MC-PDFT

Multiconfiguration pair-density functional theory (MC-PDFT) is a cost-effective post-SCF method which is able to recover the missing dynamic correlation from multiconfigurational wave functions generated through multireference methods such as CASCI or CASSCF. MC-PDFT computes a correct energy of a given reference wave function using an energy expression which contains a on-top energy functional term which depends on both the wave function’s density and on-top pair density. This approach adds minimal overhead cost to the reference multireference method while obtaining accuracy which rivals more traditional (and expensive) multireference perturbation theories such as CASPT2 or NEVPT2. Our group continues to develop MC-PDFT to tackle a wide variety of problems in photochemistry, photodynamics, catalysis, and biochemistry and integrate MC-PDFT with our automated active space selection scheme (DVS) and efficient multireference wave function ansatz (LASSCF and DMET).

The MC-PDFT program is available in several packages(Open-Molcas, Gamess, PySCF and SHARC-md) as described below.

1. Pyscf-forge

Developers: The MC-PDFT module in PySCF-forge has been developed by:

• Matthew R Hermes (University of Chicago)
• Dayou Zhang (University of Minnesota)
• Aleksandr Lykhin (University of Chicago)
• Thais R Scott (University of Chicago)
• Matthew R Hennefarth (University of Chicago)

Features:

• MC-PDFT total electronic energy calculations for wave functions of various types.
  • CASCI
  • CASSCF
  • State-averaged CASSCF (including “mixed” solver with different spins and/or point groups)
• Multi-state Extensions of MC-PDFT
  • Extended multi-state MC-PDFT (XMS-PDFT): Faraday Discuss 2020, 224, 348-372
  • Compressed multi-state MC-PDFT (CMS-PDFT): JCTC 2020, 16, 7444
  • Linearized PDFT (L-PDFT) (including “mixed solver with different spins and/or point groups”): JCTC 2023, 19, 3172
• On-the-fly generation of on-top density functionals from underlying KS-DFT ‘LDA’ or ‘GGA’ exchange-correlation functionals as defined in Libxc.
  • Translated functionals: JCTC 2014, 10, 3669
  • Fully-translated functionals: JCTC 2015, 11, 4077
  • Global hybrid functionals: JPCL 2020, 11, 10158 and JCTC 2020, 16, 2274
  • Notes:
    1. Translation of ‘meta’ KS-DFT functionals which depend on the kinetic energy density and/or Laplacian is not supported.
    2. Range-separated hybrid on-top functionals are not supported.
    3. Translation of functionals defined as global hybrids at the Libxc or PySCF level is not supported, except for ‘tPBEo’ and ‘ftPBE0’.
• Additional properties
  • Decomposition of total electronic energy into core, Coulomb, on-top components
  • Analytical nuclear gradients (non-hybrid functionals only) for:
    1. Single-state CASSCF wave function: JCTC 2018, 14, 126
    2. State-averaged CASSCF wave functions: JCP 2020, 153, 014106
    3. CMS-PDFT: Mol Phys 2022, 120
    4. L-PDFT J Chem Theory Comput, 2024, 9, 20
  • Permanent electric dipole moment (non-hybrid functionals only) for:
    1. Single-state CASSCF wave function: JCTC 2021, 17, 7586
    2. State-averaged CASSCF wave functions
    3. CMS-PDFT
  • Transition electric dipole moment (non-hybrid functionals only) for:
    1. CMS-PDFT
• Multi-configuration density-coherence functional theory (MC-DCFT) total energy: JCTC 2021, 17, 2775

License: PySCF and PySCF-forge are both licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

2. OpenMolcas

See: https://comp.chem.umn.edu/openmolcas

3. GAMESS

See: https://comp.chem.umn.edu/MC-PDFT_in_GAMESS