.. _perturbation: .. program:: perturbation .. default-role:: option ============ perturbation ============ All subroutines in ``*.irp.f`` starting with `pt2_` in the current directory are perturbation computed using the routine `i_H_psi`. Other cases are not allowed. The arguments of the `pt2_` are always: .. code-block:: fortran subroutine pt2_...( & psi_ref, & psi_ref_coefs, & E_refs, & det_pert, & c_pert, & e_2_pert, & H_pert_diag, & Nint, & Ndet, & N_st ) integer , intent(in) :: Nint,Ndet,N_st integer(bit_kind), intent(in) :: psi_ref(Nint,2,Ndet) double precision , intent(in) :: psi_ref_coefs(Ndet,N_st) double precision , intent(in) :: E_refs(N_st) integer(bit_kind), intent(in) :: det_pert(Nint,2) double precision , intent(out) :: c_pert(N_st),e_2_pert(N_st),H_pert_diag `psi_ref` bitstring of the determinants present in the various `N_st` states `psi_ref_coefs` coefficients of the determinants on the various `N_st` states `E_refs` Energy of the various `N_st` states `det_pert` Perturber determinant `c_pert` Perturbative coefficients for the various states `e_2_pert` Perturbative energetic contribution for the various states `H_pert_diag` Diagonal |H| matrix element of the perturber `Nint` Should be equal to `N_int` `Ndet` Number of determinants `i` in |Psi| on which we apply `N_st` Number of states EZFIO parameters ---------------- .. option:: do_pt2 If `True`, compute the |PT2| contribution Default: True .. option:: pt2_max The selection process stops when the largest |PT2| (for all the state) is lower than `pt2_max` in absolute value Default: 0.0001 .. option:: pt2_relative_error Stop stochastic |PT2| when the relative error is smaller than `PT2_relative_error` Default: 0.005 .. option:: correlation_energy_ratio_max The selection process stops at a fixed correlation ratio (useful for getting same accuracy between molecules). Defined as :math:`{E_{CI}-E_{HF}}/{E_{CI}+E_{PT2} - E_{HF}}`. Default: 1.00 .. option:: h0_type Type of zeroth-order Hamiltonian [ EN | Barycentric | Variance | SOP ] Default: EN Providers --------- .. c:var:: fill_h_apply_buffer_selection .. code:: text subroutine fill_H_apply_buffer_selection(n_selected,det_buffer,e_2_pert_buffer,coef_pert_buffer, & N_st,Nint,iproc,select_max_out) File: :file:`selection.irp.f` Fill the H_apply buffer with determiants for the selection .. c:var:: max_exc_pert .. code:: text integer :: max_exc_pert File: :file:`exc_max.irp.f` .. c:var:: selection_criterion .. code:: text double precision :: selection_criterion double precision :: selection_criterion_min double precision :: selection_criterion_factor File: :file:`selection.irp.f` Threshold to select determinants. Set by selection routines. .. c:var:: selection_criterion_factor .. code:: text double precision :: selection_criterion double precision :: selection_criterion_min double precision :: selection_criterion_factor File: :file:`selection.irp.f` Threshold to select determinants. Set by selection routines. .. c:var:: selection_criterion_min .. code:: text double precision :: selection_criterion double precision :: selection_criterion_min double precision :: selection_criterion_factor File: :file:`selection.irp.f` Threshold to select determinants. Set by selection routines. .. c:var:: var_pt2_ratio .. code:: text double precision :: var_pt2_ratio File: :file:`var_pt2_ratio_provider.irp.f` The selection process stops when the energy ratio variational/(variational+PT2) is equal to var_pt2_ratio Subroutines / functions ----------------------- .. c:function:: perturb_buffer_by_mono_dummy .. code:: text subroutine perturb_buffer_by_mono_dummy(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``dummy`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_by_mono_epstein_nesbet .. code:: text subroutine perturb_buffer_by_mono_epstein_nesbet(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``epstein_nesbet`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_by_mono_epstein_nesbet_2x2 .. code:: text subroutine perturb_buffer_by_mono_epstein_nesbet_2x2(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``epstein_nesbet_2x2`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_by_mono_epstein_nesbet_2x2_no_ci_diag .. code:: text subroutine perturb_buffer_by_mono_epstein_nesbet_2x2_no_ci_diag(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``epstein_nesbet_2x2_no_ci_diag`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_by_mono_h_core .. code:: text subroutine perturb_buffer_by_mono_h_core(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``h_core`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_by_mono_moller_plesset .. code:: text subroutine perturb_buffer_by_mono_moller_plesset(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``moller_plesset`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_by_mono_moller_plesset_general .. code:: text subroutine perturb_buffer_by_mono_moller_plesset_general(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``moller_plesset_general`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_by_mono_qdpt .. code:: text subroutine perturb_buffer_by_mono_qdpt(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``qdpt`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_dummy .. code:: text subroutine perturb_buffer_dummy(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``dummy`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_epstein_nesbet .. code:: text subroutine perturb_buffer_epstein_nesbet(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``epstein_nesbet`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_epstein_nesbet_2x2 .. code:: text subroutine perturb_buffer_epstein_nesbet_2x2(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``epstein_nesbet_2x2`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_epstein_nesbet_2x2_no_ci_diag .. code:: text subroutine perturb_buffer_epstein_nesbet_2x2_no_ci_diag(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``epstein_nesbet_2x2_no_ci_diag`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_h_core .. code:: text subroutine perturb_buffer_h_core(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``h_core`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_moller_plesset .. code:: text subroutine perturb_buffer_moller_plesset(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``moller_plesset`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_moller_plesset_general .. code:: text subroutine perturb_buffer_moller_plesset_general(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``moller_plesset_general`` to the buffer of determinants generated in the H_apply routine. .. c:function:: perturb_buffer_qdpt .. code:: text subroutine perturb_buffer_qdpt(i_generator,buffer,buffer_size,e_2_pert_buffer,coef_pert_buffer,sum_e_2_pert,sum_norm_pert,sum_H_pert_diag,N_st,Nint,key_mask,fock_diag_tmp,electronic_energy) File: :file:`perturbation.irp.f_shell_13` Applly pertubration ``qdpt`` to the buffer of determinants generated in the H_apply routine. .. c:function:: pt2_dummy .. code:: text subroutine pt2_dummy (electronic_energy,det_ref,det_pert,fock_diag_tmp,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pt2_equations.irp.f_template_360` Dummy perturbation to add all connected determinants. .. c:function:: pt2_epstein_nesbet .. code:: text subroutine pt2_epstein_nesbet (electronic_energy,det_ref,det_pert,fock_diag_tmp,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pt2_equations.irp.f_template_360` Compute the standard Epstein-Nesbet perturbative first order coefficient and second order energetic contribution for the various N_st states. `c_pert(i)` = :math:`\frac{\langle i|H|\alpha \rangle}{ E_n - \langle \alpha|H|\alpha \rangle }` . `e_2_pert(i)` = :math:`\frac{\langle i|H|\alpha \rangle^2}{ E_n - \langle \alpha|H|\alpha \rangle }` . .. c:function:: pt2_epstein_nesbet_2x2 .. code:: text subroutine pt2_epstein_nesbet_2x2 (electronic_energy,det_ref,det_pert,fock_diag_tmp,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pt2_equations.irp.f_template_360` Computes the Epstein-Nesbet 2x2 diagonalization coefficient and energetic contribution for the various N_st states. `e_2_pert(i)` = :math:`\frac{1}{2} ( \langle \alpha|H|\alpha \rangle - E_n) - \sqrt{ (\langle \alpha|H|\alpha \rangle - E_n)^2 + 4 \langle i|H|\alpha \rangle^2 }` . `c_pert(i)` = `e_2_pert(i)` :math:`\times \frac{1}{ \langle i|H|\alpha \rangle}` . .. c:function:: pt2_epstein_nesbet_2x2_no_ci_diag .. code:: text subroutine pt2_epstein_nesbet_2x2_no_ci_diag(electronic_energy,det_ref,det_pert,fock_diag_tmp,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pt2_equations.irp.f_template_360` compute the Epstein-Nesbet 2x2 diagonalization coefficient and energetic contribution for the various N_st states. e_2_pert(i) = 0.5 * (( - E(i) ) - sqrt( ( - E(i)) ^2 + 4 ^2 ) c_pert(i) = e_2_pert(i)/ .. c:function:: pt2_h_core .. code:: text subroutine pt2_h_core(det_pert,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pert_single.irp.f` compute the standard Epstein-Nesbet perturbative first order coefficient and second order energetic contribution for the various N_st states. c_pert(i) = /( E(i) - ) e_2_pert(i) = ^2/( E(i) - ) .. c:function:: pt2_moller_plesset .. code:: text subroutine pt2_moller_plesset (electronic_energy,det_ref,det_pert,fock_diag_tmp,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pt2_equations.irp.f_template_360` Computes the standard Moller-Plesset perturbative first order coefficient and second order energetic contribution for the various N_st states. `c_pert(i)` = :math:`\frac{\langle i|H|\alpha \rangle}{\text{difference of orbital energies}}` . `e_2_pert(i)` = :math:`\frac{\langle i|H|\alpha \rangle^2}{\text{difference of orbital energies}}` . .. c:function:: pt2_moller_plesset_general .. code:: text subroutine pt2_moller_plesset_general (electronic_energy,det_ref,det_pert,fock_diag_tmp,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pt2_equations.irp.f_template_360` Computes the standard Moller-Plesset perturbative first order coefficient and second order energetic contribution for the various N_st states. `c_pert(i)` = :math:`\frac{\langle i|H|\alpha \rangle}{\text{difference of orbital energies}}` . `e_2_pert(i)` = :math:`\frac{\langle i|H|\alpha \rangle^2}{\text{difference of orbital energies}}` . .. c:function:: pt2_qdpt .. code:: text subroutine pt2_qdpt (electronic_energy,det_ref,det_pert,fock_diag_tmp,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st,minilist,idx_minilist,N_minilist) File: :file:`pt2_equations.irp.f_template_360` Computes the QDPT first order coefficient and second order energetic contribution for the various N_st states. `c_pert(i)` = :math:`\frac{\langle i|H|\alpha \rangle}{\langle i|H|i \rangle - \langle \alpha|H|\alpha \rangle}` . .. c:function:: remove_small_contributions .. code:: text subroutine remove_small_contributions File: :file:`selection.irp.f` Remove determinants with small contributions. N_states is assumed to be provided. .. c:function:: repeat_all_e_corr .. code:: text double precision function repeat_all_e_corr(key_in) File: :file:`pert_sc2.irp.f`