qmckl/org/qmckl_determinant.org

Slater Determinant

• Context
  • Data structure
  • Access functions
  • Initialization functions
  • Fortran Interfaces
  • Test
• Computation
  • Get
  • Provide
  • Compute
  • Test

The slater deteminant is required for the calculation of the wavefunction, gradient, and derivatives. These quantities will be used to calculate the local Energy (\[E_L\]).

ψ(x) = det|ϕ₁(x₁)…ϕᵢ(yᵢ)…ϕₙ(xₙ)|

Concerning the gradient and laplacian, in fact what is actually calculated is the ratio of the gradient/laplacian and the determinant of the slater matrix:

∇ψ(x)/ψ(x)

and

∇²ψ(x)/ψ(x)

This avoids the unnecessary multiplication and division of by the determinant ψ(x).

Context

The following arrays are stored in the context:

type	char	α ('A') or β ('B') determinant
walk_num	int64_t	Number of walkers
det_num	int64_t	Number of determinants per walker
fermi_num	int64_t	Number of number of fermions
mo_index_list	mo_index[walk_num][det_num]	Index of MOs for each walker

Computed data:

det_matrix_list	[walk_num][det_num][mo_num][fermi_num]	The slater matrix for each determinant of each walker.
det_vgl	[5][walk_num][det_num]	Value, gradients, Laplacian of the MOs at electron positions
det_vgl_date	int64_t	Late modification date of Value, gradients, Laplacian of the MOs at electron positions

Data structure

typedef struct qmckl_determinant_struct {
char      type;
int64_t  walk_num;  
int64_t  det_num;  
int64_t  fermi_num;  
int64_t* mo_index_list;

double  * det_matrix_list;
double  * det_vgl;
int64_t   det_vgl_date;

int32_t   uninitialized;
bool      provided;
} qmckl_determinant_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.

Access functions

When all the data for the slater determinants have been provided, the following function returns true.

bool      qmckl_mo_basis_provided           (const qmckl_context context);

#+NAME:post

Initialization functions

To set the basis set, all the following functions need to be called.

qmckl_exit_code  qmckl_set_determinant_type             (const qmckl_context context, const char *t);
qmckl_exit_code  qmckl_set_determinant_walk_num         (const qmckl_context context, const int64_t walk_num);
qmckl_exit_code  qmckl_set_determinant_det_num          (const qmckl_context context, const int64_t det_num);
qmckl_exit_code  qmckl_set_determinant_fermi_num        (const qmckl_context context, const int64_t fermi_num);
qmckl_exit_code  qmckl_set_determinant_mo_index_list    (const qmckl_context context, const int64_t* mo_index_list);

#+NAME:pre2

#+NAME:post2

When the basis set is completely entered, other data structures are computed to accelerate the calculations.

Fortran Interfaces

Test

Computation

Get

qmckl_context	context	in	Global state
double	det_vgl[5][walk_num][det_num]	out	Value, gradients and Laplacian of the MOs

qmckl_exit_code qmckl_get_determinant_det_vgl(qmckl_context context, double* const det_vgl);

qmckl_exit_code qmckl_compute_get_determinant_det_vgl (
const qmckl_context context,
double* const det_vgl );

Provide

Compute

Test