Ultrafast and long-time excited state kinetics of an NIR-emissive vanadium(iii) complex II. Elucidating triplet-to-singlet excited-state dynamics

We report the non-adiabatic dynamics of VIIICl3(ddpd), a complex based on the Earth-abundant first-row transition metal vanadium with a d2 electronic configuration which is able to emit phosphorescence in solution in the near-infrared spectral region. Trajectory surface-hopping dynamics based on linear vibronic coupling potentials obtained with CASSCF provide molecular-level insights into the intersystem crossing from triplet to singlet metal-centered states. While the majority of the singlet population undergoes back-intersystem crossing to the triplet manifold, 1–2% remains stable during the 10 ps simulation time, enabling the phosphorescence described in Dorn et al. Chem. Sci., 2021, DOI: 10.1039/D1SC02137K. Competing with intersystem crossing, two different relaxation channels via internal conversion through the triplet manifold occur. The nuclear motion that drives the dynamics through the different electronic states corresponds mainly to the increase of all metal–ligand bond distances as well as the decrease of the angles of trans-coordinated ligand atoms. Both motions lead to a decrease in the ligand-field splitting, which stabilizes the interconfigurational excited states populated during the dynamics. Analysis of the electronic character of the states reveals that increasing and stabilizing the singlet population, which in turn can result in enhanced phosphorescence, could be accomplished by further increasing the ligand-field strength.


Contents
Supporting Information S1 S1 Optimized Geometry   Figure S1 shows the orbitals included in the (10,13) active space used to setup the LVC Hamiltonian. In panel (a) the orbitals are plotted with the commonly used isovalue of 0.05.
As can be seen, the orbitals appear as four ligand π orbitals, 5 metal d orbitals, and 4 ligand π * orbitals, where the π and π * orbitals are located on the ddpd ligand. We use this orbital classification in the majority of this work. In panel (b) the same orbitals are plotted at the looser isovalue of 0.01. Interestingly, most orbitals show additional contributions not apparent before. Importantly, the five orbitals labeled as metal d orbitals show admixture of ligand orbitals, both from the π orbitals of the ddpd ligand as well as from the p orbitals of the chlorido ligands. This observation can explain the participation of the chlorido ligands in the charge flow in the excited-state dynamics discussed in the main paper. Attempts to include an extra p orbital of the chlorido ligand in the active space for the triplet states were unsuccessful, as during the optimization, the added p orbital was always rotated out of the active space to favor another ddpd π orbital. For the singlet states, the extra chlorido p orbital could be added.
The CASSCF energies for the triplet and singlet states with the different (12,14) active spaces are shown in Table S2. Adding the extra ddpd π orbital has negligible influence on the CASSCF energies of the triplet states, with maximal changes of 0.01 eV. In contrast, for the singlet states, adding the chlorido p orbital leads to lowering of all excitation energies by

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(a) Orbitals in the (10,13) Active Space: Isovalue = 0.05 (b) Orbitals in the (10,13) Active Space: Isovalue = 0.01 Figure S1: Orbitals included in the (10,13) active space in the CASSCF calculations. (a) Isovalue of 0.05. (b) Isovalue of 0.01 Table S2: CASSCF excitation energies in eV obtained with a (10,13) and a (12,14) active space. Orbitals of the (10,13) active space shown in Figure S1. The additional orbital in the (12,14) active space was a π orbital on the ddpd ligand for the triplet states and a p orbital on the chlorido ligand for the singlet states.

S2.2 Number of States
Using the (10,13) active space, we have performed CASSCF calculations varying the number of states included in the state averaging. The resulting energies for 12-17 triplet states and 11-16 singlet states are compiled in Table S3. As can be seen, the number of states in these ranges has only little effect on the excitation energies of all states. Furthermore, there is a pronounced energy gap between states T 15 and T 16 as well as between states S 15 and S 16 of 0.6-0.7 eV. Thus, we decided to use 16 triplet and 15 singlet states in the dynamics simulations, as these states, both, cover a sufficient energy range and are well-separated from further higher-lying excited states, that might become intruder states.

S2.3 Characterization of the Electronic Excited States
The natural occupation numbers of the 16 triplet and 15 singlet states calculated with CASSCF(10,13) are collected in Table S4. These numbers allow us to assign the principal electron configuration for each state, collected in Table S5.
From As summarized in Table S5, the triplet states T 0 -T 9 correspond to metal-centered states with a d 2 configuration. The triplet states T 10 -T 15 are characterized by a hole in one of the ligand π orbitals and an excited electron in a ligand π * orbital, i.e., they resemble ligand-centered excited states. In the singlet manifold, states S 1 -S 12 correspond to metalcentered d 2 states, whereas S 13 -S 15 appear as ligand-centered excitations. We note that the states T 10 -T 15 and S 13 -S 15 , however, cannot be described simply by a π → π * excitation as will be discussed in more detail below. The orbitals denoted in Table S5 are classified according to Figure S1(a), i.e., following only their main contribution. This neglects, e.g., contribution of the chlorido p orbitals to some of the metal d orbitals. Thus, this is only a qualitative characterization of the CASSCF results. A more quantitative description of the state characters can be obtained when analyzing the transition densities between the electronic states, as discussed in Section S2.4.
The metal-centered states can now qualitatively be classified in terms of octahedral ligand-field term symbols. For this, we show in Figure S2 the Tanabe-Sugano diagram of a d 2 configuration. We can now compare the expected order of ligand-field terms with the energies of the triplet and singlet states obtained in the CASSCF calculations (Table S2).
As can be seen, the first three triplet states (T 0 -T 2 ) are nearly degenerate with anr energetic S10 Table S4: Natural orbital occupation numbers of the (10,13) active space orbitals for 16 triplet and 15 singlet states. State Tanabe-Sugano Diagram for the d 2 Configuration Figure S2: Tanabe-Sugano diagram for the d 2 Configuration S13 splitting of 0.11 eV. These states correspond to the 3 T 1 ground-state term. At 1.54-1.81 eV, another grouping of three triplet states appears. Based on the Tanabe-Sugano diagram, these states should correspond to the 3T 2 term (of the parent 3 F term). Next, a group of four states follows at energies 3.14-3.50 eV. Based on the Tanabe-Sugano diagram, a 3T 1 term (of 3 P origin, threefold-degenerate) and a 3 A 1 term (of 3 F origin, one component) is expected next. Thus, these states T 7 -T 10 likely correspond to the 3 T 1 and 3 A 1 terms. From Table S5, we can see that states T 7 -T 9 share a (t 2g ) 1 (e g ) 1 electron configuration, while T 10 possesses a (e g ) 2 configuration. Thus, we will assign states T 7 -T 9 to the 3 T 1 term whereas T 10 corresponds to the 3 A 1 term.
Similar to the metal-centered triplet states, we can classify the singlet states in terms of ligand-field terms. The results are shown in Table S5 alongside the results of the triplet states. Note that for the states S 1 -S 5 , we cannot distinguish between the components of the 1 T 1 and 1 E terms. All calculated states share a (t 2g ) 2 configuration and their energetic splitting only amounts to 0.13 eV (between energies of 1.53-1.66 eV). Two of these states, the S 1 and S 2 , are found at the same energy. At first, this might suggest that these two states correspond to the components of the 1 E term. However, when considering that the components all other degenerate terms are split by energies of the order of 0.1 eV, the degeneracy of the S 1 and S 2 seems coincidentally rather than as a proof of their belonging to the 1 E term. S14

S2.4 Transition Density Analysis
To further investigate the character of the electronic states, we have analyzed the transition densities γ IJ of all states using the TheoDORE routine 1 integrated in the WFA module in OpenMolcas. 2 We thereby divided the complex [V III (Cl) 3 (ddpd)] into three fragments: the metal atom M, the organic ddpd ligand (L1), and the three chlorido ligands (L2) [see      Tables S9 and S10 list the two sets of obtained MS-CASPT2 energies of the triplet and singlet states alongside the CASSCF(10,13) reference as well as the CASSCF-CASPT2 energy differences in eV and cm −1 , respectively. Additionally, the results are pictorially shown in Figure S3    In addition, we also note that the 1 MC 3 state is stabilized in energy when going from CASSCF to IPEA-CASPT2 and NOIPEA-CASPT2 by 0.47 and 0.58 eV, respectively. Interestingly, we find that IPEA-CASPT2 predicts larger excitation energies compared to NOIPEA-CASPT2, as it was found for organic molecules. 5 These differences are of the order of 0.1 eV for the MC states, while they can be 0.4-0.5 eV for the DL states.
While it is computationally unfeasible to perform the LVC parameterization using the CASPT2 level of theory, we will discuss later the possible implications on the excited-state dynamics of the here observed differences between CASSCF and CASPT2 results.

S4.1.1 Spin-Adiabatic Populations
In Figure S4, we show the time evolution of the spin-adiabatic triplet and singlet states.
Spin-adiabatic states are states characterized by their spin value and their energetic ordering.
This representation is complementary to the diabatic representation (see Fig. 4 in the main paper), in which the states can be distinguished by their electronic character.  Figure S4: Time-evolution of spin-adiabatic electronic states from the LVC dynamics of [V III (Cl) 3 (ddpd)] started at an excitation energy range between 3.0-3.5 eV.

S4.1.2 Singlet Diabatic Populations
In Figure S5, we show the time evolution of the diabatic singlet state populations, where the states are characterized according to Table S5. As can be seen, except for early simulation times, the singlet population is almost completely in the 1 MC 1 states, which correspond to the 1 T 2 and 1 E components of the (t 2g ) 2 configuration.

S4.2 Diabatic Character of Trajectories
In the main paper, we show the diabatic character of sample trajectories for simulation times up to 1 ps (Figure 4). Figure  we assigned a diabatic state character to a trajectory, if its diabatic population of a specific character exceeded a threshold of c 2 = 0.6. The influence of this threshold is analysed in Figure S7, we we compare results for 1 ps using the stricter threshold of c 2 = 0.7. As can be seen, using c 2 = 0.7, the amount of time steps where a trajectory cannot be assigned to a specific diabatic states increases, i.e., from 5 % to 13 % of the steps. However, overall, no large differences are apparent when comparing both thresholds. Thus, we used the threshold c 2 = 0.6 in the main paper.

S4.3 Kinetics
In Figure S8, we show the results of the kinetic model based on eqs. 4-6 from the main paper.
For early simulation times, the fit for the 3 MC 3 state populations decreases too rapidly compared to the actual 3 MC 3 population. In addition, the fit of the 3 MC 2 population decreases too rapidly at later simulation times. For these reasons, the decays of both populations were rather described by a biexponential possessing a fast and slow component, as discussed in the main paper.

S4.4 Possible Influence of CASPT2 Energies on the Dynamics
The dynamics simulations presented in he main paper are based on LVC potentials parameterized at the CASSCF level of theory. Unfortunately, it is computationally unfeasible to perform this parameterization at the MS-CASPT2 level of theory; however, here we would like to discuss how the found differences between the CASSCF and MS-CASPT2 excited state energies at the equilibrium geometry (recall Section S3) could affect the non-adiabatic dynamics.
First, we noted that the 3 MC 4 state appears at higher energies at the CASPT2 level of theory. This would likely quench the main relaxation pathway 3 MC 3 → 3 MC 4 to some extent, channeling more population through the 3 MC 3 → 3 DL 1 and 3 MC 3 → 1 MC pathways. Second, we noted that the lowest-excited singlet state, 1 MC 1 , which is also the state that accounts for the majority of the total singlet population, is lowered in energy at the MS-CASPT2 level of theory, while the lowest-excited triplet state, 3 MC 2 , is found at higher energies. Since, in our kinetic model the 1 MC states are partly depopulated to the 3 MC 2 state via back-ISC, the energetic shift when going from CASSCF to MS-CASPT2 could quench this depopulation.
Third, since the 1 MC 3 state is stabilized by ca. 0.5 eV at the MS-CASPT2 level of theory, it may play a larger role in the dynamics leading to an overall larger singlet population.
Thus, we can presume that, both, the fraction of population initially undergoing ISC from the 3 MC 4 to the 1 MC states, as well as the fraction of population then staying in the 1 MC states are underestimated in the CASSCF-based dynamics. Accordingly, the present results serve only to establish lower bounds for these quantities, and the true yield of singlet population leading to the experimentally observed phosphorescence can be larger.

S4.5 Triplet Density of States of Initial Conditions
The majority of the electronic population in the dynamics simulation is initially excited in the 3 MC 3 and 3 MC 4 states (97.5 %), with the remaining population being excited in the 3 DL 1 states (2.5 %). According to the energies of these states at the FC geometry ( Figure 2 in the main paper, Table S3 in the SI), the 3 DL 1 states lie ca. 1 eV higher in energy than the 3 MC 3,4 states. Nevertheless, the dynamics simulation show population flow from the 3 MC 3 to the 3 DL 1 states which increases the population of these states temporarily up to ca. 10 % ( Figure 4 in the main paper). This population flow is enabled due to the broad density of states of the 3 DL 1 states. To demonstrate this, we show in Figure S9 the density of states (DOS) of the individual triplet states at the geometries considered in the initial conditions -these are shown alongside as a superposition in Figure S9. As can be seen, the density of the 3 DL states (negative axis) is considerably broader than that of the 3 MC states. For the 3 DL 1 states, this DOS spans an interval of ca. 2 eV (from ca. 3 to 5 eV). In contrast, the spread of the DOS of the 3 MC 3 states, for example, is much smaller, with most DOS between 3.0 and 3.5 eV. The larger spread of the DOS of the 3 DL states can be understood by considering the geometries included in the initial conditions (right-hand side of Figure S9).
As can be seen, the geometries deviate from FC geometry primarily through motion in the ddpd ligand, while, e.g., the V−X distances to the ligating atoms (X = N, Cl) coordinated to the central V atom as well as their bonding angles X−V−Y remain almost fixed (X, Y, = N, Cl). As the 3 DL states are described in large parts by π → π * excitations at the ddpd ligand, the energy of these states is varied already in the initial conditions, i.e., geometries that are sampled from a Wigner distribution around the FC geometry. In contrast, the 3 MC are not affected by the motion in the ligand. They will only be influenced by the dynamics in the excited states which will change the V−X bond distances and X−V−Y bond angles as is discussed in Section 3.2 in the main paper. The time evolution of the internal coordinates V-X bond stretches and X-V-Y bond angles are discussed in the main paper. Here we comment on the wagging motion of the methyl groups, which is less important. To analyze the wagging motion of the methyl groups, we followed the time evolution of different pyramidalization angles including the methyl N atoms, the methyl C atom, and the two carbon atoms from the pyridine units that are bound to the respective nitrogen atom. For a combination of atoms A-B-C-D, the pyramidalization angle p is defined as 90 • minus the angle between the bond of A-B and the normal vector of the plane B-C-D. The time evolution of the so-calculated angles p are shown in Figure S10.
As can be seen, all remain close to the reference value of the ground-state geometry.

S4.7 Internal Coordinate Analysis
In the main paper, we show the time evolution of selected internal coordinates for the full simulation time of 0-10 ps in Figure 5. Here, we zoom into the 0-200 fs time window for the same coordinates in Figure S12 In addition, we have analyzed the time evolution of selected internal coordinates of trajectories exclusively in singlet states, see Figure S13. This was done by selecting trajectories where the active state possesses a spin expectation value of S 2 > 0.5. We can see that the time evolution of the trajectories in the singlet states is similar to that of the whole ensemble -which is representative for the trajectories in the triplet states, as these account for at least 90 % of all trajectories at all simulation times (see Figure 4 in the main paper.) However, notable differences can be seen for the first 5 ps, e.g., in the magnitude of the V−N distances, that are smaller for the singlet trajectories than for the whole ensemble. This can be explained considering that most of the ensemble traverses the 3

S4.8 CASSCF vs. LVC Potential Energy Curves
In this work, we have used LVC potentials parameterized at the CASSCF level of theory. The parameterization was performed at the Franck-Condon geometry of the T 0 ground state. It is now interesting to investigate how well the LVC potentials can approximate the CASSCF potentials at geometries displaced from the FC geometry. To test this, we have computed one-dimensional potential energy curves of the triplet states along some of the most active normal modes -as identified in Section S4.6. The calculations have been performed at the CASSCF(10,13) level of theory and using the parameterized LVC models. The resulting PES for the normal modes 7, 9, 12, 32, 36, and 39 are shown in Figure S14 alongside the average displacement (plus standard deviation) of the trajectories during the dynamics (repeated from Figure S11). The CASSCF curves are thereby given as solid lines, while the LVC curves are presented as dashed lines. As can be seen, for modes 7, 9, 12, 36, and 39, the LVC potentials approximate the CASSCF potentials also for large normal mode displacements well for all 16 triplet states. For normal mode 32, the LVC potential can approximate the CASSCF potential only well for negative displacements. This mode can be mainly characterized by an antisymmetric Cl 41 −V−N 2 stretching vibration (see also the vcl3ddpd.molden file given as additional supporting information), whereby a negative displacement increases the V N2 distance and decreases the C−41−V distance. For positive displacements (shortened V N distance, prolonged Cl 41 −V distance), the LVC curves increase too slowly for displacements larger than 2 arb. units. Thus, one may suspect, that in the dynamics using the LVC potentials, the trajectories could reach artificially large displacements along this normal mode coordinate. However, as can be seen next to the curves of mode 32, the average normal mode displacement of the trajectories throughout the dynamics lies between −0.1 and 0.5 with the standard deviation typically accounting for an interval of ±1.5. Thus, the fraction or trajectories of the ensemble that reaches the regions of displacements > +2 where the LVC potentials deviate considerably from the CASSCF potentials is very small. Importantly, such large displacements are only reached at later times in the dynamics -after ca. 3 ps -and, S43 thus, do not influence on the ISC processes.