%ly(ncgf), &
                                                gto_basis_set%lz(ncgf)/))
            END DO
            DO m = -lshell, lshell
               nsgf = nsgf+1
               gto_basis_set%m(nsgf) = m
               gto_basis_set%sgf_symbol(nsgf) = &
                  sgf_symbol(n(ishell, iset), lshell, m)
            END DO
         END DO
      END DO

      DEALLOCATE (gcc, l, lmax, lmin, n, npgf, nshell, zet)

      CALL timestop(handle)

   END SUBROUTINE

END MODULE mp2_optimize_ri_basis

