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Nucleus

Table of Contents

1 Context

The following data stored in the context:

uninitialized int32t Keeps bit set for uninitialized data
num int64t Total number of nuclei
provided bool If true, nucleus is valid
charge qmcklvector Nuclear charges
coord qmcklmatrix Nuclear coordinates, in transposed format
coord_date int64t Nuclear coordinates, date if modified
rescale_factor_kappa double The distance scaling factor

Computed data:

nn_distance qmcklmatrix Nucleus-nucleus distances
nn_distance_date int64t Date when Nucleus-nucleus distances were computed
nn_distance_rescaled qmcklmatrix Nucleus-nucleus rescaled distances
nn_distance_rescaled_date int64t Date when Nucleus-nucleus rescaled distances were computed
repulsion double Nuclear repulsion energy
repulsion_date int64t Date when the nuclear repulsion energy was computed

1.1 Data structure

typedef struct qmckl_nucleus_struct {
  int64_t      num;
  int64_t      repulsion_date;
  int64_t      nn_distance_date;
  int64_t      nn_distance_rescaled_date;
  int64_t      coord_date;
  qmckl_vector charge;
  qmckl_matrix coord;
  qmckl_matrix nn_distance;
  qmckl_matrix nn_distance_rescaled;
  double       repulsion;
  double       rescale_factor_kappa;
  int32_t      uninitialized;
  bool         provided;
} qmckl_nucleus_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_nucleus(qmckl_context context);

qmckl_exit_code qmckl_init_nucleus(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->nucleus.uninitialized = (1 << 3) - 1;

  /* Default values */
  ctx->nucleus.rescale_factor_kappa = 1.0;

  return QMCKL_SUCCESS;
}

1.2 Access functions

When all the data relative to nuclei have been set, the following function returns true. 

bool qmckl_nucleus_provided (const qmckl_context context);

1.3 Initialization functions

To set the data relative to the nuclei in the context, the following functions need to be called. 

qmckl_exit_code
qmckl_set_nucleus_num(qmckl_context context,
                      const int64_t num);

Sets the number of nuclei. 

qmckl_exit_code
qmckl_set_nucleus_charge(qmckl_context context,
                         const double* charge,
                         const int64_t size_max);

Sets the nuclear charges of all the atoms. 

qmckl_exit_code
qmckl_set_nucleus_coord(qmckl_context context,
                        const char transp,
                        const double* coord,
                        const int64_t size_max);

Sets the nuclear coordinates of all the atoms. The coordinates are be given in atomic units. 

qmckl_exit_code
qmckl_set_nucleus_rescale_factor(qmckl_context context,
                                 const double kappa);

Sets the rescale parameter for the nuclear distances.

1.4 Test

const double*   nucl_charge   = chbrclf_charge;
const double*   nucl_coord    = &(chbrclf_nucl_coord[0][0]);
const double    nucl_rescale_factor_kappa = 2.0;

/* --- */

qmckl_exit_code rc;

assert(!qmckl_nucleus_provided(context));

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


rc = qmckl_set_nucleus_num (context, chbrclf_nucl_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_nucleus_provided(context));

rc = qmckl_get_nucleus_num (context, &n);
assert(rc == QMCKL_SUCCESS);
assert(n == chbrclf_nucl_num);

double k;
rc = qmckl_get_nucleus_rescale_factor (context, &k);
assert(rc == QMCKL_SUCCESS);
assert(k == 1.0);


rc = qmckl_set_nucleus_rescale_factor (context, nucl_rescale_factor_kappa);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_get_nucleus_rescale_factor (context, &k);
assert(rc == QMCKL_SUCCESS);
assert(k == nucl_rescale_factor_kappa);

double nucl_coord2[3*chbrclf_nucl_num];

rc = qmckl_get_nucleus_coord (context, 'T', nucl_coord2, 3*chbrclf_nucl_num);
assert(rc == QMCKL_NOT_PROVIDED);

rc = qmckl_set_nucleus_coord (context, 'T', &(nucl_coord[0]), 3*chbrclf_nucl_num);
assert(rc == QMCKL_SUCCESS);

assert(!qmckl_nucleus_provided(context));

rc = qmckl_get_nucleus_coord (context, 'N', nucl_coord2, 3*chbrclf_nucl_num);
assert(rc == QMCKL_SUCCESS);
for (size_t k=0 ; k<3 ; ++k) {
  for (int64_t i=0 ; i<chbrclf_nucl_num ; ++i) {
    assert( nucl_coord[chbrclf_nucl_num*k+i] == nucl_coord2[3*i+k] );
  }
}

rc = qmckl_get_nucleus_coord (context, 'T', nucl_coord2, 3*chbrclf_nucl_num);
assert(rc == QMCKL_SUCCESS);
for (int64_t i=0 ; i<3*chbrclf_nucl_num ; ++i) {
  assert( nucl_coord[i] == nucl_coord2[i] );
}

double nucl_charge2[chbrclf_nucl_num];

rc = qmckl_get_nucleus_charge(context, nucl_charge2, chbrclf_nucl_num);
assert(rc == QMCKL_NOT_PROVIDED);

rc = qmckl_set_nucleus_charge(context, nucl_charge, chbrclf_nucl_num);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_get_nucleus_charge(context, nucl_charge2, chbrclf_nucl_num);
assert(rc == QMCKL_SUCCESS);
for (int64_t i=0 ; i<chbrclf_nucl_num ; ++i) {
  assert( nucl_charge[i] == nucl_charge2[i] );
 }
assert(qmckl_nucleus_provided(context));

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 Nucleus-nucleus distances

2.1.1 Get

qmckl_exit_code
qmckl_get_nucleus_nn_distance(qmckl_context context,
                              double* distance,
                              const int64_t size_max);

2.1.2 Compute

qmcklcontext context in Global state
int64t nuclnum in Number of nuclei
double coord[3][nuclnum] in Nuclear coordinates (au)
double nndistance[nuclnum][nuclnum] out Nucleus-nucleus distances (au) 
integer function qmckl_compute_nn_distance_f(context, nucl_num, coord, nn_distance) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: nucl_num
  double precision      , intent(in)  :: coord(nucl_num,3)
  double precision      , intent(out) :: nn_distance(nucl_num,nucl_num)

  integer*8 :: k

  info = QMCKL_SUCCESS

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

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

  info = qmckl_distance(context, 'T', 'T', nucl_num, nucl_num, &
          coord, nucl_num, &
          coord, nucl_num, &
          nn_distance, nucl_num)

end function qmckl_compute_nn_distance_f

2.1.3 Test

/* Reference input data */

assert(qmckl_nucleus_provided(context));

double distance[chbrclf_nucl_num*chbrclf_nucl_num];
rc = qmckl_get_nucleus_nn_distance(context, distance, chbrclf_nucl_num*chbrclf_nucl_num);
assert(distance[0] == 0.);
assert(distance[1] == distance[chbrclf_nucl_num]);
assert(fabs(distance[1]-2.070304721365169) < 1.e-12);

2.2 Nucleus-nucleus rescaled distances

2.2.1 Get

qmckl_exit_code
qmckl_get_nucleus_nn_distance_rescaled(qmckl_context context,
                                       double* distance_rescaled,
                                       const int64_t size_max);

2.2.2 Compute

qmcklcontext context in Global state
int64t nuclnum in Number of nuclei
double coord[3][nuclnum] in Nuclear coordinates (au)
double nndistancerescaled[nuclnum][nuclnum] out Nucleus-nucleus rescaled distances (au) 
integer function qmckl_compute_nn_distance_rescaled_f(context, nucl_num, rescale_factor_kappa, coord, nn_distance_rescaled) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: nucl_num
  double precision      , intent(in)  :: rescale_factor_kappa
  double precision      , intent(in)  :: coord(nucl_num,3)
  double precision      , intent(out) :: nn_distance_rescaled(nucl_num,nucl_num)

  integer*8 :: k

  info = QMCKL_SUCCESS

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

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

  info = qmckl_distance_rescaled(context, 'T', 'T', nucl_num, nucl_num, &
          coord, nucl_num, &
          coord, nucl_num, &
          nn_distance_rescaled, nucl_num, rescale_factor_kappa)

end function qmckl_compute_nn_distance_rescaled_f

2.2.3 Test

/* Reference input data */
/* TODO */

//assert(qmckl_nucleus_provided(context));
//
//double distance[nucl_num*nucl_num];
//rc = qmckl_get_nucleus_nn_distance(context, distance, nucl_num*nucl_num);
//assert(distance[0] == 0.);
//assert(distance[1] == distance[nucl_num]);
//assert(fabs(distance[1]-2.070304721365169) < 1.e-12);

2.3 Nuclear repulsion energy

\[ V_{NN} = \sum_{A=1}^{N-1} \sum_{B>A}^N \frac{Q_A Q_B}{R_{AB}} \]

2.3.1 Get

qmckl_exit_code qmckl_get_nucleus_repulsion(qmckl_context context, double* const energy);

2.3.2 Compute

qmcklcontext context in Global state
int64t nuclnum in Number of nuclei
double charge[nuclnum] in Nuclear charges (au)
double nndistance[nuclnum][nuclnum] in Nucleus-nucleus distances (au)
double energy out Nuclear repulsion energy 
integer function qmckl_compute_nucleus_repulsion_f(context, nucl_num, charge, nn_distance, energy) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in)  :: context
  integer*8             , intent(in)  :: nucl_num
  double precision      , intent(in)  :: charge(nucl_num)
  double precision      , intent(in)  :: nn_distance(nucl_num,nucl_num)
  double precision      , intent(out) :: energy

  integer*8 :: i, j

  info = QMCKL_SUCCESS

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

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

  energy = 0.d0
  do j=2, nucl_num
     do i=1, j-1
        if (dabs(nn_distance(i,j)) > 1e-5) then
          energy = energy + charge(i) * charge(j) / nn_distance(i,j)
        endif
     end do
  end do

end function qmckl_compute_nucleus_repulsion_f

2.3.3 Test

/* Reference input data */

assert(qmckl_nucleus_provided(context));

double rep;
rc = qmckl_get_nucleus_repulsion(context, &rep);
assert(rep - 318.2309879436158 < 1.e-10);

Author: TREX CoE

Created: 2022-08-07 Sun 13:45

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