Electrons

1. Context
2. Computation

1 Context

The following data stored in the context:

Variable	Type	Description
`uninitialized`	`int32_t`	Keeps bit set for uninitialized data
`num`	`int64_t`	Total number of electrons
`up_num`	`int64_t`	Number of up-spin electrons
`down_num`	`int64_t`	Number of down-spin electrons
`provided`	`bool`	If true, `electron` is valid
`walker`	`qmckl_point`	Current set of walkers
`walker_old`	`qmckl_point`	Previous set of walkers

Computed data:

Variable	Type	Description
`ee_distance`	`double[walker.num][num][num]`	Electron-electron distances
`ee_distance_date`	`uint64_t`	Last modification date of the electron-electron distances
`en_distance`	`double[walker.num][nucl_num][num]`	Electron-nucleus distances
`en_distance_date`	`uint64_t`	Last modification date of the electron-electron distances
`ee_potential`	`double[walker.num]`	Electron-electron potential energy
`ee_potential_date`	`uint64_t`	Last modification date of the electron-electron potential
`en_potential`	`double[walker.num]`	Electron-nucleus potential energy
`en_potential_date`	`int64_t`	Date when the electron-nucleus potential energy was computed

1.1 Data structure

typedef struct qmckl_walker_struct {
  int64_t num;
  qmckl_point_struct point;
} qmckl_walker;

typedef struct qmckl_electron_struct {
  int64_t        num;
  int64_t        up_num;
  int64_t        down_num;
  qmckl_walker   walker;
  qmckl_walker   walker_old;
  uint64_t       ee_distance_date;
  uint64_t       en_distance_date;
  uint64_t       ee_potential_date;
  uint64_t       en_potential_date;
  double*        ee_distance;
  double*        en_distance;
  double*        ee_potential;
  double*        en_potential;
  int32_t        uninitialized;
  bool           provided;
} qmckl_electron_struct;

The uninitialized integer contains one bit set to one for each initialization function which has not been called. It becomes equal to zero after all initialization functions have been called. The struct is then initialized and provided == true. Some values are initialized by default, and are not concerned by this mechanism.

qmckl_exit_code qmckl_init_electron(qmckl_context context);

qmckl_exit_code qmckl_init_electron(qmckl_context context) {

  if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
    return false;
  }

  qmckl_context_struct* const ctx = (qmckl_context_struct*) context;
  assert (ctx != NULL);

  ctx->electron.uninitialized = (1 << 1) - 1;

  return QMCKL_SUCCESS;
}

bool qmckl_electron_provided (const qmckl_context context);

1.2 Initialization functions

To set the data relative to the electrons in the context, the following functions need to be called. When the data structure is initialized, the internal coord_new and coord_old arrays are both not allocated.

qmckl_exit_code qmckl_set_electron_num      (qmckl_context context, const int64_t up_num, const int64_t down_num);
qmckl_exit_code qmckl_set_electron_coord    (qmckl_context context, const char transp, const int64_t walk_num, const double* coord, const int64_t size_max);

To set the number of electrons, we give the number of up-spin and down-spin electrons to the context and we set the number of walkers.

interface
  integer(c_int32_t) function qmckl_set_electron_num(context, alpha, beta) bind(C)
    use, intrinsic :: iso_c_binding
    import
    implicit none

    integer (c_int64_t) , intent(in)  , value :: context
    integer (c_int64_t) , intent(in)  , value :: alpha
    integer (c_int64_t) , intent(in)  , value :: beta
  end function
end interface

The following function sets the electron coordinates of all the walkers. When this is done, the pointers to the old and new sets of coordinates are swapped, and the new coordinates are overwritten. This can be done only when the data relative to electrons have been set.

size_max should be equal equal or geater than elec_num * walker.num * 3, to be symmetric with qmckl_get_electron_coord.

Important: changing the electron coordinates increments the date in the context.

interface
  integer(c_int32_t) function qmckl_set_electron_coord(context, transp, walk_num, coord, size_max) bind(C)
    use, intrinsic :: iso_c_binding
    import
    implicit none

    integer (c_int64_t) , intent(in)  , value :: context
    character           , intent(in)  , value :: transp
    integer (c_int64_t) , intent(in)  , value :: walk_num
    double precision    , intent(in)          :: coord(*)
    integer (c_int64_t) , intent(in)  , value :: size_max
  end function
end interface

1.3 Access functions

Access functions return QMCKL_SUCCESS when the data has been successfully retrieved. It returnes QMCKL_INVALID_CONTEXT when the context is not a valid context, and QMCKL_NOT_PROVIDED when the data has not been provided. If the function returns successfully, the variable pointed by the pointer given in argument contains the requested data. Otherwise, this variable is untouched.

1.3.1 Number of electrons

1.3.2 Number of walkers

A walker is a set of electron coordinates that are arguments of the wave function. walk_num is the number of walkers.

1.3.3 Electron coordinates

Returns the current electron coordinates. The pointer is assumed to point on a memory block of size size_max ≥ 3 * elec_num * walker.num. The order of the indices is:

	Normal	Transposed
C	`[walker.num*elec_num][3]`	`[3][walker.num*elec_num]`
Fortran	`(3,walker.num*elec_num)`	`(walker.num*elec_num, 3)`

As the walker attribute is equal to points, returning the current electron coordinates is equivalent to returning the current points.

1.4 Test

/* Reference input data */
int64_t walk_num      = chbrclf_walk_num;
int64_t elec_num      = chbrclf_elec_num;
int64_t elec_up_num   = chbrclf_elec_up_num;
int64_t elec_dn_num   = chbrclf_elec_dn_num;
int64_t nucl_num      = chbrclf_nucl_num;
double* charge        = chbrclf_charge;
double* nucl_coord    = &(chbrclf_nucl_coord[0][0]);

double* elec_coord    = &(chbrclf_elec_coord[0][0][0]);


/* --- */

qmckl_exit_code rc;

assert(!qmckl_electron_provided(context));

int64_t n;
rc = qmckl_get_electron_num (context, &n);
assert(rc == QMCKL_NOT_PROVIDED);

rc = qmckl_get_electron_up_num (context, &n);
assert(rc == QMCKL_NOT_PROVIDED);

rc = qmckl_get_electron_down_num (context, &n);
assert(rc == QMCKL_NOT_PROVIDED);


rc = qmckl_set_electron_num (context, elec_up_num, elec_dn_num);
qmckl_check(context, rc);
assert(qmckl_electron_provided(context));

rc = qmckl_get_electron_up_num (context, &n);
qmckl_check(context, rc);
assert(n == elec_up_num);

rc = qmckl_get_electron_down_num (context, &n);
qmckl_check(context, rc);
assert(n == elec_dn_num);

rc = qmckl_get_electron_num (context, &n);
qmckl_check(context, rc);
assert(n == elec_num);


int64_t w = 0;
rc = qmckl_get_electron_walk_num (context, &w);
qmckl_check(context, rc);
assert(w == 0);


assert(qmckl_electron_provided(context));

rc = qmckl_set_electron_coord (context, 'N', walk_num, elec_coord, walk_num*elec_num*3);
qmckl_check(context, rc);

rc = qmckl_get_electron_walk_num (context, &w);
qmckl_check(context, rc);
assert(w == walk_num);

double elec_coord2[walk_num*3*elec_num];

rc = qmckl_get_electron_coord (context, 'N', elec_coord2, walk_num*3*elec_num);
qmckl_check(context, rc);
for (int64_t i=0 ; i<3*elec_num*walk_num ; ++i) {
  printf("%f %f\n",  elec_coord[i],  elec_coord2[i]);
  assert( elec_coord[i] == elec_coord2[i] );
 }

2 Computation

The computed data is stored in the context so that it can be reused by different kernels. To ensure that the data is valid, for each computed data the date of the context is stored when it is computed. To know if some data needs to be recomputed, we check if the date of the dependencies are more recent than the date of the data to compute. If it is the case, then the data is recomputed and the current date is stored.

2.1 Electron-electron distances

2.1.1 Get

qmckl_exit_code qmckl_get_electron_ee_distance(qmckl_context context, double* const distance);

2.1.2 Compute

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`elec_num`	`int64_t`	in	Number of electrons
`walk_num`	`int64_t`	in	Number of walkers
`coord`	`double[3][walk_num][elec_num]`	in	Electron coordinates
`ee_distance`	`double[walk_num][elec_num][elec_num]`	out	Electron-electron distances

integer function qmckl_compute_ee_distance_f(context, elec_num, walk_num, coord, ee_distance) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: elec_num
  integer*8             , intent(in)  :: walk_num
  double precision      , intent(in)  :: coord(elec_num,walk_num,3)
  double precision      , intent(out) :: ee_distance(elec_num,elec_num,walk_num)

  integer*8 :: k, i, j
  double precision :: x, y, z

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (elec_num <= 0) then
     info = QMCKL_INVALID_ARG_2
     return
  endif

  if (walk_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  do k=1,walk_num
     info = qmckl_distance(context, 'T', 'T', elec_num, elec_num, &
          coord(1,k,1), elec_num * walk_num, &
          coord(1,k,1), elec_num * walk_num, &
          ee_distance(1,1,k), elec_num)
     if (info /= QMCKL_SUCCESS) then
        exit
     endif
  end do

end function qmckl_compute_ee_distance_f

2.1.3 Test

assert(qmckl_electron_provided(context));


double ee_distance[walk_num * elec_num * elec_num];
rc = qmckl_get_electron_ee_distance(context, ee_distance);

// (e1,e2,w)
// (0,0,0) == 0.
assert(ee_distance[0] == 0.);

// (1,0,0) == (0,1,0)
assert(ee_distance[1] == ee_distance[elec_num]);

// value of (1,0,0)
assert(fabs(ee_distance[1]-7.152322512964209) < 1.e-12);

// (0,0,1) == 0.
assert(ee_distance[elec_num*elec_num] == 0.);

// (1,0,1) == (0,1,1)
assert(ee_distance[elec_num*elec_num+1] == ee_distance[elec_num*elec_num+elec_num]);

// value of (1,0,1)
assert(fabs(ee_distance[elec_num*elec_num+1]-6.5517646321055665) < 1.e-12);

2.2 Electron-electron potential

ee_potential is given by

\[ \mathcal{V}_{ee} = \sum_{i=1}^{N_e}\sum_{j>i}^{N_e}\frac{1}{r_{ij}} \]

where \(\mathcal{V}_{ee}\) is the ee potential and \[r_{ij}\] the ee distance.

2.2.1 Get

qmckl_exit_code qmckl_get_electron_ee_potential(qmckl_context context, double* const ee_potential);

2.2.2 Compute

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`elec_num`	`int64_t`	in	Number of electrons
`walk_num`	`int64_t`	in	Number of walkers
`ee_distance`	`double[walk_num][elec_num][elec_num]`	in	Electron-electron distances
`ee_potential`	`double[walk_num]`	out	Electron-electron potential

integer function qmckl_compute_ee_potential_f(context, elec_num, walk_num, &
     ee_distance, ee_potential) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: elec_num
  integer*8             , intent(in)  :: walk_num
  double precision      , intent(in)  :: ee_distance(elec_num,elec_num,walk_num)
  double precision      , intent(out) :: ee_potential(walk_num)

  integer*8 :: nw, i, j

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (elec_num <= 0) then
     info = QMCKL_INVALID_ARG_2
     return
  endif

  if (walk_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  ee_potential = 0.0d0
  do nw=1,walk_num
    do j=2,elec_num
      do i=1,j-1
        if (dabs(ee_distance(i,j,nw)) > 1e-5) then
          ee_potential(nw) = ee_potential(nw) + 1.0d0/(ee_distance(i,j,nw))
        endif
      end do
    end do
  end do

end function qmckl_compute_ee_potential_f

qmckl_exit_code qmckl_compute_ee_potential (
      const qmckl_context context,
      const int64_t elec_num,
      const int64_t walk_num,
      const double* ee_distance,
      double* const ee_potential );

2.2.3 Test

double ee_potential[walk_num];

rc = qmckl_get_electron_ee_potential(context, &(ee_potential[0]));
qmckl_check(context, rc);

2.3 Electron-nucleus distances

2.3.1 Get

qmckl_exit_code qmckl_get_electron_en_distance(qmckl_context context, double* distance);

2.3.2 Compute

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`elec_num`	`int64_t`	in	Number of electrons
`nucl_num`	`int64_t`	in	Number of nuclei
`walk_num`	`int64_t`	in	Number of walkers
`elec_coord`	`double[3][walk_num][elec_num]`	in	Electron coordinates
`nucl_coord`	`double[3][elec_num]`	in	Nuclear coordinates
`en_distance`	`double[walk_num][nucl_num][elec_num]`	out	Electron-nucleus distances

integer function qmckl_compute_en_distance_f(context, elec_num, nucl_num, walk_num, elec_coord, nucl_coord, en_distance) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: elec_num
  integer*8             , intent(in)  :: nucl_num
  integer*8             , intent(in)  :: walk_num
  double precision      , intent(in)  :: elec_coord(elec_num,walk_num,3)
  double precision      , intent(in)  :: nucl_coord(nucl_num,3)
  double precision      , intent(out) :: en_distance(elec_num,nucl_num,walk_num)

  integer*8 :: k

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (elec_num <= 0) then
     info = QMCKL_INVALID_ARG_2
     return
  endif

  if (nucl_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  if (walk_num <= 0) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  do k=1,walk_num
     info = qmckl_distance(context, 'T', 'T', elec_num, nucl_num, &
          elec_coord(1,k,1), elec_num * walk_num, &
          nucl_coord, nucl_num, &
          en_distance(1,1,k), elec_num)
     if (info /= QMCKL_SUCCESS) then
        exit
     endif
  end do

end function qmckl_compute_en_distance_f

2.3.3 Test

assert(!qmckl_nucleus_provided(context));
assert(qmckl_electron_provided(context));

rc = qmckl_set_nucleus_num (context, nucl_num);
qmckl_check(context, rc);

rc = qmckl_set_nucleus_charge (context, charge, nucl_num);
qmckl_check(context, rc);

rc = qmckl_set_nucleus_coord (context, 'T', nucl_coord, 3*nucl_num);
qmckl_check(context, rc);

assert(qmckl_nucleus_provided(context));

double en_distance[walk_num][nucl_num][elec_num];

rc = qmckl_get_electron_en_distance(context, &(en_distance[0][0][0]));
qmckl_check(context, rc);

// (e,n,w) in Fortran notation
// (1,1,1)
assert(fabs(en_distance[0][0][0] - 7.546738741619978) < 1.e-12);

// (1,2,1)
assert(fabs(en_distance[0][1][0] - 8.77102435246984) < 1.e-12);

// (2,1,1)
assert(fabs(en_distance[0][0][1] - 3.698922010513608) < 1.e-12);

// (1,1,2)
assert(fabs(en_distance[1][0][0] - 5.824059436060509) < 1.e-12);

// (1,2,2)
assert(fabs(en_distance[1][1][0] - 7.080482110317645) < 1.e-12);

// (2,1,2)
assert(fabs(en_distance[1][0][1] - 3.1804527583077356) < 1.e-12);

2.4 Electron-nucleus potential

en_potential stores the en potential energy

\[ \mathcal{V}_{en} = -\sum_{i=1}^{N_e}\sum_{A=1}^{N_n}\frac{Z_A}{r_{iA}} \]

where \(\mathcal{V}_{en}\) is the en potential, \[r_{iA}\] the en distance and \[Z_A\] is the nuclear charge.

2.4.1 Get

qmckl_exit_code qmckl_get_electron_en_potential(qmckl_context context, double* const en_potential);

2.4.2 Compute

Variable	Type	In/Out	Description
`context`	`qmckl_context`	in	Global state
`elec_num`	`int64_t`	in	Number of electrons
`nucl_num`	`int64_t`	in	Number of nuclei
`walk_num`	`int64_t`	in	Number of walkers
`charge`	`double[nucl_num]`	in	charge of nucleus
`en_distance`	`double[walk_num][nucl_num][elec_num]`	in	Electron-electron rescaled distances
`en_potential`	`double[walk_num]`	out	Electron-electron potential

integer function qmckl_compute_en_potential_f(context, elec_num, nucl_num, walk_num, &
     charge, en_distance, en_potential) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: elec_num
  integer*8             , intent(in)  :: nucl_num
  integer*8             , intent(in)  :: walk_num
  double precision      , intent(in)  :: charge(nucl_num)
  double precision      , intent(in)  :: en_distance(elec_num,nucl_num,walk_num)
  double precision      , intent(out) :: en_potential(walk_num)

  integer*8 :: nw, i, j

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (elec_num <= 0) then
     info = QMCKL_INVALID_ARG_2
     return
  endif

  if (walk_num <= 0) then
     info = QMCKL_INVALID_ARG_3
     return
  endif

  en_potential = 0.0d0
  do nw=1,walk_num
    do j=1,nucl_num
      do i=1,elec_num
        if (dabs(en_distance(i,j,nw)) > 1e-5) then
          en_potential(nw) = en_potential(nw) - charge(j)/(en_distance(i,j,nw))
        endif
      end do
    end do
  end do

end function qmckl_compute_en_potential_f

qmckl_exit_code qmckl_compute_en_potential (
      const qmckl_context context,
      const int64_t elec_num,
      const int64_t nucl_num,
      const int64_t walk_num,
      const double* charge,
      const double* en_distance,
      double* const en_potential );

2.4.3 Test

double en_potential[walk_num];

rc = qmckl_get_electron_en_potential(context, &(en_potential[0]));
qmckl_check(context, rc);