Computing Reaction Kinetics with MC-PDFT–OPESf: Combining Multireference Electronic Structure Theory and Enhanced Sampling

Seal, Aniruddha; Gagliardi, Laura; Ferguson, Andrew L.

doi:10.1021/acs.jpclett.5c02966

Computing Reaction Kinetics with MC-PDFT–OPESf: Combining Multireference Electronic Structure Theory and Enhanced Sampling

Journal Article · Mon Oct 27 04:00:00 EDT 2025 · Journal of Physical Chemistry Letters

DOI:https://doi.org/10.1021/acs.jpclett.5c02966· OSTI ID:3005503

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University of Chicago, IL (United States)

Accurate rate constants are crucial for understanding and optimizing catalytic reactions mediated by enzymes, metalloproteins, and heterogeneous catalysts. These systems frequently present a dual computational challenge. Multiconfigurational reaction sites require multireference techniques for the accurate treatment of the electronic structure, and high activation barriers prevent efficient sampling of unbiased reactive transitions. In this work, we combine multiconfiguration pair-density functional theory (MC-PDFT) as an accurate and efficient multireference electronic structure method with on-the-fly probability-enhanced sampling flooding (OPESf) as an enhanced sampling method capable of accelerating reactive transitions. We demonstrate the approach on the Diels–Alder [4+2] cycloaddition between cis-butadiene and ethene as a reaction characterized by a large activation barrier and multireference character. MC-PDFT–OPESf provides reaction rates in agreement with experiments at a fraction of the computational cost required by conventional unbiased ab initio calculations. Here, we propose MC-PDFT–OPESf as an efficient approach for computing kinetics in strongly correlated molecular systems.

View Accepted Manuscript (DOE)

Research Organization:: University of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

Grant/Contract Number:: SC0023383

OSTI ID:: 3005503

Journal Information:: Journal of Physical Chemistry Letters, Journal Name: Journal of Physical Chemistry Letters Journal Issue: 44 Vol. 16; ISSN 1948-7185

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (57)

The Complete Active Space Self-Consistent Field Method and its Applications in Electronic Structure Calculations Roos, Björn O. Advances in Chemical Physics https://doi.org/10.1002/9780470142943.ch7	book	January 1987
Bifurcations on Potential Energy Surfaces of Organic Reactions Ess, Daniel H.; Wheeler, Steven E.; Iafe, Robert G. Angewandte Chemie International Edition, Vol. 47, Issue 40 https://doi.org/10.1002/anie.200800918	journal	September 2008
Protein Flexibility and Dissociation Pathway Differentiation Can Explain Onset of Resistance Mutations in Kinases** Shekhar, Mrinal; Smith, Zachary; Seeliger, Markus A. Angewandte Chemie International Edition, Vol. 61, Issue 28 https://doi.org/10.1002/anie.202200983	journal	May 2022
The Diels–Alder Reaction of Ethene and 1,3‐Butadiene: An Extended Multireference ab initio Investigation Lischka, Hans; Ventura, Elizete; Dallos, Michal ChemPhysChem, Vol. 5, Issue 9 https://doi.org/10.1002/cphc.200400104	journal	September 2004
E−Z Isomerization in Guanidine: Second‐order Saddle Dynamics, Non‐statisticality, and Time‐frequency Analysis Rashmi, Richa; Yadav, Pankaj Kumar; Seal, Aniruddha ChemPhysChem, Vol. 24, Issue 2 https://doi.org/10.1002/cphc.202200640	journal	November 2022
Active space and basis set effects in CASPT2 models of the 1,3‐butadiene‐ethene cycloaddition and the 1,3‐butadiene dimerization Scarborough, David L. A.; Kobayashi, Rika; Thompson, Christopher D. International Journal of Quantum Chemistry, Vol. 115, Issue 15 https://doi.org/10.1002/qua.24933	journal	April 2015
P y SCF: the Python-based simulations of chemistry framework : The PySCF program Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1 https://doi.org/10.1002/wcms.1340	journal	September 2017
Direct Dynamics Method for the Calculation of Reaction Rates Truhlar, Donald G. The Reaction Path in Chemistry: Current Approaches and Perspectives https://doi.org/10.1007/978-94-015-8539-2_10	book	January 1995
A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach Roos, Björn O.; Taylor, Peter R.; Sigbahn, Per E. M. Chemical Physics, Vol. 48, Issue 2 https://doi.org/10.1016/0301-0104(80)80045-0	journal	May 1980
PLUMED: A portable plugin for free-energy calculations with molecular dynamics Bonomi, Massimiliano; Branduardi, Davide; Bussi, Giovanni Computer Physics Communications, Vol. 180, Issue 10 https://doi.org/10.1016/j.cpc.2009.05.011	journal	October 2009
PLUMED 2: New feathers for an old bird Tribello, Gareth A.; Bonomi, Massimiliano; Branduardi, Davide Computer Physics Communications, Vol. 185, Issue 2 https://doi.org/10.1016/j.cpc.2013.09.018	journal	February 2014
Kinetic View of Enzyme Catalysis from Enhanced Sampling QM/MM Simulations Ray, Dhiman; Das, Sudip; Raucci, Umberto Journal of Chemical Information and Modeling, Vol. 64, Issue 9 https://doi.org/10.1021/acs.jcim.4c00475	journal	April 2024
Exploration vs Convergence Speed in Adaptive-Bias Enhanced Sampling Invernizzi, Michele; Parrinello, Michele Journal of Chemical Theory and Computation, Vol. 18, Issue 6 https://doi.org/10.1021/acs.jctc.2c00152	journal	May 2022
Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection King, Daniel S.; Hermes, Matthew R.; Truhlar, Donald G. Journal of Chemical Theory and Computation, Vol. 18, Issue 10 https://doi.org/10.1021/acs.jctc.2c00630	journal	September 2022
Rare Event Kinetics from Adaptive Bias Enhanced Sampling Ray, Dhiman; Ansari, Narjes; Rizzi, Valerio Journal of Chemical Theory and Computation, Vol. 18, Issue 11 https://doi.org/10.1021/acs.jctc.2c00806	journal	October 2022
Kinetics from Metadynamics: Principles, Applications, and Outlook Ray, Dhiman; Parrinello, Michele Journal of Chemical Theory and Computation, Vol. 19, Issue 17 https://doi.org/10.1021/acs.jctc.3c00660	journal	August 2023
Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment Choudhury, Arpan; Santra, Supriyo; Ghosh, Debashree Journal of Chemical Theory and Computation, Vol. 20, Issue 12 https://doi.org/10.1021/acs.jctc.4c00027	journal	June 2024
Assessing Generic Collective Variables for Determining Reaction Rates in Metadynamics Simulations Fu, Christopher D.; Oliveira, Luiz F. L.; Pfaendtner, Jim Journal of Chemical Theory and Computation, Vol. 13, Issue 3 https://doi.org/10.1021/acs.jctc.7b00038	journal	February 2017
Analytic Gradients for Complete Active Space Pair-Density Functional Theory Sand, Andrew M.; Hoyer, Chad E.; Sharkas, Kamal Journal of Chemical Theory and Computation, Vol. 14, Issue 1 https://doi.org/10.1021/acs.jctc.7b00967	journal	December 2017
Application of Multiconfiguration Pair-Density Functional Theory to the Diels–Alder Reaction Mitchell, Erica C.; Scott, Thais R.; Bao, Jie J. The Journal of Physical Chemistry A, Vol. 126, Issue 47 https://doi.org/10.1021/acs.jpca.2c06433	journal	November 2022
New Approach for Investigating Reaction Dynamics and Rates with Ab Initio Calculations Fleming, Kelly L.; Tiwary, Pratyush; Pfaendtner, Jim The Journal of Physical Chemistry A, Vol. 120, Issue 2 https://doi.org/10.1021/acs.jpca.5b10667	journal	January 2016
Subsurface Nitrogen Dissociation Kinetics in Lithium Metal from Metadynamics Ludwig, Thomas; Singh, Aayush R.; Nørskov, Jens K. The Journal of Physical Chemistry C, Vol. 124, Issue 48 https://doi.org/10.1021/acs.jpcc.0c09108	journal	November 2020
Rethinking Metadynamics: From Bias Potentials to Probability Distributions Invernizzi, Michele; Parrinello, Michele The Journal of Physical Chemistry Letters, Vol. 11, Issue 7 https://doi.org/10.1021/acs.jpclett.0c00497	journal	March 2020
Multiconfiguration Pair-Density Functional Theory Is as Accurate as CASPT2 for Electronic Excitation Hoyer, Chad E.; Ghosh, Soumen; Truhlar, Donald G. The Journal of Physical Chemistry Letters, Vol. 7, Issue 3 https://doi.org/10.1021/acs.jpclett.5b02773	journal	January 2016
Variational Flooding Study of a S _N 2 Reaction Piccini, GiovanniMaria; McCarty, James J.; Valsson, Omar The Journal of Physical Chemistry Letters, Vol. 8, Issue 3 https://doi.org/10.1021/acs.jpclett.6b02852	journal	January 2017
Collective Variables from Local Fluctuations Mendels, Dan; Piccini, GiovanniMaria; Parrinello, Michele The Journal of Physical Chemistry Letters, Vol. 9, Issue 11 https://doi.org/10.1021/acs.jpclett.8b00733	journal	May 2018
Accurate Quantum Chemical Free Energies at Affordable Cost Piccini, GiovanniMaria; Parrinello, Michele The Journal of Physical Chemistry Letters, Vol. 10, Issue 13 https://doi.org/10.1021/acs.jpclett.9b01301	journal	June 2019
Beyond Density Functional Theory: The Multiconfigurational Approach To Model Heterogeneous Catalysis Gaggioli, Carlo Alberto; Stoneburner, Samuel J.; Cramer, Christopher J. ACS Catalysis, Vol. 9, Issue 9 https://doi.org/10.1021/acscatal.9b01775	journal	August 2019
Organic Reactivity Made Easy and Accurate with Automated Multireference Calculations Wardzala, Jacob J.; King, Daniel S.; Ogunfowora, Lawal ACS Central Science https://doi.org/10.1021/acscentsci.3c01559	journal	March 2024
Assessing the Reliability of the Dynamics Reconstructed from Metadynamics Salvalaglio, Matteo; Tiwary, Pratyush; Parrinello, Michele Journal of Chemical Theory and Computation, Vol. 10, Issue 4 https://doi.org/10.1021/ct500040r	journal	March 2014
Multiconfiguration Pair-Density Functional Theory Li Manni, Giovanni; Carlson, Rebecca K.; Luo, Sijie Journal of Chemical Theory and Computation, Vol. 10, Issue 9 https://doi.org/10.1021/ct500483t	journal	August 2014
Second-order perturbation theory with a CASSCF reference function Andersson, Kerstin.; Malmqvist, Per Aake.; Roos, Bjoern O. The Journal of Physical Chemistry, Vol. 94, Issue 14 https://doi.org/10.1021/j100377a012	journal	July 1990
Chemical Kinetics and Mechanisms of Complex Systems: A Perspective on Recent Theoretical Advances Klippenstein, Stephen J.; Pande, Vijay S.; Truhlar, Donald G. Journal of the American Chemical Society, Vol. 136, Issue 2 https://doi.org/10.1021/ja408723a	journal	January 2014
Dual-Level Direct Dynamics Study on the Diels−Alder Reaction of Ethylene and 1,3-Butadiene Huang, Chun-Huei; Tsai, Li-Chao; Hu, Wei-Ping The Journal of Physical Chemistry A, Vol. 105, Issue 43 https://doi.org/10.1021/jp012740f	journal	October 2001
Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy Weigend, Florian; Ahlrichs, Reinhart Physical Chemistry Chemical Physics, Vol. 7, Issue 18, p. 3297-3305 https://doi.org/10.1039/b508541a	journal	January 2005
Kinetics of diene reactions at high temperatures Rowley, D.; Steiner, H. Discussions of the Faraday Society, Vol. 10 https://doi.org/10.1039/df9511000198	journal	January 1951
Introduction of n -electron valence states for multireference perturbation theory Angeli, C.; Cimiraglia, R.; Evangelisti, S. The Journal of Chemical Physics, Vol. 114, Issue 23 https://doi.org/10.1063/1.1361246	journal	June 2001
The Activated Complex in Chemical Reactions Eyring, Henry The Journal of Chemical Physics, Vol. 3, Issue 2 https://doi.org/10.1063/1.1749604	journal	February 1935
Rate constants from the reaction path Hamiltonian. I. Reactive flux simulations for dynamically correct rates Peters, Baron; Bell, Alexis T.; Chakraborty, Arup The Journal of Chemical Physics, Vol. 121, Issue 10 https://doi.org/10.1063/1.1778161	journal	September 2004
A method for accelerating the molecular dynamics simulation of infrequent events Voter, Arthur F. The Journal of Chemical Physics, Vol. 106, Issue 11 https://doi.org/10.1063/1.473503	journal	March 1997
Recent developments in the P y SCF program package Sun, Qiming; Zhang, Xing; Banerjee, Samragni The Journal of Chemical Physics, Vol. 153, Issue 2 https://doi.org/10.1063/5.0006074	journal	July 2020
Analytic gradients for multiconfiguration pair-density functional theory with density fitting: Development and application to geometry optimization in the ground and excited states Scott, Thais R.; Oakley, Meagan S.; Hermes, Matthew R. The Journal of Chemical Physics, Vol. 154, Issue 7 https://doi.org/10.1063/5.0039258	journal	February 2021
Ab initio metadynamics determination of temperature-dependent free-energy landscape in ultrasmall silver clusters Sucerquia, Daniel; Parra, Cristian; Cossio, Pilar The Journal of Chemical Physics, Vol. 156, Issue 15 https://doi.org/10.1063/5.0082332	journal	April 2022
Density functional theory in surface chemistry and catalysis Norskov, J. K.; Abild-Pedersen, F.; Studt, F. Proceedings of the National Academy of Sciences, Vol. 108, Issue 3 https://doi.org/10.1073/pnas.1006652108	journal	January 2011
Weighted active space protocol for multireference machine-learned potentials Seal, Aniruddha; Perego, Simone; Hennefarth, Matthew R. Proceedings of the National Academy of Sciences, Vol. 122, Issue 38 https://doi.org/10.1073/pnas.2513693122	journal	September 2025
The atomic simulation environment—a Python library for working with atoms Hjorth Larsen, Ask; Jørgen Mortensen, Jens; Blomqvist, Jakob Journal of Physics: Condensed Matter, Vol. 29, Issue 27 https://doi.org/10.1088/1361-648X/aa680e	journal	June 2017
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Predicting slow structural transitions in macromolecular systems: Conformational flooding Grubmüller, Helmut Physical Review E, Vol. 52, Issue 3 https://doi.org/10.1103/PhysRevE.52.2893	journal	September 1995
From Metadynamics to Dynamics Tiwary, Pratyush; Parrinello, Michele Physical Review Letters, Vol. 111, Issue 23 https://doi.org/10.1103/PhysRevLett.111.230602	journal	December 2013
Variationally Optimized Free-Energy Flooding for Rate Calculation McCarty, James; Valsson, Omar; Tiwary, Pratyush Physical Review Letters, Vol. 115, Issue 7 https://doi.org/10.1103/PhysRevLett.115.070601	journal	August 2015
Unified Approach to Enhanced Sampling Invernizzi, Michele; Piaggi, Pablo M.; Parrinello, Michele Physical Review X, Vol. 10, Issue 4 https://doi.org/10.1103/PhysRevX.10.041034	journal	November 2020
Reaction-rate theory: fifty years after Kramers Hänggi, Peter; Talkner, Peter; Borkovec, Michal Reviews of Modern Physics, Vol. 62, Issue 2 https://doi.org/10.1103/RevModPhys.62.251	journal	April 1990
Density functional theory: Its origins, rise to prominence, and future Jones, R. O. Reviews of Modern Physics, Vol. 87, Issue 3 https://doi.org/10.1103/RevModPhys.87.897	journal	August 2015
How and when does an anticancer drug leave its binding site? Tiwary, Pratyush; Mondal, Jagannath; Berne, B. J. Science Advances, Vol. 3, Issue 5 https://doi.org/10.1126/sciadv.1700014	journal	May 2017
Insights into Current Limitations of Density Functional Theory Cohen, A. J.; Mori-Sanchez, P.; Yang, W. Science, Vol. 321, Issue 5890 https://doi.org/10.1126/science.1158722	journal	August 2008
Multiconfiguration Pair-Density Functional Theory Sharma, Prachi; Bao, Jie J.; Truhlar, Donald G. Annual Review of Physical Chemistry, Vol. 72, Issue 1 https://doi.org/10.1146/annurev-physchem-090419-043839	journal	April 2021
Advanced simulations with PLUMED: OPES and Machine Learning Collective Variables Trizio, Enrico; Rizzi, Andrea; Piaggi, Pablo M. arXiv https://doi.org/10.48550/arXiv.2410.18019	preprint	January 2024

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Computing Reaction Kinetics with MC-PDFT–OPESf: Combining Multireference Electronic Structure Theory and Enhanced Sampling

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