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620 lines
11 KiB
ReStructuredText
620 lines
11 KiB
ReStructuredText
.. _ao_two_e_ints:
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.. program:: ao_two_e_ints
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.. default-role:: option
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==================
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ao_two_e_ints
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==================
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Here, all two-electron integrals (:math:`1/r_{12}`) are computed.
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As they have 4 indices and many are zero, they are stored in a map, as defined
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in :file:`utils/map_module.f90`.
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To fetch an |AO| integral, use the
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`get_ao_two_e_integral(i,j,k,l,ao_integrals_map)` function.
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The conventions are:
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* For |AO| integrals : (ij|kl) = (11|22) = <ik|jl> = <12|12>
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EZFIO parameters
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----------------
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.. option:: io_ao_two_e_integrals
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Read/Write |AO| integrals from/to disk [ Write | Read | None ]
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Default: None
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.. option:: ao_integrals_threshold
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If | (pq|rs) | < `ao_integrals_threshold` then (pq|rs) is zero
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Default: 1.e-15
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.. option:: do_direct_integrals
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Compute integrals on the fly (very slow, only for debugging)
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Default: False
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Providers
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---------
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.. c:var:: ao_integrals_cache
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.. code:: text
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double precision, allocatable :: ao_integrals_cache (0:64*64*64*64)
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File: :file:`map_integrals.irp.f`
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Cache of AO integrals for fast access
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.. c:var:: ao_integrals_cache_max
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.. code:: text
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integer :: ao_integrals_cache_min
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integer :: ao_integrals_cache_max
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File: :file:`map_integrals.irp.f`
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Min and max values of the AOs for which the integrals are in the cache
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.. c:var:: ao_integrals_cache_min
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.. code:: text
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integer :: ao_integrals_cache_min
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integer :: ao_integrals_cache_max
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File: :file:`map_integrals.irp.f`
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Min and max values of the AOs for which the integrals are in the cache
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.. c:var:: ao_integrals_map
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.. code:: text
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type(map_type) :: ao_integrals_map
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File: :file:`map_integrals.irp.f`
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AO integrals
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.. c:var:: ao_two_e_integral_schwartz
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.. code:: text
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double precision, allocatable :: ao_two_e_integral_schwartz (ao_num,ao_num)
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File: :file:`two_e_integrals.irp.f`
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Needed to compute Schwartz inequalities
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.. c:var:: ao_two_e_integrals_in_map
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.. code:: text
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logical :: ao_two_e_integrals_in_map
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File: :file:`two_e_integrals.irp.f`
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Map of Atomic integrals i(r1) j(r2) 1/r12 k(r1) l(r2)
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.. c:var:: gauleg_t2
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.. code:: text
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double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2)
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double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2)
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File: :file:`gauss_legendre.irp.f`
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t_w(i,1,k) = w(i) t_w(i,2,k) = t(i)
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.. c:var:: gauleg_w
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.. code:: text
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double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2)
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double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2)
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File: :file:`gauss_legendre.irp.f`
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t_w(i,1,k) = w(i) t_w(i,2,k) = t(i)
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.. c:var:: general_primitive_integral
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.. code:: text
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double precision function general_primitive_integral(dim, &
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P_new,P_center,fact_p,p,p_inv,iorder_p, &
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Q_new,Q_center,fact_q,q,q_inv,iorder_q)
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File: :file:`two_e_integrals.irp.f`
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Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
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.. c:var:: i_x1_new
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.. code:: text
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recursive subroutine I_x1_new(a,c,B_10,B_01,B_00,res,n_pt)
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File: :file:`two_e_integrals.irp.f`
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recursive function involved in the two-electron integral
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.. c:var:: i_x1_pol_mult_a1
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.. code:: text
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recursive subroutine I_x1_pol_mult_a1(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
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File: :file:`two_e_integrals.irp.f`
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recursive function involved in the two-electron integral
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.. c:var:: i_x1_pol_mult_a2
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.. code:: text
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recursive subroutine I_x1_pol_mult_a2(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
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File: :file:`two_e_integrals.irp.f`
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recursive function involved in the two-electron integral
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.. c:var:: i_x1_pol_mult_recurs
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.. code:: text
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recursive subroutine I_x1_pol_mult_recurs(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
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File: :file:`two_e_integrals.irp.f`
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recursive function involved in the two-electron integral
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.. c:var:: i_x2_new
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.. code:: text
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recursive subroutine I_x2_new(c,B_10,B_01,B_00,res,n_pt)
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File: :file:`two_e_integrals.irp.f`
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recursive function involved in the two-electron integral
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.. c:var:: i_x2_pol_mult
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.. code:: text
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recursive subroutine I_x2_pol_mult(c,B_10,B_01,B_00,C_00,D_00,d,nd,dim)
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File: :file:`two_e_integrals.irp.f`
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recursive function involved in the two-electron integral
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Subroutines / functions
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-----------------------
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.. c:function:: ao_l4
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.. code:: text
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integer function ao_l4(i,j,k,l)
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File: :file:`two_e_integrals.irp.f`
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Computes the product of l values of i,j,k,and l
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.. c:function:: ao_two_e_integral
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.. code:: text
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double precision function ao_two_e_integral(i,j,k,l)
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File: :file:`two_e_integrals.irp.f`
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integral of the AO basis <ik|jl> or (ij|kl) i(r1) j(r1) 1/r12 k(r2) l(r2)
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.. c:function:: ao_two_e_integral_schwartz_accel
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.. code:: text
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double precision function ao_two_e_integral_schwartz_accel(i,j,k,l)
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File: :file:`two_e_integrals.irp.f`
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integral of the AO basis <ik|jl> or (ij|kl) i(r1) j(r1) 1/r12 k(r2) l(r2)
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.. c:function:: ao_two_e_integrals_in_map_collector
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.. code:: text
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subroutine ao_two_e_integrals_in_map_collector(zmq_socket_pull)
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File: :file:`integrals_in_map_slave.irp.f`
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Collects results from the AO integral calculation
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.. c:function:: ao_two_e_integrals_in_map_slave
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.. code:: text
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subroutine ao_two_e_integrals_in_map_slave(thread,iproc)
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File: :file:`integrals_in_map_slave.irp.f`
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Computes a buffer of integrals
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.. c:function:: ao_two_e_integrals_in_map_slave_inproc
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.. code:: text
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subroutine ao_two_e_integrals_in_map_slave_inproc(i)
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File: :file:`integrals_in_map_slave.irp.f`
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Computes a buffer of integrals. i is the ID of the current thread.
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.. c:function:: ao_two_e_integrals_in_map_slave_tcp
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.. code:: text
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subroutine ao_two_e_integrals_in_map_slave_tcp(i)
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File: :file:`integrals_in_map_slave.irp.f`
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Computes a buffer of integrals. i is the ID of the current thread.
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.. c:function:: clear_ao_map
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.. code:: text
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subroutine clear_ao_map
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File: :file:`map_integrals.irp.f`
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Frees the memory of the AO map
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.. c:function:: compute_ao_integrals_jl
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.. code:: text
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subroutine compute_ao_integrals_jl(j,l,n_integrals,buffer_i,buffer_value)
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File: :file:`two_e_integrals.irp.f`
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Parallel client for AO integrals
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.. c:function:: compute_ao_two_e_integrals
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.. code:: text
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subroutine compute_ao_two_e_integrals(j,k,l,sze,buffer_value)
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File: :file:`two_e_integrals.irp.f`
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Compute AO 1/r12 integrals for all i and fixed j,k,l
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.. c:function:: dump_ao_integrals
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.. code:: text
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subroutine dump_ao_integrals(filename)
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File: :file:`map_integrals.irp.f`
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Save to disk the |AO| integrals
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.. c:function:: eri
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.. code:: text
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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)
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File: :file:`two_e_integrals.irp.f`
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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)
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.. c:function:: gauleg
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.. code:: text
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subroutine gauleg(x1,x2,x,w,n)
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File: :file:`gauss_legendre.irp.f`
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Gauss-Legendre
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.. c:function:: get_ao_map_size
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.. code:: text
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function get_ao_map_size()
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File: :file:`map_integrals.irp.f`
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Returns the number of elements in the AO map
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.. c:function:: get_ao_two_e_integral
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.. code:: text
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double precision function get_ao_two_e_integral(i,j,k,l,map) result(result)
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File: :file:`map_integrals.irp.f`
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Gets one AO bi-electronic integral from the AO map
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.. c:function:: get_ao_two_e_integrals
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.. code:: text
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subroutine get_ao_two_e_integrals(j,k,l,sze,out_val)
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File: :file:`map_integrals.irp.f`
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Gets multiple AO bi-electronic integral from the AO map . All i are retrieved for j,k,l fixed.
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.. c:function:: get_ao_two_e_integrals_non_zero
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.. code:: text
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subroutine get_ao_two_e_integrals_non_zero(j,k,l,sze,out_val,out_val_index,non_zero_int)
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File: :file:`map_integrals.irp.f`
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Gets multiple AO bi-electronic integral from the AO map . All non-zero i are retrieved for j,k,l fixed.
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.. c:function:: give_polynom_mult_center_x
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.. code:: text
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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)
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File: :file:`two_e_integrals.irp.f`
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subroutine that returns the explicit polynom in term of the "t" variable of the following polynomw : I_x1(a_x, d_x,p,q) * I_x1(a_y, d_y,p,q) * I_x1(a_z, d_z,p,q)
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.. c:function:: i_x1_pol_mult
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.. code:: text
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subroutine I_x1_pol_mult(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
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File: :file:`two_e_integrals.irp.f`
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recursive function involved in the two-electron integral
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.. c:function:: insert_into_ao_integrals_map
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.. code:: text
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subroutine insert_into_ao_integrals_map(n_integrals,buffer_i, buffer_values)
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File: :file:`map_integrals.irp.f`
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Create new entry into AO map
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.. c:function:: integrale_new
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.. code:: text
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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)
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File: :file:`two_e_integrals.irp.f`
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calculate the integral of the polynom :: I_x1(a_x+b_x, c_x+d_x,p,q) * I_x1(a_y+b_y, c_y+d_y,p,q) * I_x1(a_z+b_z, c_z+d_z,p,q) between ( 0 ; 1)
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.. c:function:: load_ao_integrals
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.. code:: text
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integer function load_ao_integrals(filename)
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File: :file:`map_integrals.irp.f`
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Read from disk the |AO| integrals
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.. c:function:: n_pt_sup
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.. code:: text
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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)
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File: :file:`two_e_integrals.irp.f`
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Returns the upper boundary of the degree of the polynomial involved in the bielctronic integral : Ix(a_x,b_x,c_x,d_x) * Iy(a_y,b_y,c_y,d_y) * Iz(a_z,b_z,c_z,d_z)
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.. c:function:: push_integrals
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.. code:: text
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subroutine push_integrals(zmq_socket_push, n_integrals, buffer_i, buffer_value, task_id)
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File: :file:`integrals_in_map_slave.irp.f`
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Push integrals in the push socket
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.. c:function:: two_e_integrals_index
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.. code:: text
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subroutine two_e_integrals_index(i,j,k,l,i1)
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File: :file:`map_integrals.irp.f`
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.. c:function:: two_e_integrals_index_reverse
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.. code:: text
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subroutine two_e_integrals_index_reverse(i,j,k,l,i1)
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File: :file:`map_integrals.irp.f`
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