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39 KiB
39 KiB
Molecular Orbitals
The molecular orbitals (MOs) are defined in the basis of AOs along with a AO to MO coefficient matrix \[C\]. Using these coefficients (e.g. from Hartree Fock SCF method) the MOs are defined as follows:
\[ \phi_i(\mathbf{r}) = C_i * \chi_i (\mathbf{r}) \]
In this section we demonstrate how to use the QMCkl specific DGEMM function to calculate the MOs.
Context
The following arrays are stored in the context:
mo_num |
Number of MOs | |
coefficient |
[mo_num][ao_num] |
Orbital coefficients |
coefficient_t |
[ao_num][mo_num] |
Transposed of the Orbital coefficients |
Computed data:
mo_vgl |
[point_num][5][mo_num] |
Value, gradients, Laplacian of the MOs at point positions |
mo_vgl_date |
uint64_t |
Late modification date of Value, gradients, Laplacian of the MOs at point positions |
Data structure
typedef struct qmckl_mo_basis_struct {
int64_t mo_num;
double * restrict coefficient;
double * restrict coefficient_t;
double * restrict mo_vgl;
uint64_t mo_vgl_date;
int32_t uninitialized;
bool provided;
} qmckl_mo_basis_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_mo_basis(qmckl_context context);qmckl_exit_code qmckl_init_mo_basis(qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return false;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
ctx->mo_basis.uninitialized = (1 << 2) - 1;
return QMCKL_SUCCESS;
}Access functions
When all the data for the AOs have been provided, the following
function returns true.
bool qmckl_mo_basis_provided (const qmckl_context context);Fortran interfaces
interface
integer(c_int32_t) function qmckl_get_mo_basis_mo_num (context, &
mo_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: mo_num
end function qmckl_get_mo_basis_mo_num
end interface
interface
integer(c_int32_t) function qmckl_get_mo_basis_coefficient(context, &
coefficient, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
double precision, intent(out) :: coefficient(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_mo_basis_coefficient
end interfaceInitialization functions
To set the basis set, all the following functions need to be called.
qmckl_exit_code qmckl_set_mo_basis_mo_num (qmckl_context context, const int64_t mo_num);
qmckl_exit_code qmckl_set_mo_basis_coefficient (qmckl_context context, const double * coefficient);#+NAME:pre
#+NAME:post
When the basis set is completely entered, other data structures are computed to accelerate the calculations.
Computation
Computation of MOs
Get
qmckl_exit_code
qmckl_get_mo_basis_mo_vgl(qmckl_context context,
double* const mo_vgl,
const int64_t size_max);Uses the given array to compute the VGL.
qmckl_exit_code
qmckl_get_mo_basis_mo_vgl_inplace (qmckl_context context,
double* const mo_vgl,
const int64_t size_max);Provide
Compute
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
ao_num |
int64_t |
in | Number of AOs |
mo_num |
int64_t |
in | Number of MOs |
point_num |
int64_t |
in | Number of points |
coef_normalized_t |
double[mo_num][ao_num] |
in | Transpose of the AO to MO transformation matrix |
ao_vgl |
double[point_num][5][ao_num] |
in | Value, gradients and Laplacian of the AOs |
mo_vgl |
double[point_num][5][mo_num] |
out | Value, gradients and Laplacian of the MOs |
The matrix of AO values is very sparse, so we use a sparse-dense matrix multiplication instead of a dgemm, as exposed in https://dx.doi.org/10.1007/978-3-642-38718-0_14.
integer function qmckl_compute_mo_basis_mo_vgl_doc_f(context, &
ao_num, mo_num, point_num, &
coef_normalized_t, ao_vgl, mo_vgl) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: ao_num, mo_num
integer*8 , intent(in) :: point_num
double precision , intent(in) :: ao_vgl(ao_num,5,point_num)
double precision , intent(in) :: coef_normalized_t(mo_num,ao_num)
double precision , intent(out) :: mo_vgl(mo_num,5,point_num)
integer*8 :: i,j,k
double precision :: c1, c2, c3, c4, c5
do j=1,point_num
mo_vgl(:,:,j) = 0.d0
do k=1,ao_num
if (ao_vgl(k,1,j) /= 0.d0) then
c1 = ao_vgl(k,1,j)
c2 = ao_vgl(k,2,j)
c3 = ao_vgl(k,3,j)
c4 = ao_vgl(k,4,j)
c5 = ao_vgl(k,5,j)
do i=1,mo_num
mo_vgl(i,1,j) = mo_vgl(i,1,j) + coef_normalized_t(i,k) * c1
mo_vgl(i,2,j) = mo_vgl(i,2,j) + coef_normalized_t(i,k) * c2
mo_vgl(i,3,j) = mo_vgl(i,3,j) + coef_normalized_t(i,k) * c3
mo_vgl(i,4,j) = mo_vgl(i,4,j) + coef_normalized_t(i,k) * c4
mo_vgl(i,5,j) = mo_vgl(i,5,j) + coef_normalized_t(i,k) * c5
end do
end if
end do
end do
end function qmckl_compute_mo_basis_mo_vgl_doc_fqmckl_exit_code qmckl_compute_mo_basis_mo_vgl (
const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl );qmckl_exit_code qmckl_compute_mo_basis_mo_vgl_doc (
const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl );qmckl_exit_code
qmckl_compute_mo_basis_mo_vgl (const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl )
{
#ifdef HAVE_HPC
return qmckl_compute_mo_basis_mo_vgl_hpc (context, ao_num, mo_num, point_num, coef_normalized_t, ao_vgl, mo_vgl);
#else
return qmckl_compute_mo_basis_mo_vgl_doc (context, ao_num, mo_num, point_num, coef_normalized_t, ao_vgl, mo_vgl);
#endif
}HPC version
#ifdef HAVE_HPC
qmckl_exit_code
qmckl_compute_mo_basis_mo_vgl_hpc (const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl );
#endif#ifdef HAVE_HPC
qmckl_exit_code
qmckl_compute_mo_basis_mo_vgl_hpc (const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* restrict coef_normalized_t,
const double* restrict ao_vgl,
double* restrict const mo_vgl )
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for (int64_t ipoint=0 ; ipoint < point_num ; ++ipoint) {
double* restrict const vgl1 = &(mo_vgl[ipoint*5*mo_num]);
const double* restrict avgl1 = &(ao_vgl[ipoint*5*ao_num]);
double* restrict const vgl2 = vgl1 + mo_num;
double* restrict const vgl3 = vgl1 + (mo_num << 1);
double* restrict const vgl4 = vgl1 + (mo_num << 1) + mo_num;
double* restrict const vgl5 = vgl1 + (mo_num << 2);
const double* restrict avgl2 = avgl1 + ao_num;
const double* restrict avgl3 = avgl1 + (ao_num << 1);
const double* restrict avgl4 = avgl1 + (ao_num << 1) + ao_num;
const double* restrict avgl5 = avgl1 + (ao_num << 2);
for (int64_t i=0 ; i<mo_num ; ++i) {
vgl1[i] = 0.;
vgl2[i] = 0.;
vgl3[i] = 0.;
vgl4[i] = 0.;
vgl5[i] = 0.;
}
int64_t nidx=0;
int64_t idx[ao_num];
double av1[ao_num];
double av2[ao_num];
double av3[ao_num];
double av4[ao_num];
double av5[ao_num];
for (int64_t k=0 ; k<ao_num ; ++k) {
const double* restrict ck1 = coef_normalized_t + k*mo_num;
if (avgl1[k] != 0.) {
idx[nidx] = k;
av1[nidx] = avgl1[k];
av2[nidx] = avgl2[k];
av3[nidx] = avgl3[k];
av4[nidx] = avgl4[k];
av5[nidx] = avgl5[k];
++nidx;
}
}
int64_t n;
for (n=0 ; n < nidx-4 ; n+=4) {
int64_t k = idx[n];
const double* restrict ck1 = coef_normalized_t + idx[n ]*mo_num;
const double* restrict ck2 = coef_normalized_t + idx[n+1]*mo_num;
const double* restrict ck3 = coef_normalized_t + idx[n+2]*mo_num;
const double* restrict ck4 = coef_normalized_t + idx[n+3]*mo_num;
const double a11 = av1[n ];
const double a21 = av1[n+1];
const double a31 = av1[n+2];
const double a41 = av1[n+3];
const double a12 = av2[n ];
const double a22 = av2[n+1];
const double a32 = av2[n+2];
const double a42 = av2[n+3];
const double a13 = av3[n ];
const double a23 = av3[n+1];
const double a33 = av3[n+2];
const double a43 = av3[n+3];
const double a14 = av4[n ];
const double a24 = av4[n+1];
const double a34 = av4[n+2];
const double a44 = av4[n+3];
const double a15 = av5[n ];
const double a25 = av5[n+1];
const double a35 = av5[n+2];
const double a45 = av5[n+3];
#ifdef HAVE_OPENMP
#pragma omp simd
#endif
for (int64_t i=0 ; i<mo_num ; ++i) {
vgl1[i] = vgl1[i] + ck1[i] * a11 + ck2[i] * a21 + ck3[i] * a31 + ck4[i] * a41;
vgl2[i] = vgl2[i] + ck1[i] * a12 + ck2[i] * a22 + ck3[i] * a32 + ck4[i] * a42;
vgl3[i] = vgl3[i] + ck1[i] * a13 + ck2[i] * a23 + ck3[i] * a33 + ck4[i] * a43;
vgl4[i] = vgl4[i] + ck1[i] * a14 + ck2[i] * a24 + ck3[i] * a34 + ck4[i] * a44;
vgl5[i] = vgl5[i] + ck1[i] * a15 + ck2[i] * a25 + ck3[i] * a35 + ck4[i] * a45;
}
}
int64_t n0 = nidx-4;
n0 = n0 < 0 ? 0 : n0;
for (int64_t n=n0 ; n < nidx ; n+=1) {
const double* restrict ck = coef_normalized_t + idx[n]*mo_num;
const double a1 = av1[n];
const double a2 = av2[n];
const double a3 = av3[n];
const double a4 = av4[n];
const double a5 = av5[n];
#ifdef HAVE_OPENMP
#pragma omp simd
#endif
for (int64_t i=0 ; i<mo_num ; ++i) {
vgl1[i] += ck[i] * a1;
vgl2[i] += ck[i] * a2;
vgl3[i] += ck[i] * a3;
vgl4[i] += ck[i] * a4;
vgl5[i] += ck[i] * a5;
}
}
}
return QMCKL_SUCCESS;
}
#endif