1.1. OpenMolcas Website
OpenMolcas is a quantum chemistry package available at
https://gitlab.com/Molcas/OpenMolcas
The OpenMolcas online manual is available at
Website: https://molcas.gitlab.io/OpenMolcas/sphinx
PDF: https://molcas.gitlab.io/OpenMolcas/Manual.pdf
1.2. Reference
The citation for OpenMolcas is the following:
"OpenMolcas: From Source Code to Insight," I. F. Galván, M. Vacher, A. Alavi, C. Angeli, J. Autschbach, J. J. Bao, S. I. Bokarev, N. A. Bogdanov, R. K. Carlson, L. F. Chibotaru, J. Creutzberg, N. Dattani, M. G. Delcey, S. S. Dong, A. Dreuw, L. Freitag, L. M. Frutos, L. Gagliardi, F. Gendron, A. Giussani, L. González, G. Grell, M. Guo, C. E. Hoyer , M. Johansson, E. Källman, S. Keller, S. Knecht, G. Kovacevic, G. Li Manni, M. Lundberg, Y. Ma, S. Mai, J. P. Malhado, P. Å. Malmqvist, P. Marquetand, S. A. Mewes, J. Norell, M. Olivucci, , M. Oppel, Q. M. Phung, K. Pierloot, F. Plasser, M. Reiher, A. M. Sand, I. Schapiro, P. Sharma, L. K. Sørensen, C. Stein, D. G. Truhlar, M. Ugandi, L. Ungur, A. Valentini, S. Vancoillie, V. Veryazov, P.-O. Widmark, S. Wouters, J. P. Zobel, and R. Lindh, Journal of Chemical Theory and Computation, 15, 5925-5964 (2019). doi.org/10.1021/acs.jctc.9b00532
OpenMolcas evolved from Molcas. The final version of Molcas was 8.2, and it was described in the following article:
"Molcas 8: New Capabilities for Multiconfigurational Quantum Chemical Calculations across the Periodic Table," F. Aquilante, J. Autschbach, R. K. Carlson, L. Chibotaru, M. G. Delcey, L. De Vico, I. F. Galván, N. Ferré, L. M. Frutos, L. Gagliardi, M. Garavelli, A. Giussani, C. E. Hoyer, G. Li Manni, H. Lischka, D. Ma, P.-Å. Malmqvist, T. Müller, A. Nenov, M. Olivucci, T. B. Pedersen , D. Peng, F. Plasser, B. Pritchard, M. Reiher, I. Rivalta, I. Schapiro, J. Segarra-Martí, M. Stenrup, D. G. Truhlar, L. Ungur, A. Valentini, S. Vancoillie, V. Veryazov, V. P. Vysotskiy, O. Weingart, F. Zapata, R. Lindh, Journal of Computational Chemistry 37, 506-541 (2016). doi.org/10.1002/jcc.24221
*Minnesota coauthors (at Minnesota at the time the work was done) of Molcas 8.2 are R. K. Carlson, L. Gagliardi, M. Hermes, C. E. Hoyer, G. Li Manni, D. Ma, and D. G. Truhlar.
1.3. libxc Capability
The OpenMOLCAS master branch was updated on January 26, 2022 with respect to some syntax changes associated with MC-PDFT calculations. This was done in order to enable the use of translation or full translation of any LSDA or GA (i.e., GGA or NGA) that is in libxc. As of this update, such MC-PDFT calculations will prefix the KS-DFT functionals with T: or FT: (for example, the previous syntax TPBE becomes T:PBE). New MC-PDFT functionals that are translated or fully translated from KS-DFT functionals no longer need to be hardcoded into the program provided that the LSDA or GA is available in libxc.
OpenMolcas has all or most of the capabilites described in that article plus several new ones contributed by many workers at many institutions. At Minnesota we have made several enhancements beyond what is in version 8.2.
We list the Minnesota enhancements of OpenMolcas that are fully available from the Gitlab site.
2.1.1. Introduction to Theory
Multiconfiguration pair-density functional theory (MC-PDFT) is a post-MCSCF method that evaluates the energy of a state with on-top pair-density function theory.
Readers may refer to the two following references for the details of the theory.
"Multiconfiguration Pair-Density Functional Theory," G. Li Manni, R. K. Carlson, S. Luo, D. Ma, J. Olsen, D. G. Truhlar, and L. Gagliardi, Journal of Chemical Theory and Computation 10, 3669-3680 (2014). doi.org/10.1021/ct500483t
"Multiconfiguration Pair-Density Functional Theory: A New Way to Treat Strongly Correlated Systems," L. Gagliardi, D. G. Truhlar, G. Li Manni, R. K. Carlson, C. E. Hoyer, and J. L. Bao, Accounts of Chemical Research 50, 66-73 (2017). doi.org/10.1021/acs.accounts.6b00471
In addition, we provide a description of MC-PDFT capabilities in OpenMolcas (as of 2018 November 9) and some input examples.
2.1.2. MC-PDFT Reference Wave Functions
The reference wave function for a MC-PDFT calculation include state-averaged or state-specific CASSCF, RASSCF, GASSCF, CAS-CI, RAS-CI, and GAS-CI wave functions.
MC-PDFT can be used in conjunction with the density matrix renormalization group (DMRG) method. For DMRG-PDFT calculations, an interface between OpenMolcas and QCMaquis (https://gitlab.com/qc-maquis/) is required. A DMRG-PDFT sample input file for N_{2} molecule with symmetry is shown here. Examples of DMRG-PDFT calculations are given in the following references:
"Density Matrix Renormalization Group Pair-Density Functional Theory (DMRG-PDFT): Singlet-Triplet Gaps in Polyacenes and Polyacetylenes," P. Sharma, V. Bernales, S. Knecht, D. G. Truhlar, and L. Gagliardi, Chemical Science 10, 1716-1723 (2019). doi.org/10.1039/C8SC03569E
"Multiconfiguration Pair-Density Functional Theory for Iron Porphyrin with CAS, RAS, and DMRG Active Spaces," C. Zhou, L. Gagliardi, and D. G. Truhlar, Journal of Physical Chemistry A 123, 3389-3394 (2019). doi.org/10.1021/acs.jpca.8b12479
"Magnetic Coupling in a Tris-hydroxo-Bridged Chromium Dimer Occurs Through Ligand Mediated Superexchange in Conjunction with Through- Space Coupling," P. Sharma, D. G. Truhlar, and L. Gagliardi, Journal of the American Chemical Society 142, 16644-16650 (2020). doi.org/10.1021/jacs.0c06399
A zip file containing sample input files and orbitals for the calculations in the third reference is available here.
2.1.3. MC-PDFT On-Top Functionals
The following on-top density functionals are available for MC-PDFT: tLSDA, ftLSDA, tPBE, ftPBE, trevPBE, ftrevPBE, tBLYP, ftBLYP, tOPBE, and ftOPBE.
2.1.4. A Special Note
Please use the keyword 'NoGr' (No Gradient) to avoid additional cost to compute gradients if gradients are not needed.
When several electronic states are closely coupled, due to near degeneracy or close to a conical intersection, the states should be treated by a model-space diagonalization, as in multi-configuration quasidegenerate perturbation theory. The multistate pair-density functional theory (MS-PDFT) is a category of methods that produce the right topology of potential energy surfaces. (SI-PDFT done by Andrew M. Sand, XMS-PDFT and CMS-PDFT done by Jie J. Bao)
The SI-PDFT is the first MS-PDFT method developed. This method is described in the following reference:
"State-Interaction Pair-Density Functional Theory," A. M. Sand, C. E. Hoyer, D. G. Truhlar, and L. Gagliardi, The Journal of Chemical Physics 149, 024106 (2018). doi.org/10.1063/1.5036727
The XMS-PDFT method is the most efficient MS-PDFT method. This method is described in the reference below. The manual of the XMS-PDFT method can be found here. Note that there are certain cases where XMS-PDFT can fail. See Section S3 of the supplementary file for the following reference.
"Multi-state pair-density functional theory," J. J. Bao, C. Zhou, Z. Varga, S. Kanchanakungwankul, L. Gagliardi, D. G. Truhlar, Faraday Discussions 224, 348-372 (2020). doi.org/10.1039/D0FD00037J
The CMS-PDFT method is the most robust MS-PDFT method and is the recommended one to use. This method is described in the reference below. The manual of the CMS-PDFT method can be found here.
"Compressed-state multistate pair-density functional theory," J. J. Bao, C. Zhou, D. G. Truhlar, The Journal of Chemical Theory and Computation 16, 7444-7452 (2020). doi.org/10.1021/acs.jctc.0c00908
2.3.1. Fast analytic gradients of MC-PSDFT and CMS-PDFT in OpenMolcas
Fast analytic gradients for MC-PDFT (Section 2.3.2), SA-PDFT (Section 2.3.2), and CMS-PDFT (Section 2.3.3) are all available in the OpenMolcas repository as of January 1st, 2022, in commit SHAR1=b99d61a3, or later. (See this page for the history of SHAR1 numbers.)
More details about the acceleration can be found in this pdf document.
2.3.2. MC-PDFT Analytic Gradient
The gradient of MC-PDFT obtained from a single-state (SS) reference wave function is different from that obtained from a state in a state-averaged (SA) calculation. (SS-PDFT gradient by Andrew M. Sand, SA-PDFT gradient and the density fitting by Thais R. Scott)
State-specific CASSCF-PDFT analytic gradients as described in:
"Analytic Gradients for Complete Active Space Pair-Density Functional Theory," A. M. Sand, C. E. Hoyer, K. Sharkas, K. M. Kidder, R. Lindh, D. G. Truhlar, and L. Gagliardi, Journal of Chemical Theory and Computation 14, 126-138 (2018). doi.org/10.1021/acs.jctc.7b00967
State-average CASSCF-PDFT analytic gradients as described in:
"Analytic Gradients for State-Averaged Multiconfiguration Pair-Density Functional Theory," T. R. Scott, M. R. Hermes, A. M. Sand, M. S. Oakley, D. G. Truhlar and L. Gagliardi, The Journal of Chemical Physics 153, 014106 (2020). https://doi.org/10.1063/5.0007040
You may find a sample input for optimizing the geometry of ethylene using MC-PDFT.
MC-PDFT analytic gradient can also be calculated with density fitting. The details are described in the following paper:
"Analytic Gradients for Multiconfiguration Pair-Density Functional Theory with Density Fitting: Development and Application to Geometry Optimization in the Ground and Excited States," T. R. Scott, M. S. Oakley, M. R. Hermes, A. M. Sand, R. Lindh, D. G. Truhlar and L. Gagliardi,The Journal of Chemical Physics 154, 074108 (2021). https://doi.org/10.1063/5.0039258
2.3.3. CMS-PDFT Analytic Gradient
The CMS-PDFT analytic gradient starting with an SA-CASSCF calculations is now available on OpenMolcas. CMS-PDFT analytic gradient calculation does not require additional keywords and will be triggered when one uses the keywords for CMS-PDFT calculation together with the keyword for MC-PDFT gradient calculation. CMS-PDFT analytic gradient currently does not support density fitting.
You may find a sample input and the key information of the corresponding output for the gradient calculation with CMS-PDFT for LiF.
The details of the CMS-PDFT analytic gradient can be found in the following paper:
"Analytical Gradient for Compressed-State Multistate Pair-Density Functional Theory" J. J. Bao, M. R. Hermes, T. R. Scott, A. M. Sand, R. Lindh, L. Gagliardi and D. G. Truhlar, Wolniewicz Special Issue of Molecular Physics. https://doi.org/10.1080/00268976.2022.2110534
The user can run a natural transition orbital calculation in the RASSI module in OpenMolcas. (by Jie J. Bao)
For methodology, usage, keywords and examples, one may refer to the manual for the NTO calculation in the RASSI module.
2.5.1. Introduction
The user can scale the exchange terms (by a factor of f_exch) and/or the correlation term (by a factor of f_corr) for a density functionals. This scaling works for KS-DFT calculations and MC-PDFT calculations that use translated or fully translated functionals. (by Sijia S. Dong)
2.5.2. Keyword and Usage
Keyword: DFCF
Usage: DFCF=f_exch f_corr
Default: DFCF=1.0 1.0
*Note: By setting f_exch as 1.25 and f_corr as 0.5 one can get a High Local Exchange (HLE) density functional
2.5.3. Examples
Example 1:
&SCF;
KSDFT=BLYP;
DFCF=1.0 0.9
Example 2:
&MCPDFT;
KSDFT=TPBE;
DFCF=1.25 0.5
Orbital contributions of properties can be calculated by the SEWARD module for all orbitals (including virtuals), such as orbital moments. Controlled by the new keyword ORBAll in &SEWARD. (by Sijia S. Dong)
The MC-PDFT module prints out individual energy components of the MC-PDFT total energy by default. (by Prachi Sharma)
J. J. Bao, S. S. Dong, C. E. Hoyer, A. Sand, T. Scott, K. Sharkas, P. Sharma, C. Zhou, L. Gagliardi, and D. G. Truhlar.