Bug-fixes and upgrades to the Active Space Module

- bug fixes of some incorrect indices
- extension to support UKS calculations
- implementation of an FCIDump checksum to ease testing
- addition of regression tests
- minor documentation improvements

After this PR, the active space module can be used in conjunction with HF-style calculations. This includes:

- GAPW with the ALL electron potential
- GAPW with the GTH-HF potential
- GPW with the GTH-HF potential

Regression tests for all of the above scenarios have been added in `tests/QS/regtest-as-1`.
```
% ../tools/regtesting/do_regtest -cp2kdir ../ -version sdbg -arch local -nobuild -restrictdir QS/regtest-as-1
<...>
--------------------------------- Summary --------------------------------
Number of FAILED  tests 0
Number of WRONG   tests 0
Number of CORRECT tests 26
Total number of   tests 26
GREPME 0 0 26 0 26 X

Summary: correct: 26 / 26; 3min
Status: OK
```

src/qs_active_space_types.F

@@ -71,10 +71,10 @@ MODULE qs_active_space_types
    END TYPE eri_type_eri_element_func
 
    TYPE active_space_type
-      INTEGER                       :: nactive
-      INTEGER                       :: ninactive
-      INTEGER, DIMENSION(2)         :: ninspin
-      INTEGER, DIMENSION(2)         :: nelectrons
+      INTEGER                       :: nelec_active
+      INTEGER                       :: nelec_inactive
+      INTEGER, DIMENSION(2)         :: nelec_inactive_spinwise
+      INTEGER, DIMENSION(2)         :: nelec_total
       INTEGER                       :: multiplicity
       INTEGER                       :: nspins
       LOGICAL                       :: molecule
@@ -86,7 +86,7 @@ MODULE qs_active_space_types
       TYPE(mo_set_p_type), DIMENSION(:), POINTER  :: mos_active
       TYPE(mo_set_p_type), DIMENSION(:), POINTER  :: mos_inactive
       TYPE(eri_type)                :: eri
-      TYPE(cp_fm_p_type), DIMENSION(:), POINTER   :: p_ref
+      TYPE(cp_fm_p_type), DIMENSION(:), POINTER   :: p_active
       TYPE(cp_fm_p_type), DIMENSION(:), POINTER   :: ks_sub
       TYPE(cp_fm_p_type), DIMENSION(:), POINTER   :: vxc_sub
       TYPE(cp_fm_p_type), DIMENSION(:), POINTER   :: h_sub
@@ -118,8 +118,8 @@ END FUNCTION eri_type_eri_element_func_interface
 CONTAINS
 
 ! **************************************************************************************************
-!> \brief ...
-!> \param active_space_env ...
+!> \brief Creates an active space environment type, nullifying all quantities.
+!> \param active_space_env the active space environment to be initialized
 ! **************************************************************************************************
    SUBROUTINE create_active_space_type(active_space_env)
       TYPE(active_space_type), POINTER                   :: active_space_env
@@ -130,15 +130,15 @@ SUBROUTINE create_active_space_type(active_space_env)
 
       ALLOCATE (active_space_env)
       NULLIFY (active_space_env%mos_active, active_space_env%mos_inactive)
-      NULLIFY (active_space_env%ks_sub, active_space_env%p_ref)
+      NULLIFY (active_space_env%ks_sub, active_space_env%p_active)
       NULLIFY (active_space_env%vxc_sub, active_space_env%h_sub)
       NULLIFY (active_space_env%fock_sub, active_space_env%pmat_inactive)
 
    END SUBROUTINE create_active_space_type
 
 ! **************************************************************************************************
-!> \brief ...
-!> \param active_space_env ...
+!> \brief Releases all quantities in the active space environment.
+!> \param active_space_env the active space environment to be released
 ! **************************************************************************************************
    SUBROUTINE release_active_space_type(active_space_env)
       TYPE(active_space_type), POINTER                   :: active_space_env
@@ -163,11 +163,11 @@ SUBROUTINE release_active_space_type(active_space_env)
 
          CALL release_eri_type(active_space_env%eri)
 
-         IF (ASSOCIATED(active_space_env%p_ref)) THEN
-            DO isp = 1, SIZE(active_space_env%p_ref)
-               CALL cp_fm_release(active_space_env%p_ref(isp)%matrix)
+         IF (ASSOCIATED(active_space_env%p_active)) THEN
+            DO isp = 1, SIZE(active_space_env%p_active)
+               CALL cp_fm_release(active_space_env%p_active(isp)%matrix)
             END DO
-            DEALLOCATE (active_space_env%p_ref)
+            DEALLOCATE (active_space_env%p_active)
          END IF
 
          IF (ASSOCIATED(active_space_env%ks_sub)) THEN
@@ -207,8 +207,8 @@ SUBROUTINE release_active_space_type(active_space_env)
    END SUBROUTINE release_active_space_type
 
 ! **************************************************************************************************
-!> \brief ...
-!> \param eri_env ...
+!> \brief Releases the ERI environment type.
+!> \param eri_env the ERI environment to be released
 ! **************************************************************************************************
    SUBROUTINE release_eri_type(eri_env)
       TYPE(eri_type)                                     :: eri_env
@@ -279,8 +279,8 @@ END SUBROUTINE csr_idx_from_combined
 
 ! **************************************************************************************************
 !> \brief calculates index range for processor in group mp_group
-!> \param nindex ...
-!> \param mp_group ...
+!> \param nindex the number of indices
+!> \param mp_group message-passing group ID
 !> \return a range tuple
 !> \par History
 !>      04.2016 created [JGH]

tests/QS/regtest-as-1/TEST_FILES

@@ -0,0 +1,33 @@
+# runs are executed in the same order as in this file
+# the second field tells which test should be run in order to compare with the last available output
+# e.g. 0 means do not compare anything, running is enough
+#      1 compares the last total energy in the file
+#      for details see cp2k/tools/do_regtest
+#
+h2_gapw_2-2.inp                                        1      1e-12              -1.12703481947359
+h2_gapw_2-2.inp                                       92      1e-8                4.08762365
+h2_gapw_2-3.inp                                        1      1e-12              -1.12703481947359
+h2_gapw_2-3.inp                                       92      1e-8                6.34129968
+h2_gapw_2-4.inp                                        1      1e-12              -1.12703481947359
+h2_gapw_2-4.inp                                       92      1e-8               10.57997133
+h2_gapw_pp_2-2.inp                                     1      1e-12              -1.12609343153655
+h2_gapw_pp_2-2.inp                                    92      1e-8                4.08439200
+h2_gapw_pp_2-3.inp                                     1      1e-12              -1.12609343153655
+h2_gapw_pp_2-3.inp                                    92      1e-8                6.33490411
+h2_gapw_pp_2-4.inp                                     1      1e-12              -1.12609343153655
+h2_gapw_pp_2-4.inp                                    92      1e-8               10.58497448
+h2_gpw_pp_2-2.inp                                      1      1e-12              -1.12622646044780
+h2_gpw_pp_2-2.inp                                     92      1e-8                4.08480362
+h2_gpw_pp_2-3.inp                                      1      1e-12              -1.12622646044780
+h2_gpw_pp_2-3.inp                                     92      1e-8                6.33542725
+h2_gpw_pp_2-4.inp                                      1      1e-12              -1.12622646044780
+h2_gpw_pp_2-4.inp                                     92      1e-8               10.58532335
+h2o_gapw_2-2.inp                                       1      1e-12             -76.011970410506123
+h2o_gapw_2-2.inp                                      92      1e-8               77.48403361
+ch2_gapw_2-3.inp                                       1      1e-12             -38.91914381184247
+ch2_gapw_2-3.inp                                      92      1e-8               50.38752107
+ch2_gapw_pp_2-3.inp                                    1      1e-12              -6.51646227467145
+ch2_gapw_pp_2-3.inp                                   92      1e-8               17.95445655
+ch2_gpw_pp_2-3.inp                                     1      1e-12              -6.51682932586237
+ch2_gpw_pp_2-3.inp                                    92      1e-8               17.95513412
+#EOF

tests/QS/regtest-as-1/ch2_gapw_2-3.inp

@@ -0,0 +1,78 @@
+&FORCE_EVAL
+  METHOD Quickstep
+  &DFT
+    &QS
+      METHOD GAPW
+    &END QS
+    UKS TRUE
+    MULTIPLICITY 3
+    &XC
+      &XC_FUNCTIONAL NONE
+      &END XC_FUNCTIONAL
+      &HF 1.0
+      &END HF
+    &END XC
+    &POISSON
+      POISSON_SOLVER ANALYTIC
+      PERIODIC NONE
+    &END POISSON
+    &MGRID
+      CUTOFF 500
+    &END MGRID
+    &SCF
+      ADDED_MOS 17
+      MAX_SCF 20
+      &PRINT
+        &RESTART OFF
+        &END RESTART
+      &END PRINT
+    &END SCF
+    &PRINT
+      &AO_MATRICES
+        CORE_HAMILTONIAN TRUE
+        KINETIC_ENERGY TRUE
+        POTENTIAL_ENERGY TRUE
+      &END AO_MATRICES
+      &ACTIVE_SPACE
+        ACTIVE_ELECTRONS 2
+        ACTIVE_ORBITALS 3 3
+        INACTIVE_ELECTRONS 3 3
+        ISOLATED_SYSTEM TRUE
+        &ERI
+          METHOD FULL_GPW
+          PERIODICITY 0 0 0
+        &END ERI
+        &ERI_GPW
+          CUTOFF 500
+        &END ERI_GPW
+        &FCIDUMP
+          FILENAME __STD_OUT__
+        &END FCIDUMP
+      &END ACTIVE_SPACE
+    &END PRINT
+  &END DFT
+  &SUBSYS
+    &CELL
+      ABC 6.0 6.0 6.0
+      PERIODIC NONE
+    &END CELL
+    &COORD
+      C 0.000  0.000  0.112
+      H 0.000  0.974  0.335
+      H 0.000 -0.974 -0.335
+    &END COORD
+    &KIND H
+      BASIS_SET 6-31G*
+      POTENTIAL ALL
+    &END KIND
+    &KIND C
+      BASIS_SET 6-31G*
+      POTENTIAL ALL
+    &END KIND
+  &END SUBSYS
+&END FORCE_EVAL
+&GLOBAL
+  RUN_TYPE ENERGY
+  PRINT_LEVEL LOW
+  PROJECT ch2_gapw
+&END GLOBAL

tests/QS/regtest-as-1/ch2_gapw_pp_2-3.inp

@@ -0,0 +1,78 @@
+&FORCE_EVAL
+  METHOD Quickstep
+  &DFT
+    &QS
+      METHOD GAPW
+    &END QS
+    UKS TRUE
+    MULTIPLICITY 3
+    &XC
+      &XC_FUNCTIONAL NONE
+      &END XC_FUNCTIONAL
+      &HF 1.0
+      &END HF
+    &END XC
+    &POISSON
+      POISSON_SOLVER ANALYTIC
+      PERIODIC NONE
+    &END POISSON
+    &MGRID
+      CUTOFF 500
+    &END MGRID
+    &SCF
+      ADDED_MOS 17
+      MAX_SCF 20
+      &PRINT
+        &RESTART OFF
+        &END RESTART
+      &END PRINT
+    &END SCF
+    &PRINT
+      &AO_MATRICES
+        CORE_HAMILTONIAN TRUE
+        KINETIC_ENERGY TRUE
+        POTENTIAL_ENERGY TRUE
+      &END AO_MATRICES
+      &ACTIVE_SPACE
+        ACTIVE_ELECTRONS 2
+        ACTIVE_ORBITALS 3 3
+        INACTIVE_ELECTRONS 2 2
+        ISOLATED_SYSTEM TRUE
+        &ERI
+          METHOD FULL_GPW
+          PERIODICITY 0 0 0
+        &END ERI
+        &ERI_GPW
+          CUTOFF 500
+        &END ERI_GPW
+        &FCIDUMP
+          FILENAME __STD_OUT__
+        &END FCIDUMP
+      &END ACTIVE_SPACE
+    &END PRINT
+  &END DFT
+  &SUBSYS
+    &CELL
+      ABC 6.0 6.0 6.0
+      PERIODIC NONE
+    &END CELL
+    &COORD
+      C 0.000  0.000  0.112
+      H 0.000  0.974  0.335
+      H 0.000 -0.974 -0.335
+    &END COORD
+    &KIND H
+      BASIS_SET 6-31G*
+      POTENTIAL GTH-HF
+    &END KIND
+    &KIND C
+      BASIS_SET 6-31G*
+      POTENTIAL GTH-HF
+    &END KIND
+  &END SUBSYS
+&END FORCE_EVAL
+&GLOBAL
+  RUN_TYPE ENERGY
+  PRINT_LEVEL LOW
+  PROJECT ch2_gapw_pp
+&END GLOBAL

tests/QS/regtest-as-1/ch2_gpw_pp_2-3.inp

@@ -0,0 +1,78 @@
+&FORCE_EVAL
+  METHOD Quickstep
+  &DFT
+    &QS
+      METHOD GPW
+    &END QS
+    UKS TRUE
+    MULTIPLICITY 3
+    &XC
+      &XC_FUNCTIONAL NONE
+      &END XC_FUNCTIONAL
+      &HF 1.0
+      &END HF
+    &END XC
+    &POISSON
+      POISSON_SOLVER ANALYTIC
+      PERIODIC NONE
+    &END POISSON
+    &MGRID
+      CUTOFF 500
+    &END MGRID
+    &SCF
+      ADDED_MOS 17
+      MAX_SCF 20
+      &PRINT
+        &RESTART OFF
+        &END RESTART
+      &END PRINT
+    &END SCF
+    &PRINT
+      &AO_MATRICES
+        CORE_HAMILTONIAN TRUE
+        KINETIC_ENERGY TRUE
+        POTENTIAL_ENERGY TRUE
+      &END AO_MATRICES
+      &ACTIVE_SPACE
+        ACTIVE_ELECTRONS 2
+        ACTIVE_ORBITALS 3 3
+        INACTIVE_ELECTRONS 2 2
+        ISOLATED_SYSTEM TRUE
+        &ERI
+          METHOD FULL_GPW
+          PERIODICITY 0 0 0
+        &END ERI
+        &ERI_GPW
+          CUTOFF 500
+        &END ERI_GPW
+        &FCIDUMP
+          FILENAME __STD_OUT__
+        &END FCIDUMP
+      &END ACTIVE_SPACE
+    &END PRINT
+  &END DFT
+  &SUBSYS
+    &CELL
+      ABC 6.0 6.0 6.0
+      PERIODIC NONE
+    &END CELL
+    &COORD
+      C 0.000  0.000  0.112
+      H 0.000  0.974  0.335
+      H 0.000 -0.974 -0.335
+    &END COORD
+    &KIND H
+      BASIS_SET 6-31G*
+      POTENTIAL GTH-HF
+    &END KIND
+    &KIND C
+      BASIS_SET 6-31G*
+      POTENTIAL GTH-HF
+    &END KIND
+  &END SUBSYS
+&END FORCE_EVAL
+&GLOBAL
+  RUN_TYPE ENERGY
+  PRINT_LEVEL LOW
+  PROJECT ch2_gpw_pp
+&END GLOBAL