Article pubs.acs.org/JCTC
Exploring the Mechanism of Ultrafast Intersystem Crossing in Rhenium(I) Carbonyl Bipyridine Halide Complexes: Key Vibrational Modes and Spin−Vibronic Quantum Dynamics Yu Harabuchi,†,‡ Julien Eng,§ Etienne Gindensperger,*,§ Tetsuya Taketsugu,†,‡ Satoshi Maeda,*,†,‡ and Chantal Daniel*,§ †
Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan CREST, Japan Science and Technology Agency, Tokyo 102-8666, Japan § Laboratoire de Chimie Quantique, Institut de Chimie Strasbourg, UMR-7177 CNRS/Université de Strasbourg, 1 Rue Blaise Pascal BP 296/R8, F-67008 Strasbourg, France ‡
S Supporting Information *
ABSTRACT: The mechanism of ultrafast intersystem crossing in rhenium(I) carbonyl bipyridine halide complexes Re(X)(CO)3(bpy) (X = Cl, Br, I) is studied by exploring the structural deformations when going from Franck−Condon (FC) to critical geometries in the low-lying singlet and triplet excited states and by selecting the key vibrational modes. The luminescent decay observed in [Re(Br)(CO)3(bpy)] is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. The dominant coordinates underlying the nonradiative decay process are extracted from minima, minimum energy seam of crossing (MESX) and minimum energy conical intersection (MECI) geometries obtained by the seam model function (SMF)/single-component artificial force induced reaction (SC-AFIR) approach. By choosing the normal modes used in MCTDH from the MECI and MESX geometries, not only the degenerate energy points but also the low-energy-gap regions are included. For this purpose a careful vibrational analysis is performed at each critical geometry and analyzed under the light of the pertinent nonadiabatic coupling terms obtained from the linear vibronic coupling (LVC) model augmented by spin−orbit coupling (SOC) in the electronic diabatic representation.
1. INTRODUCTION Ultrafast processes play a central role in transition metal complexes’ photophysics and photochemistry.1−3 Related experiments based on picosecond (ps) and femtosecond (fs) transient absorption/emission spectroscopies, and on optical laser pump−X-ray probe techniques using ps and fs X-ray pulses,4−6 are difficult to interpret and subject to unresolved questions. One key point is the interplay between spin−orbit coupling (SOC) and vibronic coupling. Indeed, spin−orbit and vibronic couplings directly influence the probability of elementary processes such as internal conversions and intersystem crossing (ISC). The interpretation of ultrafast structural changes, time-resolved spectra, quantum yields, and time scales of elementary processes or transient lifetimes not only need robust theoretical tools in quantum chemistry but developments in quantum dynamics for solving the electronic and nuclear problems. Quantum dynamics has to treat dynamical processes that are not confined to a single electronic potential energy surface (PES) and that violate the Born− Oppenheimer (BO) separation of electronic and nuclear motions, taking into account nonadiabatic coupling between two or more electronic states via several vibrational modes. Up to now three types of dynamical simulations, far from being routine, have needed specific developments to be © XXXX American Chemical Society
applicable to transition metal complexes and ultrafast phenomena circumscribed by spin−vibronic coupling: (i) the time-dependent formalism within the Condon approximation;7,8 (ii) the nonadiabatic surface-hopping semiclassical method;9 (iii) the multimode quantum wavepacket dynamics.10 In a recent study we have proposed a qualitative mechanism for the ultrafast luminescence decay and intersystem crossing processes through the seven low-lying singlet and triplet excited states of [Re(X)(CO)3(bpy)] (X = Cl, Br, I; bpy = 2,2′bipyridine) on the basis of time-dependent density functional theory (TD-DFT) electronic structures calculations performed in acetonitrile and including SOC effects.11 We have shown that the S2 absorbing state at 400 nm is responsible for the ultrafast decay observed in the first few tens of fs, whereas the intermediate luminescent signal observed between 550 and 600 nm is attributed to the low-lying S1 and T2 states. The longlived emission at 600−610 nm originates into the deactivation of the lowest triplet T1. In order to simulate and interpret the ultrafast luminescence decays observed experimentally in this series of molecules we have developed an effective matrix Hamiltonian for solving an 11 electronic states multimode Received: January 22, 2016
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DOI: 10.1021/acs.jctc.6b00080 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX
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Journal of Chemical Theory and Computation
local minima. An application of SC-AFIR to the SMF therefore gives many approximate MECI/MESX structures. True MECI/ MESX structures can then be optimized by any MECI/MESX optimization method starting from these approximate structures. S2/S1-MECIs, S2/T3-MESXs, S2/T2-MESXs, S2/T1-MESXs, S1/T3-MESXs, S1/T2-MESXs, S1/T1-MESXs, T3/T2-MECIs, and T2/T1-MECIs in [Re(Br)(CO)3(bpy)] complexes were explored by the SMF/SC-AFIR method. These searches were initiated from the FC structure. MECIs and MESXs that were found to be important in [Re(Br)(CO)3(bpy)] were optimized in [Re(X)(CO)3(bpy)] (X = Cl, I) using structures obtained for the case of X = Br as initial guesses. In applications of the SC-AFIR method, the collision energy parameter of 100 kJ/mol was adopted as suggested in our previous study. It was assumed that structural deformation occurs around the Re center, and 14 atoms, i.e., Re, X (Cl, Br, I), atoms in the three CO ligands, two nitrogen atoms in the bipyridine ligand, and four carbon atoms bonded to the nitrogen atoms, were chosen as the target atoms in the SC-AFIR search (see ref 17 for the meanings of the collision energy parameter and the target atoms). Energies and gradients were computed by the TDDFT with B3LYP functional.25,26 Solvent effects of acetonitrile were included by the conductor-like polarizable continuum model (CPCM).27−30 The SOC was not considered in geometry optimizations, since the SOC effect is reported not to be significant for minimum energy geometries at least for Cl and Br.11,12 The initial automated searches were performed using small basis sets (Re and I, SDD; H, C, N, and O, 6-31G; Cl and Br, 6-31G*), and all of the obtained geometries were further optimized with the larger ones (Re, SDD; H, C, N, O, Cl, and Br, cc-pVDZ; I, cc-pVDZ-pp). We also note that at all MECIs and MESXs the energy gap between two states is smaller than 0.0006 eV. In order to see connections between obtained structures, meta-IRC calculations (the steepest descent path in the mass-weighted coordinate) were performed starting from the most stable MECI and MESX geometries on the corresponding two electronic states. In these static calculations, all electronic structure calculations were performed using the Gaussian09 program.31 Structural deformations and optimizations were performed using a developmental version of the GRRM program,32 which has been developed to systematically explore local minima and first-order saddles on the PES and on the seam of a crossing hypersurface in combination with various electronic structure calculation program packages. It should be noted that all MECIs and MESXs shown below are fully optimized MECI and MESX structures that are optimized without artificial force of the AFIR method. TD-DFT S0 → Sn and Sn,Tn → S0 vertical transition energies are calculated on the initial state, namely, S0, Sn, and Tn, optimized geometries. The geometries of the critical points obtained by the SMF/ SC-AFIR are used in the vibrational mode selection for the development of a 14-dimensional potential functions to run MCTDH dynamics simulations discussed in section 3.5. The nonadiabatic coupling and SOC entering the model Hamiltonian for the dynamics along these selected modes are taken from our previous work (see ref 12) and discussion in section 3.4.
problem including both vibronic coupling and SOC within the linear vibronic coupling (LVC) approximation and the assumption of harmonic potentials.12 The first application to the study of [Re(Br)(CO)3(bpy)] complex after excitation at 400 nm allowed us to confirm that the fast decay of the initially populated electronic state is mainly due to vibronic coupling with a time scale of the order of the experimental one deduced from the time-resolved emission spectra. Six vibrational modes were included in this first quantum treatment of ultrafast ISC in a transition metal complex. [Re(X)(CO)3(bpy)] complexes possess 78 internal degrees of freedom, and the selection of vibrational modes included in the model for quantum dynamics is challenging. One way to improve our model is to explore the potential energy surfaces (PESs) associated with the relevant electronic excited states in order to determine critical geometries. Indeed, ultrafast nonradiative decays occur efficiently in regions where two states are nearly degenerated. Therefore, conical intersection (CI) between two states of the same spin and space symmetries as well as seam of crossing (SX) between two states of different spin and/or space symmetries will play an important role in ultrafast processes. Especially, minimum energy CI (MECI) geometries and minimum energy SX (MESX) geometries have been optimized as the most favorable points from the energetic point of view.13,14 MECIs and MESXs can be explored by using automated searching methods with the seam model function (SMF).15 The details of the SMF search for the small molecules are summarized in a previous review.16 More recently, the applicability of the S0/S1-MECI search was tremendously improved by using single-component artificial force induced reaction (SC-AFIR)17 (denoted SMF/ SC-AFIR) combined with the spin−flip (SF) TD-DFT.18,19 It is now possible to perform MECI search from the Franck− Condon (FC) point.20,21 The framework of the SC-AFIR/SMF approach can also be expanded to the search for MECI and MESX geometries between arbitrary pairs of electronic excited states at the TDDFT level. In the present work the ultrafast decay observed in [Re(Br)(CO)3(bpy)], a case study for this class of complexes, is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method.22−24 The dominant coordinates underlying the nonradiative decay process are extracted from minima, MECI and MESX geometries obtained by the SC-AFIR/SMF approach. By choosing the normal modes used in MCTDH from the MECI and MESX geometries, not only the degenerate energies points but also the low-energy-gap regions are included. For this purpose a careful vibrational analysis is performed at each critical geometry and analyzed under the light of the pertinent nonadiabatic coupling terms.
2. COMPUTATIONAL DETAILS In this section, computational details for exploration of critical points on the PES using the SC-AFIR method are described. This calculation resulted in minima on seams of crossing hypersurface between two different electronic states, i.e., MECIs and MESXs. SC-AFIR is a method to explore local minima and first-order saddles on a given function of molecular geometry. In this study, SC-AFIR was applied to the SMF rather than to the PES. The SMF is a model function which is composed of PESs of the two target electronic states. Its functional form was designed so that approximate MECI or MESX structures were obtained as
3. RESULTS AND DISCUSSION 3.1. [Re(X)(CO)3(bpy)] (X = Cl, Br, I) Critical Geometries and Energy Profiles. By the SMF/SC-AFIR searches, in total seven MECIs and four MESXs (one S2/S1-MECI, four T3/T2B
DOI: 10.1021/acs.jctc.6b00080 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX
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Journal of Chemical Theory and Computation MECIs, two T2/T1-MECIs, two S2/T3-MESXs, and two S1/T2MESXs) were found for the case of X = Br. Cartesian coordinates for all of the MECIs and MESXs as well as local minima obtained by the meta-IRC calculations from the MECIs and MESXs are listed in the Supporting Information. In Figure 1a−c, the relative energies of the S0, S1, S2, T1, and T2 state are indicated for the important geometries along the dominant decay path from FC to T1 minimum. The energy differences between the target state and the ground state are indicated in eV (in nm) for each point. As shown in Figure 1, the relative order of the T1, T2, S1, and S2 excited state at FC from the S0 electronic ground state is respected as compared to previous studies33,34,11 and ranges in the same domain of energy for the three complexes. Barely the decay path after photoexcitation to S2 is considered here. Exploring the MESXs between S2 and T3 states put in evidence a (S2/T3)-MESX higher in energy than the (S2/S1)-MECI justifying the neglect of T3 in the dominant decay path. An energy profile including a decay path through the stable S2/T3-MESX in the case of X = Br is shown in the Supporting Information (Figure S1). Assuming an ultrafast S2 → S1 → T2 → T1 decay, the pathway was determined following the nuclear relaxation from FC to (T1)min, via (S2)min → (S2/ S1) → (S1)min → (S1/T2) → (T2)min → (T2/T1) as indicated in gray shades in Figure 1a−c. The decay process can be divided into three different regions based on the energy gaps with S0 along the decay pathways for the three complexes. The first region is (S2)min 2.32 eV (X = Cl), 2.32 eV (X = Br), and 2.29 eV (X = I) above S0. The second region is (S1)min ∼ (T2)min 2.09−2.17 eV (X = Cl), 2.12−2.19 eV (X = Br), and 2.12−2.18 eV (X = I) above S0. The third region is (T1)min 1.94 eV (X = Cl), 1.97 eV (X = Br), and 2.01 eV (X = I) above S0. Although it is generally difficult to discuss time constants directly only from potential profiles, we try to compare the profiles here to previous experimental and theoretical knowledge to justify further use of critical points along the profiles in dynamics studies. The positions of S2 and T2 minima, inside S2/ S1 and T2/T1 intersections, corroborate the occurrence of an ultrafast S2 → S1 → T2 → T1 decay as observed experimentally. Long-time-scale phosphorescence (>150 ps) will result from T1 minimum decay as previously proposed.11 The potential energy profiles depicted in Figure 1a−c confirm the qualitative mechanism of luminescence proposed on the basis of optimized minima in the excited states only.11 Indeed the three time domains determined experimentally can be attributed to the three domains of energy: (i) an ultrafast decay within a few tens of fs from the S2 state at about 530 nm; (ii) an intermediate decay within a few hundreds of fs from S1 and T2 at about 575 nm; (iii) a long-time-scale phosphorescence (>150 ps) from T1 at 610 nm. In order to go further into the interpretation of the time-resolved emission spectroscopy observed for the three complexes a dynamical approach is mandatory. This qualitative matching between the theoretical potential profiles and experimental results justifies the use of the critical points obtained along the profiles in development of the potential functions used in MCTDH simulations, sections 3.4 and 3.5. The optimized geometries of each critical point described in Figure 1a−c are depicted in Figure 2 showing the important internal coordinates, rReX, rReCax, aXReCeq, aCeqReCeq, and aCaxReCeq. Significant geometrical deformations are localized around the coordination sphere centered on the Re atom. The Re−X bond stretching due to the mixed MLCT/XLCT11 nature of the first excited state characterizes the structural deformation from FC
Figure 1. Variations of the potential energy (eV) as a function of the critical geometries for [ReX(CO)3(bpy)] (X = Cl, Br, I). (a) X = Cl, (b) X = Br, and (c) X = I. Calculated absorption and emission wavelengths for each structure are also indicated in eV (in nm) (in red, singlet states; in blue, triplet states). Note that (S2)min and (T2)min are located inside the corresponding CIs, i.e., S 2 /S 1 and T 2 /T 1 intersections, respectively; the geometries for (S2)min and (T2)min are identical to S2/S1 and T2/T1 MECI geometries.
to S1 minimum. The structural deformations when going from the electronic ground state to the relaxed low-lying singlet and triplet excited states are quite small. After nuclear relaxation into the potential wells of the excited states S1 and T1 the Re− X shortening amounts to ∼0.10 Å whatever the spin state is. This value reproduces quite well the one obtained previously C
DOI: 10.1021/acs.jctc.6b00080 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX
Article
Journal of Chemical Theory and Computation
Figure 2. Structural changes along the decay path for [ReX(CO)3(bpy)] (X = Cl, Br, I). (a) X = Cl, (b) X = Br, and (c) X = I. Dihedral angles, Bond lengths, rReX and rReCax, and angles, aXReCeq, aCeqReCeq, and aCaxReCeq, are indicated. Note that (S2)min and (T2)min are located inside the corresponding CIs, i.e., S2/S1 and T2/T1 intersections, respectively; the geometries for (S2)min and (T2)min are identical to S2/S1 and T2/T1 MECI geometries.
Table 1. Vertical TD-DFT S0 → Sn and Sn, Tn → S0 Transition Energies (eV) and Associated Absorption/Emission Wavelengths (nm) of [ReX(CO)3(bpy)] (X = Cl, Br, I) in Acetonitrilea transition energies (eV)
abs/emission wavelengths (nm)b
exptl visible absc (nm)
exptl emission maximumd (nm)
decay timed
X = Cl S0 → S2 S0 → S1 S2 → S0 S1 → S0 T2 → S0 T1 → S0
2.98 2.84 2.32 2.09 2.10 1.94
415 437 536 592 590 638
(393) (418) (505/496)e (557/575)e (558/575)e (596/610)e
450−350, λmax = 371 450−350, λmax = 371
S0 → S2 S0 → S1 S2 → S0 S1 → S0 T2 → S0 T1 → S0
2.93 2.81 2.32 2.12 2.12 1.97
424 442 535 584 585 628
(399) (422) (522/505)e (553/576)e (571/587)e (592/609)e
450−350, λmax = 375 450−350, λmax = 375
S0 → S2 S0 → S1 S2 → S0 S1 → S0 T2 → S0 T1 → S0
2.77 2.70 2.29 2.14 2.12 2.01
448 459 541 578 585 617
(424) (438) (536/577)e (552/595)e (596/620)e (587/620)e
450−350, λmax = 385 450−350, λmax = 385
525 575 575 600−610
85 fs 340 fs
530 570
128 fs 470 fs
600−610
>150 ps
525 575
152 fs 1180 fs
600−620
>150 ps
>150 ps
X = Br
X=I
a
Note that (S2)min and (T2)min are located inside the corresponding CIs, i.e., S2/S1 and T2/T1 intersections, respectively; the geometries for (S2)min and (T2)min are identical to S2/S1 and T2/T1 MECI geometries. bIn parentheses previous work from ref 11. cFrom ref 34. dFrom ref 33. eWith/ without SOC.
The T1 and T2 triplet states in the bromide and iodide substituted complexes are the seat of a moderate bending of the halide−Re−Cax angle complemented by an opening of the NReX angle. This effect increases with the XLCT character. The difference in the experimental lifetime for X = Cl, Br, and I at the first stage of the decay process may be qualitatively explained on the basis of the structural deformation between FC and S1 geometries. Because the stretching mode for the heavier atom should be slower, the lifetime at the first stage
for the S1 and S2 singlet states (
