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quantum_package/docs/source/modules/fci.rst
Anthony Scemama 123de0381e Added modules
2018-12-28 19:50:28 +01:00

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.. _fci:
.. program:: fci
.. default-role:: option
===
fci
===
Selected Full Configuration Interaction.
The :command:`FCI` program starts with a single determinant, or with the wave
function in the |EZFIO| database if :option:`determinants read_wf` is |true|.
Then, it will iteratively:
* Select the most important determinants from the external space and add them to the
internal space
* If :option:`determinants s2_eig` is |true|, add all the necessary
determinants to allow the eigenstates of |H| to be eigenstates of |S^2|
* Diagonalize |H| in the enlarged internal space
* Compute (stochastically) the second-order perturbative contribution to the energy
* Extrapolate the variational energy by fitting
:math:`E=E_\text{FCI} - \alpha\, E_\text{PT2}`
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:`IterativeSave` 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.
EZFIO parameters
----------------
.. option:: energy
Calculated Selected |FCI| energy
.. option:: energy_pt2
Calculated |FCI| energy + |PT2|
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_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`
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:: fci
.. code:: text
subroutine fci
File: :file:`fci.irp.f`
Selected Full Configuration Interaction.
.. 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_m0
.. code:: text
subroutine get_m0(gen, phasemask, bannedOrb, vect, mask, h, p, sp, coefs)
File: :file:`selection.irp.f`
.. c:function:: get_m1
.. code:: text
subroutine get_m1(gen, phasemask, bannedOrb, vect, mask, h, p, sp, coefs)
File: :file:`selection.irp.f`
.. c:function:: get_m2
.. code:: text
subroutine get_m2(gen, phasemask, bannedOrb, vect, 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:: pt2
.. code:: text
subroutine pt2
File: :file:`pt2.irp.f`
Second order perturbative correction to the wave function contained in the EZFIO directory.
.. c:function:: pt2_collector
.. code:: text
subroutine pt2_collector(zmq_socket_pull, E, relative_error, pt2, error, variance, norm)
File: :file:`pt2_stoch_routines.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)
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, 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:: 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:: 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)
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`
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