Abstract
We present a nonadiabatic statistical theory (NAST) package for predicting kinetics of spin-dependent processes, such as intersystem crossings, spin-forbidden unimolecular reactions, and spin crossovers. The NAST package can calculate the probabilities and rates of transitions between the electronic states of different spin multiplicities. Both the microcanonical (energy-dependent) and canonical (temperature-dependent) rate constants can be obtained. Quantum effects, including tunneling, zero-point vibrational energy, and reaction path interference, can be accounted for. In the limit of an adiabatic unimolecular reaction proceeding on a single electronic state, NAST reduces to the traditional transition state theory. Because NAST requires molecular properties at only a few points on potential energy surfaces, it can be applied to large molecular systems, used with accurate high-level electronic structure methods, and employed to study slow nonadiabatic processes. The essential NAST input data include the nuclear Hessian at the reactant minimum, as well as the nuclear Hessians, energy gradients, and spin–orbit coupling at the minimum energy crossing point (MECP) between two states. The additional computational tools included in the NAST package can be used to extract the required input data from the output files of electronic structure packages, calculate the effective Hessian at the MECP, and fit the reaction coordinate for more advanced NAST calculations. We describe the theory, its implementation, and three examples of application to different molecular systems.
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Availability of data and material
The input files for the electronic structure, NAST and MESMER calculations discussed in the main text are available in the SI.
Code availability
The source code of the NAST package is available free of charge at https://github.com/svarganov/NAST.
References
Schröder D, Shaik S, Schwarz H (2000) Two-state reactivity as a new concept in organometallic chemistry. Acc Chem Res 33:139–145. https://doi.org/10.1021/ar990028j
Liao P, Carter EA (2013) New concepts and modeling strategies to design and evaluate photo-electro-catalysts based on transition metal oxides. Chem Soc Rev 42:2401–2422. https://doi.org/10.1039/c2cs35267b
Sun Y, Tang H, Chen K et al (2016) Two-state reactivity in low-valent iron-mediated C-H activation and the implications for other first-row transition metals. J Am Chem Soc 138:3715–3730. https://doi.org/10.1021/jacs.5b12150
Lykhin AO, Kaliakin DS, DePolo GE et al (2016) Nonadiabatic transition state theory: application to intersystem crossings in the active sites of metal-sulfur proteins. Int J Quantum Chem 116:750–761. https://doi.org/10.1002/qua.25124
Goodrow A, Bell AT, Head-Gordon M (2009) Are spin-forbidden crossings a bottleneck in methanol oxidation? J Phys Chem C 113:19361–19364. https://doi.org/10.1021/jp906603r
Kaliakin DS, Zaari RR, Varganov SA (2015) Effect of H2 binding on the nonadiabatic transition probability between singlet and triplet states of the [NiFe]-hydrogenase active site. J Phys Chem A 119:1066–1073. https://doi.org/10.1021/jp510522z
Pohlman AJ, Kaliakin DS, Varganov SA, Casey SM (2020) Spin controlled surface chemistry: alkyl desorption from Si(100)-2×1 by nonadiabatic hydrogen elimination. Phys Chem Chem Phys 22:16641–16647. https://doi.org/10.1039/d0cp01913e
Zhao J, Wu W, Sun J, Guo S (2013) Triplet photosensitizers: from molecular design to applications. Chem Soc Rev 42:5323–5351. https://doi.org/10.1039/c3cs35531d
Zhao J, Chen K, Hou Y et al (2018) Recent progress in heavy atom-free organic compounds showing unexpected intersystem crossing (ISC) ability. Org Biomol Chem 16:3692–3701. https://doi.org/10.1039/c8ob00421h
Pordel S, Pickens RN, White JK (2021) Release of CO and production of 1O2 from a Mn-BODIPY Photoactivated CO releasing molecule with visible light. Organometallics 40:2983–2994. https://doi.org/10.1021/acs.organomet.1c00331
Bogani L, Wernsdorfer W (2008) Molecular spintronics using single-molecule magnets. Nat Mater 7:179–186. https://doi.org/10.1038/nmat2133
Gaita-Ariño A, Luis F, Hill S, Coronado E (2019) Molecular spins for quantum computation. Nat Chem 11:301–309. https://doi.org/10.1038/s41557-019-0232-y
Goldman ML, Doherty MW, Sipahigil A et al (2015) State-selective intersystem crossing in nitrogen-vacancy centers. Phys Rev B 91:1–11. https://doi.org/10.1103/PhysRevB.91.165201
Bayliss SL, Laorenza DW, Mintun PJ et al (2020) Optically addressable molecular spins for quantum information processing. Science 370:1309–1312. https://doi.org/10.1126/science.abb9352
Ullah A, Cerdá J, Baldoví JJ et al (2019) In silico molecular engineering of dysprosocenium-based complexes to decouple spin energy levels from molecular vibrations. J Phys Chem Lett 10:7678–7683. https://doi.org/10.1021/acs.jpclett.9b02982
Mitschke U, Bäuerle P (2000) The electroluminescence of organic materials. J Mater Chem 10:1471–1507. https://doi.org/10.1039/a908713c
Goushi K, Yoshida K, Sato K, Adachi C (2012) Organic light-emitting diodes employing efficient reverse intersystem crossing for triplet-to-singlet state conversion. Nat Photonics 6:253–258. https://doi.org/10.1038/nphoton.2012.31
Endo A, Ogasawara M, Takahashi A et al (2009) Thermally activated delayed fluorescence from Sn4+-porphyrin complexes and their application to organic light-emitting diodes—a novel mechanism for electroluminescence. Adv Mater 21:4802–4806. https://doi.org/10.1002/adma.200900983
Bergmann L, Hedley GJ, Baumann T et al (2016) Direct observation of intersystem crossing in a thermally activated delayed fluorescence copper complex in the solid state. Sci Adv 2:1–7. https://doi.org/10.1126/sciadv.1500889
Wada Y, Nakagawa H, Matsumoto S et al (2020) Organic light emitters exhibiting very fast reverse intersystem crossing. Nat Photonics 14:643–649. https://doi.org/10.1038/s41566-020-0667-0
Franzen S, Kiger L, Poyart C, Martin JL (2001) Heme photolysis occurs by ultrafast excited state metal-to-ring charge transfer. Biophys J 80:2372–2385. https://doi.org/10.1016/S0006-3495(01)76207-8
Wang W, Ye X, Demidov AA et al (2000) Femtosecond multicolor pump-probe spectroscopy of ferrous cytochrome C. J Phys Chem B 104:10789–10801. https://doi.org/10.1021/jp0008602
Dunietz BD, Dreuw A, Head-Gordon M (2003) Initial steps of the photodissociation of the CO ligated heme group. J Phys Chem B 107:5623–5629. https://doi.org/10.1021/jp0226376
Mara MW, Hadt RG, Reinhard ME et al (2017) Metalloprotein entatic control of ligand-metal bonds quantified by ultrafast x-ray spectroscopy. Science 356:1276–1280. https://doi.org/10.1126/science.aam6203
Falahati K, Tamura H, Burghardt I, Huix-Rotllant M (2018) Ultrafast carbon monoxide photolysis and heme spin-crossover in myoglobin via nonadiabatic quantum dynamics. Nat Commun 9:1–8. https://doi.org/10.1038/s41467-018-06615-1
Harvey JN, Aschi M (2003) Modelling spin-forbidden reactions: recombination of carbon monoxide with iron tetracarbonyl. Faraday Discuss 124:129–143. https://doi.org/10.1039/b211871h
Yang B, Gagliardi L, Truhlar DG (2018) Transition states of spin-forbidden reactions. Phys Chem Chem Phys 20:4129–4136. https://doi.org/10.1039/c7cp07227a
Jensen KP, Ryde U (2004) How O2 binds to heme. Reasons for rapid binding and spin inversion. J Biol Chem 279:14561–14569. https://doi.org/10.1074/jbc.M314007200
Strickland N, Harvey JN (2007) Spin-forbidden ligand binding to the ferrous-heme group: Ab initio and DFT studies. J Phys Chem B 111:841–852. https://doi.org/10.1021/jp064091j
Harvey JN (2004) Spin-forbidden CO ligand recombination in myoglobin. Faraday Discuss 127:165–177. https://doi.org/10.1039/b314768a
Kahn O, Martinez CJ (1998) Spin-transition polymers: from molecular materials toward memory devices. Science 279:44–48. https://doi.org/10.1126/science.279.5347.44
Halder GJ, Kepert CJ, Moubaraki B et al (2002) Guest-dependent spin crossover in a nanoporous molecular framework material. Science 298:1762–1765. https://doi.org/10.1126/science.1075948
Gütlich PGH (2004) Spin crossover in transition metal compounds I-III. Top Curr Chem 23(234):235
Halcrom MA (2013) Spin-crossover materials, properities and applications. Wiley, Hoboken
Senthil Kumar K, Ruben M (2017) Emerging trends in spin crossover (SCO) based functional materials and devices. Coord Chem Rev 346:176–205. https://doi.org/10.1016/j.ccr.2017.03.024
Real JA, Gaspar AB, Carmen Muñoz M (2005) Thermal, pressure and light switchable spin-crossover materials. Dalt Trans 12:2062–2079. https://doi.org/10.1039/b501491c
Bonhommeau S, Molnár G, Galet A et al (2005) One shot laser pulse induced reversible spin transition in the spin-crossover complex [Fe(C4H4N2){Pt(CN)4}] at room temperature. Angew Chemie Int Ed 44:4069–4073. https://doi.org/10.1002/anie.200500717
Gaspar AB, Ksenofontov V, Seredyuk M, Gütlich P (2005) Multifunctionality in spin crossover materials. Coord Chem Rev 249:2661–2676. https://doi.org/10.1016/j.ccr.2005.04.028
Muller RN, Vander EL, Laurent S (2003) Spin transition molecular materials: Intelligent contrast agents for magnetic resonance imaging. J Am Chem Soc 125:8405–8407. https://doi.org/10.1021/ja0349599
Beck M (2000) The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets. Phys Rep 324:1–105. https://doi.org/10.1016/S0370-1573(99)00047-2
Barbatti M (2011) Nonadiabatic dynamics with trajectory surface hopping method. Wiley Interdiscip Rev Comput Mol Sci 1:620–633. https://doi.org/10.1002/wcms.64
Curchod BFE, Martinez TJ (2018) Ab initio nonadiabatic quantum molecular dynamics. Chem Rev 118:3305–3336. https://doi.org/10.1021/acs.chemrev.7b00423
Mai S, Marquetand P, González L (2018) Nonadiabatic dynamics: the SHARC approach. Wiley Interdiscip Rev Comput Mol Sci 8:1–23. https://doi.org/10.1002/wcms.1370
Hammes-Schiffer S, Tully JC (1995) Nonadiabatic transition state theory and multiple potential energy surface molecular dynamics of infrequent events. J Chem Phys 103:8513–8527. https://doi.org/10.1063/1.470162
Shenvi N, Subotnik JE, Yang W (2011) Simultaneous-trajectory surface hopping: a parameter-free algorithm for implementing decoherence in nonadiabatic dynamics. J Chem Phys 134:144102. https://doi.org/10.1063/1.3575588
Curchod BFE, Rauer C, Marquetand P et al (2016) Communication: GAIMS—generalized ab initio multiple spawning for both internal conversion and intersystem crossing processes. J Chem Phys 144:101102. https://doi.org/10.1063/1.4943571
Fedorov DA, Pruitt SR, Keipert K et al (2016) Ab initio multiple spawning method for intersystem crossing dynamics: spin-forbidden transitions between 3B1 and 1A1 states of GeH2. J Phys Chem A 120:2911–2919. https://doi.org/10.1021/acs.jpca.6b01406
Fedorov DA, Lykhin AO, Varganov SA (2018) Predicting intersystem crossing rates with AIMS-DFT molecular dynamics. J Phys Chem A 122:3480–3488
Mukherjee S, Fedorov DA, Varganov SA (2021) Modeling spin-crossover dynamics. Annu Rev Phys Chem 72:515–540. https://doi.org/10.1146/annurev-physchem-101419-012625
Harvey JN (2007) Understanding the kinetics of spin-forbidden chemical reactions. Phys Chem Chem Phys 9:331–343. https://doi.org/10.1039/b614390c
Harvey JN, Aschi M (1999) Spin-forbidden dehydrogenation of methoxy cation: a statistical view. Phys Chem Chem Phys 1:5555–5563. https://doi.org/10.1039/a907723e
Harvey JN (2014) Spin-forbidden reactions: Computational insight into mechanisms and kinetics. Wiley Interdiscip Rev Comput Mol Sci 4:1–14. https://doi.org/10.1002/wcms.1154
Cui Q, Morokuma K, Bowman JM, Klippenstein SJ (1999) The spin-forbidden reaction CH(2Π)+N2→HCN+N(4S) revisited. II. Nonadiabatic transition state theory and application. J Chem Phys 110:9469–9482. https://doi.org/10.1063/1.478949
Lorquet JC, Leyh-Nihant B (1988) Nonadiabatic unimolecular reactions. 1. A statistical formulation for the rate constants. J Phys Chem 92:4778–4783. https://doi.org/10.1021/j100327a043
Nikitin EE, Umanskii SY (1984) Theory of slow atomic collisions. Springer, Berlin
Zhao Y, Mil’nikov G, Nakamura H (2004) Evaluation of canonical and microcanonical nonadiabatic reaction rate constants by using the Zhu-Nakamura formulas. J Chem Phys 121:8854–8860. https://doi.org/10.1063/1.1801971
Marks AJ (2001) Nonadiabatic transition-state theory: a Monte Carlo study of competing bond fission processes in bromoacetyl chloride. J Chem Phys 114:1700–1708. https://doi.org/10.1063/1.1333702
McLafferty FJ, George TF (1976) On nonadiabatic transition state theory. Chem Phys Lett 37:67–71. https://doi.org/10.1016/0009-2614(76)80163-7
Lykhin AO, Varganov SA (2020) Intersystem crossing in tunneling regime: T1→S0 relaxation in thiophosgene. Phys Chem Chem Phys 22:5500–5508. https://doi.org/10.1039/c9cp06956a
Truhlar DG, Garrett BC, Klippenstein SJ (1996) Current status of transition-state theory. J Phys Chem 100:12771–12800. https://doi.org/10.1021/jp953748q
Truhlar DG, Garrett BC (1984) Variational transition state theory. Ann Rev Phys Chem 35:159–189. https://doi.org/10.1146/annurev.pc.35.100184.001111
Laidler KJ, King MC (1983) The development of transition-state theory. J Phys Chem 87:2657–2664. https://doi.org/10.1021/j100238a002
Garrett BC, Truhlar DG (1979) Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules. J Phys Chem 83:1052–1079. https://doi.org/10.1021/j100471a031
Miller WH (1998) “Direct” and “correct” calculation of canonical and microcanonical rate constants for chemical reactions. J Phys Chem A 102:793–806. https://doi.org/10.1021/jp973208o
Bao JL, Truhlar DG (2017) Variational transition state theory: Theoretical framework and recent developments. Chem Soc Rev 46:7548–7596. https://doi.org/10.1039/c7cs00602k
Marian CM (2012) Spin-orbit coupling and intersystem crossing in molecules. Wiley Interdiscip Rev Comput Mol Sci 2:187–203. https://doi.org/10.1002/wcms.83
Fedorov DG, Koseki S, Schmidt MW, Gordon MS (2003) Spin-orbit coupling in molecules: chemistry beyond the adiabatic approximation. Int Rev Phys Chem 22:551–592. https://doi.org/10.1080/0144235032000101743
Marian CM (2001) Spin-orbit coupling in molecules. In: Lipkowitz KB, Boyd DB (eds) Reviews in computational chemistry. Wiley, Hoboken, pp 99–204
Marian CM (2021) Understanding and controlling intersystem crossing in molecules. Annu Rev Phys Chem 72:617–640. https://doi.org/10.1146/annurev-physchem-061020-053433
Zhu C, Nakamura H (1994) Theory of nonadiabatic transition for general two-state curve crossing problems. I. Nonadiabatic tunneling case. J Chem Phys 101:10630–10647. https://doi.org/10.1063/1.467877
Fernández-Ramos A, Ellingson BA, Meana-Pañeda R et al (2007) Symmetry numbers and chemical reaction rates. Theor Chem Acc 118:813–826. https://doi.org/10.1007/s00214-007-0328-0
Lykhin AO (2019) Predicting kinetics of spin-forbidden unimolecular reactions with nonadiabatic transition state theory. Ph.D. Dissertation, University of Nevada, Reno
Delos JB (1973) On the reactions of N2 with O. J Chem Phys 59:2365–2369. https://doi.org/10.1063/1.1680345
Dashevskaya EI, Nikitin EE (2017) Uniform airy approximation for nonadiabatic transitions in a curve-crossing weak-coupling. Z Phys Chem 232:311–323. https://doi.org/10.1515/zpch-2017-1025
Nakamura H (2012) Nonadiabatic transition: concepts, basic theories and applications, 2nd edn. World Scientific, Berlin
Zhu C, Teranishi Y, Nakamura H (2001) Nonadiabatic transitions due to curve crossings: complete solutions of the landau‐zener‐stueckelberg problems and their applications. In: Prigogine I, Rice SA (eds) Advances in chemical physics. Wiley Online Librabry, pp 127–133
Zhu C, Nakamura H, Re N, Aquilanti V (1992) The two-state linear curve crossing problems revisited. I. Analysis of Stokes phenomenon and expressions for scattering matrices. J Chem Phys 97:1892–1904. https://doi.org/10.1063/1.463178
Zhu C, Nakamura H (1992) The two-state linear curve crossing problems revisited. II. Analytical approximations for the Stokes constant and scattering matrix: the Landau-Zener case. J Chem Phys 97:8497–8514. https://doi.org/10.1063/1.464814
Zhu C, Nakamura H (1994) Two-state linear curve crossing problems revisited. IV. The best analytical formulas for scattering matrices. J Chem Phys 101:4855–4866. https://doi.org/10.1063/1.468505
Melissas VS, Truhlar DG, Garrett BC (1992) Optimized calculations of reaction paths and reaction-path functions for chemical reactions. J Chem Phys 96:5758–5772. https://doi.org/10.1063/1.462674
Kuki A (1993) Adiabaticity factor for electron transfer in the multimode case: an energy velocity perspective. J Phys Chem 97:13107–13116. https://doi.org/10.1021/j100152a013
Bracewell RN (2000) The fourier transform and its applications, 3d edn. McGraw-Hill, New York
Baer T, Hase WL (1996) Unimolecular reaction dynamics: theory and experiments. Oxford University Press, Oxford
Green NJB (2003) Unimolecular kinetics part 1. The reaction step. Elsevier, Hoboken
Lykhin AO, Truhlar DG, Gagliardi L (2021) Role of triplet states in the photodynamics of aniline. J Am Chem Soc 143:5878–5889. https://doi.org/10.1021/jacs.1c00989
Galano A, Alvarez-Idaboy JR (2013) A computational methodology for accurate predictions of rate constants in solution: application to the assessment of primary antioxidant activity. J Comput Chem 34:2430–2445. https://doi.org/10.1002/jcc.23409
Dzib E, Cabellos JL, Ortíz-Chi F et al (2019) Eyringpy: a program for computing rate constants in the gas phase and in solution. Int J Quant Chem 119:11–13. https://doi.org/10.1002/qua.25686
Garrett BC, Schenter GK (1994) Variational transition state theory for activated chemical reactions in solution. Int Rev Phys Chem 13:263–289. https://doi.org/10.1080/01442359409353296
Truhlar D, Pliego JR (2008) Transition state theory and chemical reaction dynamics in solution. In: Mennucci B, Cammi R (eds) Continuum solvation models in chemical physics: theory and application. Wiley, Hoboken
Hall DG (1986) The status of transition-state theory in non-ideal solutions and application of Kirkwood-Buff theory to the transition state. J Chem Soc Faraday Trans 2: Mol Chem Phys 82:1297–1303. https://doi.org/10.1039/F29868201297
Henriksen NE, Hansen FY (2018) Static solvent effects, transition-state theory. Theories of molecular reaction dynamics: the microscopic foundation of chemical kinetics. Oxford University Press, Oxford
Barca GMJ, Bertoni C, Carrington L et al (2020) Recent developments in the general atomic and molecular electronic structure system. J Chem Phys 152:154102. https://doi.org/10.1063/5.0005188
Werner HJ, Knowles PJ, Manby FR et al (2020) The Molpro quantum chemistry package. J Chem Phys 152:144107. https://doi.org/10.1063/5.0005081
Dubnikova F, Lifshitz A (2000) Isomerization of propylene oxide. Quantum chemical calculations and kinetic modeling. J Phys Chem A 104:4489–4496. https://doi.org/10.1021/jp004038+
Lifshitz A, Tamburu C (1994) Isomerization and decomposition of propylene oxide. Studies with a single-pulse shock tube. J Phys Chem 98:1161–1170. https://doi.org/10.1021/j100055a020
McGarvey JJ, Wilson J (1975) Photochemical perturbation and chemical relaxation of the planar—tetrahedral equilibrium in a di(tertiary phosphine) complex of nickel(II). J Am Chem Soc 97:2531–2532. https://doi.org/10.1021/ja00842a034
Miller JA, Klippenstein SJ (2003) From the multiple-well master equation to phenomenological rate coefficients: reactions on a C3H4 potential energy surface. J Phys Chem A 107:2680–2692. https://doi.org/10.1021/jp0221082
Glowacki DR, Liang CH, Morley C et al (2012) MESMER: an open-source master equation solver for multi-energy well reactions. J Phys Chem A 116:9545–9560. https://doi.org/10.1021/jp3051033
Acknowledgements
This work was supported by the National Science Foundation through a CAREER Award (CHE-1654547). We acknowledge Dr. Ryan Zaari for his contributions to the earlier version of the NAST package and thank Drs. Danil Kaliakin and Saikat Mukherjee for fruitful discussions.
Funding
This work was supported by the National Science Foundation through a CAREER Award (CHE 1654547).
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S.A.V. supervised the NAST package development. V.D.D., M.R., I.D.D., A.O.L. and R.C.M. wrote different parts of the code. V.D.D, M.R. and I.D.D. performed the electronic structure and kinetics calculations. All authors contributed to the preparation of the manuscript.
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Dergachev, V.D., Rooein, M., Dergachev, I.D. et al. NAST: Nonadiabatic Statistical Theory Package for Predicting Kinetics of Spin-Dependent Processes. Top Curr Chem (Z) 380, 15 (2022). https://doi.org/10.1007/s41061-022-00366-w
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DOI: https://doi.org/10.1007/s41061-022-00366-w