RCISD

This is a concise step-by-step guide to different CI calculations available in PyBEST. An example input file for the water molecule can be found in the section Examples.

12.1.1. Preliminaries

Before proceeding, it’s imperative to review the general introduction outlined in General Remarks concerning Post-Hartree-Fock Calculations. This part of the Documentation builds upon it. PyBEST allows you also to perform Restricted Configuration Interaction calculations on top of any single-reference wave function. Similar to the previous modules, we will assume the following names for all PyBEST objects

lf:

A LinalgFactory instance (see Preliminaries).

occ_model:

An Aufbau occupation model of the AufbauOccModel class

kin:

The kinetic energy integrals

ne:

The nucleus-electron attraction integrals

eri:

The two-electron repulsion integrals

Currently, PyBEST supports the following variants of CI calculations

restricted Configuration Interaction Singles (RCIS)

restricted Configuration Interaction Doubles (RCID)

restricted Configuration Interaction Singles and Doubles (RCISD)

For all methods with an RHF reference function, PyBEST supports two calculation techniques that introduce the wave function as a Slater determinant (SD) or configuration state function (CSF). The CSF is the default.

12.1.2. RCI on top of RHF

We assume that you have performed a restricted Hartree-Fock calculation, whose results are stored in the IOData container hf_out (see The Self-Consistent Field Module). The code snippet below demonstrates how to perform default RCIS/RCID/RCISD calculations with an RHF reference function in PyBEST,

rcis = RCIS(lf, occ_model)
rcis_out = rcis(kin, ne, eri, hf_out)

rcid = RCID(lf, occ_model)
rcid_out = rcid(kin, ne, eri, hf_out)

rcisd = RCISD(lf, occ_model)
rcisd_out = rcisd(kin, ne, eri, hf_out)

Note

By default, only one root is calculated. That is, for RCIS only the lowest-lying excited state is determined, while for RCID and RCISD only the ground-state root is optimized. See Summary of keyword arguments for more details.

The results are returned as an IOData container and can be found in the ./pybest-results directory, where all data is stored in the checkpoint_CIS.h5, checkpoint_CID.h5, and checkpoint_CISD.h5 files, respectively. Specifically, the IOData container contains the following attributes

e_corr:

The RCIS/RCID/RCISD correlation energy

civ:

The eigenvectors of the RCIS/RCID/RCISD Hamiltonian

e_ref:

The energy of the reference determinant (here, the Hartree-Fock determinant)

12.1.3. RCI on top of pCCD

If you use this module, please cite [nowak2023].

We assume that you have performed a restricted pCCD calculation, whose results are stored in the IOData container pccd_out (see The pCCD module). The code snippet below demonstrates how to perform default pCCD-CID/pCCD-CISD calculations with a pCCD reference function in PyBEST,

rcid = RpCCDCID(lf, occ_model)
rcid_out = rcid(kin, ne, er, pccd_out)

rcisd = RpCCDCISD(lf, occ_model)
rcisd_out = rcisd(kin, ne, er, pccd_out)

Note

By default, only one root is calculated. That is, only the ground-state root is optimized. See Summary of keyword arguments for more details.

Note

By default, electron-pair excitations are excluded. Thus, all CID-type corrections do not consider electron-pair excitations in their ansatz.

The results are returned as an IOData container and can be found in the ./pybest-results directory, where all data is stored in the checkpoint_pCCD-CID.h5 and checkpoint_pCCD-CISD.h5 files, respectively. Specifically, the IOData container contains the following attributes

e_ci:

The RCID/RCISD correlation energy

civ:

The eigenvectors of the RCID/RCISD Hamiltonian

e_ref:

The energy of the reference pCCD wave function