Strong Influence of Decoherence Corrections and Momentum Rescaling in Surface Hopping Dynamics of Transition Metal Complexes Felix Plasser, Sebastian Mai, Maria Fumanal, Etienne Gindensperger, Chantal Daniel, Leticia González To cite this version: Felix Plasser, Sebastian Mai, Maria Fumanal, Etienne Gindensperger, Chantal Daniel, et al.. Strong Influence of Decoherence Corrections and Momentum Rescaling in Surface Hopping Dynamics of Transition Metal Complexes. Journal of Chemical Theory and Computation, American Chemical Society, 2019, 15 (9), pp.5031-5045. 10.1021/acs.jctc.9b00525. hal-03037918 HAL Id: hal-03037918 https://hal.archives-ouvertes.fr/hal-03037918 Submitted on 14 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. 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Strong Influence of Decoherence Corrections and Momentum Rescaling in Surface Hopping Dynamics of Transition Metal Complexes , , Felix Plasser,∗ y { Sebastian Mai,y Maria Fumanal,z Etienne Gindensperger,z Chantal Daniel,z and Leticia Gonzálezy Institute for Theoretical Chemistry, Faculty of Chemistry, University of Vienna, y Währingerstr. 17, 1090 Vienna, Austria Laboratoire de Chimie Quantique, Institut de Chimie Strasbourg, UMR7177 CNRS/Universitéz de Strasbourg 4 Rue Blaise Pascal BP296/R8, F-67008 Strasbourg, France Department of Chemistry, Loughborough University, Loughborough, LE11 3TU, U.K. { E-mail: [email protected] Abstract portance of the often neglected parameters in surface hopping and shows that there is still The reliability of different parameters in the need for simple, robust, and generally applica- surface hopping method is assessed for a vi- ble correction schemes. bronic coupling model of a challenging transi- tion metal complex, where a large number of electronic states of different multiplicities are 1 Introduction met within a small energy range. In particular, the effect of two decoherence correction schemes Many important processes in photochemistry and of various strategies for momentum rescal- and electrochemistry are governed by nonadi- 1–6 ing and treating frustrating hops during the dy- abatic transitions between electronic states, namics is investigated and compared against an at which the Born-Oppenheimer approximation accurate quantum dynamics simulation. The breaks down, meaning that electronic and nu- results show that small differences in the sur- clear degrees of freedom can no longer be sepa- 7 face hopping protocol can strongly affect the rated. The surface hopping dynamics method results. We find a clear preference for momen- has become a popular approach to describe tum rescaling along the nonadiabatic coupling nonadiabatic processes due to its conceptual vector and trace this effect back to an enhanced simplicity and the intuitive interpretation of the number of frustrated hops. Furthermore, reflec- results in a quasi-classical picture. As a result, tion of the momentum after frustrated hops is surface hopping is widely applied in many dif- shown to work better than to ignore the com- ferent application areas and and a large body 3,8–15 pletely. The study also highlights the impor- of recent work exists. The simplicity of tance of the decoherence correction but neither the classical picture is deceptive as it never- of the two methods employed, energy based de- theless needs to mimic non-trivial underlying coherence and augmented fewest switches sur- quantum processes, such as (i) the branching of face hopping, performs completely satisfactory. the wavepacket onto different electronic states, More generally, the study emphasises the im- (ii) the loss of electronic coherence due to inter- actions with the nuclei or the environment, (iii) 1 the exchange of energy and momentum between of surface-hoping could be only assessed on sim- electronic and nuclear degrees of freedom, and ple systems where accurate reference values are (iv) classically forbidden transitions. available. In contrast, a reference for realistic Point (i) is treated by the surface hopping large systems is much more difficult to obtain. algorithm itself meaning that rather than de- In this paper, we introduce a new and gen- scribing the whole wavepacket branching onto erally applicable strategy to assess the qual- different potential energy surfaces (PES), one ity of surface hopping on complex large sys- of the surfaces is selected by using an stochas- tems using high-dimensional, many-state vi- tic algorithm and only this branch is further bronic coupling models. Since their introduc- propagated; an ensemble of trajectories follow- tion in the 80s,38 vibronic coupling models have ing the different branches is then needed to re- been very successful39–44 in reproducing ex- semble a bifurcating quantum wavepacket. The perimental work, particularly in combination fact that only one branch is propagated, auto- with the multiconfigurational time-dependent matically means that it is not possible to model Hartree (MCTDH) method.45–47 Recently, we the interactions between different branches and implemented an algorithm to perform surface their eventual loss of coherence (ii), and this hopping based on vibronic coupling models,48 has led to the introduction of decoherence cor- and showed that it can be extremely cheap com- rections on top of the surface hopping algo- putationally while still capturing the main fea- rithm.16–20 An exchange of energy and momen- tures of a variety of photophysical processes. tum (iii) should occur during surface hops and Here, we shall use a linear vibronic coupling different schemes of redistributing energy and (LVC) model to compare the results of sur- momentum have been developed. Here, a new face hopping against an accurate MCTDH ref- + complication (iv) comes into play if the quan- erence for [Re(im)(CO)3(phen)] (im = imida- tum and classical descriptions lead to incom- zole, phen = phenanthroline, see Fig. 1). patible results and the quantum propagation The choice of a transition metal complex as requires a classically forbidden hop, also called a test bed is purposely, as such systems fea- a "frustrated hop".18,21 In order to deal with ture a high number of excited electronic states the above-mentioned formal problems as well of different multiplicities in a limited domain as additional numerical problems22 a number of of energy and the description of its dynam- different flavours of the surface hopping method ics represent a particularly challenging case have been developed,9,12,14,23 able to work un- for spin-vibronic models.49 Moreover, the dy- + der different circumstances. namics of [Re(im)(CO)3(phen)] is particularly While surface hopping simulations can de- rich, as due to the presence of an intermedi- 3 pend strongly on the electronic structure ate intra-ligand triplet state IL (T3) that cou- method employed for the underlying on-the- ples strongly with the initially populated second fly calculations,24,25 it is often forgotten that singlet metal-to-ligand charge transfer 1MLCT changes in the surface hopping algorithm can (S2) state, spin-orbit coupling (SOC) effects are also have its consequences. The reliability of dominant at the early time of the dynamics (< surface hopping algorithms has been tested 50 fs) while vibronic effects lead to populate 3 particularly on idealized model systems, such the lowest MLCT (T1) state by exchange with 26–28 ? as spin-boson models, a quantum os- T3. Depending on the character and relative cillator,29 a two-level system in a classical positions of the low-lying states the early time bath,30 or on low-dimensional scattering prob- spin-vibronic mechanism will be driven essen- lems31–33 and the one-dimensional LiH sys- tially either by vibronic effects43,50 or by SOC tem.34 There also exist a few studies using effects.51 realistic high-dimensional PES via on-the-fly Studies based on the LVC model performed dynamics,18,35–37 but in this case it is more on a series of rhenium (I) carbonyl α-diimine challenging to find an accurate reference to complexes revealed the dominant normal modes compare with. Generally speaking, the validity and associated (spin) vibronic couplings that 2 drive the ultra-fast decay (< 200 fs) within 2.1 Wavefunction representations the low-lying singlet and triplet states.43,50–53 An important ingredient of SHARC is the op- Previous simulations on [Re(im)(CO) (phen)]+ 3 timal use of the possible representations of the showed that the key normal modes are the phen electronic wavefunctions.9 To ease the discus- and carbonyl vibrations whereas the imidazole sion, we establish here the name conventions ligand is a spectator.54? Here we employ a employed,9,55,56 see Figure 2. Most quantum model of 2 singlet and 4 triplet states, vibron- chemistry codes work with an electronic Hamil- ically coupled via 15 normal modes, as well tonian that includes molecular Coulomb inter- as three additional models with a reduced set actions but neither external fields nor SOC. of electronic states. In each case, 13 different We label this operator the molecular Coulomb surface hopping protocols are compared to the Hamiltonian (MCH) and its eigenfunctions MCTDH reference. The 200 trajectories prop- form the MCH basis (Figure 2 (b)). In this rep- agated over 500 fs are equivalent to a total of resentation, states possessing distinct multiplic- more than ten million formal electronic struc- ity are labelled as S ;S ;:::;T ;T ;:::. States ture computations. Doing this would be hardly 1 2 1 2 of the same spin-multiplicity do not cross in a feasible with on-the-fly dynamics but it requires one-dimensional picture whereas states of dif- negligible computational effort with our new ferent multiplicities do.