ao_two_e_ints
Here, all two-electron integrals (\(1/r_{12}\)) are computed.
As they have 4 indices and many are zero, they are stored in a map, as defined
in utils/map_module.f90
.
To fetch an AO integral, use the
get_ao_two_e_integral(i,j,k,l,ao_integrals_map)
function.
The conventions are: * For AO integrals : (ij|kl) = (11|22) = <ik|jl> = <12|12>
EZFIO parameters
- io_ao_two_e_integrals
Read/Write AO integrals from/to disk [ Write | Read | None ]
Default: None
- ao_integrals_threshold
If | (pq|rs) | <
ao_integrals_threshold
then (pq|rs) is zeroDefault: 1.e-15
- do_direct_integrals
Compute integrals on the fly (very slow, only for debugging)
Default: False
Providers
- ao_integrals_cache
File :
ao_two_e_ints/map_integrals.irp.f
double precision, allocatable :: ao_integrals_cache (0:64*64*64*64)
Cache of AO integrals for fast access
Needs:
ao_integrals_cache_min
ao_integrals_map
ao_two_e_integrals_in_map
- ao_integrals_cache_max
File :
ao_two_e_ints/map_integrals.irp.f
integer :: ao_integrals_cache_min integer :: ao_integrals_cache_max
Min and max values of the AOs for which the integrals are in the cache
Needs:
ao_num
Needed by:
ao_integrals_cache
ao_integrals_cache_periodic
- ao_integrals_cache_min
File :
ao_two_e_ints/map_integrals.irp.f
integer :: ao_integrals_cache_min integer :: ao_integrals_cache_max
Min and max values of the AOs for which the integrals are in the cache
Needs:
ao_num
Needed by:
ao_integrals_cache
ao_integrals_cache_periodic
- ao_integrals_cache_periodic
File :
ao_two_e_ints/map_integrals.irp.f
complex*16, allocatable :: ao_integrals_cache_periodic (0:64*64*64*64)
Cache of AO integrals for fast access
Needs:
ao_integrals_cache_min
ao_integrals_map
ao_two_e_integrals_in_map
- ao_integrals_map
File :
ao_two_e_ints/map_integrals.irp.f
type(map_type) :: ao_integrals_map
AO integrals
Needs:
ao_num
Needed by:
ao_integrals_cache
ao_integrals_cache_periodic
ao_two_e_integrals_in_map
mo_two_e_integral_jj_from_ao
mo_two_e_integrals_in_map
mo_two_e_integrals_vv_from_ao
- ao_two_e_integral_schwartz
File :
ao_two_e_ints/two_e_integrals.irp.f
double precision, allocatable :: ao_two_e_integral_schwartz (ao_num,ao_num)
Needed to compute Schwartz inequalities
Needs:
ao_coef_normalized_ordered_transp
ao_expo_ordered_transp
ao_nucl
ao_num
ao_power
ao_prim_num
n_pt_max_integrals
nucl_coord
- ao_two_e_integrals_in_map
File :
ao_two_e_ints/two_e_integrals.irp.f
logical :: ao_two_e_integrals_in_map
- Map of Atomic integrals
i(r1) j(r2) 1/r12 k(r1) l(r2)
Needs:
ao_coef_normalized_ordered_transp
ao_expo_ordered_transp
ao_integrals_map
ao_nucl
ao_num
ao_power
ao_prim_num
ezfio_filename
io_ao_two_e_integrals
mpi_master
n_pt_max_integrals
nproc
nucl_coord
read_ao_two_e_integrals
zmq_context
zmq_socket_pull_tcp_address
zmq_state
Needed by:
ao_integrals_cache
ao_integrals_cache_periodic
mo_two_e_integral_jj_from_ao
mo_two_e_integrals_in_map
mo_two_e_integrals_vv_from_ao
- gauleg_t2
File :
ao_two_e_ints/gauss_legendre.irp.f
double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2) double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2)
t_w(i,1,k) = w(i) t_w(i,2,k) = t(i)
Needs:
n_pt_max_integrals
- gauleg_w
File :
ao_two_e_ints/gauss_legendre.irp.f
double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2) double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2)
t_w(i,1,k) = w(i) t_w(i,2,k) = t(i)
Needs:
n_pt_max_integrals
- general_primitive_integral:
File :
ao_two_e_ints/two_e_integrals.irp.f
double precision function general_primitive_integral(dim, & P_new,P_center,fact_p,p,p_inv,iorder_p, & Q_new,Q_center,fact_q,q,q_inv,iorder_q)
Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
Calls:
add_poly_multiply()
give_polynom_mult_center_x()
multiply_poly()
- i_x1_new:
File :
ao_two_e_ints/two_e_integrals.irp.f
recursive subroutine I_x1_new(a,c,B_10,B_01,B_00,res,n_pt)
recursive function involved in the two-electron integral
Needs:
n_pt_max_integrals
Called by:
i_x1_new()
i_x2_new()
integrale_new()
Calls:
i_x1_new()
i_x2_new()
- i_x1_pol_mult_a1:
File :
ao_two_e_ints/two_e_integrals.irp.f
recursive subroutine I_x1_pol_mult_a1(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
Recursive function involved in the two-electron integral
Called by:
i_x1_pol_mult()
i_x1_pol_mult_a2()
i_x1_pol_mult_recurs()
Calls:
i_x2_pol_mult()
multiply_poly()
- i_x1_pol_mult_a2:
File :
ao_two_e_ints/two_e_integrals.irp.f
recursive subroutine I_x1_pol_mult_a2(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
Recursive function involved in the two-electron integral
Called by:
i_x1_pol_mult()
i_x1_pol_mult_recurs()
Calls:
i_x1_pol_mult_a1()
i_x2_pol_mult()
multiply_poly()
- i_x1_pol_mult_recurs:
File :
ao_two_e_ints/two_e_integrals.irp.f
recursive subroutine I_x1_pol_mult_recurs(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
Recursive function involved in the two-electron integral
Called by:
i_x1_pol_mult()
i_x1_pol_mult_recurs()
Calls:
i_x1_pol_mult_a1()
i_x1_pol_mult_a2()
i_x1_pol_mult_recurs()
multiply_poly()
- i_x2_new:
File :
ao_two_e_ints/two_e_integrals.irp.f
recursive subroutine I_x2_new(c,B_10,B_01,B_00,res,n_pt)
recursive function involved in the two-electron integral
Needs:
n_pt_max_integrals
Called by:
i_x1_new()
Calls:
i_x1_new()
- i_x2_pol_mult:
File :
ao_two_e_ints/two_e_integrals.irp.f
recursive subroutine I_x2_pol_mult(c,B_10,B_01,B_00,C_00,D_00,d,nd,dim)
Recursive function involved in the two-electron integral
Called by:
i_x1_pol_mult()
i_x1_pol_mult_a1()
i_x1_pol_mult_a2()
i_x2_pol_mult()
Calls:
i_x2_pol_mult()
multiply_poly()
Subroutines / functions
- ao_idx2_sq:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine ao_idx2_sq(i,j,ij)
Called by:
two_e_integrals_index_2fold()
- ao_idx2_sq_rev:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine ao_idx2_sq_rev(i,k,ik)
reverse square compound index
Called by:
two_e_integrals_index_reverse_2fold()
- ao_idx2_tri_key:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine ao_idx2_tri_key(i,j,ij)
Called by:
two_e_integrals_index_2fold()
- ao_idx2_tri_rev_key:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine ao_idx2_tri_rev_key(i,k,ik)
return i<=k
Called by:
two_e_integrals_index_reverse_2fold()
- ao_l4:
File :
ao_two_e_ints/two_e_integrals.irp.f
integer function ao_l4(i,j,k,l)
Computes the product of l values of i,j,k,and l
Needs:
ao_l
- ao_two_e_integral:
File :
ao_two_e_ints/two_e_integrals.irp.f
double precision function ao_two_e_integral(i,j,k,l)
- integral of the AO basis <ik|jl> or (ij|kl)
i(r1) j(r1) 1/r12 k(r2) l(r2)
Needs:
ao_coef_normalized_ordered_transp
ao_expo_ordered_transp
ao_nucl
ao_power
ao_prim_num
n_pt_max_integrals
nucl_coord
Calls:
give_explicit_poly_and_gaussian()
- ao_two_e_integral_schwartz_accel:
File :
ao_two_e_ints/two_e_integrals.irp.f
double precision function ao_two_e_integral_schwartz_accel(i,j,k,l)
- integral of the AO basis <ik|jl> or (ij|kl)
i(r1) j(r1) 1/r12 k(r2) l(r2)
Needs:
ao_coef_normalized_ordered_transp
ao_expo_ordered_transp
ao_integrals_threshold
ao_nucl
ao_power
ao_prim_num
n_pt_max_integrals
nucl_coord
Calls:
give_explicit_poly_and_gaussian()
- ao_two_e_integral_zero:
File :
ao_two_e_ints/screening.irp.f
logical function ao_two_e_integral_zero(i,j,k,l)
Needs:
ao_integrals_threshold
ao_overlap_abs
ao_two_e_integral_schwartz
is_periodic
read_ao_two_e_integrals
- ao_two_e_integrals_in_map_collector:
File :
ao_two_e_ints/integrals_in_map_slave.irp.f
subroutine ao_two_e_integrals_in_map_collector(zmq_socket_pull)
Collects results from the AO integral calculation
Needs:
ao_integrals_map
ao_num
Called by:
ao_two_e_integrals_in_map
Calls:
end_zmq_to_qp_run_socket()
insert_into_ao_integrals_map()
- ao_two_e_integrals_in_map_slave:
File :
ao_two_e_ints/integrals_in_map_slave.irp.f
subroutine ao_two_e_integrals_in_map_slave(thread,iproc)
Computes a buffer of integrals
Needs:
ao_num
Called by:
ao_two_e_integrals_in_map_slave_inproc()
ao_two_e_integrals_in_map_slave_tcp()
Calls:
compute_ao_integrals_jl()
end_zmq_push_socket()
end_zmq_to_qp_run_socket()
push_integrals()
- ao_two_e_integrals_in_map_slave_inproc:
File :
ao_two_e_ints/integrals_in_map_slave.irp.f
subroutine ao_two_e_integrals_in_map_slave_inproc(i)
Computes a buffer of integrals. i is the ID of the current thread.
Called by:
ao_two_e_integrals_in_map
Calls:
ao_two_e_integrals_in_map_slave()
- ao_two_e_integrals_in_map_slave_tcp:
File :
ao_two_e_ints/integrals_in_map_slave.irp.f
subroutine ao_two_e_integrals_in_map_slave_tcp(i)
Computes a buffer of integrals. i is the ID of the current thread.
Calls:
ao_two_e_integrals_in_map_slave()
- clear_ao_map:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine clear_ao_map
Frees the memory of the AO map
Needs:
ao_integrals_map
Calls:
map_deinit()
- compute_ao_integrals_jl:
File :
ao_two_e_ints/two_e_integrals.irp.f
subroutine compute_ao_integrals_jl(j,l,n_integrals,buffer_i,buffer_value)
Parallel client for AO integrals
Needs:
ao_integrals_threshold
ao_num
Called by:
ao_two_e_integrals_in_map_slave()
Calls:
two_e_integrals_index()
- compute_ao_two_e_integrals:
File :
ao_two_e_ints/two_e_integrals.irp.f
subroutine compute_ao_two_e_integrals(j,k,l,sze,buffer_value)
Compute AO 1/r12 integrals for all i and fixed j,k,l
Needs:
ao_num
Called by:
mo_two_e_integral_jj_from_ao
mo_two_e_integrals_vv_from_ao
- eri:
File :
ao_two_e_ints/two_e_integrals.irp.f
double precision function ERI(alpha,beta,delta,gama,a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z)
- ATOMIC PRIMTIVE two-electron integral between the 4 primitives ::
primitive_1 = x1**(a_x) y1**(a_y) z1**(a_z) exp(-alpha * r1**2) primitive_2 = x1**(b_x) y1**(b_y) z1**(b_z) exp(- beta * r1**2) primitive_3 = x2**(c_x) y2**(c_y) z2**(c_z) exp(-delta * r2**2) primitive_4 = x2**(d_x) y2**(d_y) z2**(d_z) exp(- gama * r2**2)
Calls:
integrale_new()
- gauleg:
File :
ao_two_e_ints/gauss_legendre.irp.f
subroutine gauleg(x1,x2,x,w,n)
Gauss-Legendre
Called by:
gauleg_t2
- get_ao_map_size:
File :
ao_two_e_ints/map_integrals.irp.f
function get_ao_map_size()
Returns the number of elements in the AO map
Needs:
ao_integrals_map
- get_ao_two_e_integral:
File :
ao_two_e_ints/map_integrals.irp.f
double precision function get_ao_two_e_integral(i,j,k,l,map) result(result)
Gets one AO bi-electronic integral from the AO map
Needs:
ao_integrals_cache
ao_integrals_cache_min
ao_two_e_integrals_in_map
Calls:
map_get()
two_e_integrals_index()
- get_ao_two_e_integral_periodic:
File :
ao_two_e_ints/map_integrals.irp.f
complex*16 function get_ao_two_e_integral_periodic(i,j,k,l,map) result(result)
Gets one AO bi-electronic integral from the AO map
Needs:
ao_integrals_cache_min
ao_integrals_cache_periodic
ao_integrals_map
ao_two_e_integrals_in_map
Calls:
map_get()
two_e_integrals_index_2fold()
- get_ao_two_e_integrals:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine get_ao_two_e_integrals(j,k,l,sze,out_val)
Gets multiple AO bi-electronic integral from the AO map . All i are retrieved for j,k,l fixed. physicist convention : <ij|kl>
Needs:
ao_integrals_map
ao_two_e_integrals_in_map
Called by:
add_integrals_to_map()
add_integrals_to_map_no_exit_34()
add_integrals_to_map_three_indices()
- get_ao_two_e_integrals_non_zero:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine get_ao_two_e_integrals_non_zero(j,k,l,sze,out_val,out_val_index,non_zero_int)
Gets multiple AO bi-electronic integral from the AO map . All non-zero i are retrieved for j,k,l fixed.
Needs:
ao_integrals_map
ao_integrals_threshold
ao_two_e_integrals_in_map
Called by:
mo_two_e_integral_jj_from_ao
mo_two_e_integrals_vv_from_ao
Calls:
map_get()
two_e_integrals_index()
- get_ao_two_e_integrals_non_zero_jl:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine get_ao_two_e_integrals_non_zero_jl(j,l,thresh,sze_max,sze,out_val,out_val_index,non_zero_int)
Gets multiple AO bi-electronic integral from the AO map . All non-zero i are retrieved for j,k,l fixed.
Needs:
ao_integrals_map
ao_two_e_integrals_in_map
Calls:
map_get()
two_e_integrals_index()
- get_ao_two_e_integrals_non_zero_jl_from_list:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine get_ao_two_e_integrals_non_zero_jl_from_list(j,l,thresh,list,n_list,sze_max,out_val,out_val_index,non_zero_int)
Gets multiple AO two-electron integrals from the AO map . All non-zero i are retrieved for j,k,l fixed.
Needs:
ao_integrals_map
ao_two_e_integrals_in_map
Calls:
map_get()
two_e_integrals_index()
- get_ao_two_e_integrals_periodic:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine get_ao_two_e_integrals_periodic(j,k,l,sze,out_val)
Gets multiple AO bi-electronic integral from the AO map . All i are retrieved for j,k,l fixed. physicist convention : <ij|kl>
Needs:
ao_integrals_map
ao_two_e_integrals_in_map
- give_polynom_mult_center_x:
File :
ao_two_e_ints/two_e_integrals.irp.f
subroutine give_polynom_mult_center_x(P_center,Q_center,a_x,d_x,p,q,n_pt_in,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,d,n_pt_out)
subroutine that returns the explicit polynom in term of the “t” variable of the following polynomw :
$I_{x_1}(a_x,d_x,p,q) , I_{x_1}(a_y,d_y,p,q) I_{x_1}(a_z,d_z,p,q)$
Called by:
general_primitive_integral()
Calls:
i_x1_pol_mult()
- i_x1_pol_mult:
File :
ao_two_e_ints/two_e_integrals.irp.f
subroutine I_x1_pol_mult(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
Recursive function involved in the two-electron integral
Called by:
give_polynom_mult_center_x()
Calls:
i_x1_pol_mult_a1()
i_x1_pol_mult_a2()
i_x1_pol_mult_recurs()
i_x2_pol_mult()
- idx2_tri_int:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine idx2_tri_int(i,j,ij)
- idx2_tri_rev_int:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine idx2_tri_rev_int(i,k,ik)
return i<=k
- insert_into_ao_integrals_map:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine insert_into_ao_integrals_map(n_integrals,buffer_i, buffer_values)
Create new entry into AO map
Needs:
ao_integrals_map
Called by:
ao_two_e_integrals_in_map_collector()
Calls:
map_append()
- integrale_new:
File :
ao_two_e_ints/two_e_integrals.irp.f
subroutine integrale_new(I_f,a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z,p,q,n_pt)
Calculates the integral of the polynomial :
$I_{x_1}(a_x+b_x,c_x+d_x,p,q) , I_{x_1}(a_y+b_y,c_y+d_y,p,q) , I_{x_1}(a_z+b_z,c_z+d_z,p,q)$ in $( 0 ; 1)$
Needs:
gauleg_t2
n_pt_max_integrals
Called by:
eri()
Calls:
i_x1_new()
- n_pt_sup:
File :
ao_two_e_ints/two_e_integrals.irp.f
integer function n_pt_sup(a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z)
Returns the upper boundary of the degree of the polynomial involved in the two-electron integral :
$I_x(a_x,b_x,c_x,d_x) , I_y(a_y,b_y,c_y,d_y) , I_z(a_z,b_z,c_z,d_z)$
- push_integrals:
File :
ao_two_e_ints/integrals_in_map_slave.irp.f
subroutine push_integrals(zmq_socket_push, n_integrals, buffer_i, buffer_value, task_id)
Push integrals in the push socket
Called by:
ao_two_e_integrals_in_map_slave()
- two_e_integrals_index:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine two_e_integrals_index(i,j,k,l,i1)
Gives a unique index for i,j,k,l using permtuation symmetry. i <-> k, j <-> l, and (i,k) <-> (j,l) for non-periodic systems
Called by:
ao_integrals_cache
ao_integrals_map
banned_excitation
compute_ao_integrals_jl()
four_idx_novvvv()
get_ao_two_e_integral()
get_ao_two_e_integrals_non_zero()
get_ao_two_e_integrals_non_zero_jl()
get_ao_two_e_integrals_non_zero_jl_from_list()
get_two_e_integral()
mo_integrals_cache
mo_integrals_map
- two_e_integrals_index_2fold:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine two_e_integrals_index_2fold(i,j,k,l,i1)
Called by:
ao_integrals_cache_periodic
get_ao_two_e_integral_periodic()
Calls:
ao_idx2_sq()
ao_idx2_tri_key()
- two_e_integrals_index_reverse:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine two_e_integrals_index_reverse(i,j,k,l,i1)
Computes the 4 indices $i,j,k,l$ from a unique index $i_1$. For 2 indices $i,j$ and $i le j$, we have $p = i(i-1)/2 + j$. The key point is that because $j < i$, $i(i-1)/2 < p le i(i+1)/2$. So $i$ can be found by solving $i^2 - i - 2p=0$. One obtains $i=1 + sqrt{1+8p}/2$ and $j = p - i(i-1)/2$. This rule is applied 3 times. First for the symmetry of the pairs (i,k) and (j,l), and then for the symmetry within each pair.
- two_e_integrals_index_reverse_2fold:
File :
ao_two_e_ints/map_integrals.irp.f
subroutine two_e_integrals_index_reverse_2fold(i,j,k,l,i1)
Calls:
ao_idx2_sq_rev()
ao_idx2_tri_rev_key()