Nonadiabatic Quantum Dynamics - ACS Publications - American

Article pubs.acs.org/JCTC

Ultrafast Excited-State Decays in [Re(CO)3(N,N)(L)]n+: Nonadiabatic Quantum Dynamics Maria Fumanal, Etienne Gindensperger, and Chantal Daniel* 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 ultrafast luminescent decay of [Re(CO)3(phen)(im)]+, representative of Re(I) carbonyl α-diimine photosensitizers, is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. On the basis of electronic structure data obtained at the time-dependent density functional theory (TD-DFT) level, the luminescence decay is simulated by solving a 14 electronic states multimode problem including both vibronic and spin−orbit coupling (SOC) up to 15 vibrational modes. A careful analysis of the results provides the key features of the mechanism of the intersystem crossing (ISC) in this complex. The intermediate state, detected by means of fs - ps timeresolved spectroscopies, is assigned to the T3 state corresponding to the triplet intraligand (3IL) transition localized on the phen ligand. By switching off/on SOC and vibronic coupling in the model it is shown that efficient population transfer occurs from the optically active metal-to-ligand-charge-transfer1,3MLCT states to T3 and to the lowest long-lived phosphorescent 3MLCT (T1) state. The early ultrafast SOC-driven decay followed by a T3/T1 equilibration controlled by vibronic coupling underlies the photoluminescent properties of [Re(CO)3(phen)(im)]+. The impact of the axial and N,N ligands on the photophysics of this class of Re(I) complexes is further rationalized on the basis of their calculated optical properties. The relative position of the 3IL and upper 3MLCT states with respect to the optically active singlet state is influenced by the N,N ligand and affects the relaxation dynamics.

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INTRODUCTION Rhenium(I) carbonyl-diimine complexes have been extensively studied in the past decades for their fascinating photophysical and photochemical properties used in a wide range of chemical and biological applications.1,2 Advanced spectroscopic studies have enabled to follow excited states decay and associated primary events occurring in the first ps.3−5 A series of [Re(CO)3(N,N)(X)] (X = Cl, Br, I) and [Re(CO)3(N,N)(im)]+ (im = imidazole; N,N = 2,2′-bipyridine (bpy); 1,10phenanthroline (phen); 4,7-dimethyl-phen (dmp)) complexes have been investigated combining fluorescence up-conversion, time-resolved UV/vis absorption, and IR spectroscopies with density functional theory6−8 providing valuable information on (i) the electronic and structural properties of the optically populated excited states; (ii) the ps time-scale decay kinetics and associated elementary steps; (iii) the role of spin−orbit, vibronic, and solvation effects. On the basis of the characteristics of time-resolved luminescence and absorption spectra measured for the different molecules a general mechanism (Scheme 1) has been suggested for describing the ultrafast excited states dynamics of these Re(I) photosensitizers. According to the proposed mechanism the low-lying metalto-ligand-charge-transfer 1MLCTNN states optically active at 400 nm decay via intersystem crossing (ISC) within 100−150 fs to two triplet states, namely the long-lived phosphorescent © 2017 American Chemical Society

MLCTNN and an intermediate one. The Re-X/Rei-m vibrational frequencies play a role in this first elementary step that is independent of the N,N ligand and is marginally influenced by spin−orbit coupling (SOC). Time-resolved infrared (TRIR) spectra reveal a simultaneous sub-ps population of the two triplet states, the intermediate one being predominantly 3ILNN. The second decay lifetime occurring within 1−5 ps has not been correlated to any specific elementary step and should include spin-vibronic relaxation and equilibration between the two triplet states. Late vibrational relaxation and solvation dynamics contribute to the slow kinetic component of a few tens of ps observed in the time-resolved absorption spectra.8 The static picture of the luminescent properties of this class of Re(I) complexes based on accurate quantum chemical calculations of the electronic and photophysical properties of the reference molecules [Re(CO) 3 (bpy)(X)] and [Re (CO)3(phen)(im)]+ correlates nicely with the three experimental luminescent decay domains (Scheme 1), as discussed previously.9−11 In order to interpret the ultrafast decays observed in [Re(CO)3(bpy)(Br)] complex we have recently developed a method able to simulate ISC and internal conversion (IC) Received: December 9, 2016 Published: February 13, 2017 1293

DOI: 10.1021/acs.jctc.6b01203 J. Chem. Theory Comput. 2017, 13, 1293−1306

Article

Journal of Chemical Theory and Computation

rationalization of the influence of the different ligands on the ultrafast decay mechanism is performed on the basis of the theoretical optical properties of [Re (CO)3 (N,N)(L)] n complexes with L = imidazole or halide and N,N = phenanthroline or bipyridine complexes.

Scheme 1. Qualitative Mechanism of Ultrafast Decay in Re(I) Carbonyl α-Diimine Complexes and Associated Emissive Domains of Energy Based on Experimental Data from Ref 8a

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COMPUTATIONAL DETAILS Model Hamiltonian. The model Hamiltonian used in the present work has been introduced recently12,13 and includes vibronic and SOC within the linear vibronic coupling (LVC) model.15,16 The Hamiltonian reads Η = (TN + V0)1 + W

where V0 is the ground state potential energy surface, here taken to be harmonic with vibrational frequencies ωi along dimensionless normal coordinates Qi, TN is the kinetic energy of the nuclei, 1 is the identity matrix, and W is the potential energy matrix that contains the SOC and vibronic coupling terms. The vibronic interactions are constructed from the diabatic electronic representation including the intrastate, κ(n), and interstate, λ(n,m), coupling constants where n and m label the electronic states. These coupling terms are extracted from the gradients and Hessians of the excited states, evaluated at the Franck−Condon point (FC, Qi = 0) and correspond to the following expressions, where Vn is the adiabatic potential energy surface of the state n obtained from quantum chemistry calculations.15 For Cs symmetry with a′ and a′′ modes, it comes

a

CT: charge-transfer; MLCT: metal-to-ligand-charge-transfer; IL: intraligand.

faster than a few ps. This method relies on quantum dynamics simulations based on the spin-vibronic model Hamiltonian12 in the electronic diabatic representation. The selection of key vibrational modes from the model13 corresponds to that obtained independently by the artificial force induced reaction (AFIR) method.14 The spin-vibronic quantum dynamics revealed that the ultrafast decay of the electronic population of the initially excited state occurs in less than 150 fs, in agreement with experimental findings.6 The population decays to an intermediate mixed singlet−triplet MLCT/XLCT state, which in turn relaxes to the lowest triplet state from which long-lived luminescence is observed.6 The aim of the present paper is to go beyond the static picture and to interpret the experimental kinetics of the elementary steps, depicted in Scheme 1, for the [Re(CO)3(phen)(im)]+ complex. To decipher the role of SOC and vibronic effects in the ultrafast dynamics we exploit the spin-vibronic model to perform wavepacket propagations on the constructed coupled diabatic potentials. We restrict here our investigation to the conformer of Cs symmetry (Scheme 2). A detailed vibrational analysis and various normal modes selections are presented, and the associated time-dependent electronic population dynamics is discussed. Decay time-scales are compared to experimental findings.8 Finally, a tentative

κi(n) =

λi(n , m)

∂Vn ∂Q i

for i ∈ a′ 0

⎛ 1 ∂2 ⎞1/2 2 (|Vm − Vn| )⎟⎟ , = ⎜⎜ 2 ⎝ 8 ∂Q i ⎠

n≠m

0

The later equation gives, when developed, two distinct equations for a′ and a′′ modes, depending on the symmetry of the electronic states involved λi(n , m)

⎛ε − ε ⎛ 2 ⎞1/2 ∂ 2 ⎞⎟ m n⎜ ∂ ⎜ =⎜ V − Vn⎟⎟ ⎜ 2 m ∂Q i2 ⎠⎟⎠ ⎝ 4 ⎝ ∂Q i

0

for i ∈ a″ and states n and m of different spatial symmetry and 1/2 ⎛ε − ε ⎛ 2 (m) (n) 2 ⎞ ∂ 2 ⎞ (κi − κi ) ⎟ n⎜ ∂ ⎟ λi(n , m) = ⎜⎜ m − − V V n⎟ ⎜ 2 m ⎟ 8 ∂Q i2 ⎠ ⎝ 4 ⎝ ∂Q i ⎠

0

for i ∈ a′ and n and m of the same spatial symmetry, with n ≠ m. εn is the “spin-orbit free” vertical transition energy of state n. The last term in the right-hand-side of the last equation comes from the fact that the gradients are nonzero along totally symmetric a′ modes. The contributions of the κ(n) in the i for i ∈ a′ will lead to interesting effects which equation for λ(n,m) i will be discussed later in the section dedicated to the Results and Discussion. We can already notice that if κ(m) = κ(n) i i , for states n ≠ m but of the same symmetry, then the contributions of the gradients vanishe. Also, if one κ(n) is large compared to i κ(m) or vice versa, this will lower and even suppress (imaginary i

Scheme 2. Structure of [Re(CO)3(phen)(im)]+ Conformer A of Cs Symmetry

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Table 1. Calculated Transition Energies (in eV) Associated with the Six “Spin-Orbit Free” and 14 Low-Lying “Spin-Orbit” States (and Composition) of [Re(CO)3(phen)(im)]+

a

SO-freestate

TD-DFT transition energies

SOstate

composition

TD-DFT/SOC transition energies

model compositiona

model/SOC transition energiesa

Δa

T1 (A″) T2 (A′) S1 (A″) T3 (A″) S2 (A′) T4 (A′)

2.98 3.07 3.10 3.24 3.35 3.42

E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14

T1 75% T2 18% T1 75% T2 18% T1 90% S1 43% T2 48% T2 75% T1 20% T2 75% T1 20% S1 45% T2 50% T3 88% T3 88% T3 88% S2 64% T4 15% T5 60% T4 22% T5 54% T4 30% T5 55% T4 19%

2.91 2.92 2.93 2.99 3.09 3.09 3.15 3.22 3.24 3.24 3.35 3.39 3.39 3.40

T1 85% T2 11% T1 85% T2 11% T1 86% T2 11% S1 45% T2 41% T2 89% T1 10% T2 88% T1 10% S1 44% T2 47% T3 94% T3 95% T3 95% S2 88% T4 6% T4 92% T4 92% T4 85%

2.96 2.96 2.97 3.06 3.08 3.08 3.10 3.24 3.24 3.24 3.38 3.44 3.44 3.45

0.05 0.04 0.04 0.07 −0.01 −0.01 −0.05 0.02 0.00 0.00 0.03 0.05 0.05 0.05

The composition and values obtained after truncation within the model Hamiltonian and the difference Δ are provided for comparison.

value of λ(n,m) ) the interstate coupling between two states of the i same symmetry. Six low-lying “spin-orbit free” excited states of [Re(CO)3(phen)(im)]+ are potentially involved in the ultrafast relaxation process studied herein, two singlets S1 (a1A″) and S2 (b1A′) and four triplets T1 (A3A″), T2 (A3A′), T3 (B3A″), and T4 (B3A′) (see discussion in section 1.1 of Results). Therefore, the W matrix reads as follows, where the star stands for the conjugate transpose: ⎛ WT1,T1 ⎜ ⎜ W *T1,T2 ⎜ ⎜ W *T1,S1 W=⎜ ⎜ W *T1,T3 ⎜ ⎜ W *T1,S2 ⎜ ⎝ W *T1,T4

WT1,T2

WT1,S1 WT1,T3

WT2,T2

WT2,S1 WT2,T3

W *T2,S1 W S1,S1

W S1,T3

W *T2,T3 W *S1,T3 WT3,T3 W *T2,S2 W *S1,S2 W *T3,S2 W *T2,T4 W *S1,T4 W *T3,T4

WT1,S2 WT1,T4 ⎞⎟ WT2,S2 WT2,T4 ⎟ ⎟ W S1,S2 W S1,T4 ⎟ ⎟ WT3,S2 WT3,T4 ⎟ ⎟ W S2,S2 W S2,T4 ⎟ ⎟ W *S2,T4 WT4,T4 ⎠

∑ κi(n)Q i i∈a′

W S1,S2 =

λj(S1,S2)Q j

∑ j ∈ a ′′

W Sn(A ′),Tm(A ′) = W Sn(A ′′),Tm(A ′′) = (0; ηSn,Tm ; 0)

Tm(A ′),Sn(A ′)

W

Tm(A ′′),Sn(A ′′)

=W

⎛ 0 ⎞ ⎜ ⎟ = ⎜ ηSn,Tm ⎟ ⎜ ⎟ ⎝ 0 ⎠

* ; 0; η W Sn(A ′),Tm(A ′′) = W Sn(A ′′),Tm(A ′) = (ηSn,Tm ) Sn,Tm

WTm(A ′),Sn(A ′′) = WTm(A ′′),Sn(A ′)

⎞ ⎟ ⎟ ⎟ ηTn,Tm ⎟ ⎟ ⎟ (Tn,Tm) Q j⎟ ∑ λj ⎟ j ∈ a ′′ ⎠

WTn(A ′′),Tm(A ′′) = WTn(A ′),Tm(A ′) = ⎛ (Tn,Tm) Q i+ηTn,Tm 0 ⎜ ∑ λi ∈ ′ i a ⎜ ⎜ 0 ∑ λi(Tn,Tm)Q i ⎜ i∈a′ ⎜ ⎜ 0 0 ⎜ ⎝

⎞ ⎟ ⎟ ⎟ 0 ⎟ ⎟ ⎟ * ⎟ ∑ λi(Tn,Tm)Q i+ηTn,Tm ⎠ i∈a′

0

0

where the SOC ηn,m constants (complex-valued) are obtained from electronic structure calculations at FC. The latter are kept constant in the wavepacket propagations. Notice that, due to symmetry selection rules, only a′ modes will give nonzero κ(n) i and interstate coupling λ(n,m) between states of the same spacial i symmetry (T1/T3 and T2/T4), while only a a′′ mode will couple states of different special symmetries. Electronic Structure. The electronic structure data used in this work are reported in detail in our recent papers.10,11 The Cs optimum structure of the electronic ground state (Scheme 2) and low-lying excited states was obtained by means of DFT including solvent corrections (water) using a conductor-like screening model (COSMO).17−19 The calculations were performed using the B3LYP functional,20 the D3 parametrization of Grimme,21 and all electron triple-ξ basis set.22 The scalar relativistic effects were taken into account within the zeroth-order regular approximation (ZORA).23 The vertical transition energies were computed within TD-DFT24,25 at the same level described above under the Tamm-Dancoff approximation (TDA).26 The TD-DFT results were validated by SA-CASSCF/CASPT2 calculations.10 In this recent article it is shown that TD-DFT as well as SA-CASSCF(10,10)/ CASPT2 gives rather good transition energies and a correct assignment of the lowest excited states, more specifically the broad MLCT band observed in the experimental spectrum between 420 and 330 nm, region of interest in the present

Note that we explicitly consider the triplet’s components, yielding a 14 states W matrix. The different submatrices are defined as follows: W n,n = εn +

WTn(A ′),Tm(A ′′) = WTn(A ′′),Tm(A ′) ⎛ (Tn,Tm) Qj ηTn,Tm ⎜ ∑ λj ⎜ j ∈ a ′′ ⎜ * ∑ λj(Tn,Tm)Q j = ⎜ − ηTn,Tm ⎜ j ∈ a ′′ ⎜ * ⎜ − ηTn,Tm 0 ⎜ ⎝

⎛η* ⎞ ⎜ Sn,Tm ⎟ =⎜ 0 ⎟ ⎜⎜ ⎟⎟ ⎝ ηSn,Tm ⎠ 1295


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the 14 × 14 W matrix at FC. In all cases the difference is less than 0.07 eV in absolute value, thus, they have not been adjusted in the model. The SOC terms between the aforementioned six lowest singlet and triplet states are given in Table 2. It can be seen that

study. The SOC effects were introduced according to a simplified relativistic perturbative TD-DFT formalism.27,28 The normal modes of the ground singlet state S0 (a1A′) are used herein to build the model multidimensional potential energy surfaces. All calculations were done with the ADF2013 code.29 Wavepacket Propagation. The time-dependent Schrödinger equation for the nuclei is solved by employing the multiconfiguration time-dependent Hartree (MCTDH) method.30−32 Here the multiconfiguration nuclear wave function is expressed as a linear construction of Hartree products of timedependent basis functions, known as single-particle functions (SPF). The wavepacket ansatz adapted to the present nonadiabatic problem corresponds to the multiset formulation.31 The mode combination, number of primitive basis, and SPF used in the largest simulation are given in Table S1 (SI section). The choice is adapted to the small energy differences between the excited states and to the small displacement of the potentials due to modest κ(n) coupling terms. Harmonicoscillator basis sets were employed. The initial wavepacket corresponds to the harmonic ground vibrational state of the ground electronic state S0, promoted at time zero to the S2 absorbing state. The Heidelberg MCTDH Package is used (version 8.4.10).33

Table 2. SOC Terms (in cm−1) at Franck-Condon between the Six Lowest Singlet and Triplet Electronic Excited States of [Re(CO)3(phen)(im)]+a state set

SOC η

state set

SOC η

S1T1 S1T2 S1T3 S1T4 S2T1 S2T2 S2T3

0−2i (2) −126−369i (390) 0 + 4i (4) −586−48i (588) −281−397i (487) 0 + 138i (138) 96 + 94i (134)

S2T4 T1T2 T1T3 T1T4 T2T3 T2T4 T3T4

0−498i (498) −109−318i (336) 0−0i (0) −528−65i (531) 56 + 170i (179) 0−453i (453) 201−40i (205)

a

Only one component is given in each case (see text). The modulus is shown in parentheses.

the largest SOC values correspond to the sets S1T2, S1T4, S2T1, and S2T4. However, the E11 state displays significant S2/T4 mixing and does not show S2/T1 mixing because of the large energy difference between the S2 and T1 states. The E4 and E7 states show half-and-half S1/T2 composition and lack of S1/T4 mixing because of the same reason (see Table 1). The T1 and T2 states display a large mixing in the lowest “spin-orbit” excited states due to strong SOC and small energy difference. It is worth noting that the E12, E13, and E14 states are characterized by a large contribution of T5 at the TD-DFT level. However, this state is not involved in the main absorbing state, and the resulting shift in the excitation energies is only about 0.05 eV. Moreover, when including the T5 state in the Hamiltonian the early time dynamics is basically not modified (results not shown). Vibrational Analysis and Normal Modes Selection. [Re(CO)3(phen)(im)]+ has a total of 108 internal degrees of freedom, 60 of which are of a′ symmetry and 48 are of a″ symmetry. However, the dimensionality of the system has to be reduced in order to efficiently perform quantum dynamics simulations. For symmetry reasons, only the totally symmetric a′ normal modes induce intrastate κ(n) coupling and interstate λ(n,m) vibronic coupling between electronic states of the same spatial symmetry. The nontotally symmetric a″ normal modes contribute to the interstate λ(n,m) vibronic coupling between electronic states of different spatial symmetry. Considering the ground state potential (V0) as the reference potential, the excited states diabatic potentials are represented by shifted harmonic oscillators along the a′ normal modes. The shifts in equilibrium position and in energy along a particular (n)2 mode i are given by −κ(n) i /ωi and κi /(2ωi), respectively. These shifts in position and in energy correspond to the displacements and energy-scaled contributions, respectively, along a′ normal modes. A selection is performed in order to include the a′ normal modes that contribute most importantly to the geometrical deformation and energy shift of the excited state minimum energy points. However, it is also of prime importance to consider modes that lead to large differences in the κ(n) i values of the excited states, in particular, those that led to a different sign of κ(n) i shifting the excited states in opposite directions from the FC point.12,13 Ultimately, this may induce low-energy crossing points between the diabatic potentials

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RESULTS AND DISCUSSION Electronic Excited States and Spin−Orbit Coupling. The electronic properties of [Re(CO)3(phen)(im)]+ have been extensively analyzed in recent articles.10,11 The experimental absorption spectrum reported for this complex shows the maximum of the visible broad band at about 375 nm,34 which was attributed to the S2 (b1A′) excited state. Therefore, all the excited states up to S2 can potentially participate in the ultrafast luminescence decay after irradiation into the visible, namely T1 (A3A″), T2 (A3A′), T3 (B3A″), and S1 (a1A″). However, previous theoretical studies10,11 have shown that the main absorbing S2 state is mixed with T4 (B3A′) by SOC, slightly higher in energy, indicating that this additional state should be taken into account in the model Hamiltonian as well. The lowest “spin-orbit free” excited-state energies are reported in Table 1. The six lowest excited states are of predominant MLCT character from Re(I) d-like occupied molecular orbitals to π*phen low-lying unoccupied orbitals. However, the T3 excited state is also characterized by an important π → π* ILphen contribution (about 30% at FC). Remarkably, the electronic characteristics between S1 and T1 (and between S2 and T2) are nearly identical and involve the same d → π* MLCT electron excitation.11 Fourteen “spin-orbit” Ei states arise from the six “spin-orbit” free states when SOC is taken into account. According to the spin CS double group symmetry rules, T1 (A3A″) and T3 (B3A″) states generate two A′ and one A″ “spin-orbit” states, T2 (A3A′) and T4 (B3A′) states generate two A″ and one A′ states, S1 (a1A″) generates one A″ state, and S2 (b1A′) generates one A′ Ei state. The 14 “spin-orbit” excited state energies are reported in Table 1. As a consequence of the truncation performed on the number of states considered in the model Hamiltonian, the associated “spin-orbit” excited state energies can be artificially shifted with respect to the TD-DFT results. In Table 1, the values within the model restrained to the six lowest excited states are given and compared to those obtained when computing 50 singlet and triplets states at the TD-DFT level.10 These values are extracted from the diagonalization of 1296


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Figure 1. Nuclear deformations associated with the most relevant a′ and a″ normal modes of [Re(CO)3(phen)(im)]+ selected for the quantum dynamics simulations.

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Figure 2. Diabatic potential energy curves along Qi for the nine most relevant a′ normal modes of [Re(CO)3(phen)(im)]+. Each triplet state is triply degenerate in the diabatic representation.

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Table 3. Intrastate Coupling Values κ(n) (in eV) Associated with Each Excited State n, and Interstate Coupling Values λ(n,m) (in eV) between T1/T3 and T2/T4, Determined for the Selected a′ Normal Modesa

a

mode

ω (cm‑1)

ω (eV)

S1

S2

T1

T2

T3

T4

9a′ 18a′ 22a′ 27a′ 32a′ 38a′ 70a′ 77a′ 81a′ 88a′ 91a′ 93a′

93 235 439 498 552 637 1174 1336 1444 1554 1623 1660

0.0115 0.0291 0.0545 0.0618 0.0684 0.0790 0.1456 0.1656 0.1790 0.1926 0.2013 0.2058

0.0230 −0.0569 0.0104 −0.0891 0.0148 −0.0304 0.0728 0.1070 0.0824 −0.1850 0.1298 −0.0498

−0.0264 −0.0339 −0.0016 −0.0736 −0.0141 0.0485 0.0542 0.1070 0.0884 −0.1503 0.1058 −0.0171

0.0174 −0.0447 0.0123 −0.0777 0.0111 −0.0239 0.0593 0.1119 0.0919 −0.1726 0.1139 −0.0110

−0.0166 −0.0289 −0.0062 −0.0562 −0.0244 0.0315 0.0469 0.1517 0.1161 −0.1687 0.0907 0.0572

−0.0041 −0.0229 −0.0608 −0.0317 −0.0112 0.0089 −0.0652 0.1510 0.1806 0.0539 −0.0808 0.2367

−0.0029 −0.0179 0.0119 −0.0883 0.0049 −0.0019 0.0539 0.1116 0.0809 −0.1510 0.0917 −0.0224

T1/T3

T2/T4 0.0059

0.0056

0.0167 0.0149

0.0202

0.0195 0.0177

0.0142

The frequency ω (in cm−1 and eV) is indicated for each normal mode.

at 93, 439, 498, 637, 1174, 1444, 1554, 1623, and 1660 cm−1 show low-energy intersections between S2 and T3 and between T3 and the low-lying S1/T2/T1 states. From this static picture of the excited potential energy profiles along Qi one can anticipate the efficiency of ultrafast S2 → T3 decay. As previously mentioned, the a′ normal modes only contribute to the interstate vibronic coupling between excited states of the same symmetry, while the a″ normal modes contribute to the interstate vibronic coupling between excited states of different symmetry. Here, we include the two a″ normal modes calculated at 90 and 475 cm−1, that have been shown to be important in our previous studies.12,13 They involve symmetry breaking motions of the carbonyl groups and strongly couple S1 with S2, T1 with T2, and T3 with T4. In addition, we also include two a″ coupling modes at 621 and 631 cm−1. The κ(n) and λ(n,m) values of the most relevant a′ and a″ modes are reported in Table 3 and Table 4, whereas the

around the FC region opening efficient pathways for ultrafast population transfers within the electronic excited states manifold. Figures S1 and S2 (SI section) show the displacements and energy-scaled contributions of the a′ normal modes for the considered electronic excited states of [Re(CO)3(phen)(im)]+, namely S2, T4, T3, S1, T2, and T1. The larger displacement contributions are found in the lower frequencies modes, while important energy-scaled contributions appear both in the lowand high-energy region. From a careful analysis of all contributions, 20 a′ normal modes are potentially important in the excited-state relaxation process. The nuclear deformations associated with the relevant modes are depicted in Figure 1. It can be seen that some modes mainly correspond to Re-CO motion (modes calculated at 67, 80, 93, 95, 498, 637, and 2039 cm−1), some to the deformation of the imidazole ligand (modes at 173 and 228 cm−1), and the others mostly to phen deformations (modes calculated at 235 and 439 cm−1 and from 749 to 1660 cm−1). Finally, normal modes with mixed contributions are associated with collective nuclear relaxation. Interestingly, the normal modes calculated at 67, 80, 93, and 637 cm−1 associated with the carbonyl motions lead to a different sign of κ(n) i for S1 and S2 and also for T1 and T2. This is in agreement with the normal-mode analysis reported for the [Re(CO)3(bpy)(Br)] compound12,13 and highlights the different impact of these motions on the electronic densities associated with MLCT states. In contrast, the modes that imply imidazole or phen deformations lead to same-sign κi(n) constants and, thus, induce displacement shifts in the same direction from FC; see for instance modes at 173 and 235 cm−1 in Figure 1. However, the ILphen character of T3 is manifested in its different behavior with active normal modes associated with pure phen nuclear deformations, as the modes calculated at 1174 and 1554 cm−1. An analysis of the excited state potential energy surfaces (PES) along these Qi modes is performed in order to determine the dominant coordinates underlying the nonradiative decay process. The excited-state diabatic potentials have been constructed as a function of a given Qi coordinate on the coupling basis of the transition energies at FC and the κ(n) i terms. The potential profiles for the 20 normal modes of a′ symmetry depicted in Figure 1 are shown in Figure S3 (SI section). Among these modes, nine of them clearly provide efficient pathways for the photodecay process from the absorbing S2 excited state (Figure 2). The modes calculated

Table 4. Interstate Vibronic Coupling λ(n,m) (in eV) between S1/S2, T1/T2, and T3/T4 Excited States Determined for the Selected a″ Normal Modesa mode

ω (cm‑1)

ω (eV)

S1/S2

T1/T2

T3/T4

8a″ 24a″ 36a″ 37a″

90 475 621 631

0.0112 0.0589 0.0769 0.0783

0.0137 0.0258 0.0259 0.0304

0.0061 0.0378 0.0129 0.0186

0.0129 0.0057 0.0289 0.0196

The frequency ω (in cm−1 and eV) is indicated for each normal mode.

a

associated nuclear deformations are depicted in Figure 1. It is noticeable that, even though there is a low-energy crossing between T1 and T3, for instance with mode 93a′ at 1660 cm−1 (see Figure 2), there is no direct coupling between T1 and T3 along this mode (see Table 3). In fact, the value of κ(T3) is large as compared to the one of κ(T1) and thus, according to the equation for λ(n,m), leads to no coupling at first order between these two states of A″ symmetry (see the discussion in the Model Hamiltonian section.) This can be understood as follows. The interstate coupling λ is a measure of the repulsion of the two coupled states15 at FC. This repulsion is lowered by the relative displacement of the potential energy curves due to large intrastate coupling κ, while at the same time this relative displacement allows for low-energy crossing. The large difference between κ(T1) and κ(T3) reflects the different nature 1299


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Figure 3. Diabatic electronic populations of the six low-lying excited states of [Re(CO)3(phen)(im)]+ as a function of time: (a) 6-modes Model-1 with 4 a′ (93 cm−1, 439 cm−1, 498 cm−1, 637 cm−1) and 2 a″ (90 cm−1, 475 cm−1) modes, (b) 4-modes Model-2 with 4 a′ (93 cm−1, 439 cm−1, 498 cm−1, 637 cm−1) modes, excluding the vibronic coupling between same-symmetry states, (c) 9-modes Model-3 with 7 a′ (93 cm−1, 439 cm−1, 498 cm−1, 637 cm−1, 1444 cm−1, 1554 cm−1, 1660 cm−1) and 2 a″ (90 cm−1, 475 cm−1) modes, and (d) 15-modes Model-4 with 12 a′ (93 cm−1, 235 cm−1, 439 cm−1, 498 cm−1, 552 cm−1, 637 cm−1, 1336 cm−1, 1444 cm−1, 1554 cm−1, 1660 cm−1, 1174 cm−1, 1623 cm−1) modes and 3 a″ (90 cm−1, 475 cm−1, 621 + 631 cm−1) modes. The triplet contributions are summed up.

Quantum Wavepacket Propagations. The evolution of the diabatic electronic populations of the low-lying S1, S2, T1, T2, T3, and T4 excited states of [Re(CO)3(phen)(im)]+ as a function of time has been obtained by wavepacket propagations. Different models including from six to fifteen normal modes have been used in accordance with the selection discussed in the previous section. The results obtained after initial excitation of S2 are shown in Figure 3. Note that populations of the triplet components are summed up. The four low-energy a′ normal modes at 93, 439, 498, and 637 cm−1 were chosen as an appropriate initial set to explore the convergence of the dynamics with the number of selected normal modes. Moreover, the a″ modes calculated at 90 and 475 cm−1 were also included in Model-1 (Figure 3a). The results show that the S2 population drops very quickly to mainly populate T4 and T3 and slightly T1. The population transfer during the very first fs to T4 and T1 is purely due to the strong S2T4 and S2T1 SOC (Table 2), while the slightly delayed increase in T3 can be originated also from the T4 population via spin and/or vibronic coupling. After the initial decay, S2 and T4

of the electronic states (ILphen and MLCT). They are affected differently by the vibrational mode in question which involves only motion of the phen moiety, especially atoms far away from the central Re(I) atom (see Figure 1). As a consequence, they are less likely to repel one another and truly intersect in this case. In other words, despite a low-energy crossing, these two states are not directly coupled by this vibrational mode. Of course, this is in balance with the difference of the Hessians: if the later difference is large enough (strong repulsion), then the κ may not be able to compensate. In contrast, the mode 81a′ at 1444 cm−1, for instance, does exhibit a direct T1/T3 coupling, even though the crossing is higher in energy. While this mode also involves motion of the phen moiety, the motion is closer to the central Re(I) atom and also affects the MLCT states. The difference between the κ is consequently less important and allows for the direct coupling: The two states are not sufficiently pulled apart by the gradients (κ), and/or the repulsion is high enough, so that T1 and T3 interact directly via interstate coupling λ along this mode. 1300


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Figure 4. Diabatic electronic populations of the six low-lying excited states of [Re(CO)3(phen)(im)]+ as a function of time (a) excluding the interstate vibronic coupling among states of the same symmetry (b) including these contributions. The S2/T4 populations are summed up.

1554, and 1660 cm−1 were all considered in Model-3 in addition to those included in Model-1. The same results are obtained at the very early fs dynamics (Figure 3c), namely a fast decay of S2 population to T4 and, to a lesser extent, to T1, a rapid increase of T3 population. The S2 and T4 potentials remain strongly coupled, and their population is reduced to 10% within 100 fs. On the contrary, the T1 population continues growing up to the limit of the simulation. Interestingly, the population of T1 increases slightly faster than in Model-1. As a consequence, the crossing point between T3 and T1 is observed at about 300 fs, and the overall population amounts to about 70% (30% in T3 vs 40% in T1) within the first 500 fs. When increasing the number of modes to 15 (Model-4) the diabatic electronic population profiles as a function of time are not dramatically affected as illustrated in Figure 3d. Indeed, the results are similar to the ones reported for 9 modes (Model-3), therefore supporting the reliability of the reduced dimensionality picture for the early dynamics. In this case, the maximum of the T3 population at 100 fs is slightly reduced as compared to Model-3 (about 60% at 100 fs) and decreases slowly within the next 400 fs. Furthermore, the S2 decay time is extended to larger values up to 150 fs, when the ISC event with T1 is complete. Overall, the triplet population exceeds 80% after 350 fs and mainly corresponds to T3 and T1 states. The excited-state population dynamics presented herein correlate well with the mechanism proposed by El Nahhas et al. to interpret the relaxation dynamics of this complex (Scheme 1).8 Their experiments performed in DMF report an ultrafast decay τ1 = 144 ± 7 fs followed by a second decay τ2 = 1.5 ± 0.2 ps attributed to an earlier populated triplet excited state at 550 nm of mixed 3IL/CT character. It was proposed that this intermediate state and the long-lived phosphorescent 3MLCT state at 600 nm are populated simultaneously and equilibrate thermally after a few picoseconds relaxation period. Longer time-scale propagation corroborates this mechanism as illustrated in Figure 4 where we show the time-evolution within 1 ps for Model-4 including 15 normal modes. Here, the populations of S2 and T4 are summed up because in the spin− orbit picture T4 acquires some oscillator strength.10 This would correspond to the E11 spin−orbit state appearing in Table 1.

populations further decrease together manifesting the strong coupling between these two potentials. Indeed, the fast oscillations observed in their populations are induced by this strong SOC between their nearly parallel PES (Figure 2). The T3 population reaches a peak at about 70 fs, where it starts to rapidly decrease, while in turn population of the lowest excited state T1 grows up to the limit of the simulation. A crossing point between the T1 and T3 populations appears at about 400 fs within this model. The population of the S1 and T2 excited states slightly increases at the early time dynamics because of their coupling with T1 and T3 but remains marginal. The role of the vibronic coupling between S1/S2, T1/T2, and T3/T4 can now be considered excluding the a″ normal modes that account for them in the model (Model-2), as well as the role of the vibronic coupling between T1/T3 and T2/T4 by turning off their coupling along the a′ modes. The population profiles are represented in Figure 3b where it can be seen that the population of the T3 state is slightly overestimated as a consequence of the decrease in T2 and S1 (the latter being completely withdrawn), the overall picture being preserved. From these results, it can be concluded that the ultrafast ISC from S2 to T3 and T1 in this complex is not significantly altered by the presence of vibronic coupling. Nevertheless, the vibronic coupling between S1/S2 and T1/T2 controls the population transfer to S1 and T2 and should be included for describing the complete photophysical process as already discussed in the case of [Re(CO)3(bpy)(Br)].12 At this point, the reliability of Model-1 is still subject to its reduced dimensionality in terms of the number of included a′ normal modes limited to four. Additional a′ modes were selected (according to the discussion in the previous section) for improving our model. A total of 16 a′ modes were individually considered in order to determine their effect in the excited-state population profiles as compared to Model-1. A comparison between the electronic diabatic populations of the six electronic excited states (Figure S4, SI section) indicates that essentially five modes, that provide low-energy crossing points around FC (Figure 2), display a significant effect on the quantum dynamics (0−500 fs). In contrast, the addition of the other modes does not improve or modify significantly the description of the ISC pathways. The a′ normal modes at 1444, 1301


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the decay rate of T3 population (see Figure 6c and 6d, respectively). This corroborates the hypothesis of both pathways, namely an efficient direct T3 → T1 pathway that participates in their equilibration process driven by vibronic coupling and an indirect pathway via S2/T4 at the early stage activated by SOC. Overall, both direct and indirect population transfer pathways explain the main features of the luminescence properties of this system, that is, the earlier photoemission ascribed to an intermediate triplet state of marked IL character (T3) followed by an equilibration process that drives to the lowest emitting MLCT triplet state (T1). With the aim of evaluating the impact on the dynamics of the specific a′ normal modes considered in Model-1, additional simulations have been performed in which they are simply neglected. The normal modes calculated at 93, 498, and 637 cm−1 mainly correspond to carbonyl motions (see Figure 1), while the mode at 439 cm−1 is associated with the deformation of the phen. By comparing Figure 3a with Figure 7a, it can be observed that the very early population transfer from S2/T4 to T3 is highly reduced when the mode calculated at 498 cm−1 is not included. However, the mode calculated at 439 cm−1 is of prime importance to allow the population transfer to T1, which otherwise gets only weakly populated (Figure 7b). Finally, the modes calculated at 93 and 637 cm−1 that improve the nuclear conformational space description do not imply significant changes of the population time-evolution profiles (Figure S5, SI section). This can be well understood by looking at the excitedstate potential energy profiles along these particular normal modes (Figure 2). Influence of the Axial and Ancillary Ligands. Once the main routes for the ultrafast ISC processes are determined, examining how ligand effects control the relaxation mechanism can reveal important clues for the design of new Re-based sensitizers. In this section we compare the results previously reported by some of us for [Re(CO)3(bpy)(Br)]12,13 with the ones obtained in the present work for [Re(CO)3(phen)(im)]+. The excited-state wavepacket quantum dynamics performed for [Re(CO)3(bpy)(Br)] shows an ultrafast ISC from the main absorbing S2 (b1A′) state to the lowest triplet T1 (A3A″) excited state achieved in a few hundreds of femtoseconds. A systematic analysis of the PES associated with the involved excited states indicated the occurrence of S2 → S1/T2 → T1 luminescent decay via the S2/S1 and T2/T1 conical intersections. This was corroborated by a simulation excluding some normal modes that induce energetically accessible S2/S1 and T2/T1 crossings near FC, inhibiting the population transfer.13 In contrast, we have observed that neither S1 nor T2 directly participate in the ultrafast ISC in [Re(CO)3(phen)(im)]+. Indeed, the deactivation pathways that contribute to the population transfer are represented by the network depicted in Figure 5. In order to establish the influence of various ligands on the photophysics of this class of Re(I) tricarbonyl α-diimine complexes, we present here a systematic comparison between the four possible combinations of equatorial phen/bpy and axial im/Br ligand compounds, that is, between [Re(CO)3(bpy)(Br)], [Re(CO)3(phen)(im)]+, [Re(CO)3(phen)(Br)], and [Re(CO)3(bpy)(im)]+. Their low-lying singlet and triplet excited state energies are reported in Table 5. In all cases the main absorbing excited state is S2 corresponding mainly to the HOMO−1 to LUMO one-electron excitation. However, the absorption energy is reduced by about 0.2 eV for the halide Br complexes whatever the equatorial ancillary ligand is. This is due to the different shape and energy of the molecular orbitals

From this simulation, based on electronic structure data calculated in water for the Cs conformer of [Re(CO)3(phen)(im)]+, we extracted an ultrafast decay time-scale for S2/T4 of 75 fs that cannot be directly compared to the experimental τ1 value obtained in DMF (144 fs).8 Indeed changing the solvent may significantly influence the decay lifetimes as illustrated by a number of experiments reported in various solvents.7,8 However, this influence is more pronounced on τ2, as exemplified by the [Re(CO)3(bpy)(Cl)] complex.7,8 Moreover the coexistence of nearly degenerate conformers of Cs and C1 symmetry10 in the experiment may modify the observed dynamics within the first ps. Nevertheless, even if not quantitative, the good order of magnitude for the τ1 ultrafast time-scale is recovered within our model. The initial ultrafast decay is essentially driven by SOC, with little influence of the vibronic coupling. The time evolutions of the population of T3, the intermediate state, and of T1, the long-lived phosphorescent state, depicted in Figure 4, indicate a T3/T1 equilibrium starting between 200 fs and 1 ps. The T1/T3 vibronic coupling controls this equilibration as shown by the different profiles obtained without (Figure 4a) and with (Figure 4b) coupling. Of course, by including more normal modes or by improving our current model we may reach a better quantitative agreement with the experimental findings, themselves subject to carefulness analysis. However, this should not affect the main conclusions as far as the mechanism underlying the observed ultrafast time scales τ1 and τ2 is concerned. The potential deactivation pathways that characterize the population transfer among the excited states are depicted schematically in Figure 5. In order to identify the most relevant

Figure 5. Schematic deactivation pathways that contribute to the population transfer among the diabatic excited states and characterize the relaxation dynamics of [Re(CO)3(phen)(im)]+.

routes, the spin−orbit coupling between the initially populated excited state S2 (and T4) and the two low-lying emitting triplet T3 and T1 states has been systematically turned to zero in additional wavepacket propagations. Model-1 has been used for these quantum dynamics. Although slightly constrained, this six-mode model captures the essence of all the transfer processes and allows performing the tests at a reasonable computational cost. The allowed transfer routes in each model are depicted as the inset of Figure 6. Note that neither S1 nor T2 states are considered in the analysis although they have been included in the simulations: their populations remain minor in all considered cases. The population dynamics are depicted in Figure 6 and reveal the relative importance of both direct, S2 → T1, and indirect, S2 → T4 → T1, deactivation pathways to T1 (see Figure 6a and 6b, respectively). Notably, one would expect that when S2/T3 (or T4/T3) SOC is turned to zero, the transfer rate to T1 increases at the expense of the transfer to T3 due to the lack of one of its two direct accepting pathways, namely S2 to T3 or T4 to T3. In contrast, the increase in T1 population is even slower as well as 1302


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Figure 6. Diabatic electronic populations as a function of time for different models arising from the 6-modes Model-1 and excluding SOC as indicated. The triplet contributions are summed up. Inset: schematic deactivation pathways contributing to the population transfer among the diabatic excited states.

Figure 7. Diabatic electronic populations as a function of time for different 5-modes models arising from the 6-modes Model-1 and excluding the normal modes Q27 and Q22. The triplet contributions are summed up.

This is a consequence of the lack of participation of the two extra carbon atoms of the phen with respect to the bpy. On the other hand, the HOMO−1 orbital corresponds to an almost pure d-like orbital for the two imidazole-substituted com-

involved in the one-electron excitations associated with S2, which are depicted in Figure S6 and Figure S7 (SI section). On the one hand, the LUMO is a N,N π* orbital, the shape and energy of which are almost equivalent in the four complexes. 1303


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Table 5. TD-DFT/TDA Transition Energies (eV) Associated with the Low-Lying Spin-Orbit Free Singlet and Triplet Excited states of [Re(CO)3(phen)(im)]+, [Re(CO)3(bpy)(im)]+, [Re(CO)3(phen)(Br)], and [Re(CO)3(bpy)(Br)] [Re(CO)3(phen)(im)]+

[Re(CO)3(bpy)(im)]+

[Re(CO)3(phen)(Br)]

T1 A″

2.98

MLCT

T1 A″

2.96

MLCT

T1 A″

2.95

T2 A′

3.07

MLCT

S1 A″

3.07

MLCT

T2 A′

2.97

S1 A″

3.10

MLCT

T2 A′

3.20

MLCT

S1 A″

3.07

T3 A″

3.24

T3 A″

3.31

IL

S2 A′

3.16

S2 A′

3.35

MLCT IL MLCT

S2 A′

3.37

MLCT

T3 A″

3.18

T4 A′

3.42

MLCT

T4 A′

3.38

MLCT

T4 A′

3.37

MLCT XLCT MLCT XLCT MLCT XLCT MLCT XLCT MLCT XLCT IL MLCT XLCT

[Re(CO)3(bpy)(Br)] T1 A″

2.94

T2 A′

3.03

S1 A″

3.04

S2 A′

3.17

T3 A″

3.32

MLCT XLCT MLCT XLCT MLCT XLCT MLCT XLCT IL

T4 A′

3.41

MLCT

significant role in the early ultrafast decay. In the same way, T4, S2, and T3 excited states being very close in energy in [Re(CO)3(bpy)(im)]+ will clearly contribute to the early time dynamics.

pounds but displays a large contribution of the p(Br) orbital for the two halide substituted complexes leading to partial XLCT character. The interaction between the d-Re and p(Br) units is antibonding and destabilizes the HOMO−1 energy, which ultimately results in a lower excitation energy for S2. This is in agreement with the absorption properties reported experimentally.7 The destabilization of the HOMO−1 orbital leads to an important difference of the excited state pattern at FC in the Br substituted complexes, in which the relative stability between the optically active S2 state and the T3 excited state is reversed. For both halide complexes T3 is above S2, while for the imidazole-based compounds it remains below in energy. This implies that T3 can play a different role in the ultrafast process that characterizes the luminescence decay of these systems. Moreover, depending on the equatorial phen/bpy ligand that is used, the character of T3 can be modulated as well as its relative stability with respect to S2. In the case of bpy complexes, T3 corresponds to a pure IL excited state, while for the two phensubstituted compounds the IL character is reduced to about 30%. This will imply immediate consequences in the potential energy landscape of the excited states along specific nuclear motions and in their coupling modes. From this analysis one can anticipate that in [Re(CO)3(bpy)(Br)] neither T3 nor T4 actively participate in the ultrafast ISC from S2 to T1 because their relative energies are significantly higher than the main absorbing state. Therefore, only T2 and S1 will account for the main deactivation pathway as corroborated by quantum dynamics simulations.12,13 In contrast, more complex excited-state dynamics could be expected for [Re(CO)3(phen)(im)]+ as long as T4 is only 0.07 eV higher in energy than S2 and strongly coupled by SOC with T3. The wavepacket propagations performed in this work have allowed for elucidation of the mechanism and the main routes for the two ISC ultrafast kinetic components of [Re(CO)3(phen)(im)]+. Finally, on the basis of the relative energies of the low-lying excited states at FC of [Re(CO)3(bpy)(im)]+ and [Re(CO)3(phen)(Br)] (Table 5) we may infer some important features as far as the excited-state dynamics is concerned. Indeed, the main difference between [Re(CO)3(phen)(Br)] and [Re(CO)3(bpy)(Br)] is the stabilization of T3, which becomes almost degenerate with S2 due to its MLCT/XLCT character in the phen substituted molecule. As a consequence, T3 will strongly interact with S2 and thus should play a

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CONCLUSIONS Ultrafast excited-state decay in [Re(CO)3(phen)(im)]+ has been investigated by nonadiabatic quantum dynamics based on six low-lying singlet and triplet excited states coupled vibronically and by SOC. We have shown that low-frequency normal modes contribute essentially to large displacements of the potentials associated with selected electronic excited states, while both low- and high-frequency normal modes are critical for describing the potential energy shifts. Twenty a′ normal modes are potentially important in the ultrafast excited-state relaxation processes. Among these modes seven are associated with CO ligands motion. They contribute to intrastate coupling constants, the sign of which varies from one electronic state to the other, favoring the generation of excited-state potentials crossing. The thirteen modes connected to the imidazole group and phen deformations contribute also to the intrastate coupling constants but without modifying their sign leading to quasi parallel excited-state energy shifts (except for T3, which has a marked IL character). The interstate coupling constants between different symmetry states are included via three a″ normal modes, two of them being counterparts of the two a′ low-frequency CO normal modes. On the basis of a series of wavepacket propagations we have shown that nine a′ modes are especially relevant in the generation of excited-state potential crossing points and display significant effects on the electronic diabatic populations of the six considered electronic excited states within the first 500 fs. The photophysics of [Re(CO)3(phen)(im)]+ is characterized by an ultrafast decay, within a few tens of fs, from the S2 (1MLCT) optically active state to T4 and T1 (3MLCT) followed by a fast population of the intermediate T3 (3IL) state. After 350 fs the population of T1 and T3 accounts for 80%. This mechanism corroborates the experimental findings suggesting that the long-lived phosphorescence of the lowest MLCT triplet excited state at about 600 nm is preceded by an intermediate emission at about 550 nm originated from an earlier populated triplet excited state of mixed 3IL/CT character. It was proposed that these two low-lying excited states are populated simultaneously and equilibrate thermally 1304



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within less than a picosecond relaxation period in agreement with the results of our wavepacket simulations. Switching on/off vibronic and spin−orbit coupling in our model has enabled us to get deep insight into the mechanism of population transfer within the triplet manifold. It is shown that the combination of S2/T4 (1,3MLCT) → T3 (3IL) and S2/T4 (1,3MLCT)→ T1 (3MLCT) population transfers via SOC followed by the T3/T1 (3IL/3MLCT) equilibration explains the photoluminescent properties of [Re(CO)3(phen)(im)]+. Vibronic coupling controls the direct T3 → T1 (3IL → 3MLCT) pathway driving their equilibration process. The influence of the axial and N,N ligands on the photophysics of this class of Re(I) carbonyl α-diimine complexes is tentatively rationalized on the basis of their calculated optical properties. More particularly, the relative position of the upper 3MLCT and 3IL excited states with respect to the optically active singlet state controlled by the ancillary ligand will modify the mechanism, whereas the axial ligand may have a significant effect on the early dynamics as illustrated by the series of [Re(CO)3(bpy)(X)] (X = Cl, Br, I) studied both experimentally6 and theoretically.12,13

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REFERENCES

(1) Kirgan, R. A.; Sullivan, B. P.; Rillema, D. P. Photochemistry and Photophysics of Coordination Compounds: Rhenium. Top. Curr. Chem. 2007, 281, 45−100. (2) Kumar, A.; Sun, S. − S; Lees, A. J. Photophysics and Photochemistry of Organometallic Rhenium Diimine Complexes. Top. Organomet. Chem. 2009, 29, 37−71. (3) Vlček, A., Jr Ultrafast Excited-State Processes in Re(I) CarbonylDiimine Complexes: From Excitation to Photochemistry. Top. Organomet. Chem. 2009, 29, 115−158. (4) Vlček, A., Jr; Busby, M. Ultrafast ligand-to-ligand electron and Energy transfer in the complexes fac-[ReI(L) (CO)3(bpy)]n+. Coord. Chem. Rev. 2006, 250, 1755−1762. (5) Vlček, A., Jr; Kvapilová, H.; Towrie, M.; Záliš, S. Electron-transfer acceleration investigated by time resolved infrared spectroscopy. Acc. Chem. Res. 2015, 48, 868−876. (6) Cannizzo, A.; Blanco-Rodríguez, A. M.; El Nahhas, A.; Šebera, J.; Zàliš, S.; Vlček, A., Jr.; Chergui, M. Femtosecond fluorescence and intersystem crossing in rhenium(I) carbonyl-bipyridine complexes. J. Am. Chem. Soc. 2008, 130, 8967−8974. (7) El Nahhas, A.; Cannizzo, A.; van Mourik, F.; Blanco-Rodríguez, A. M.; Záliš, S.; Vlček, A., Jr.; Chergui, M. Ultrafast excited-state dynamics of [Re(L) (CO)3(bpy)]n complexes: involvement of the solvent. J. Phys. Chem. A 2010, 114, 6361−6369. (8) El Nahhas, A.; Consani, C.; Blanco-Rodríguez, A. M.; Lancaster, K. M.; Braem, O.; Cannizzo, A.; Towrie, M.; Clark, I. P.; Záiš, S.; Chergui, M.; Vlček, A., Jr Ultrafast excited-state dynamics of rhenium(I) photosensitizers [Re(Cl) (CO)3(N,N)] and [Re(imidazole) (CO)3(N,N)]+: diimine effects. Inorg. Chem. 2011, 50, 2932−2943. (9) Gourlaouen, C.; Eng, J.; Otsuka, M.; Gindensperger, E.; Daniel, C. Quantum Chemical Interpretation of Ultrafast Luminescence Decay and Intersystem Crossings in Rhenium(I) Carbonyl Bipyridine Complexes. J. Chem. Theory Comput. 2015, 11, 99−110. (10) Fumanal, M.; Daniel, C. Description of Excited States in [Re(Imidazole) (CO)3(Phen)]+ Including Solvent and Spin-Orbit Coupling Effects: Density Functional Theory Versus Multiconfigurational Wavefunction Approach. J. Comput. Chem. 2016, 37, 2454− 2466. (11) Fumanal, M.; Daniel, C. Electronic and Photophysical Properties of [Re (L) (CO)3(phen)]+ and [Ru(L)2(bpy)2]2+ (L = imidazole), Building Units for Long-Range Electron Transfer in Modified Blue Copper Proteins. J. Phys. Chem. A 2016, 120, 6934− 6943. (12) Eng, J.; Gourlaouen, C.; Gindensperger, E.; Daniel, C. SpinVibronic Quantum Dynamics for Ultrafast Excited States Processes. Acc. Chem. Res. 2015, 48, 809−817. (13) Harabuchi, Y.; Eng, J.; Gindensperger, E.; Taketsugu, T.; Maeda, S.; Daniel, C. Exploring the Mechanism of Ultrafast Intersystem Crossing in Rhenium (I) Carbonyl Bipyridine Halide Complexes: Key Vibrational Modes and Spin-Vibronic Quantum Dynamics. J. Chem. Theory Comput. 2016, 12, 2335−2345. (14) Maeda, S.; Taketsugu, T.; Morokuma, K. Exploring Transition State Structures for Intramolecular Pathways by the Artificial Force induced Reaction Method. J. Comput. Chem. 2014, 35, 166−173. (15) Köppel, H.; Domcke, W.; Cederbaum, L. S. Multimode molecular dynamics beyond the Born-Oppenheimer approximation. Adv. Chem. Phys. 1984, 57, 59−246. (16) Köppel, H.; Domcke, W. Vibronic dynamics of polyatomic molecules. In Encyclopedia in Computational Chemistry; von Ragué Schleyer, P., Ed.; Wiley: New York, 1998; p 3166. (17) Klamt, A.; Schüürmann, G. COSMO: a New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 2, 799−805. (18) Klamt, A. Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224−2235.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.6b01203. Table S1, computational details; Figure S1, displacement contributions of the a′ normal modes; Figure S2, energyscaled contributions of the a′ normal modes; Figure S3, diabatic potential energy curves along the 20 Qi most relevant a′ normal modes; Figure S4, diabatic electronic populations as a function of time for different models; Figure S5, diabatic electronic populations as a function of time, for different 5-modes models arising from the 6modes Model-1 and excluding the normal mode indicated; Figure S6, Kohn−Sham frontier orbitals of (a) [Re(CO)3(phen)(im)]+ and (b) [Re(CO)3(bpy)(im)]+ in water; Figure S7, Kohn−Sham frontier orbitals of (a) [Re(CO)3(phen)(Br)] and (b) [Re(CO)3(bpy)(Br)] in water (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Chantal Daniel: 0000-0002-0520-2969 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the reviewers for their enlightening comments and Horst Köppel for stimulating discussions. This work has been supported by Labex CSC (ANR-10-LABX0026_CSC) and French/Austrian ANR-15-CE29-0027-01 DeNeTheor. The calculations have been performed at the High Performance Computer Centre (HPC), University of Strasbourg and on the nodes cluster of the Laboratoire de Chimie Quantique (CNRS/University of Strasbourg). 1305


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