qmckl/org/qmckl_electron.org

Electrons

• Context
  • Data structure
  • Access functions
    • Number of electrons
    • Number of walkers
    • Scaling factors Kappa
    • Electron coordinates
  • Initialization functions
  • Test
• Computation
  • Electron-electron distances
    • Get
    • Compute
    • Test
  • Electron-electron rescaled distances
    • Get
    • Compute
    • Test
  • Electron-electron rescaled distance gradients and Laplacian with respect to electron coords
    • Get
    • Compute
    • Test
  • Electron-electron potential
    • Get
    • Compute
    • Test
  • Electron-nucleus distances
    • Get
    • Compute
    • Test
  • Electron-nucleus rescaled distances
    • Get
    • Compute
    • Test
  • Electron-nucleus rescaled distance gradients and laplacian with respect to electron coords
    • Get
    • Compute
    • Test
  • Electron-nucleus potential
    • Get
    • Compute
    • Test
  • Generate initial coordinates

In conventional QMC simulations, up-spin and down-spin electrons are different. The electron data structure contains the number of up-spin and down-spin electrons, and the electron coordinates.

The electrons are stored as points in the following order: for each walker, first up-spin electrons and then down-spin electrons.

If the points are set with the 'N' flag, the order of the components is [ (x,y,z), (x,y,z), ... ] Using the 'T' flage, it is [ (x,x,x,...), (y,y,y,...), (z,z,z,...) ]

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
rescale_factor_kappa_ee	double	The distance scaling factor
rescale_factor_kappa_en	double	The distance scaling factor
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_distance_rescaled	double[walker.num][num][num]	Electron-electron rescaled distances
ee_distance_rescaled_date	uint64_t	Last modification date of the electron-electron distances
ee_distance_rescaled_deriv_e	double[walker.num][4][num][num]	Electron-electron rescaled distances derivatives
ee_distance_rescaled_deriv_e_date	uint64_t	Last modification date of the electron-electron distance derivatives
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
en_distance_rescaled	double[walker.num][nucl_num][num]	Electron-nucleus distances
en_distance_rescaled_date	uint64_t	Last modification date of the electron-electron distances
en_distance_rescaled_deriv_e	double[walker.num][4][nucl_num][num]	Electron-electron rescaled distances derivatives
en_distance_rescaled_deriv_e_date	uint64_t	Last modification date of the electron-electron distance derivatives

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;
double         rescale_factor_kappa_ee;
double         rescale_factor_kappa_en;
uint64_t        ee_distance_date;
uint64_t        en_distance_date;
uint64_t        ee_potential_date;
uint64_t        en_potential_date;
uint64_t        ee_distance_rescaled_date;
uint64_t        ee_distance_rescaled_deriv_e_date;
uint64_t        en_distance_rescaled_date;
uint64_t        en_distance_rescaled_deriv_e_date;
double*        ee_distance;
double*        en_distance;
double*        ee_potential;
double*        en_potential;
double*        ee_distance_rescaled;
double*        ee_distance_rescaled_deriv_e;
double*        en_distance_rescaled;
double*        en_distance_rescaled_deriv_e;
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;

/* Default values */
ctx->electron.rescale_factor_kappa_ee = 1.0;
ctx->electron.rescale_factor_kappa_en = 1.0;

return QMCKL_SUCCESS;
}

bool qmckl_electron_provided (const qmckl_context context);

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.

#+NAME:post

Number of electrons

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.

Scaling factors Kappa

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.

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);

qmckl_exit_code qmckl_set_electron_rescale_factor_ee (qmckl_context context, const double kappa_ee);
qmckl_exit_code qmckl_set_electron_rescale_factor_en (qmckl_context context, const double kappa_en);

#+NAME:pre2

#+NAME:post2

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.

Next we set the rescale parameter for the rescaled distance metric.

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

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;
double  rescale_factor_kappa_ee   = 1.0;
double  rescale_factor_kappa_en   = 1.0;
double  nucl_rescale_factor_kappa = 1.0;
double* elec_coord    = &(chbrclf_elec_coord[0][0][0]);

int64_t  nucl_num      = chbrclf_nucl_num;
double*  charge        = chbrclf_charge;
double*  nucl_coord    = &(chbrclf_nucl_coord[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);
assert(rc == QMCKL_SUCCESS);
assert(qmckl_electron_provided(context));

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

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

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

double k_ee = 0.;
double k_en = 0.;
rc = qmckl_get_electron_rescale_factor_ee (context, &k_ee);
assert(rc == QMCKL_SUCCESS);
assert(k_ee == 1.0);

rc = qmckl_get_electron_rescale_factor_en (context, &k_en);
assert(rc == QMCKL_SUCCESS);
assert(k_en == 1.0);

rc = qmckl_set_electron_rescale_factor_en(context, rescale_factor_kappa_en);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_electron_rescale_factor_ee(context, rescale_factor_kappa_ee);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_get_electron_rescale_factor_ee (context, &k_ee);
assert(rc == QMCKL_SUCCESS);
assert(k_ee == rescale_factor_kappa_ee);

rc = qmckl_get_electron_rescale_factor_en (context, &k_en);
assert(rc == QMCKL_SUCCESS);
assert(k_en == rescale_factor_kappa_en);


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


assert(qmckl_electron_provided(context));

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

rc = qmckl_get_electron_walk_num (context, &w);
assert(rc == QMCKL_SUCCESS);
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);
assert(rc == QMCKL_SUCCESS);
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] );
}

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.

Electron-electron distances

Get

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

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

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);

Electron-electron rescaled distances

ee_distance_rescaled stores the matrix of the rescaled distances between all pairs of electrons:

\[ C_{ij} = \left( 1 - \exp{-\kappa C_{ij}}\right)/\kappa \]

where \(C_{ij}\) is the matrix of electron-electron distances.

Get

qmckl_exit_code qmckl_get_electron_ee_distance_rescaled(qmckl_context context, double* const distance_rescaled);

Compute

Variable	Type	In/Out	Description
context	qmckl_context	in	Global state
elec_num	int64_t	in	Number of electrons
rescale_factor_kappa_ee	double	in	Factor to rescale ee distances
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 rescaled distances

integer function qmckl_compute_ee_distance_rescaled_f(context, elec_num, rescale_factor_kappa_ee, walk_num, &
 coord, ee_distance_rescaled) &
 result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in)  :: context
integer*8             , intent(in)  :: elec_num
double precision      , intent(in)  :: rescale_factor_kappa_ee
integer*8             , intent(in)  :: walk_num
double precision      , intent(in)  :: coord(elec_num,walk_num,3)
double precision      , intent(out) :: ee_distance_rescaled(elec_num,elec_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 (walk_num <= 0) then
 info = QMCKL_INVALID_ARG_3
 return
endif

do k=1,walk_num
 info = qmckl_distance_rescaled(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_rescaled(1,1,k), elec_num, rescale_factor_kappa_ee)
 if (info /= QMCKL_SUCCESS) then
    exit
 endif
end do

end function qmckl_compute_ee_distance_rescaled_f

Test

assert(qmckl_electron_provided(context));


double ee_distance_rescaled[walk_num * elec_num * elec_num];
rc = qmckl_get_electron_ee_distance_rescaled(context, ee_distance_rescaled);

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

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

// value of (1,0,0)
assert(fabs(ee_distance_rescaled[1]-0.9992169566605263) < 1.e-12);

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

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

// value of (1,0,1)
assert(fabs(ee_distance_rescaled[elec_num*elec_num+1]-0.9985724058042633) < 1.e-12);

Electron-electron rescaled distance gradients and Laplacian with respect to electron coords

The rescaled distances which is given as $R = (1 - \exp{-\kappa r})/\kappa$ needs to be perturbed with respect to the electorn coordinates. This data is stored in the ee_distance_rescaled_deriv_e tensor. The The first three elements of this three index tensor [4][num][num] gives the derivatives in the x, y, and z directions $dx, dy, dz$ and the last index gives the Laplacian $\partial x^2 + \partial y^2 + \partial z^2$.

Get

qmckl_exit_code qmckl_get_electron_ee_distance_rescaled_deriv_e(qmckl_context context, double* const distance_rescaled_deriv_e);

Compute

Variable	Type	In/Out	Description
context	qmckl_context	in	Global state
elec_num	int64_t	in	Number of electrons
rescale_factor_kappa_ee	double	in	Factor to rescale ee distances
walk_num	int64_t	in	Number of walkers
coord	double[3][walk_num][elec_num]	in	Electron coordinates
ee_distance_deriv_e	double[walk_num][4][elec_num][elec_num]	out	Electron-electron rescaled distance derivatives

integer function qmckl_compute_ee_distance_rescaled_deriv_e_f(context, elec_num, rescale_factor_kappa_ee, walk_num, &
 coord, ee_distance_rescaled_deriv_e) &
 result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in)  :: context
integer*8             , intent(in)  :: elec_num
double precision      , intent(in)  :: rescale_factor_kappa_ee
integer*8             , intent(in)  :: walk_num
double precision      , intent(in)  :: coord(elec_num,walk_num,3)
double precision      , intent(out) :: ee_distance_rescaled_deriv_e(4,elec_num,elec_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 (walk_num <= 0) then
 info = QMCKL_INVALID_ARG_3
 return
endif

do k=1,walk_num
 info = qmckl_distance_rescaled_deriv_e(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_rescaled_deriv_e(1,1,1,k), elec_num, rescale_factor_kappa_ee)
 if (info /= QMCKL_SUCCESS) then
    exit
 endif
end do

end function qmckl_compute_ee_distance_rescaled_deriv_e_f

Test

assert(qmckl_electron_provided(context));


double ee_distance_rescaled_deriv_e[4 * walk_num * elec_num * elec_num];
rc = qmckl_get_electron_ee_distance_rescaled_deriv_e(context, ee_distance_rescaled_deriv_e);

// TODO: Get exact values
//// (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);

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.

Get

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

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 rescaled 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 );

Test

double ee_potential[walk_num];

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

Electron-nucleus distances

Get

qmckl_exit_code qmckl_get_electron_en_distance(qmckl_context context, double* distance);

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

Test

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

rc = qmckl_set_nucleus_num (context, nucl_num);
assert(rc == QMCKL_SUCCESS);

rc = qmckl_set_nucleus_charge (context, charge, nucl_num);
assert (rc == QMCKL_SUCCESS);

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

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]));
assert (rc == QMCKL_SUCCESS);

// (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);

Electron-nucleus rescaled distances

en_distance_rescaled stores the matrix of the rescaled distances between electrons and nuclei.

\[ C_{ij} = \left( 1 - \exp{-\kappa C_{ij}}\right)/\kappa \]

where \(C_{ij}\) is the matrix of electron-nucleus distances.

Get

qmckl_exit_code qmckl_get_electron_en_distance_rescaled(qmckl_context context, double* distance_rescaled);

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
rescale_factor_kappa_en	double	in	The factor for rescaled distances
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_rescaled	double[walk_num][nucl_num][elec_num]	out	Electron-nucleus distances

integer function qmckl_compute_en_distance_rescaled_f(context, elec_num, nucl_num, rescale_factor_kappa_en, walk_num, elec_coord, &
 nucl_coord, en_distance_rescaled) &
 result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in)  :: context
integer*8             , intent(in)  :: elec_num
integer*8             , intent(in)  :: nucl_num
double precision      , intent(in)  :: rescale_factor_kappa_en
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_rescaled(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

! TODO: comparison with 0
!if (rescale_factor_kappa_en <= 0) then
!   info = QMCKL_INVALID_ARG_4
!   return
!endif

if (walk_num <= 0) then
 info = QMCKL_INVALID_ARG_5
 return
endif

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

end function qmckl_compute_en_distance_rescaled_f

Test

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

double en_distance_rescaled[walk_num][nucl_num][elec_num];

rc = qmckl_get_electron_en_distance_rescaled(context, &(en_distance_rescaled[0][0][0]));

assert (rc == QMCKL_SUCCESS);

// (e,n,w) in Fortran notation
// (1,1,1)
assert(fabs(en_distance_rescaled[0][0][0] - 0.9994721712909764) < 1.e-12);

// (1,2,1)
assert(fabs(en_distance_rescaled[0][1][0] - 0.9998448354439821) < 1.e-12);

// (2,1,1)
assert(fabs(en_distance_rescaled[0][0][1] - 0.9752498074577688) < 1.e-12);

// (1,1,2)
assert(fabs(en_distance_rescaled[1][0][0] - 0.9970444172399963) < 1.e-12);

// (1,2,2)
assert(fabs(en_distance_rescaled[1][1][0] - 0.9991586325813303) < 1.e-12);

// (2,1,2)
assert(fabs(en_distance_rescaled[1][0][1] - 0.9584331688679852) < 1.e-12);

Electron-nucleus rescaled distance gradients and laplacian with respect to electron coords

The rescaled distances which is given as $R = (1 - \exp{-\kappa r})/\kappa$ needs to be perturbed with respect to the nuclear coordinates. This data is stored in the en_distance_rescaled_deriv_e tensor. The The first three elements of this three index tensor [4][nucl_num][elec_num] gives the derivatives in the x, y, and z directions $dx, dy, dz$ and the last index gives the Laplacian $\partial x^2 + \partial y^2 + \partial z^2$.

Get

qmckl_exit_code qmckl_get_electron_en_distance_rescaled_deriv_e(qmckl_context context, double* distance_rescaled_deriv_e);

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
rescale_factor_kappa_en	double	in	The factor for rescaled distances
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_rescaled_deriv_e	double[walk_num][nucl_num][elec_num][4]	out	Electron-nucleus distance derivatives

integer function qmckl_compute_en_distance_rescaled_deriv_e_f(context, elec_num, nucl_num, &
 rescale_factor_kappa_en, walk_num, elec_coord, &
 nucl_coord, en_distance_rescaled_deriv_e) &
 result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in)  :: context
integer*8             , intent(in)  :: elec_num
integer*8             , intent(in)  :: nucl_num
double precision      , intent(in)  :: rescale_factor_kappa_en
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_rescaled_deriv_e(4,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

! TODO: comparison with 0
!if (rescale_factor_kappa_en <= 0) then
!   info = QMCKL_INVALID_ARG_4
!   return
!endif

if (walk_num <= 0) then
 info = QMCKL_INVALID_ARG_5
 return
endif

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

end function qmckl_compute_en_distance_rescaled_deriv_e_f

Test

assert(qmckl_electron_provided(context));

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

assert(qmckl_nucleus_provided(context));

double en_distance_rescaled_deriv_e[walk_num][4][nucl_num][elec_num];

rc = qmckl_get_electron_en_distance_rescaled_deriv_e(context, &(en_distance_rescaled_deriv_e[0][0][0][0]));

assert (rc == QMCKL_SUCCESS);

// TODO: check exact values
//// (e,n,w) in Fortran notation
//// (1,1,1)
//assert(fabs(en_distance_rescaled[0][0][0] - 7.546738741619978) < 1.e-12);
//
//// (1,2,1)
//assert(fabs(en_distance_rescaled[0][1][0] - 8.77102435246984) < 1.e-12);
//
//// (2,1,1)
//assert(fabs(en_distance_rescaled[0][0][1] - 3.698922010513608) < 1.e-12);
//
//// (1,1,2)
//assert(fabs(en_distance_rescaled[1][0][0] - 5.824059436060509) < 1.e-12);
//
//// (1,2,2)
//assert(fabs(en_distance_rescaled[1][1][0] - 7.080482110317645) < 1.e-12);
//
//// (2,1,2)
//assert(fabs(en_distance_rescaled[1][0][1] - 3.1804527583077356) < 1.e-12);

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.

Get

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

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 );

Test

double en_potential[walk_num];

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

Generate initial coordinates