.. : PyBEST: Pythonic Black-box Electronic Structure Tool : Copyright (C) 2016-- The PyBEST Development Team : : This file is part of PyBEST. : : PyBEST is free software; you can redistribute it and/or : modify it under the terms of the GNU General Public License : as published by the Free Software Foundation; either version 3 : of the License, or (at your option) any later version. : : PyBEST is distributed in the hope that it will be useful, : but WITHOUT ANY WARRANTY; without even the implied warranty of : MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the : GNU General Public License for more details. : : You should have received a copy of the GNU General Public License : along with this program; if not, see : -- .. _user_estruct_rci_hf: The Configuration Interaction Module on top of RHF ################################################## .. _rci_keywords: Summary of keyword arguments ---------------------------- The :py:class:`~pybest.ci.rci.RCIS`, :py:class:`~pybest.ci.rci.RCID`, and :py:class:`~pybest.ci.rci.RCISD` modules support various keyword arguments that allow the user to steer the process of the RCIS/RCID/RCISD Hamiltonian diagonalization. In the following, all supported keyword arguments are listed together with their default values. Please note that the default values should be sufficient to reach convergence in simple systems. :nroot: (int) The number of states (default: 1; ground state for RCID/RCISD; first excited state for RCIS) :nguessv: (int) Total number of guess vectors (default: (nroot-1)*4+1) :tolerance: (float) Tolerance for energies (default: 1e-6) :tolerancev: (float) Tolerance for eigenvectors (default: 1e-5) :maxiter: (int) Maximum number of iterations (default: 200). :threshold: (float) Printing tolerance for contributions of RCI wave function (default: 0.1). :maxvectors: (int) Maximum number of Davidson vectors (default: nroot*10) :scc: (boolean) Determines whether a size-consistency correction is to be calculated (default: True) :threshold_c_0: A threshold that helps to verify the accuracy of Davidson-type corrections :print_csf: (boolean) Davidson-typeecides in which variant (True: CSF; False: SD) the results will be printed (default: False) .. _rci_csf: Relation between Configuration State Function and Slater Determinant -------------------------------------------------------------------- A Configuration State Function (CSF) is a symmetry-adapted linear combination of Slater determinants (SD). Below, we illustrate the exact relations between CSF and SD for singly- and doubly-excited configurations. To distinguish between the SD and CSF representation, the individual components of an SD will be denoted with normal size letters, while capitalized letters are used for CSFs. The relation for single excitations is as follows .. math:: :label: single sd/csf \vert ^{\textrm{A}} _{\textrm{I}}\rangle = \frac{1}{\sqrt{2}} (\vert ^a_i \rangle + \vert ^{\bar{a}} _{\bar{i}} \rangle), while the relation for double excitations is more complicated and can be expressed as a set of equations .. math:: :label: doubles pairs \vert ^{\textrm{A} \textrm{A}} _{\textrm{I}\textrm{I}}\rangle = \vert ^{a \bar{a}} _{i\bar{i}}\rangle .. math:: :label: doubles iiab \vert ^{\textrm{A} \textrm{B}} _{\textrm{I} \textrm{I}}\rangle = \frac{1}{\sqrt{2}} (\vert ^{a \bar{b}} _{i\bar{i}} \rangle + \vert ^{b \bar{a}} _{i\bar{i}} \rangle), .. math:: :label: doubles ijaa \vert ^{\textrm{A} \textrm{A}} _{\textrm{I} \textrm{J}}\rangle = \frac{1}{\sqrt{2}} (\vert ^{a \bar{a}} _{i\bar{j}} \rangle + \vert ^{a \bar{a}} _{j\bar{i}} \rangle), .. math:: :label: doubles A _{A}\vert ^{\textrm{A} \textrm{B}} _{\textrm{I} \textrm{J}}\rangle = \frac{1}{\sqrt{12}} (\vert ^{ab} _{ij} \rangle + \vert ^{\bar{a} \bar{b}} _{\bar{i}\bar{j}} \rangle + \vert ^{a \bar{b}} _{i\bar{j}} \rangle + \vert ^{b \bar{a}} _{j\bar{i}} \rangle - \vert ^{a \bar{b}} _{j\bar{i}} \rangle - \vert ^{b \bar{a}} _{i\bar{j}} \rangle), .. math:: :label: doubles B _{B}\vert ^{\textrm{A} \textrm{B}} _{\textrm{I} \textrm{J}}\rangle = \frac{1}{2} (\vert ^{a \bar{b}} _{i\bar{j}} \rangle + \vert ^{b \bar{a}} _{j\bar{i}} \rangle + \vert ^{a \bar{b}} _{j\bar{i}} \rangle + \vert ^{b \bar{a}} _{i\bar{j}} \rangle), .. _rci_csf_calc: Setting up calculations using CSFs and SDs ------------------------------------------ By default, all variants of :py:class:`~pybest.ci.rci.RCI` classes perform a calculation using the CSF representation. To change this and use an SD basis instead, the ``csf`` argument has to be set to ``False`` in the initialization of an instance of the chosen RCI class. The following code snippet shows how to use this option .. code-block:: python rcis = RCIS(lf, occ_model, csf=False) rcid = RCID(lf, occ_model, csf=False) rcisd = RCISD(lf, occ_model, csf=False) .. _rcis_frozen_core: Frozen core RCI --------------- By default, all core orbitals are frozen. To freeze some specific (occupied) orbitals, the number of frozen cores has to be specified during the initialization of some occupation module class. The code snippet below shows how to freeze the first (occupied) orbital in a :py:class:`~pybest.ci.rci.RCIS`, :py:class:`~pybest.ci.rci.RCID`, :py:class:`~pybest.ci.rci.RCISD` calculation, by specifying the ``ncore`` argument during the initialization of the chosen occupation model .. code-block:: python # Select one frozen core orbital #------------------------------- occ_model = AufbauOccModel(gobasis, ncore=1) # Perform CI calculation, ncore is stored in occ_model #----------------------------------------------------- rcis = RCIS(lf, occ_model) rcis_out = rcis(kin, ne, er, hf_out) rcid = RCID(lf, occ_model) rcid_out = rcid(kin, ne, er, hf_out) rcisd = RCISD(lf, occ_model) rcisd_out = rcisd(kin, ne, er, hf_out) .. _user_estruct_scc: Size-consistency Corrections ---------------------------- The RCI module allows you to calculate Davidson-type corrections for the ground state. The following variants of Davidson-type corrections are supported * ``Davidson:`` [davidson-corr]_ .. math:: :label: dc E_{DC}=(1-{c_{0}}^2)(E_{RCI} - E_{RF}) * ``Renormalized Davidson:`` [scc-overview]_ .. math:: :label: rdc E_{RDC}=\left(\frac{1-{c_{0}}^2}{{c_{0}}^2}\right)(E_{RCI} - E_{RF}) * ``Modified Pople:`` [scc-overview]_ .. math:: :label: pc E_{PC}=E_{RDC}\left(1-\frac{2}{n_e}\right) * ``Meissner:`` [meissner-overview]_ .. math:: :label: mc E_{MC}=E_{RDC}\left( \frac{(n_e-2)(n_e-3)}{n_e(n_e-1)} \right) * ``Duch and Diercksen:`` [duch1994]_ .. math:: :label: ddc E_{DDC}=E_{RCI}\left(\frac{1-{c_{0}}^2}{2\left(\frac{n_e-1}{n_e-2}\right)c_0^2-1} \right), where :math:`E_{RCI}` indicates the total energy of the :py:class:`~pybest.io.iodata.RCI` method, :math:`E_{RF}` is the energy of the reference method, :math:`c_0` is the contribution of the reference determinant of the reference method, and :math:`n_e` denotes the total number of electrons in the system. .. note:: Please note that PyBEST supports size-consistency calculations for two variants of the :py:class:`~pybest.ci.rci.RCI` module: :py:class:`~pybest.io.iodata.RCID` and :py:class:`~pybest.io.iodata.RCISD`. The size-consistency corrections are calculated directly by setting the ``scc`` keyword argument to True (see also :ref:`rci_keywords`). By default, all size-consistency corrections are calculated.