.. _cipsi: .. program:: cipsi .. default-role:: option ===== cipsi ===== |CIPSI| algorithm. The :c:func:`run_stochastic_cipsi` and :c:func:`run_cipsi` subroutines start with a single determinant, or with the wave function in the |EZFIO| database if :option:`determinants read_wf` is |true|. The :c:func:`run_cipsi` subroutine iteratively: * Selects the most important determinants from the external space and adds them to the internal space * If :option:`determinants s2_eig` is |true|, it adds all the necessary determinants to allow the eigenstates of |H| to be eigenstates of |S^2| * Diagonalizes |H| in the enlarged internal space * Computes the |PT2| contribution to the energy stochastically :cite:`Garniron_2017.2` or deterministically, depending on :option:`perturbation do_pt2` * Extrapolates the variational energy by fitting :math:`E=E_\text{FCI} - \alpha\, E_\text{PT2}` The difference between :c:func:`run_stochastic_cipsi` and :c:func:`run_cipsi` is that :c:func:`run_stochastic_cipsi` selects the determinants on the fly with the computation of the stochastic |PT2| :cite:`Garniron_2017.2`. Hence, it is a semi-stochastic selection. It * Selects the most important determinants from the external space and adds them to the internal space, on the fly with the computation of the PT2 with the stochastic algorithm presented in :cite:`Garniron_2017.2`. * If :option:`determinants s2_eig` is |true|, it adds all the necessary determinants to allow the eigenstates of |H| to be eigenstates of |S^2| * Extrapolates the variational energy by fitting :math:`E=E_\text{FCI} - \alpha\, E_\text{PT2}` * Diagonalizes |H| in the enlarged internal space The number of selected determinants at each iteration will be such that the size of the wave function will double at every iteration. If :option:`determinants s2_eig` is |true|, then the number of selected determinants will be 1.5x the current number, and then all the additional determinants will be added. By default, the program will stop when more than one million determinants have been selected, or when the |PT2| energy is below :math:`10^{-4}`. The variational and |PT2| energies of the iterations are stored in the |EZFIO| database, in the :ref:`iterations` module. Computation of the |PT2| energy ------------------------------- At each iteration, the |PT2| energy is computed considering the Epstein-Nesbet zeroth-order Hamiltonian: .. math:: E_{\text{PT2}} = \sum_{ \alpha } \frac{|\langle \Psi_S | \hat{H} | \alpha \rangle|^2} {E - \langle \alpha | \hat{H} | \alpha \rangle} where the |kalpha| determinants are generated by applying all the single and double excitation operators to all the determinants of the wave function :math:`\Psi_G`. When the hybrid-deterministic/stochastic algorithm is chosen (default), :math:`Psi_G = \Psi_S = \Psi`, the full wavefunction expanded in the internal space. When the deterministic algorithm is chosen (:option:`perturbation do_pt2` is set to |false|), :math:`Psi_G` is a truncation of |Psi| using :option:`determinants threshold_generators`, and :math:`Psi_S` is a truncation of |Psi| using :option:`determinants threshold_selectors`, and re-weighted by :math:`1/\langle \Psi_s | \Psi_s \rangle`. At every iteration, while computing the |PT2|, the variance of the wave function is also computed: .. math:: \sigma^2 & = \langle \Psi | \hat{H}^2 | \Psi \rangle - \langle \Psi | \hat{H} | \Psi \rangle^2 \\ & = \sum_{i \in \text{FCI}} \langle \Psi | \hat{H} | i \rangle \langle i | \hat{H} | \Psi \rangle - \langle \Psi | \hat{H} | \Psi \rangle^2 \\ & = \sum_{ \alpha } \langle |\Psi | \hat{H} | \alpha \rangle|^2. The expression of the variance is the same as the expression of the |PT2|, with a denominator of 1. It measures how far the wave function is from the |FCI| solution. Note that the absence of denominator in the Heat-Bath selected |CI| method is selection method by minimization of the variance, whereas |CIPSI| is a selection method by minimization of the energy. If :option:`perturbation do_pt2` is set to |false|, then the stochastic |PT2| is not computed, and an approximate value is obtained from the |CIPSI| selection. The calculation is faster, but the extrapolated |FCI| value is less accurate. This way of running the code should be used when the only goal is to generate a wave function, as for using |CIPSI| wave functions as trial wave functions of |QMC| calculations for example. The :command:`PT2` program reads the wave function of the |EZFIO| database and computes the energy and the |PT2| contribution. State-averaging --------------- Extrapolated |FCI| energy ------------------------- An estimate of the |FCI| energy is computed by extrapolating .. math:: E=E_\text{FCI} - \alpha\, E_\text{PT2} This extrapolation is done for all the requested states, and excitation energies are printed as energy differences between the extrapolated energies of the excited states and the extrapolated energy of the ground state. The extrapolations are given considering the 2 last points, the 3 last points, ..., the 7 last points. The extrapolated value should be chosen such that the extrpolated value is stable with the number of points. Providers --------- .. c:var:: initialize_pt2_e0_denominator .. code:: text logical :: initialize_pt2_e0_denominator File: :file:`energy.irp.f` If true, initialize pt2_E0_denominator .. c:var:: pt2_collector .. code:: text subroutine pt2_collector(zmq_socket_pull, E, relative_error, pt2, error, & variance, norm, b, N_) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_cw .. code:: text double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_e0_denominator .. code:: text double precision, allocatable :: pt2_e0_denominator (N_states) File: :file:`energy.irp.f` E0 in the denominator of the PT2 .. c:var:: pt2_f .. code:: text integer, allocatable :: pt2_f (N_det_generators) integer :: pt2_n_tasks_max File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_j .. code:: text integer, allocatable :: pt2_j (N_det_generators) integer, allocatable :: pt2_r (N_det_generators) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_mindetinfirstteeth .. code:: text integer :: pt2_n_teeth integer :: pt2_mindetinfirstteeth File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_n_0 .. code:: text double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_n_tasks .. code:: text integer :: pt2_n_tasks File: :file:`pt2_stoch_routines.irp.f` Number of parallel tasks for the Monte Carlo .. c:var:: pt2_n_tasks_max .. code:: text integer, allocatable :: pt2_f (N_det_generators) integer :: pt2_n_tasks_max File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_n_teeth .. code:: text integer :: pt2_n_teeth integer :: pt2_mindetinfirstteeth File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_r .. code:: text integer, allocatable :: pt2_j (N_det_generators) integer, allocatable :: pt2_r (N_det_generators) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_stoch_istate .. code:: text integer :: pt2_stoch_istate File: :file:`pt2_stoch_routines.irp.f` State for stochatsic PT2 .. c:var:: pt2_u .. code:: text double precision, allocatable :: pt2_u (N_det_generators) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_u_0 .. code:: text double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_w .. code:: text double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: pt2_w_t .. code:: text double precision, allocatable :: pt2_w (N_det_generators) double precision, allocatable :: pt2_cw (0:N_det_generators) double precision :: pt2_w_t double precision :: pt2_u_0 integer, allocatable :: pt2_n_0 (pt2_N_teeth+1) File: :file:`pt2_stoch_routines.irp.f` .. c:var:: selection_weight .. code:: text double precision, allocatable :: selection_weight (N_states) File: :file:`selection.irp.f` Weights in the state-average calculation of the density matrix Subroutines / functions ----------------------- .. c:function:: add_to_selection_buffer .. code:: text subroutine add_to_selection_buffer(b, det, val) File: :file:`selection_buffer.irp.f` .. c:function:: bitstring_to_list_in_selection .. code:: text subroutine bitstring_to_list_in_selection( string, list, n_elements, Nint) File: :file:`selection.irp.f` Gives the inidices(+1) of the bits set to 1 in the bit string .. c:function:: create_selection_buffer .. code:: text subroutine create_selection_buffer(N, siz_, res) File: :file:`selection_buffer.irp.f` .. c:function:: delete_selection_buffer .. code:: text subroutine delete_selection_buffer(b) File: :file:`selection_buffer.irp.f` .. c:function:: fill_buffer_double .. code:: text subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_diag_tmp, E0, pt2, variance, norm, mat, buf) File: :file:`selection.irp.f` .. c:function:: get_d0 .. code:: text subroutine get_d0(gen, phasemask, bannedOrb, banned, mat, mask, h, p, sp, coefs) File: :file:`selection.irp.f` .. c:function:: get_d1 .. code:: text subroutine get_d1(gen, phasemask, bannedOrb, banned, mat, mask, h, p, sp, coefs) File: :file:`selection.irp.f` .. c:function:: get_d2 .. code:: text subroutine get_d2(gen, phasemask, bannedOrb, banned, mat, mask, h, p, sp, coefs) File: :file:`selection.irp.f` .. c:function:: get_mask_phase .. code:: text subroutine get_mask_phase(det1, pm, Nint) File: :file:`selection.irp.f` .. c:function:: get_phase_bi .. code:: text double precision function get_phase_bi(phasemask, s1, s2, h1, p1, h2, p2, Nint) File: :file:`selection.irp.f` .. c:function:: make_selection_buffer_s2 .. code:: text subroutine make_selection_buffer_s2(b) File: :file:`selection_buffer.irp.f` .. c:function:: merge_selection_buffers .. code:: text subroutine merge_selection_buffers(b1, b2) File: :file:`selection_buffer.irp.f` Merges the selection buffers b1 and b2 into b2 .. c:function:: past_d1 .. code:: text subroutine past_d1(bannedOrb, p) File: :file:`selection.irp.f` .. c:function:: past_d2 .. code:: text subroutine past_d2(banned, p, sp) File: :file:`selection.irp.f` .. c:function:: provide_everything .. code:: text subroutine provide_everything File: :file:`slave_cipsi.irp.f` .. c:function:: pt2_find_sample .. code:: text integer function pt2_find_sample(v, w) File: :file:`pt2_stoch_routines.irp.f` .. c:function:: pt2_find_sample_lr .. code:: text integer function pt2_find_sample_lr(v, w, l_in, r_in) File: :file:`pt2_stoch_routines.irp.f` .. c:function:: pt2_slave_inproc .. code:: text subroutine pt2_slave_inproc(i) File: :file:`pt2_stoch_routines.irp.f` .. c:function:: pull_pt2_results .. code:: text subroutine pull_pt2_results(zmq_socket_pull, index, pt2, variance, norm, task_id, n_tasks, b) File: :file:`run_pt2_slave.irp.f` .. c:function:: pull_selection_results .. code:: text subroutine pull_selection_results(zmq_socket_pull, pt2, variance, norm, val, det, N, task_id, ntask) File: :file:`run_selection_slave.irp.f` .. c:function:: push_pt2_results .. code:: text subroutine push_pt2_results(zmq_socket_push, index, pt2, variance, norm, b, task_id, n_tasks) File: :file:`run_pt2_slave.irp.f` .. c:function:: push_selection_results .. code:: text subroutine push_selection_results(zmq_socket_push, pt2, variance, norm, b, task_id, ntask) File: :file:`run_selection_slave.irp.f` .. c:function:: remove_duplicates_in_selection_buffer .. code:: text subroutine remove_duplicates_in_selection_buffer(b) File: :file:`selection_buffer.irp.f` .. c:function:: run_cipsi .. code:: text subroutine run_cipsi File: :file:`cipsi.irp.f` Selected Full Configuration Interaction with deterministic selection and stochastic PT2. .. c:function:: run_pt2_slave .. code:: text subroutine run_pt2_slave(thread,iproc,energy) File: :file:`run_pt2_slave.irp.f` .. c:function:: run_selection_slave .. code:: text subroutine run_selection_slave(thread,iproc,energy) File: :file:`run_selection_slave.irp.f` .. c:function:: run_slave_cipsi .. code:: text subroutine run_slave_cipsi File: :file:`slave_cipsi.irp.f` Helper program for distributed parallelism .. c:function:: run_slave_main .. code:: text subroutine run_slave_main File: :file:`slave_cipsi.irp.f` .. c:function:: run_stochastic_cipsi .. code:: text subroutine run_stochastic_cipsi File: :file:`stochastic_cipsi.irp.f` Selected Full Configuration Interaction with Stochastic selection and PT2. .. c:function:: select_connected .. code:: text subroutine select_connected(i_generator,E0,pt2,variance,norm,b,subset,csubset) File: :file:`selection.irp.f` .. c:function:: select_singles_and_doubles .. code:: text subroutine select_singles_and_doubles(i_generator,hole_mask,particle_mask,fock_diag_tmp,E0,pt2,variance,norm,buf,subset,csubset) File: :file:`selection.irp.f` WARNING /!\ : It is assumed that the generators and selectors are psi_det_sorted .. c:function:: selection_collector .. code:: text subroutine selection_collector(zmq_socket_pull, b, N, pt2, variance, norm) File: :file:`zmq_selection.irp.f` .. c:function:: selection_slave_inproc .. code:: text subroutine selection_slave_inproc(i) File: :file:`zmq_selection.irp.f` .. c:function:: sort_selection_buffer .. code:: text subroutine sort_selection_buffer(b) File: :file:`selection_buffer.irp.f` .. c:function:: splash_pq .. code:: text subroutine splash_pq(mask, sp, det, i_gen, N_sel, bannedOrb, banned, mat, interesting) File: :file:`selection.irp.f` .. c:function:: spot_isinwf .. code:: text subroutine spot_isinwf(mask, det, i_gen, N, banned, fullMatch, interesting) File: :file:`selection.irp.f` .. c:function:: testteethbuilding .. code:: text logical function testTeethBuilding(minF, N) File: :file:`pt2_stoch_routines.irp.f` .. c:function:: zmq_pt2 .. code:: text subroutine ZMQ_pt2(E, pt2,relative_error, error, variance, norm, N_in) File: :file:`pt2_stoch_routines.irp.f` .. c:function:: zmq_selection .. code:: text subroutine ZMQ_selection(N_in, pt2, variance, norm) File: :file:`zmq_selection.irp.f`