QMCPACK provides a set of lightweight executables that address certain common problems in QMC workflow and analysis. These range from conversion utilities between different file formats and QMCPACK (e.g., ppconvert and convert4qmc), (qmc-extract-eshdf-kvectors) to postprocessing utilities (trace-density and qmcfinitesize) to many others. In this section, we cover the use cases, syntax, and features of all additional tools provided with QMCPACK.

## Postprocessing¶

### qmca¶

qmca is a versatile tool to analyze and plot the raw data from QMCPACK *.scalar.dat files. It is a Python executable and part of the Nexus suite of tools. It can be found in qmcpack/nexus/executables. For details, see Using the qmca tool to obtain total energies and related quantities.

### qmc-fit¶

qmc-fit is a curve fitting tool used to obtain statistical error bars on fitted parameters. It is useful for DMC time step extrapolation. For details, see Using the qmc-fit tool for statistical time step extrapolation and curve fitting.

### qdens¶

qdens is a command line tool to produce density files from QMCPACK’s stat.h5 output files. For details, see Using the qdens tool to obtain electron densities.

### qmcfinitesize¶

qmcfinitesize is a utility to compute many-body finite-size corrections to the energy. It is a C++ executable that is built alongside the QMCPACK executable. It can be found in build/bin.

## Converters¶

### convert4qmc¶

Convert4qmc allows conversion of orbitals and wavefunctions from quantum chemistry output files to QMCPACK XML and HDF5 input files. It is a small C++ executable that is built alongside the QMCPACK executable and can be found in build/bin.

To date, convert4qmc supports the following codes: GAMESS [SBB+93], PySCF [SBB+18] and QP2 [GAG+19] natively, and NWCHEM , TURBOMOLE [FAH+14], PSI4 [TSP+12], CFOUR 2.0beta [MCH+20], ORCA 3.X - 4.X [Nee18], DALTON2016 [AAB+14], MOLPRO [WKK+12], DIRAC [DIR], RMG [RMG], and QCHEM 4.X [SGE+15] through the molden2qmc converter (see molden2qmc).

#### General use¶

General use of convert4qmc can be prompted by running with no options:

>convert4qmc

Defaults : -gridtype log -first 1e-6 -last 100 -size 1001 -ci required -threshold 0.01 -TargetState 0 -prefix sample

convert [-gaussian|gamess|-orbitals|-dirac|-rmg]
filename
[-nojastrow -hdf5 -prefix title -addCusp -production -NbImages NimageX NimageY NimageZ]
[-psi_tag psi0 -ion_tag ion0 -gridtype log|log0|linear -first ri -last rf]
[-size npts -ci file.out -threshold cimin -TargetState state_number
Defaults : -gridtype log -first 1e-6 -last 100 -size 1001 -ci required
-threshold 0.01 -TargetState 0 -prefix sample
When the input format is missing, the  extension of filename is used to determine
the format
*.Fchk -> gaussian; *.out -> gamess; *.h5 -> hdf5 format


As an example, to convert a GAMESS calculation using a single determinant, the following use is sufficient:

convert4qmc -gamess MyGamessOutput.out


By default, the converter will generate multiple files:

convert4qmc output:

output

file type

default

description

*.qmc.in-wfs.xml

XML

default

Main input file for QMCPACK

*.qmc.in-wfnoj.xml

XML

default

Main input file for QMCPACK

*.structure.xml

XML

default

File containing the structure of the system

*.wfj.xml

XML

default

Wavefunction file with 1-, 2-, and 3-body Jastrows

*.wfnoj.xml

XML

default

Wavefunction file with no Jastrows

*.orbs.h5

HDF5

with -hdf5

HDF5 file containing all wavefunction data

If no -prefix option is specified, the prefix is taken from the input file name. For instance, if the GAMESS output file is Mysim.out, the files generated by convert4qmc will use the prefix Mysim and output files will be Mysim.qmc.in-wfs.xml, Mysim.structure.xml, and so on.

• Files .in-wfs.xml and .in-wfnoj.xml

These are the input files for QMCPACK. The geometry and the wavefunction are stored in external files *.structure.xml and *.wfj.xml (referenced from *.in-wfs.xml) or *.qmc.wfnoj.xml (referenced from *.qmc.in-wfnoj.xml). The Hamiltonian section is included, and the presence or lack of presence of an ECP is detected during the conversion. If use of an ECP is detected, a default ECP name is added (e.g., H.qmcpp.xml), and it is the responsibility of the user to modify the ECP name to match the one used to generate the wavefunction.

  <?xml version="1.0"?>
<simulation>
<!--

Example QMCPACK input file produced by convert4qmc

parameters based on the measured energies, variance, and statistics.

-->
<!--Name and Series number of the project.-->
<project id="gms" series="0"/>
<!--Link to the location of the Atomic Coordinates and the location of
the Wavefunction.-->
<include href="gms.structure.xml"/>
<include href="gms.wfnoj.xml"/>
<!--Hamiltonian of the system. Default ECP filenames are assumed.-->
<hamiltonian name="h0" type="generic" target="e">
<pairpot name="ElecElec" type="coulomb" source="e" target="e"
physical="true"/>
<pairpot name="IonIon" type="coulomb" source="ion0" target="ion0"/>
<pairpot name="PseudoPot" type="pseudo" source="ion0" wavefunction="psi0"
format="xml">
<pseudo elementType="H" href="H.qmcpp.xml"/>
<pseudo elementType="Li" href="Li.qmcpp.xml"/>
</pairpot>
</hamiltonian>

The qmc.in-wfnoj.xml file will have one VMC block with a
minimum number of blocks to reproduce the HF/DFT energy used to
generate the trial wavefunction.

::

<qmc method="vmc" move="pbyp" checkpoint="-1">
<estimator name="LocalEnergy" hdf5="no"/>
<parameter name="warmupSteps">100</parameter>
<parameter name="blocks">20</parameter>
<parameter name="steps">50</parameter>
<parameter name="substeps">8</parameter>
<parameter name="timestep">0.5</parameter>
<parameter name="usedrift">no</parameter>
</qmc>
</simulation>


If the qmc.in-wfj.xml file is used, Jastrow optimization blocks followed by a VMC and DMC block are included. These blocks contain default values to allow the user to test the accuracy of a system; however, they need to be updated and optimized for each system. The initial values might only be suitable for a small molecule.

  <loop max="4">
<qmc method="linear" move="pbyp" checkpoint="-1">
<estimator name="LocalEnergy" hdf5="no"/>
<parameter name="warmupSteps">100</parameter>
<parameter name="blocks">20</parameter>
<parameter name="timestep">0.5</parameter>
<parameter name="walkers">1</parameter>
<parameter name="samples">16000</parameter>
<parameter name="substeps">4</parameter>
<parameter name="usedrift">no</parameter>
<parameter name="MinMethod">OneShiftOnly</parameter>
<parameter name="minwalkers">0.0001</parameter>
</qmc>
</loop>
<!--

Example follow-up VMC optimization using more samples for greater accuracy:

-->
<loop max="10">
<qmc method="linear" move="pbyp" checkpoint="-1">
<estimator name="LocalEnergy" hdf5="no"/>
<parameter name="warmupSteps">100</parameter>
<parameter name="blocks">20</parameter>
<parameter name="timestep">0.5</parameter>
<parameter name="walkers">1</parameter>
<parameter name="samples">64000</parameter>
<parameter name="substeps">4</parameter>
<parameter name="usedrift">no</parameter>
<parameter name="MinMethod">OneShiftOnly</parameter>
<parameter name="minwalkers">0.3</parameter>
</qmc>
</loop>
<!--

Production VMC and DMC:

Examine the results of the optimization before running these blocks.
For example, choose the best optimized jastrow from all obtained, put in the
wavefunction file, and do not reoptimize.

-->
<qmc method="vmc" move="pbyp" checkpoint="-1">
<estimator name="LocalEnergy" hdf5="no"/>
<parameter name="warmupSteps">100</parameter>
<parameter name="blocks">200</parameter>
<parameter name="steps">50</parameter>
<parameter name="substeps">8</parameter>
<parameter name="timestep">0.5</parameter>
<parameter name="usedrift">no</parameter>
<!--Sample count should match targetwalker count for
DMC. Will be obtained from all nodes.-->
<parameter name="samples">16000</parameter>
</qmc>
<qmc method="dmc" move="pbyp" checkpoint="20">
<estimator name="LocalEnergy" hdf5="no"/>
<parameter name="targetwalkers">16000</parameter>
<parameter name="reconfiguration">no</parameter>
<parameter name="warmupSteps">100</parameter>
<parameter name="timestep">0.005</parameter>
<parameter name="steps">100</parameter>
<parameter name="blocks">100</parameter>
<parameter name="nonlocalmoves">yes</parameter>
</qmc>
</simulation>

• File .structure.xml

This file will be referenced from the main QMCPACK input. It contains the geometry of the system, position of the atoms, number of atoms, atomic types and charges, and number of electrons.

• Files .wfj.xml and .wfnoj.xml

These files contain the basis set detail, orbital coefficients, and the 1-, 2-, and 3-body Jastrow (in the case of .wfj.xml). If the wavefunction is multideterminant, the expansion will be at the end of the file. We recommend using the option -hdf5 when large molecules are studied to store the data more compactly in an HDF5 file.

• File .orbs.h5 This file is generated only if the option -hdf5 is added as follows:

convert4qmc -gamess MyGamessOutput.out -hdf5


In this case, the .wfj.xml or .wfnoj.xml files will point to this HDF file. Information about the basis set, orbital coefficients, and the multideterminant expansion is put in this file and removed from the wavefunction files, making them smaller.

convert4qmc input type:

option name

description

-orbitals

Generic HDF5 input file. Mainly automatically generated from QP2, Pyscf and all codes in molden2qmc

-gamess

Gamess code

-gaussian

Gaussian code

-dirac

get spinors from DIRAC code

-rmg

RMG code

#### Command line options¶

convert4qmc command line options:

Option Name

Value

default

description

-nojastrow

Force no Jastrow. qmc.in.wfj will not be generated

-hdf5

Force the wf to be in HDF5 format

-prefix

string

All created files will have the name of the string

-multidet

string

HDF5 file containing a multideterminant expansion

-addCusp

Force to add orbital cusp correction (ONLY for all-electron)

-production

Generates specific blocks in the input

-psi_tag

string

psi0

Name of the electrons particles inside QMCPACK

-ion_tag

string

ion0

Name of the ion particles inside QMCPACK

• -multidet

This option is to be used when a multideterminant expansion (mainly a CI expansion) is present in an HDF5 file. The trial wavefunction file will not display the full list of multideterminants and will add a path to the HDF5 file as follows (full example for the C2 molecule in qmcpack/tests/molecules/C2_pp).

<?xml version="1.0"?>
<qmcsystem>
<wavefunction name="psi0" target="e">
<determinantset type="MolecularOrbital" name="LCAOBSet" source="ion0" transform="yes" href="C2.h5">
<sposet basisset="LCAOBSet" name="spo-up" size="58">
<occupation mode="ground"/>
<coefficient size="58" spindataset="0"/>
</sposet>
<sposet basisset="LCAOBSet" name="spo-dn" size="58">
<occupation mode="ground"/>
<coefficient size="58" spindataset="0"/>
</sposet>
<multideterminant optimize="no" spo_up="spo-up" spo_dn="spo-dn">
<detlist size="202" type="DETS" nca="0" ncb="0" nea="4" neb="4" nstates="58" cutoff="1e-20" href="C2.h5"/>
</multideterminant>
</determinantset>
</wavefunction>
</qmcsystem>


To generate such trial wavefunction, the converter has to be invoked as follows:

> convert4qmc -orbitals C2.h5 -multidet C2.h5

• -nojastrow

This option generates only an input file, *.qmc.in.wfnoj.xml, containing no Jastrow optimization blocks and references a wavefunction file, *.wfnoj.xml, containing no Jastrow section.

• -hdf5

This option generates the *.orbs.h5 HDF5 file containing the basis set and the orbital coefficients. If the wavefunction contains a multideterminant expansion from QP2, it will also be stored in this file. This option minimizes the size of the *.wfj.xml file, which points to the HDF file, as in the following example:

 <?xml version="1.0"?>
<qmcsystem>
<wavefunction name="psi0" target="e">
<determinantset type="MolecularOrbital" name="LCAOBSet" source="ion0"
transform="yes" href="test.orbs.h5">
<slaterdeterminant>
<determinant id="updet" size="39">
<occupation mode="ground"/>
<coefficient size="411" spindataset="0"/>
</determinant>
<determinant id="downdet" size="35">
<occupation mode="ground"/>
<coefficient size="411" spindataset="0"/>
</determinant>
</slaterdeterminant>
</determinantset>
</wavefunction>
</qmcsystem>


Jastrow functions will be included if the option “-nojastrow” was not specified. Note that when initially optimization a wavefunction, we recommend temporarily removing/disabling the 3-body Jastrow.

• -prefix

Sets the prefix for all output generated by convert4qmc. If not specified, convert4qmc will use the defaults for the following:

• Gamess If the Gamess output file is named “Name.out” or “Name.output,” all files generated by convert4qmc will carry Name as a prefix (i.e., Name.qmc.in.xml).

• Generic HDF5 input If a generic HDF5 file is named “Name.H5,” all files generated by convert4qmc will carry Name as a prefix (i.e., Name.qmc.in.xml).

This option is very important for all-electron (AE) calculations. In this case, orbitals have to be corrected for the electron-nuclear cusp. The cusp correction scheme follows the algorithm described by Ma et al. [MTDN05] When this option is present, the wavefunction file has a new set of tags:

qmcsystem>
<wavefunction name="psi0" target="e">
<determinantset type="MolecularOrbital" name="LCAOBSet" source="ion0"
transform="yes" cuspCorrection="yes">
<basisset name="LCAOBSet">


The tag “cuspCorrection” in the wfj.xml (or wfnoj.xml) wavefunction file will force correction of the orbitals at the beginning of the run. In the “orbitals“ section of the wavefunction file, a new tag “cuspInfo” will be added for orbitals spin-up and orbitals spin-down:

 <slaterdeterminant>
<determinant id="updet" size="2"
cuspInfo="../updet.cuspInfo.xml">
<occupation mode="ground"/>
<coefficient size="135" id="updetC">

<determinant id="downdet" size="2"
cuspInfo="../downdet.cuspInfo.xml">
<occupation mode="ground"/>
<coefficient size="135" id="downdetC">


These tags will point to the files updet.cuspInfo.xml and downdet.cuspInfo.xml. By default, the converter assumes that the files are located in the relative path ../. If the files are not present in the parent directory, QMCPACK will run the cusp correction algorithm to generate both files in the current run directory (not in ../). If the files exist, then QMCPACK will apply the corrections to the orbitals.

Important notes:

The cusp correction implementations has been parallelized and performance improved. However, since the correction needs to be applied for every ion and then for every orbital on that ion, this operation can be costly (slow) for large systems. We recommend saving and reusing the computed cusp correction files updet.cuspInfo.xml and downdet.cuspInfo.xml, and transferring them between computer systems where relevant.

• -psi_tag

QMCPACK builds the wavefunction as a named object. In the vast majority of cases, one wavefunction is simulated at a time, but there may be situations where we want to distinguish different parts of a wavefunction, or even use multiple wavefunctions. This option can change the name for these cases.

<wavefunction name="psi0" target="e">

• -ion_tag

Although similar to -psi_tag, this is used for the type of ions.

<particleset name="ion0" size="2">

• -production

Without this option, input files with standard optimization, VMC, and DMC blocks are generated. When the “-production” option is specified, an input file containing complex options that may be more suitable for large runs at HPC centers is generated. This option is for users who are already familiar with QMC and QMCPACK. We encourage feedback on the standard and production sample inputs.

The following options are specific to using MCSCF multideterminants from Gamess.

convert4qmc MCSCF arguments:

Option Name

Value

default

description

-ci

String

none

Name of the file containing the CI expansion

-threshold

double

1e-20

Cutoff of the weight of the determinants

-TargetState

int

none

?

-NaturalOrbitals

int

none

?

-optDetCoeffs

no

Enables the optimization of CI coefficients

• keyword -ci Path/name of the file containing the CI expansion in a Gamess Format.

• keyword -threshold The CI expansion contains coefficients (weights) for each determinant. This option sets the maximum coefficient to include in the QMC run. By default it is set to 1e-20 (meaning all determinants in an expansion are taken into account). At the same time, if the threshold is set to a different value, for example $$1e-5$$, any determinant with a weight $$|weight| < 1e-5$$ will be discarded and the determinant will not be considered.

• keyword -TargetState ?

• keyword -NaturalOrbitals ?

• keyword -optDetCoeffs This flag enables optimization of the CI expansion coefficients. By default, optimization of the coefficients is disabled during wavefunction optimization runs.

Examples and more thorough descriptions of these options can be found in the lab section of this manual: Lab 3: Advanced molecular calculations.

#### Grid options¶

These parameters control how the basis set is projected on a grid. The default parameters are chosen to be very efficient. Unless you have a very good reason, we do not recommend modifying them.

 Tags keyword Value default description -gridtype log|log0|linear log Grid type -first double 1e-6 First point of the grid -last double 100 Last point of the grid -size int 1001 Number of point in the grid
• -gridtype Grid type can be logarithmic, logarithmic base 10, or linear

• -first First value of the grid

• -last Last value of the grid

• -size Number of points in the grid between “first” and “last.”

#### Supported codes¶

• PySCF

PySCF [SBB+18] is an all-purpose quantum chemistry code that can run calculations from simple Hartree-Fock to DFT, MCSCF, and CCSD, and for both isolated systems and periodic boundary conditions. PySCF can be downloaded from https://github.com/sunqm/pyscf. Many examples and tutorials can be found on the PySCF website, and all types of single determinants calculations are compatible with , thanks to active support from the authors of PySCF. A few additional steps are necessary to generate an output readable by convert4qmc.

This example shows how to run a Hartree-Fock calculation for the $$LiH$$ dimer molecule from PySCF and convert the wavefunction for QMCPACK.

• Python path

PySCF is a Python-based code. A Python module named PyscfToQmcpack containing the function savetoqmcpack is provided by and is located at qmcpack/src/QMCTools/PyscfToQmcpack.py. To be accessible to the PySCF script, this path must be added to the PYTHONPATH environment variable. For the bash shell, this can be done as follows:

export PYTHONPATH=/PATH_TO_QMCPACK/qmcpack/src/QMCTools:\\$PYTHONPATH

• PySCF Input File

Copy and paste the following code in a file named LiH.py.

#! /usr/bin/env python3
from pyscf import gto, scf, df
import numpy

cell = gto.M(
atom ='''
Li 0.0 0.0 0.0
H  0.0 0.0 3.0139239778''',
basis ='cc-pv5z',
unit="bohr",
spin=0,
verbose = 5,
cart=False,
)
mf = scf.ROHF(cell)
mf.kernel()

###SPECIFIC TO QMCPACK###
title='LiH'
from PyscfToQmcpack import savetoqmcpack

savetoqmcpack(cell,mf,title)


The arguments to the function savetoqmcpack are:

• cell This is the object returned from gto.M, containing the type of atoms, geometry, basisset, spin, etc.

• mf This is an object representing the PySCF level of theory, in this example, ROHF. This object contains the orbital coefficients of the calculations.

• title The name of the output file generated by PySCF. By default, the name of the generated file will be “default” if nothing is specified.

By adding the three lines below the “SPECIFIC TO QMCPACK” comment in the input file, the script will dump all the necessary data for QMCPACK into an HDF5 file using the value of “title” as an output name. PySCF is run as follows:

>python LiH.py


The generated HDF5 can be read by convert4qmc to generate the appropriate QMCPACK input files.

• Generating input files

As described in the previous section, generating input files for PySCF is as follows:

> convert4qmc -pyscf LiH.h5


The HDF5 file produced by “savetoqmcpack” contains the wavefunction in a form directly readable by QMCPACK. The wavefunction files from convert4qmc reference this HDF file as if the “-hdf5” option were specified (converting from PySCF implies the “-hdf5” option is always present).

Periodic boundary conditions with Gaussian orbitals from PySCF is fully supported for Gamma point and kpoints.

• Quantum Package

QP2 [GAG+19] is a quantum chemistry code developed by the LCPQ laboratory in Toulouse, France, and Argonne National Laboratory for the PBC version. It can be downloaded from https://github.com/QuantumPackage/qp2, and the tutorial within is quite extensive. The tutorial section of QP2 can guide you on how to install and run the code.

After a QP2 calculation, the data needed for convert4qmc can be generated through

qp_run save_for_qmcpack Myrun.ezfio


This command will generate an HDF5 file in the QMCPACK format named QP2QMCPACK.h5 convert4qmc can read this file and generate the *.structure.xml, *.wfj.xml and other files needed to run QMCPACK. . For example:

convert4qmc -orbitals QP2QMCPACK.h5 -multidet QP2QMCPACK.h5 -prefix MySystem


The main reason to use QP2 is to access the CIPSI algorithm to generate a multideterminant wavefunction. CIPSI is the preferred choice for generating a selected CI trial wavefunction for QMCPACK. An example on how to use QP2 for Hartree-Fock and selected CI can be found in CIPSI wavefunction interface of this manual. The converter code is actively maintained and codeveloped by both QMCPACK and QP2 developers.

• Using -hdf5 tag

convert4qmc -gamess Myrun.out -hdf5


This option is only used/usefull with the gamess code as it is the onlycode not providing an HDF5 output The result will create QMCPACK input files but will also store all key data in the HDF5 format.

• Mixing orbitals and multideterminants

Note that the QP2QMCPACK.h5 combined with the tags -orbitals and -multidet allows the user to choose orbitals from a different code such as PYSCF and the multideterminant section from QP2. These two codes are fully compatible, and this route is also the only possible route for multideterminants for solids.

convert4qmc -orbitals MyPyscfrun.h5 -multidet QP2QMCPACK.h5

• GAMESS

QMCPACK can use the output of GAMESS [SBB+93] for any type of single determinant calculation (HF or DFT) or multideterminant (MCSCF) calculation. A description with an example can be found in the Advanced Molecular Calculations Lab (Lab 3: Advanced molecular calculations).

• DIRAC

QMCPACK can use the output of DIRAC to run spin-orbit calculations using single-particle spinor wave functions for single-determinant calculations (DFT or closed-shell Dirac HF) or multideterminant complete open-shell configuration interaction (COSCI) wavefunctions. In the case of COSCI, the desired ground or excited state can be requested with -TargetState x.

• RMG

QMCPACK can use the HDF5 output of RMG DFT calculations. To generate this HDF5 output, set write_qmcpack_restart = "true" in the RMG input (file will be written to Waves/wave.out.h5). convert4qmc will read the data from this HDF5 file and generate *.structure.xml, *.wf{j,noj}.xml, and *.qmc.in-wf{j,noj}.xml. Pseudopotential files must be generated/moved manually by the user to X.qmcpp.xml, where X is the appropriate element symbol (PP filename/path can be changed in the Hamiltonian section of *.qmc.in-wf{j,noj}.xml).

convert4qmc -rmg wave.out.h5


### pw2qmcpack.x¶

pw2qmcpack.x is an executable that converts PWSCF wavefunctions from the Quantum ESPRESSO (QE) package to QMCPACK readable HDF5 format. This utility is built alongside the QE postprocessing utilities. This utility is written in Fortran90 and is distributed as a patch of the QE source code. The patch, as well as automated QE download and patch scripts, can be found in qmcpack/external_codes/quantum_espresso. Once built, we recommend also build QMCPACK with the QE_BIN option pointing to the build pw.x and pw2qmcpack.x directory. This will enable workflow tests to be run.

pw2qmcpack can be used in serial in small systems and should be used in parallel with large systems for best performance. The K_POINT gamma optimization is not supported.

Listing 74 Sample pw2qmcpack.x input file p2q.in
&inputpp
prefix     = 'bulk_silicon'
outdir     = './'
write_psir = .false.
/


This example will cause pw2qmcpack.x to convert wavefunctions saved from PWSCF with the prefix “bulk_silicon.” Perform the conversion via, for example:

mpirun -np 1 pw2qmcpack.x < p2q.in>& p2q.out


Because of the large plane-wave energy cutoffs in the pw.x calculation required by accurate PPs and the large system sizes of interest, one limitation of QE can be easily reached: that wf_collect=.true. results in problems of writing and loading correct plane-wave coefficients on disks by pw.x because of the 32 bit integer limits. Thus, pw2qmcpack.x fails to convert the orbitals for QMCPACK. Since the release of QE v5.3.0, the converter has been fully parallelized to overcome this limitation completely.

By setting wf_collect=.false. (by default .false. in v6.1 and before and .true. since v6.2), pw.x does not collect the whole wavefunction into individual files for each k-point but instead writes one smaller file for each processor. By running pw2qmcpack.x in the same parallel setup (MPI tasks and k-pools) as the last scf/nscf calculation with pw.x, the orbitals distributed among processors will first be aggregated by the converter into individual temporal HDF5 files for each k-pool and then merged into the final file. In large calculations, users should benefit from a significant reduction of time in writing the wavefunction by pw.x thanks to avoiding the wavefunction collection.

pw2qmcpack has been included in the test suite of QMCPACK (see instructions about how to activate the tests in Installing and patching Quantum ESPRESSO). There are tests labeled “no-collect” running the pw.x with the setting wf_collect=.false. The input files are stored at examples/solids/dft-inputs-polarized-no-collect. The scf, nscf, and pw2qmcpack runs are performed on 16, 12, and 12 MPI tasks with 16, 2, and 2 k-pools respectively.

### convertpw4qmc¶

Convertpw4qmc is an executable that reads xml from a plane wave based DFT code and produces a QMCPACK readable HDF5 format wavefunction. For the moment, this supports both QBox and Quantum Epresso

In order to save the wavefunction from QBox so that convertpw4qmc can work on it, one needs to add a line to the QBox input like

save -text -serial basename.sample


after the end of a converged dft calculation. This will write an ascii wavefunction file and will avoid QBox’s optimized parallel IO (which is not currently supported).

After the wavefunction file is written (basename.sample in this case) one can use convertpw4qmc as follows:

convertpw4qmc basename.sample -o qmcpackWavefunction.h5


This reads the Qbox wavefunction and performs the Fourier transform before saving to a QMCPACK eshdf format wavefunction. Currently multiple k-points are supported, but due to difficulties with the qbox wavefunction file format, the single particle orbitals do not have their proper energies associated with them. This means that when tiling from a primitive cell to a supercell, the lowest n single particle orbitals from all necessary k-points will be used. This can be problematic in the case of a metal and this feature should be used with EXTREME caution.

In the case of Quantum ESPRESSO, QE must be compiled with HDF support. If this is the case, then an eshdf file can be generated by targeting the data-file-schema.xml file generated in the output of Quantum ESPRESSO. For example, if one is running a calculation with outdir = ‘out’ and prefix=’Pt’ then the converter can be invoked as:

convertpw4qmc out/Pt.save/data-file-schema.xml -o qmcpackWavefunction.h5


Note that this method is insensitive to parallelization options given to Quantum ESPRESSO. Additionally, it supports noncollinear magnetism and can be used to generate wavefunctions suitable for qmcpack calculations with spin-orbit coupling.

### ppconvert¶

ppconvert is a utility to convert PPs between different commonly used formats. As with all operations on pseudopotentials, great care should be exercised when using this tool. The tool is not yet considered to be fully robust and converted potentials should be examined carefully. Please report any issues. Generally DFT-derived potentials should not be used with QMC. The main intended use for the converter is to convert potentials generated for QMC calculations into formats acceptable to DFT and quantum chemistry codes for trial wavefunction generation.

Currently it converts CASINO, FHI, UPF (generated by OPIUM), BFD, and GAMESS formats to several other formats including XML (QMCPACK) and UPF (QE). See all the formats via ppconvert -h.

For output formats requiring Kleinman-Bylander projectors, the atom will be solved with DFT if the projectors are not provided in the input formats. This requires providing reference states and often needs extra tuning for heavy elements. To avoid ghost states, the local channel can be changed via the --local_channel option. Ghost state considerations are similar to those of DFT calculations but could be worse if ghost states were not considered during the original PP construction. To make the self-consistent calculation converge, the density mixing parameter may need to be reduced via the --density_mix option. Note that the reference state should include only the valence electrons. One reference state should be included for each channel in the PP.

For example, for a sodium atom with a neon core, the reference state would be “1s(1).” --s_ref needs to include a 1s state, --p_ref needs to include a 2p state, --d_ref needs to include a 3d state, etc. If not specified, a corresponding state with zero occupation is added. If the reference state is chosen as the neon core, setting empty reference states “” is technically correct. In practice, reasonable reference states should be picked with care. For PP with semi-core electrons in the valence, the reference state can be long. For example, Ti PP has 12 valence electrons. When using the neutral atom state, --s_ref, --p_ref, and --d_ref are all set as “1s(2)2p(6)2s(2)3d(2).” When using an ionized state, the three reference states are all set as “1s(2)2p(6)2s(2)” or “1s(2)2p(6)2s(2)3d(0).”

Unfortunately, if the generated UPF file is used in QE, the calculation may be incorrect because of the presence of “ghost” states. Potentially these can be removed by adjusting the local channel (e.g., by setting --local_channel 1, which chooses the p channel as the local channel instead of d. For this reason, validation of UPF PPs is always required from the third row and is strongly encouraged in general. For example, check that the expected ionization potential and electron affinities are obtained for the atom and that dimer properties are consistent with those obtained by a quantum chemistry code or a plane-wave code that does not use the Kleinman-Bylander projectors.

### molden2qmc¶

molden2qmc is a tool used to convert molden files into an HDF5 file with the QMCPACK format. Molden2qmc is a single program that can use multiple different quantum chemistry codes. It is python code developed by Vladimir Konjkov originally for the CASINO code but then extended to QMCPACK. This tool can be found at https://github.com/gjohnson3/molden2qmc.git.

#### Using molden2qmc¶

General use of molden2qmc can be prompted by running molden2qmc.py and entering the corresponding quantum chemistry code number and the molden file name:

number corresponding to the quantum chemistry code used to produce this MOLDEN file:
0 -- TURBOMOLE
1 -- PSI4
2 -- CFOUR 2.0beta
3 -- ORCA 3.X - 4.X
4 -- DALTON2016
5 -- MOLPRO
6 -- NWCHEM
7 -- QCHEM 4.X


Use the --qmcpack flag to create the file as an hdf5 file, suitable for QMCPACK. Without the --qmcpack flag, the file will become a gwfn file for CASINO. Example: molden2qmc.py 5 n4.molden --qmcpack.

## Obtaining pseudopotentials¶

### Pseudopotentiallibrary.org¶

An open website collecting community developed and tested pseudopotentials for QMC and other many-body calculations is being developed at https://pseudopotentiallibrary.org. This site includes potentials in QMCPACK format and an increasing range of electronic structure and quantum chemistry codes. We recommend using potentials from this site if available and suitable for your science application.

### Opium¶

Opium is a pseudopotential generation code available from the website http://opium.sourceforge.net/. Opium can generate pseudopotentials with either Hartree-Fock or DFT methods. Once you have a useable pseudopotential param file (for example, Li.param), generate pseudopotentials for use in Quantum ESPRESSO with the upf format as follows:

This generates a UPF-formatted pseudopotential (Li.upf, in this case) for use in Quantum ESPRESSO. The pseudopotential conversion tool ppconvert can then convert UPF to FSAtom xml format for use in QMCPACK:

Listing 75 Convert UPF-formatted pseudopotential to FSAtom xml format
ppconvert --upf_pot Li.upf --xml Li.xml


### Burkatzki-Filippi-Dolg¶

Burkatzki et al. developed a set of energy-consistent pseudopotenitals for use in QMC [BFD07, BFD08], available at http://www.burkatzki.com/pseudos/index.2.html. To convert for use in QMCPACK, select a pseudopotential (choice of basis set is irrelevant to conversion) in GAMESS format and copy the ending (pseudopotential) lines beginning with(element symbol)-QMC GEN:

Listing 76 BFD Li pseudopotential in GAMESS format
Li-QMC GEN 2 1
3
1.00000000 1 5.41040609
5.41040609 3 2.70520138
-4.60151975 2 2.07005488
1
7.09172172 2 1.34319829


Save these lines to a file (here, named Li.BFD.gamess; the exact name may be anything as long as it is passed to ppconvert after –gamess_pot). Then, convert using ppconvert with the following:

Listing 77 Convert GAMESS-formatted pseudopotential to FSAtom xml format
ppconvert --gamess_pot Li.BFD.gamess --s_ref "2s(1)" --p_ref "2p(0)" --xml Li.BFD.xml

Listing 78 Convert GAMESS-formatted pseudopotential to Quantum ESPRESSO UPF format
ppconvert --gamess_pot Li.BFD.gamess --s_ref "2s(1)" --p_ref "2p(0)" --log_grid --upf Li.BFD.upf


### CASINO¶

The QMC code CASINO also makes available its pseudopotentials available at the website https://vallico.net/casinoqmc/pplib/. To use one in QMCPACK, select a pseudopotential and download its summary file (summary.txt), its tabulated form (pp.data), and (for ppconvert to construct the projectors to convert to Quantum ESPRESSO’s UPF format) a CASINO atomic wavefunction for each angular momentum channel (awfn.data_*). Then, to convert using ppconvert, issue the following command:

Listing 79 Convert CASINO-formatted pseudopotential to Quantum ESPRESSO UPF format
ppconvert --casino_pot pp.data --casino_us awfn.data_s1_2S --casino_up awfn.data_p1_2P --casino_ud awfn.data_d1_2D --upf Li.TN-DF.upf


QMCPACK can directly read in the CASINO-formated pseudopotential (pp.data), but four parameters found in the pseudopotential summary file must be specified in the pseudo element (l-local, lmax, nrule, cutoff)[see Pseudopotentials for details]:

Listing 80 XML syntax to use CASINO-formatted pseudopotentials in QMCPACK
<pairpot type="pseudo" name="PseudoPot" source="ion0" wavefunction="psi0" format="xml">
<pseudo elementType="Li" href="Li.pp.data" format="casino" l-local="s" lmax="2" nrule="2" cutoff="2.19"/>
<pseudo elementType="H" href="H.pp.data" format="casino" l-local="s" lmax="2" nrule="2" cutoff="0.5"/>
</pairpot>


### wftester¶

While not really a stand-alone application, wftester (short for “Wave Function Tester”) is a helpful tool for testing pre-existing and experimental estimators and observables. It provides the user with derived quantities from the Hamiltonian and wave function, but evaluated at a small set of configurations.

The wftester is implemented as a QMCDriver, so one invokes QMCPACK in the normal manner with a correct input XML, the difference being the addition of an additional qmc input block. This is the main advantage of this tool–it allows testing of realistic systems and realistic combinations of observables. It can also be invoked before launching into optimization, VMC, or DMC runs, as it is a valid <qmc> block.

As an example, the following code generates a random walker configuration and compares the trial wave function ratio computed in two different ways:

Listing 81 The following executes the wavefunction ratio test in “wftester”
<qmc method="wftester">
<parameter name="ratio">    yes    </parameter>
</qmc>


Here’s a summary of some of the tests provided:

• Ratio Test. Invoked with

<parameter name="ratio">yes</parameter>


This computes the implemented wave function ratio associated with a single-particle move using two different methods.

• Clone Test. Invoked with

<parameter name="clone">yes</parameter>


This checks the cloning of TrialWaveFunction, ParticleSet, Hamiltonian, and Walkers.

• Elocal Test. Invoked with

<parameter name="printEloc">yes</parameter>


For an input electron configuration (can be random), print the value of TrialWaveFunction, LocalEnergy, and all local observables for this configuration.

• Derivative Test. Invoked with

<parameter name="ratio">deriv</parameter>}


Computes electron gradients, laplacians, and wave function parameter derivatives using implemented calls and compares them to finite-difference results.

• Ion Gradient Test. Invoked with

<parameter name="source">ion0</parameter>


Calls the implemented evaluateGradSource functions and compares them against finite-difference results.

• “Basic Test”. Invoked with

<parameter name="basic">yes</parameter>


Performs ratio, gradient, and laplacian tests against finite-difference and direct computation of wave function values.

The output of the various tests will be to standard out or “wftest.000” after successful execution of qmcpack.

DIR

DIRAC, a relativistic ab initio electronic structure program, Release DIRAC19 (2019), written by A. S. P. Gomes, T. Saue, L. Visscher, H. J. \relax Aa. Jensen, and R. Bast, with contributions from I. A. Aucar, V. Bakken, K. G. Dyall, S. Dubillard, U. Ekström, E. Eliav, T. Enevoldsen, E. Faßhauer, T. Fleig, O. Fossgaard, L. Halbert, E. D. Hedegård, B. Heimlich–Paris, T. Helgaker, J. Henriksson, M. Iliaš, Ch. R. Jacob, S. Knecht, S. Komorovský, O. Kullie, J. K. Lærdahl, C. V. Larsen, Y. S. Lee, H. S. Nataraj, M. K. Nayak, P. Norman, G. Olejniczak, J. Olsen, J. M. H. Olsen, Y. C. Park, J. K. Pedersen, M. Pernpointner, R. di Remigio, K. Ruud, P. Sałek, B. Schimmelpfennig, B. Senjean, A. Shee, J. Sikkema, A. J. Thorvaldsen, J. Thyssen, J. van Stralen, M. L. Vidal, S. Villaume, O. Visser, T. Winther, and S. Yamamoto (available at http://dx.doi.org/10.5281/zenodo.3572669, see also http://www.diracprogram.org).

RMG

RMG, a real space multigrid DFT code, https://github.com/RMGDFT/rmgdft.

AAB+14

Kęstutis Aidas, Celestino Angeli, Keld L. Bak, Vebjørn Bakken, Radovan Bast, Linus Boman, Ove Christiansen, Renzo Cimiraglia, Sonia Coriani, Pål Dahle, Erik K. Dalskov, Ulf Ekström, Thomas Enevoldsen, Janus J. Eriksen, Patrick Ettenhuber, Berta Fernández, Lara Ferrighi, Heike Fliegl, Luca Frediani, Kasper Hald, Asger Halkier, Christof Hättig, Hanne Heiberg, Trygve Helgaker, Alf Christian Hennum, Hinne Hettema, Eirik Hjertenæs, Stinne Høst, Ida-Marie Høyvik, Maria Francesca Iozzi, Branislav Jansík, Hans Jørgen \relax Aa. Jensen, Dan Jonsson, Poul Jørgensen, Joanna Kauczor, Sheela Kirpekar, Thomas Kjærgaard, Wim Klopper, Stefan Knecht, Rika Kobayashi, Henrik Koch, Jacob Kongsted, Andreas Krapp, Kasper Kristensen, Andrea Ligabue, Ola B Lutnæs, Juan I. Melo, Kurt V. Mikkelsen, Rolf H. Myhre, Christian Neiss, Christian B. Nielsen, Patrick Norman, Jeppe Olsen, Jógvan Magnus H. Olsen, Anders Osted, Martin J. Packer, Filip Pawlowski, Thomas B. Pedersen, Patricio F. Provasi, Simen Reine, Zilvinas Rinkevicius, Torgeir A. Ruden, Kenneth Ruud, Vladimir V. Rybkin, Pawel Sałek, Claire C. M. Samson, Alfredo Sánchez de Merás, Trond Saue, Stephan P. A. Sauer, Bernd Schimmelpfennig, Kristian Sneskov, Arnfinn H. Steindal, Kristian O. Sylvester-Hvid, Peter R. Taylor, Andrew M. Teale, Erik I. Tellgren, David P. Tew, Andreas J. Thorvaldsen, Lea Thøgersen, Olav Vahtras, Mark A. Watson, David J. D. Wilson, Marcin Ziolkowski, and Hans Ågren. The Dalton quantum chemistry program system. WIREs Comput. Mol. Sci., 4(3):269–284, 2014. doi:10.1002/wcms.1172.

ApraBdJ+20

E. Aprá, E. J. Bylaska, W. A. de Jong, N. Govind, K. Kowalski, T. P. Straatsma, M. Valiev, H. J. J. van Dam, Y. Alexeev, J. Anchell, V. Anisimov, F. W. Aquino, R. Atta-Fynn, J. Autschbach, N. P. Bauman, J. C. Becca, D. E. Bernholdt, K. Bhaskaran-Nair, S. Bogatko, P. Borowski, J. Boschen, J. Brabec, A. Bruner, E. Cauët, Y. Chen, G. N. Chuev, C. J. Cramer, J. Daily, M. J. O. Deegan, T. H. Dunning, M. Dupuis, K. G. Dyall, G. I. Fann, S. A. Fischer, A. Fonari, H. Früchtl, L. Gagliardi, J. Garza, N. Gawande, S. Ghosh, K. Glaesemann, A. W. Götz, J. Hammond, V. Helms, E. D. Hermes, K. Hirao, S. Hirata, M. Jacquelin, L. Jensen, B. G. Johnson, H. Jónsson, R. A. Kendall, M. Klemm, R. Kobayashi, V. Konkov, S. Krishnamoorthy, M. Krishnan, Z. Lin, R. D. Lins, R. J. Littlefield, A. J. Logsdail, K. Lopata, W. Ma, A. V. Marenich, J. Martin del Campo, D. Mejia-Rodriguez, J. E. Moore, J. M. Mullin, T. Nakajima, D. R. Nascimento, J. A. Nichols, P. J. Nichols, J. Nieplocha, A. Otero-de-la-Roza, B. Palmer, A. Panyala, T. Pirojsirikul, B. Peng, R. Peverati, J. Pittner, L. Pollack, R. M. Richard, P. Sadayappan, G. C. Schatz, W. A. Shelton, D. W. Silverstein, D. M. A. Smith, T. A. Soares, D. Song, M. Swart, H. L. Taylor, G. S. Thomas, V. Tipparaju, D. G. Truhlar, K. Tsemekhman, T. Van Voorhis, Á. Vázquez-Mayagoitia, P. Verma, O. Villa, A. Vishnu, K. D. Vogiatzis, D. Wang, J. H. Weare, M. J. Williamson, T. L. Windus, K. Woliński, A. T. Wong, Q. Wu, C. Yang, Q. Yu, M. Zacharias, Z. Zhang, Y. Zhao, and R. J. Harrison. Nwchem: past, present, and future. The Journal of Chemical Physics, 152(18):184102, 2020. doi:10.1063/5.0004997.

BFD07

M. Burkatzki, C. Filippi, and M. Dolg. Energy-consistent pseudopotentials for quantum monte carlo calculations. The Journal of Chemical Physics, 126(23):–, 2007. doi:10.1063/1.2741534.

BFD08

M. Burkatzki, Claudia Filippi, and M. Dolg. Energy-consistent small-core pseudopotentials for 3d-transition metals adapted to quantum monte carlo calculations. The Journal of Chemical Physics, 129(16):–, 2008. doi:10.1063/1.2987872.

FAH+14

Filipp Furche, Reinhart Ahlrichs, Christof Hättig, Wim Klopper, Marek Sierka, and Florian Weigend. Turbomole. WIREs Computational Molecular Science, 4(2):91–100, 2014. doi:10.1002/wcms.1162.

GAG+19(1,2)

Yann Garniron, Thomas Applencourt, Kevin Gasperich, Anouar Benali, Anthony Ferté, Julien Paquier, Barthélémy Pradines, Roland Assaraf, Peter Reinhardt, Julien Toulouse, Pierrette Barbaresco, Nicolas Renon, Grégoire David, Jean-Paul Malrieu, Mickaël Véril, Michel Caffarel, Pierre-François Loos, Emmanuel Giner, and Anthony Scemama. Quantum package 2.0: an open-source determinant-driven suite of programs. Journal of Chemical Theory and Computation, 15(6):3591–3609, 2019. doi:10.1021/acs.jctc.9b00176.

MTDN05

A. Ma, M. D. Towler, N. D. Drummond, and R. J. Needs. Scheme for adding electron–nucleus cusps to gaussian orbitals. The Journal of Chemical Physics, 122(22):224322, 2005. doi:10.1063/1.1940588.

MCH+20

Devin A. Matthews, Lan Cheng, Michael E. Harding, Filippo Lipparini, Stella Stopkowicz, Thomas-C. Jagau, Péter G. Szalay, Jürgen Gauss, and John F. Stanton. Coupled-cluster techniques for computational chemistry: the cfour program package. The Journal of Chemical Physics, 152(21):214108, 2020. doi:10.1063/5.0004837.

Nee18

Frank Neese. Software update: the orca program system, version 4.0. WIREs Computational Molecular Science, 8(1):e1327, 2018. doi:10.1002/wcms.1327.

SBB+93(1,2)

Michael W. Schmidt, Kim K. Baldridge, Jerry A. Boatz, Steven T. Elbert, Mark S. Gordon, Jan H. Jensen, Shiro Koseki, Nikita Matsunaga, Kiet A. Nguyen, Shujun Su, Theresa L. Windus, Michel Dupuis, and John A. Montgomery. General atomic and molecular electronic structure system. Journal of Computational Chemistry, 14(11):1347–1363, 1993. doi:10.1002/jcc.540141112.

SGE+15

Yihan Shao, Zhengting Gan, Evgeny Epifanovsky, Andrew T.B. Gilbert, Michael Wormit, Joerg Kussmann, Adrian W. Lange, Andrew Behn, Jia Deng, Xintian Feng, Debashree Ghosh, Matthew Goldey, Paul R. Horn, Leif D. Jacobson, Ilya Kaliman, Rustam Z. Khaliullin, Tomasz Kuś, Arie Landau, Jie Liu, Emil I. Proynov, Young Min Rhee, Ryan M. Richard, Mary A. Rohrdanz, Ryan P. Steele, Eric J. Sundstrom, H. Lee Woodcock III, Paul M. Zimmerman, Dmitry Zuev, Ben Albrecht, Ethan Alguire, Brian Austin, Gregory J. O. Beran, Yves A. Bernard, Eric Berquist, Kai Brandhorst, Ksenia B. Bravaya, Shawn T. Brown, David Casanova, Chun-Min Chang, Yunqing Chen, Siu Hung Chien, Kristina D. Closser, Deborah L. Crittenden, Michael Diedenhofen, Robert A. DiStasio Jr., Hainam Do, Anthony D. Dutoi, Richard G. Edgar, Shervin Fatehi, Laszlo Fusti-Molnar, An Ghysels, Anna Golubeva-Zadorozhnaya, Joseph Gomes, Magnus W.D. Hanson-Heine, Philipp H.P. Harbach, Andreas W. Hauser, Edward G. Hohenstein, Zachary C. Holden, Thomas-C. Jagau, Hyunjun Ji, Benjamin Kaduk, Kirill Khistyaev, Jaehoon Kim, Jihan Kim, Rollin A. King, Phil Klunzinger, Dmytro Kosenkov, Tim Kowalczyk, Caroline M. Krauter, Ka Un Lao, Adèle D. Laurent, Keith V. Lawler, Sergey V. Levchenko, Ching Yeh Lin, Fenglai Liu, Ester Livshits, Rohini C. Lochan, Arne Luenser, Prashant Manohar, Samuel F. Manzer, Shan-Ping Mao, Narbe Mardirossian, Aleksandr V. Marenich, Simon A. Maurer, Nicholas J. Mayhall, Eric Neuscamman, C. Melania Oana, Roberto Olivares-Amaya, Darragh P. O’Neill, John A. Parkhill, Trilisa M. Perrine, Roberto Peverati, Alexander Prociuk, Dirk R. Rehn, Edina Rosta, Nicholas J. Russ, Shaama M. Sharada, Sandeep Sharma, David W. Small, Alexander Sodt, Tamar Stein, David Stück, Yu-Chuan Su, Alex J.W. Thom, Takashi Tsuchimochi, Vitalii Vanovschi, Leslie Vogt, Oleg Vydrov, Tao Wang, Mark A. Watson, Jan Wenzel, Alec White, Christopher F. Williams, Jun Yang, Sina Yeganeh, Shane R. Yost, Zhi-Qiang You, Igor Ying Zhang, Xing Zhang, Yan Zhao, Bernard R. Brooks, Garnet K.L. Chan, Daniel M. Chipman, Christopher J. Cramer, William A. Goddard III, Mark S. Gordon, Warren J. Hehre, Andreas Klamt, Henry F. Schaefer III, Michael W. Schmidt, C. David Sherrill, Donald G. Truhlar, Arieh Warshel, Xin Xu, Alán Aspuru-Guzik, Roi Baer, Alexis T. Bell, Nicholas A. Besley, Jeng-Da Chai, Andreas Dreuw, Barry D. Dunietz, Thomas R. Furlani, Steven R. Gwaltney, Chao-Ping Hsu, Yousung Jung, Jing Kong, Daniel S. Lambrecht, WanZhen Liang, Christian Ochsenfeld, Vitaly A. Rassolov, Lyudmila V. Slipchenko, Joseph E. Subotnik, Troy Van Voorhis, John M. Herbert, Anna I. Krylov, Peter M.W. Gill, and Martin Head-Gordon. Advances in molecular quantum chemistry contained in the q-chem 4 program package. Molecular Physics, 113(2):184–215, 2015. doi:10.1080/00268976.2014.952696.

SBB+18(1,2)

Qiming Sun, Timothy C. Berkelbach, Nick S. Blunt, George H. Booth, Sheng Guo, Zhendong Li, Junzi Liu, James D. McClain, Elvira R. Sayfutyarova, Sandeep Sharma, Sebastian Wouters, and Garnet Kin-Lic Chan. Pyscf: the python-based simulations of chemistry framework. Wiley Interdisciplinary Reviews: Computational Molecular Science, 8(1):n/a–n/a, 2018. doi:10.1002/wcms.1340.

TSP+12

Justin M. Turney, Andrew C. Simmonett, Robert M. Parrish, Edward G. Hohenstein, Francesco A. Evangelista, Justin T. Fermann, Benjamin J. Mintz, Lori A. Burns, Jeremiah J. Wilke, Micah L. Abrams, Nicholas J. Russ, Matthew L. Leininger, Curtis L. Janssen, Edward T. Seidl, Wesley D. Allen, Henry F. Schaefer, Rollin A. King, Edward F. Valeev, C. David Sherrill, and T. Daniel Crawford. Psi4: an open-source ab initio electronic structure program. WIREs Computational Molecular Science, 2(4):556–565, 2012. doi:10.1002/wcms.93.

WKK+12

Hans-Joachim Werner, Peter J. Knowles, Gerald Knizia, Frederick R. Manby, and Martin Schütz. Molpro: a general-purpose quantum chemistry program package. WIREs Computational Molecular Science, 2(2):242–253, 2012. doi:10.1002/wcms.82.