Photoinduced Low-Spin → High-Spin Mechanism of an Octahedral Fe(II) Complex Revealed by Synergistic Spin-Vibronic Dynamics

The Fe(II) low-spin (LS; 1A1g, t2g6eg0) → high-spin (HS; 5T2g, t2g4eg2) light-induced excited spin state trapping (LIESST) mechanism solely involving metal-centered states is revealed by synergistic spin-vibronic dynamics simulations. For the octahedral [Fe(NCH)6]2+ complex, we identify an initial ∼100 fs 1T1g → 3T2g intersystem crossing, controlled by vibronic coupling to antisymmetric Fe–N stretching motion. Subsequently, population branching into 3T1g, 5T2g (HS), and 1A1g (LS) is observed on a subpicosecond time scale, with the dynamics dominated by coherent Fe–N breathing wavepackets. These findings are consistent with ultrafast experiments, methodologically establish a new state of the art, and will give a strong impetus for further intriguing dynamical studies on LS → HS photoswitching.

P hotoinduced low-spin (LS) → high-spin (HS) transition in transition-metal complexes, known as light-induced excited spin state trapping (LIESST), has attracted great interest since its discovery in 1984. 1 LIESST is an intriguing phenomenon both from the point of view of the fundamentals of excited-state processes and revolutionary applicational areas, such as molecular data storage. 2 It is known that the LS-to-HS transition can also be triggered by varying the temperature, pressure, and magnetic field; 3 in fact, the first discovery of these so-called spincrossover (SCO) complexes is dated way back to 1931. 4 In the past two decades, the LIESST mechanism has been a very "hot" research topic; this is motivated by the fact that the gained knowledge may allow control of excited-state pathways and thus can lead to the design of improved functional molecules and technologies. In the case of switchable hexacoordinated complexes with a Fe II N 6 core, which by far dominate the known LIESST-exhibiting systems, irradiation of light converts the singlet ground state [ 1 A 1g (LS), t 2g 6 e g 0 ] into a quintet metastable state [ 5 T 2g (HS), t 2g 4 e g 2 ]; thus, a ΔS = 2 net change of the spin momentum occurs. The LIESST mechanism was first investigated in 1991 by Hauser 5 1 T 1g in <150 fs and decays into the 5 T 2g HS state in 1.2 ps. 6 The HS state is metastable at low temperatures (T < 50 K), and its lifetime is determined by quantum-mechanical tunneling.
Despite these valuable mechanistic insights, several unknowns remain, in most cases, because of the ambiguities in the interpretation of the experimental data. An excellent example is the more complicated case of [Fe(bipy) 3 ] 2+ (bipy = 2,2′bipyridine), a LS Fe(II) complex, which became the LS ↔ HS photoswitching prototype for time-resolved investigations.
[Fe(bipy) 3 ] 2+ is converted to the HS state in <100 fs, initiated   by irradiation into the optically active singlet metal-to-ligand charge-transfer (MLCT) band. This <100 fs time scale and the HS lifetime (ca. 650 ps in aqueous solution) are consistent for various experimental studies, but it is strongly debated how the HS state is populated. 7−9 A final consensus is yet to be established; in order to achieve this goal, theory, which has the potential to complement and support time-resolved experiments, has a crucial role. However, the computational state of the art for light-induced singlet-to-quintet transitions has so far been limited to analysis of the static potential energy surfaces (PESs) 10 /couplings 11 and estimation of the excited-state lifetimes by Fermi's golden rule. 12,13 Albeit often useful, these approaches face severe shortcomings when it comes to fast electronic relaxation such as LIESST, with a time scale comparable to that of nuclear motion. In fact, this nuclear− electronic coupling, leading to a dynamic mixing of the electronic states, is among the main sources for the complexity of the obtained time-resolved experimental data, which theory is intended to alleviate.
In this Communication, we present the first theoretical dynamics study on LS → HS photoswitching with excitation into 1 MC states ( 1 T 1g , [Fe(ptz) 6 ] 2+ prototype; Figure 1). In order to achieve feasibility at a high computational level, we investigate the excited-state dynamics of [Fe(NCH) 6 ] 2+ , a wellestablished model 14−17 for metastable Fe(II)-based SCO systems. Its validity, with a special emphasis on LIESST, is discussed in the Supporting Information (SI). Employing a synergistic spin-vibronic approach, 18,19 we achieve an invaluable mechanistic understanding, whose adequacy is assessed and confirmed by its consistency with the above-discussed experiments.
Herein, we employ a synergistic approach, which exploits the complementary character of trajectory surface hopping (TSH; full dimensionality) and quantum dynamics (QD; fully quantum description). We utilize full-dimensional TSH on potentials computed on-the-fly to select the dominant nuclear degrees of freedom and QD on high-level ab initio (CASPT2) precomputed surfaces along the selected modes for the accurate simulation of LIESST excited-state dynamics. A brief methodological description is provided in the Computational Methods section, with details given in the SI. Figure 2 presents the normal-mode activity of the vibrational motion, obtained from the excited-state TSH trajectories. As is clear from the figure, three modes, ν 13 , ν 14 , and ν 15 , dominate the excited-state nuclear motion. As shown in Figure 3, all three modes have Fe−N stretching character, but while the 2-folddegenerate ν 13 and ν 14 modes are antisymmetric, ν 15 is a totally symmetric (breathing) mode. These three Fe−N stretching modes are in excellent agreement with the natural choice of coordinates upon the occupation of e g * antibonding orbitals, shown in Figure 1, in MC excited states. Figure 4 shows the PESs along modes ν 15 and ν 14 ; the PESs along ν 13 are shown in Figure S7. While the ν 15 breathing mode is crucial to connect the LS ( 1 A 1g ) and HS ( 5 T 2g ) states ( Figure  4a), it maintains the octahedral symmetry and does not allow the different singlet and triplet MC components to cross. The reason for this is that, in the singlet and triplet excited states, a single e g * orbital is populated, which activates antisymmetric Fe−N stretching modes, while the ν 15 breathing mode is totally symmetric. Indeed, as seen in Figure 4b, the excited-state potentials split along ν 14 , allowing the possibility of singlet− triplet ISC and triplet internal conversion (IC) via the intersection of the corresponding MC PESs.
In Figure 5, we present the electronic population dynamics, as obtained from the three-dimensional QD simulation utilizing the selected modes and all relevant singlet−triplet−quintet states. As shown in the figure, the 1 T 1g population decay has two components, characterized by the 39 and 168 fs exponential time constants. These time scales are in excellent agreement with the experimentally observed <150 fs ISC. 6 As proposed by Marino et al., 6 the 1 T 1g states indeed deactivate via the 3 T 2g states. Subsequently, the excited-state population flows on a subpicosecond time scale to 3 T 1g by triplet IC and to the 5 T 2g manifold via triplet−quintet ISC; as a minor component, the ground state 1 A 1g is recovered. The 3 T 1g population is stable on the 1 ps time duration of the simulation, which is consistent with its 39 ps 6 lifetime detected experimentally. 20 Crucially, the simulated dynamics captures all important aspects of the LIESST mechanism revealed by experiments: very fast singlet−triplet ISC, the role of 3 T 2g states as intermediates, and branching into the HS/LS states. This consistency supports the presented results, which for certain aspects, such as the singlet−triplet ISC, reach even a quantitative agreement with experiment. 6 Figure 2. Dynamic normal-mode activity, as determined from the standard deviation of nuclear displacements, projected onto the ground-state normal modes. This was obtained from the singlet− triplet TSH simulations. The labels of the three dominant normal modes, ν 13 , ν 14 , and ν 15 , are depicted. As illustrated in Figure 3, the character of these three modes is Fe−N stretching. Finally, we reveal fine details of the LIESST mechanism based on the time evolution of excited-state nuclear wavepackets. We now analyze the singlet−triplet ISC along ν 14 , which is the natural choice for the involved 1 T 1g / 3 T 2g states (occupation of a single e g * orbital). Figure 6a shows snapshots of the excited-state singlet wavepacket along ν 14 for the initial 200 fs. The 1 T 1g wavepacket immediately starts to propagate away from q 14 = 0, entering the 1 T 1g / 3 T 2g crossing region. This, combined with a sizable spin−orbit coupling (∼175 and 250 cm −1 ), allows efficient ISC to the 3 T 2g manifold, which is indeed what is observed in Figure 5. On the 100−200 fs time scale, the wavepacket becomes more diffuse, which is the reason why the ISC is slower for >100 fs. These results highlight the importance of vibronic motion, as confirmed by the discrepancy between the 36 ps 1 T 1g → 3 T 2g ISC time constant of ref 13 for [Fe(mtz) 6 ] 2+ , based on Fermi's golden rule, and the <150 fs experimental 6 and simulated 39/168 fs values obtained in this work.
In Figure 6b, we analyze the wavepacket motion in the intermediate 3 T 2g state along ν 15 . Clearly, a coherent wavepacket oscillation is induced, with a period of ∼110 fs. The wavepacket dephases and spreads, and, importantly, the Gaussian full width at half-maximum (fwhm, green) does not reach the crossings with the 5 T 2g and 1 A 1g states (dashed lines in Figure 6b). This is to say that the 3 T 2g wavepacket only slightly leaks into the crossing region, which is the reason why the quintet population rises relatively slowly (in [Fe(bipy) 3 ] 2+ , the HS state is   populated in <100 fs 7,8 ). Although the wavepacket gains more access to the 3 T 2g / 5 T 2g intersection along ν 14 , this channel does not allow significant net population flow to the 5 T 2g states. This is due to very efficient 5 T 2g → 3 T 1g deactivation, favored by the energetics and easy access to the crossing region (located just at the 5 T 2g minimum) along ν 14 , as is clear from Figure 4b.
In this Communication, we revealed the Fe(II) LIESST mechanism of Fe[(NCH) 6 ] 2+ using synergistic spin-vibronic dynamics simulations. The obtained mechanistic picture is consistent with the experimental findings and includes assignment of the principal intermediate 3 T 2g , whose dynamics are controlled by the key antisymmetric (ν 14 ) and symmetric (ν 15 ) Fe−N stretching vibrations. Importantly, the present work establishes a new theoretical state of the art for LS → HS photoswitching and will certainly motivate intriguing dynamical studies, both experimental and theoretical ones.