56 KiB
Electrons
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 |
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[num][nucl_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 |
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);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);#+NAME:pre2
#+NAME:post
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 interfaceThe 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 interfaceAccess 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.
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.
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.
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] );
}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_fTest
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 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 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_fqmckl_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]));
qmckl_check(context, rc);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 |
point_num |
int64_t |
in | Number of points |
nucl_num |
int64_t |
in | Number of nuclei |
elec_coord |
double[3][point_num] |
in | Electron coordinates |
nucl_coord |
double[3][nucl_num] |
in | Nuclear coordinates |
en_distance |
double[point_num][nucl_num] |
out | Electron-nucleus distances |
integer function qmckl_compute_en_distance_f(context, point_num, nucl_num, elec_coord, nucl_coord, en_distance) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: point_num
integer*8 , intent(in) :: nucl_num
double precision , intent(in) :: elec_coord(point_num,3)
double precision , intent(in) :: nucl_coord(nucl_num,3)
double precision , intent(out) :: en_distance(nucl_num,point_num)
integer*8 :: k
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (point_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (nucl_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
info = qmckl_distance(context, 'T', 'T', nucl_num, point_num, &
nucl_coord, nucl_num, &
elec_coord, point_num, &
en_distance, nucl_num)
end function qmckl_compute_en_distance_fTest
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][elec_num][nucl_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][0][1] - 8.77102435246984) < 1.e-12);
// (2,1,1)
assert(fabs(en_distance[0][1][0] - 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][0][1] - 7.080482110317645) < 1.e-12);
// (2,1,2)
assert(fabs(en_distance[1][1][0] - 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][elec_num][nucl_num] |
in | Electron-electron 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(nucl_num,elec_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 i=1,elec_num
do j=1,nucl_num
if (dabs(en_distance(j,i,nw)) > 1.d-6) then
en_potential(nw) = en_potential(nw) - charge(j)/(en_distance(j,i,nw))
endif
end do
end do
end do
end function qmckl_compute_en_potential_fqmckl_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]));
qmckl_check(context, rc);