SpinâOrbit Coupling Drives Femtosecond Nonadiabatic Dynamics in a

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Spin-orbit Coupling Drives Femtosecond Nonadiabatic Dynamics in a Transition Metal Compound William P. Carbery, Archana Verma, and Daniel B. Turner J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b00130 • Publication Date (Web): 07 Mar 2017 Downloaded from http://pubs.acs.org on March 7, 2017

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The Journal of Physical Chemistry Letters

Spin-Orbit Coupling Drives Femtosecond Nonadiabatic Dynamics in a Transition Metal Compound William P. Carbery, Archana Verma, and Daniel B. Turner∗ Department of Chemistry, New York University, 100 Washington Square East, New York NY 10003, USA E-mail: [email protected]

∗

To whom correspondence should be addressed

1 ACS Paragon Plus Environment


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Abstract Transient absorption measurements conducted using broadband, 6-fs laser pulses reveal unexpected femtosecond dynamics in the [IrBr6 ]2− model system. Vibrational spectra and the x-ray crystal structure indicate that these dynamics are not induced by a Jahn–Teller distortion, a type of conical intersection typically associated with the spectral features of transition metal compounds. Two-dimensional electronic spectra of [IrBr6 ]2− contain 23 cross peaks, which necessarily arise from spin-orbit coupling. Real-valued 2D spectra support a spectroscopic basis where strong nonadiabatic coupling, ascribed to multiple conical intersections, mediates rapid energy relaxation to the lowest-energy excited state. Subsequent analysis gives rise to a more generalized description of a conical intersection as a degeneracy between two adiabatic states having the same total angular momentum.

Graphical TOC Entry

Keywords femtosecond dynamics, iridium(IV) hexabromide, transition metal compounds, Jahn–Teller effect, two-dimensional electronic spectroscopy, spin-orbit coupling, conical intersection


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A conical intersection is a degeneracy between two adiabatic potential energy surfaces. 1 At this point, named for its characteristic double-cone topology, the Born–Oppenheimer approximation breaks down, and nonradiative decay can proceed efficiently and at timescales as fast as tens of femtoseconds. 2 Thus conical intersections are often invoked when molecules display diagnostic properties such as negligible fluorescence, femtosecond dynamics, or high photoactivity. 3 Theoretical models and computational studies have shown the diverse utility of conical intersections in photochemical and photophysical transformations as key mechanistic drivers analogous to thermal transition states. 4–9 Most experimental studies of conical intersections have focused on the opsin family of biomolecules, 10–16 where a conical intersection promotes rapid and efficient photoisomerization. This area of research involves states of well-defined spin character, where the conical intersection is specified as a degeneracy between adiabatic potential energy surfaces of the same spin multiplicity. In contrast, very little research has been performed to investigate what role, if any, conical intersections have in compounds with large spin-orbit coupling. For many systems involving transition metals—a diverse group of compounds including enzymes, functionalized materials, and small molecule catalysts—spin-orbit coupling affects the symmetry of the electronic states and scrambles their spin character. Just as mechanistic studies rely on the accurate characterization of the thermal transition state, understanding transition metal photophysics requires accurate characterization of spin-orbit coupling and its effect on potential energy surface topology. Hexahalide, d5 heavy metal compounds are excellent molecular models for broadening the scope of experimental studies on conical intersections because they contain a single unpaired electron in a valence atomic orbital with large orbital angular momentum and have relatively few normal vibrational modes. Thus the variety of configurations for which a conical intersection might exist are intrinsically limited, and spin can be expected to play a substantial role in the photophysics. Two considerations suggest that conical intersections are both important and common in transition metal complexes generally. The first is that many



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such compounds have low fluorescence quantum yields, a diagnostic property for conical intersections. 3 The second consideration is that the Jahn–Teller effect—a well-known spectral feature of many transition metal compounds—is a special type of conical intersection. 17,18 In this report we focus on iridium(IV) hexabromide ([IrBr6 ]2− ), a few-atom molecule having spin-orbit coupling on the order of 10 THz. The linear absorption spectrum of (NBu4 )2 [IrBr6 ] is presented in Fig. (1). The six prominent ligand-to-metal charge transfer (LMCT) bands are classified as three Laporte-allowed transitions derived from an octahedral geometry split into six transitions by spin-orbit coupling. 19,20 The current assignments listed in Table (1) mimic the square-planar, D4h , electronic structure commonly used to describe the geometric distortion induced by a Jahn–Teller effect in an Oh molecule. 21,22 Table 1: Electronic transitions of (NBu4 )2 [IrBr6 ] in acetonitrile relevant to this study. Peak assignments are according to the early work of Jørgensen. 19 Symmetry designations of the ligand orbitals are presented in the Oh geometry. Symmetry designations of the ligand orbitals in the spin-orbit coupling induced splitting regime are attributed to a D4h –like geometry, while the spin-orbit coupling designations themselves are presented in parentheses. λ ν Oh (nm) (THz) (π) → T1g I IIa IIb IIc III IVa IVb

835 751 711 685 599 551 534

361 399 422 437 500 544 561

T1g (1) T1u (1) T1u T2u T2u (2) T1u (2) T1u

D4h (O*h ) (π) → B1g 0

Eg (Eg ) 0 (1) A2u (Uu ) 0 E(1) u (Eu ) 00 E(2) u (Eu ) 00 B2u (Uu ) 0 E(3) u (Eu ) 0 (2) A2u (Uu )

In recent pioneering work, 23 the Tarnovsky group measured transient absorption spectra of (NBu4 )2 [IrBr6 ] using a narrowband, 2 µm pulse to pump the d → d transition of the [IrBr6 ]2− ion and a broadband supercontinuum pulse to probe the LMCT bands. They observed no femtosecond dynamics and attributed this absence to slow, nonradiative decay from the d–orbital based excited state, |ed i, to the ground state, |gi, through intersystem crossing. Here, using broadband, 6 fs pulses that pump and probe the LMCT bands directly, we mea4 ACS Paragon Plus Environment

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ε ×10–3 (M cm–1)

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III

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600 700 wavelength (nm)

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550

IVa

600

III

650 ΔT/T (%) +1

700

IIc

0

IIb

–1

750 0

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3 4 time (ps)

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Figure 1: (top) Absorption spectrum of (NBu4 )2 [IrBr6 ] in acetonitrile and normalized laser spectrum in solid and dashed lines, respectively. (bottom) Transient absorption spectrum reveals femtosecond dynamics.



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sure transient absorption spectra of (NBu4 )2 [IrBr6 ] in acetonitrile. The bottom panel of Fig. (1) presents the transient absorption spectrum, and Supporting Information contains the two-component decay associated difference spectra (DADS). These data reveal unreported femtosecond dynamics at τ1 ' 750 fs and also match the transient absorption spectra of the prior report at τ2 ' 360 ps. 23 It is tempting to attribute the femtosecond dynamics present in the transient absorption spectrum to a previously unobserved Jahn–Teller effect. Indeed, the Tarnovsky group attributed the femtosecond dynamics observed in copper(II) tetrachloride ([CuCl4 ]2− ) to a conical intersection driven by a Jahn-Teller distortion. 23 This explanation is consistent with the large splitting of the [CuCl4 ]2− LMCT bands as well as the sensitivity of those bands to pressure and local environment. 24,25 In addition, the distortion away from Td symmetry, which breaks the degeneracy of the electronic states and gives rise to these spectral features, is readily observed by x-ray crystallography. 26 The [IrBr6 ]2− ion does share some similarities with the copper(II) system. For example, the large splitting of their LMCT bands is comparable, and nonradiative decay proceeds on the femtosecond timescale for both. Unlike [CuCl4 ]2− , however, substantial direct evidence demonstrates that [IrBr6 ]2− does not deviate from an octahedral geometry as would be expected if the femtosecond dynamics were a result of a Jahn–Teller distortion. A recent report on the [IrBr6 ]2− crystal structure with a tetra(para-tolyl)stibonium cation grown from dimethyl sulfoxide concluded that the ion was indeed octahedral, with an average Ir–Br bond length of 2.4785 ± 0.0071 ˚ A . 27 In addition, resonance Raman measurements performed on the [IrBr6 ]2− ion in solution revealed only three Raman-active stretching modes consistent with an octahedral symmetry. 28–30 As further evidence, we found that slow evaporation of (NBu4 )2 [IrBr6 ] from acetone resulted in crystals pure enough for both Raman microscopy and x-ray crystallography. These data reveal that the average Ir–Br bond length of (NBu4 )2 [IrBr6 ] is 2.471 ± 0.006 ˚ A , arranged in an octahedral geometry, and with a concomitant Raman spectrum showing


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only the three expected peaks for an Oh symmetry. The vibronic spectrum obtained from the coherent oscillations embedded in the transient absorption data also confirms two of the three low-frequency peaks at 179 cm−1 and 212 cm−1 . This combination of vibrational and x-ray data, detailed further in Supporting Information, indicate that any Jahn–Teller effect in [IrBr6 ]2− is negligible compared to the effect induced by spin-orbit coupling. In the absence of a Jahn–Teller distortion, the condensed-phase geometry of [IrBr6 ]2− becomes inconsistent with the stratified linear absorption spectrum and femtosecond dynamics. To resolve this discrepancy, and to explore the dominant role of spin-orbit coupling in this system, it is instructive to consider the conventional application of group theory to electronic transitions. In general, the transition dipole moment is given by ZZZ Mg,e =

Ψ∗e (q, Q, S)ˆ µ(Q)Ψg (q, Q, S) dqdQdS,

(1)

where q is an electronic coordinate, Q is a nuclear coordinate, S is the spin state, and subscripts g and e indicate the ground and excited states, respectively. 31 Under the Franck– Condon approximation and in the absence of spin-orbit coupling, the transition dipole operator is not a function of nuclear coordinate, µ ˆ(Q) → µ ˆ0 , the wavefunctions are crude adiabats rewritten as product states with explicit spin dependence, Ψ(q, Q, S) → ψ(q; Q0 )φ(Q)θ(S), and the integrands separate. This approximate transition dipole moment is given by

MFC g,e (µ0 )

Z = |

φ∗e (Q)φg (Q) dQ × {z

}

Franck–Condon factor

Z |

θe∗ (S)θg (S) dS {z

spin state

}

Z ×

ψe∗ (q; Q0 )ˆ µ0 ψg (q; Q0 ) dq . | {z }

(2)

transition dipole

The application of group theory simplifies this expression by replacing the product-state wavefunctions with irreducible representations of some point-group symmetry such that

MΓg,e ∝ Γe (Q) · Γg (Q) × Γe (S) · Γg (S) × Γe (q) · Γµ · Γg (q) . | {z } | {z } | {z } vibrational symmetry

spin selection rule

Laporte’s selection rule


(3)


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Group theory is a model used to predict how electronic transitions can be separated according to their intensities. Each Γg and Γe in Eqn. (3) is a vector with a symmetry designation that can be evaluated in relation to other irreducible representations or the transition dipole matrix, Γµ . If any inner product is zero, the transition dipole moment is zero, and the transition is said to be “forbidden”. Laporte’s selection rule, which states that excited-state and ground-state symmetries must transform with the dipole operator, is the most prominent of the resulting selection rules. Nevertheless, it is commonly broken by invoking atomic motion. This combines the electronic and vibrational symmetries into a single inviolable inner product representing vibronic coupling. Vibronic coupling, however, is not the only possible interaction. An alternative way to lift Laporte’s selection rule is through spin-orbit coupling. This involves combining the spin and electronic symmetries into a single inner product. Transitions that would otherwise not 0

00

transform with the dipole operator—indicated in Table (1) as originating from Uu or Uu ligand orbitals—are then allowed, and they are furthermore indifferent to atomic motion because the vibrational inner product is separate from the inner product representing spinorbit coupling. This use of group theory results in a reasonable description of the electronic properties of [IrBr6 ]2− , particularly as a way for explaining the stratified linear absorption spectrum in the absence of geometric distortion. Furthermore, the coupling between spin and electronic states likely drives the femtosecond nonradiative decay measured in the transient absorption spectrum. Pump-probe techniques, however, lack sufficient detail to assess the nature of the LMCT interactions arising from spin-orbit coupling. Therefore, we performed two-dimensional electronic spectroscopy (2D ES) on [IrBr6 ]2− to directly measure couplings among all of the LMCT transitions. The magnitude 2D spectrum at a waiting time of 6 ps, Fig. (2), contains 23 cross peaks at the locations predicted by mapping the linear absorption transitions onto the excitation and emission axes (dashed horizontal and vertical lines). Consistent with our expectation for spin-orbit coupling, all six LMCT bands are coupled.


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600

excitation frequency (THz)

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550

500

450

1

400 0 400

450 500 550 emission frequency (THz)

600

Figure 2: 2D spectrum at 6 ps, magnitude. Spin-orbit coupling induces cross peaks among all six LMCT transitions. Color scaling is logarithmic to enhance low-amplitude features.



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The real-valued 2D spectra presented in Fig. (3) reveal further details about the shortlived and long-lived dynamics measured in the transient absorption data. In addition to the persistent bleach and stimulated emission signals (red) at the intersections of the LMCT excitations and emissions (horizontal and vertical dashed lines, respectively), there are excited state absorption signals (ESA, blue) at four emission frequencies of interest (vertical dotted lines). These include: 1. three peaks at the 551 THz emission frequency coupled to the IIa (399 THz), IIc (437 THz), and IVa (544 THz) LMCT excitations that disappear by 600 fs, 2. six peaks at the 522 THz emission frequency coupled to every LMCT excitation that also diminish by 600 fs, 3. two peaks centered around the 472 THz emission frequency coupled to LMCT excitation III (500 THz) present in the 2 ps spectrum and resolved as a single peak at 6 ps, 4. and six peaks that persist from 2 ps onwards, centered at the 412 THz emission frequency, and coupled to LMCT excitations IIc, III, and IVa. The first three ESA features are unique to this report. The peaks observed at the 412 THz emission frequency, and duplicated in the long-lived DADS spectrum, match the transient absorption features of the prior report 23 past 100 fs. This frequency corresponds to a transition from the d–orbital derived excited state to the IVa and IVb LMCT excited states, which is distinct from the ESA peaks at 551 THz, 522 THz, and 472 THz that correspond to transitions from the LMCT excited states to higher-lying excited states. Crucially, the broadband excitation used in this experiment to investigate the LMCT transitions fills the vacant d–orbital that gives rise to the ESA transitions at 412 THz. In [IrBr6 ]2− , the peaks at 551 THz, 522 THz, and 472 THz can not be measured alongside peaks at 412 THz without a rapid reorganization of the excited-state populations. Therefore, we 10 ACS Paragon Plus Environment

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100 fs

600 fs

2 ps

6 ps

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500

excitation frequency (THz)

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450

400

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500 +1 450 0 −1

400 400

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550 400 450 emission frequency (THz)

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Figure 3: Phased 2D electronic spectra of (NBu4 )2 [IrBr6 ] at indicated waiting times. Longlived bleach and stimulated emission peaks (red) occur at intersections between LMCT excitations and emissions (horizontal and vertical dashed lines, respectively). Strong ESA peaks (blue) occur at emission frequencies of 522 THz and 551 THz before 2 ps, and ESA peaks at 412 THz and 472 THz after 600 fs (dotted vertical lines). Color scaling is linear.



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interpret the rapid disappearance of the bleach and ESA signals in the transient absorption, DADS, and real-valued 2D spectra, as well as the agreement between spectra measured in this report past 750 fs and the spectra obtained previously, to rapid nonadiabatic population decay from all of the LMCT states to the lowest-energy excited state, |ed i. Understanding these nonadiabatic dynamics requires a complete assessment of the [IrBr6 ]2− molecular orbitals with respect to spin-orbit coupling. Including spin-orbit coupling should yield electronic potential-energy surfaces with topographies consistent with the lifetime and yield of nonradiative decay. 7 In Eqn. (3), we used the symmetry combination of spin and orbital angular momentum to rationalize the existence of six LMCT bands in octahedral [IrBr6 ]2− . Analogously, we can diagonalize the electronic states with respect to total angular momentum and postulate adiabatic potential energy surfaces. The change in chemical identity—neither spin nor orbital angular momentum are good quantum numbers in this spectroscopic basis—could evolve with weak or strong nonadiabatic coupling. Here we are interested in the femtosecond dynamics of [IrBr6 ]2− mediated by strong nonadiabatic coupling.

|ψ7〉

Eβ

dx2–y2

Eα

dyz

dz2

dxz

|ψ8〉

|ψ9〉

|ψ1〉

|ψ2〉

|ψ4〉

|ψ5〉

|ψ10〉

E7→10

SOC E1,2

dxy |ψ3〉

6–4

|ψ6〉

E3→6

4–2–4

Figure 4: (left) The conventional d orbitals due to octahedral geometry are doubly degenerate for spin up and spin down. (right) In the coupled basis arising from an octahedral geometry and spin-orbit coupling, each eigenstate is a linear combination of spherical harmonics as well as spin. Supporting Information contains the details regarding the construction of these coupled atomic basis states for the [IrBr6 ]2− ion. The iridium d-orbitals rearrange from a 6–4 con12 ACS Paragon Plus Environment

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figuration that accounts for only the octahedral ligand field into a 4–2–4 configuration that accounts for both the octahedral ligand field and spin-orbit coupling. Fig. (4) depicts the ordering of these states, which are linear combinations of spherical harmonics having definite total angular momentum but indefinite spin character. The coupled atomic basis states |ψ1 i through |ψ6 i all have total angular momentum j = 3/2. The degenerate |ψ1 i and |ψ2 i states are singly occupied and constitute the electron-accepting orbitals of the LMCT transitions. Assessing the splitting of the 18 bromide p-orbitals induced by spin-orbit coupling is a more intensive process. Fortunately, the symmetry adapted linear combinations in an octahedral geometry are triply degenerate like the T2g states of the iridium atom, and therefore their splitting can reasonably be described using the 4–2 split of the coupled iridium states. The overall result is an agreement between the early descriptions of molecular orbital splitting in the [IrBr6 ]2− ion 19,20 and the splitting obtained by introducing the appropriate spin-orbit coupling to the metal and ligand orbitals. This agreement furthermore removes the need for a geometric distortion invoked by earlier investigations 32 to justify the six allowed LMCT bands. An updated description of the [IrBr6 ]2− molecular orbital states can be found in Supporting Information alongside relevant spectroscopic states. The 2D spectra in Fig. (3) confirm and help quantify the spin-orbit coupling in [IrBr6 ]2− . Consider the 561 THz (IVb) and 544 THz (IVa) transitions, which form the expected bleach pattern of coupled transitions—two positive diagonal peaks and two positive cross peaks in a square pattern—for all τ2 values. The splitting is about 18 THz, which under the homodimer model implies a spin-orbit coupling of 9 THz. A similarly persistent, squareshaped pattern appears between the 500 THz (III) and 437 THz (IIc) transitions, implying that their coupling is 32 THz. These two values serve as upper bounds for the spin-orbit coupling because the homodimer model may not be valid for [IrBr6 ]2− . The alternative heterodimer model would imply that some of the splitting arises from the original t2g − eg energy difference. Nevertheless, spin-orbit coupling is the dominant source of coupling in the system. The width of the central peak at 500 THz reveals that there is minimal broadened



561 544

frequency (THz)

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500

437 422

d

399

150

0

Figure 5: Proposed spectroscopic states of (a) a conventional Jahn–Teller distortion, (b) the modulation of [IrBr6 ]2− along the z-axis, (c) the proposed tuning mode of the conical intersection in [IrBr6 ]2− , and (d) all electronic states relevant to the visible-NIR electromagnetic region. 14 ACS Paragon Plus Environment

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due to vibronic coupling, relative to standard organic dye molecules. 33 A number of other d5 hexahalides with heavy metal centers such as osmium, ruthenium, rhenium, and platinum have LMCT bands split by similar magnitudes. 19 This splitting is reduced when substituting bromide ligands with chloride, and it disappears entirely when the metal center is reduced to d6 , suggesting that the majority of the splitting is indeed due to a spin state effect. In principle, extreme nonadiabatic relaxation due to strong spin-orbit coupling can be captured by the Landau–Zener model, which involves an avoided crossing between adiabatic potential energy surfaces. 34 However, the 204 cm−1 coherent vibrational oscillations near 700 nm persist for several picoseconds in the transient absorption spectrum, much longer then the femtosecond population decay. These oscillations cannot arise from ground-state vibrational wavepackets due to the bandwidth of the laser pulse. 35–38 As postulated by Shank and coworkers, 12 nonadiabatic dynamics accompanied by persistent vibrational coherences imply that the system has passed through a conical intersection. Hence we conclude that conical intersections mediate the ultrafast relaxation of the LMCT excited states to |ed i. This is unexpected because the conventional description of a conical intersection involves two adiabatic potential energy surfaces of the same spin multiplicity, coupled through symmetric atomic motion, and brought into resonance by an asymmetric atomic motion. 8,18 Due to strong spin-orbit coupling, the electronic relaxation dynamics of [IrBr6 ]2− require a more general description of a conical intersection involving two adiabatic potential energy surfaces of the same total angular momentum. This description of conical intersections in [IrBr6 ]2− is cast in the adiabatic basis, in which internal conversion is expected to proceed with no change in total angular momentum and through conical intersections with the conventional N-2 dimensionality. This contrasts with intersystem crossing mechanisms in organic molecules, where diabatic states of distinct spin multiplicity are connected by crossings with N-1 dimensionality. Computations 39,40 suggest that spin-orbit coupling is sufficient to lift a forbidden transition and overcome small energy barriers but is one or two orders of magnitude smaller than the spin-orbit



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coupling proposed here for [IrBr6 ]2− . While the LMCT excited states are described well in the strong-coupling regime as adiabats, this does not preclude the existence of intersystem crossing at timescales longer than 100 ps or at frequencies below 400 THz. Indeed, the slow ground state recovery from |ed i suggests the intriguing possibility that the final relaxation process, which proceeds almost entirely on the iridium d-orbitals, functions more like the diabatic picture of intersystem crossing or within a regime of intermediate coupling. The topology of the conical intersections in [IrBr6 ]2− can be described further. With only six normal mode vibrations available to construct the branching space of a conical intersection, any one potential energy surface crossing can be four-dimensional at most. This branching space is small enough for a qualitative discussion of the topography of the conical intersection. For a Jahn–Teller distortion of an octahedral molecule, a compression or elongation along the z-axis stabilizes the d–orbital derived T2g states by breaking the Oh symmetry of the molecule into one of two possible D4h configurations. This leads to a conical intersection at the minimum of the excited state potential energy surface as depicted in Fig. (5 (a)). Such a conical intersection will drive rapid and efficient nonradiative decay to the ground state. Without a Jahn–Teller distortion, a modulation along the z-axis of [IrBr6 ]2− is not expected to yield femtosecond dynamics, and is instead depicted in Fig. (5(b)) as the T2g and Eg states keeping their diabatic chemical identity. The measured femtosecond dynamics of [IrBr6 ]2− , however, are among the excited states of the molecule and not between the ground and excited state. The persistent bleach and ESA features of the transient absorption and real valued 2D spectra suggest the excited-state energy is thermally dissipated to the ground state through vibration, but only after a significant portion of the higher lying excited states have relaxed to the lowest energy excited state in hundreds of femtoseconds. While the molecular geometry of [IrBr6 ]2− is octahedral, the individual ‘orbitals’ of the coupled states are spatially asymmetric and do not contain an inversion center. For instance, spatial plots presented in the Supporting Information indicate the |ψ1 i and |ψ2 i states ap-


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proximately constitute the top and bottom portions, respectively, of a combined dxz and dyz orbital. Thus the rotation of |ψ2 i as |ψ1 i remains fixed should closely emulate the conformational analysis of a system like staggered ethane, where the ground-state energy is raised in the eclipsed conformation and lowered in the staggered conformation. More specifically, vibrational modes that do not alter the inversion center of [IrBr6 ]2− can be considered as coupling modes in a conical intersection branching space. These normal mode vibrations—designated as a1g , eg , and t2g —are complemented by a t1u and two t2u tuning modes that are asymmetric with respect to inversion. In addition, the spatial bifurcation of the coupled ‘orbitals’ suggests that torsions with respect to the C4 axis should cause significant modulation of the potential energy surfaces. This torsional motion is most closely described by the t2g bending motion of the molecule, with the t2u motion acting as a complementary tuning mode. The proposed modulations of the IVa and IVb excited states as a result of this motion are shown in Fig. (5(c)). The torsional displacement leads to a conical intersection that is not quite at the minimum of the excited-state potential energy surface. The conical intersection therefore mediates ultrafast dynamics less efficiently than the conical intersection of a Jahn–Teller distortion. Extrapolated to all of the LMCT bands, the proposed spectroscopic states in Fig. (5(d)) describe a system of conical intersections among all of the LMCT excited states, |e(IIa)i, |e(IIb)i, |e(IIc)i, |e(III)i, |e(IV a)i, and |e(IV b)i, brought into resonance by the torsional motion between the upper and lower halves of [IrBr6 ]2− . A conical intersection is also depicted between the LMCT states and the excited state of the d–d transition, |ed i, which is the simplest explanation for the quantitative agreement between the long-lived DADS in this report and transient absorption spectra measured using a 2 µm pump pulse. 23 Indeed, without this system of conical intersections mediating femtosecond energy relaxation in [IrBr6 ]2− , it is challenging to understand how 1.5 eV of excitation energy is lost in less than 1 ps. Further two-dimensional spectroscopic studies with bandwidths extending into the near-infrared would directly resolve a cross peak between



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each LMCT excitation and the 2 µm emission wavelength. 41 Two-dimensional electronic vibrational spectroscopy (2D EV) would make an excellent candidate for this type of study even though both the excitation and emission would be electronic transitions in this case. 42 Comparative studies on Oh transition metal compounds with proven Jahn–Teller distortions would further elaborate the topography of the potential energy surfaces, with nonradiative dynamics expected to be faster than 750 fs for these molecules. In summary, using 6-fs pulses to conduct transient absorption and two-dimensional electronic spectroscopy, we explored the effects of spin-orbit coupling on the electronic properties of the [IrBr6 ]2− ion. The measured femtosecond dynamics suggest that spin-orbit coupling alone drives nonradiative decay in [IrBr6 ]2− . By constructing the relevant total angular momentum states of the iridium center, we showed that the [IrBr6 ]2− ion has a symmetric geometric structure with orbitals that lack an inversion center, leading to a splitting of the electronic states. The resulting adiabatic potential energy surfaces are then nonadiabatically coupled throughout all of the reaction coordinates. For [IrBr6 ]2− we propose a system of spectroscopic states where each LMCT excited state, as well as the d–orbital derived excited state, is connected by a series of conical intersections and brought into resonance by a torsional motion. For systems with conical intersections, understanding the topography of the potential energy surfaces is important because small topographical changes near a conical intersection can significantly affect the quantum yield and dynamics of nonradiative decay. 7 This is evident in the difference between the Jahn–Teller and spin-orbit coupling induced conical intersections, where small differences in topography dictate order-of-magnitude differences in excited-state lifetime. Because large spin-orbit coupling is an inherent property of transition metal compounds, conical intersections should be expected in systems with a wide range of technological potential. This is particularly important in devices such as dye-sensitized solar cells, because large portions of the absorbed energy may be lost on time scales too fast to be probed by conventional tools. More fundamentally, the data in this report call into question


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the use of intersystem crossing, or indeed the use of any well-defined spin state, in systems where spin-orbit coupling dominates. This includes descriptions of conical intersections, where the affects of spin-orbit coupling are understudied. Further work on the more general description of a conical intersection, as a degeneracy between adiabatic potential energy surfaces with identical total angular momenta, will greatly aid the understanding of electronic properties in these and other transition metal compounds.

Methods Sample Preparation and Characterization We combined a sample of bulk iridium(IV) hexabromide (potassium hexabromoiridiate(IV) K2 [IrBr6 ], Alfa Aesar, 99% metals basis, 25.2% min Ir) with 2.2 molar equivalents of tetrabutylammonium bromide (NBu4 Br, Sigma-Aldrich, ACS reagent, ≥ 99.8%) in a simple metathesis reaction using a minimum of water. We dried the resultant deep purple powder, (NBu4 )2 [IrBr6 ], en vacuo and stored it under air at room temperature in the dark. We prepared solutions of (NBu4 )2 [IrBr6 ] suitable for femtosecond spectroscopy measurements with dry acetonitrile (Fischer Scientific, 99.9%, Extra Dry over Molecular Sieve, AcroSealTM ). Eliminating water from the sample environment prevents photodegradation for scans lasting several hours. The optical density at 599 nm was 0.3 in a 250-µm pathlength flow-cell cuvette, confirmed by linear absorption measurements using a Cary 100 UV-Vis instrument. Spectra of the compound before and immediately after laser femtosecond measurements showed no change.

Femtosecond Spectroscopy Prior reports describe the femtosecond spectrometer used in these measurements. 33,43,44 Briefly, a noncollinear optical parametric amplifier produced pulses spanning 520 nm to 760 nm. We routed the beam through a pair of chirped mirrors and a home-built pulse 19 ACS Paragon Plus Environment


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shaper to achieve 6.5 fs duration pulses. In the interferometer, two sets of beamsplitters separate the input pulse into four beams positioned in the BOX geometry. Two choppers and a photodiode work in an advanced chopping sequence to implement proper balanced detection for each laser shot. 33,43,44 The high-sensitivity measurement techniques allow us to obtain nonlinear signal in the visible region using < 100 nJ excitation pulses even though the maximum molar absorptivity of [IrBr6 ]2− is only ∼3000 cm−1 . Typical laser noise is less than 0.5% (standard deviation over the mean, based on shot-by-shot statistics) with an average of 1200 kinetic cycle pairs and 800 kinetic cycle quadruples acquired for each τ2 waiting time measured in transient absorption and two-dimensional electronic spectroscopy measurements, respectively. The probe intensity was 100× weaker than the pump, and the acquired signal was free of nonresonant response by about 25 fs.

Supporting Information Available X-ray crystal structure, Raman spectra, decay associated difference spectra, construction of coupled angular-momentum eigenstates and spectroscopic basis states.

This material is

available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The National Science Foundation supported this work through CAREER grant CHE–1552235. We thank Chunhua Hu for assistance with single-crystal structure determination.


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References (1) Domcke, W.; Yarkony, D. R.; Köppel, H. Conical Intersections: Electronic Structure, Dynamics & Spectroscopy; World Scientific Publishing, 2004. (2) Yarkony, D. R. Diabolical Conical Intersections. Rev. Mod. Phys. 1996, 68, 985–1013. (3) Haas, Y.; Zilberg, S. Photochemistry by Conical Intersections: A Practical Guide for Experimentalists. J. Photochem. Photobio. A 2001, 144, 221–228. (4) Bernardi, F.; Olivucci, M.; Robb, M. A. Potential Energy Surface Crossings in Organic Photochemistry. Chem. Soc. Rev. 1996, 25, 321–328. (5) Klein, S.; Bearpark, M. J.; Smith, B. R.; Robb, M. A.; Olivucci, M.; Bernardi, F. Mixed State ‘on the Fly’ Non-Adiabatic Dynamics: The Role of the Conical Intersection Topology. Chem. Phys. Lett. 1998, 292, 259–266. (6) Robb, M. A.; Olivucci, M. Photochemical Processes: Potential Energy Surface Topology and Rationalization using VB Arguments. J. Photochem. Photobio. A 2001, 5737, 1–7. (7) Toniolo, A.; Granucci, G.; Mart´ınez, T. J. Conical Intersections in Solution: A QM/MM Study Using Floating Occupation Semiempirical Configuration Interaction Wave Functions. J. Phys. Chem. A 2003, 107, 3822–3830. (8) Schapiro, I.; Melaccio, F.; Laricheva, E. N.; Olivucci, M. Using the Computer to Understand the Chemistry of Conical Intersections. Photochem. Photobiol. Sci. 2011, 10, 867–886. (9) Zilberg, S.; Haas, Y. Towards Experimental Determination of Conical Intersection Properties: A Twin State Based Comparison with Bound Excited States. Phys. Chem. Chem. Phys. 2011, 13, 11872–11877.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(10) Mathies, R. A.; Cruz, C. H. B.; Pollard, W. T.; Shank, C. V. Direct Observation of the Femtosecond Excited-State cis-trans Isomerization in Bacteriorhodopsin. Science 1988, 240, 777–779. (11) Schoenlein, R. W.; Peteanu, L. A.; Mathies, R. A.; Shank, C. V. The First Step in Vision: Femtosecond Isomerization of Rhodopsin. Science 1991, 254, 412–415. (12) Wang, Q.; Schoenlein, R. W.; Peteanu, L. A.; Mathies, R. A.; Shank, C. V. Vibrationally Coherent Photochemistry in the Femtosecond Primary Event of Vision. Science 1994, 266, 422–424. (13) Kobayashi, T.; Saito, T.; Ohtani, H. Real-Time Spectroscopy of Transition States in Bacteriorhodopsin during Retinal Isomerization. Nature 2001, 414, 531–534. (14) Polli, D.; Altoe, P.; Weingart, O.; Spillane, K. M.; Manzoni, C.; Brida, D.; Tomasello, G.; Orlandi, G.; Kukura, P.; Mathies, R. A. et al. Conical Intersection Dynamics of the Primary Photoisomerization Event in Vision. Nature 2010, 467, 440– 443. (15) Schnedermann, C.; Liebel, M.; Kukura, P. Mode-Specificity of Vibrationally Coherent Internal Conversion in Rhodopsin during the Primary Visual Event. J. Am. Chem. Soc. 2015, 137, 2866–2891. (16) Bassolino, G.; Sovdat, T.; Duarte, A. S.; Lim, J. M.; Schnedermann, C.; Liebel, M.; Odell, B.; Claridge, T. D. W.; Fletcher, S. P.; Kukura, P. Barrierless Photoisomerization of 11-cis Retinal Protonated Schiff Base in Solution. J. Am. Chem. Soc. 2015, 137, 12434–12437. (17) Teller, E. The Crossing of Potential Energy Surfaces. J. Phys. Chem. 1937, 41, 109–116. (18) Yarkony, D. R. Conical Intersections: The New Conventional Wisdom. J. Phys. Chem. A 2001, 105, 6277–6293. 22 ACS Paragon Plus Environment

Page 22 of 26

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(19) Jørgensen, C. K. Electron Transfer Spectra of Hexahalide Complexes. Molecular Physics 1959, 2, 309–332. (20) McCaffery, A. J.; Schatz, P. N.; Lester, T. E. Magnetic Circular Dichroism of IrCl2− 6 in Crystalline (CH3 NH3 )2 SnCl6 . J. Chem. Phys. 1969, 50, 379–385. (21) Jørgensen, C. K. Solvent Effects on the Absorption Bands of Iridium(IV)hexabromide and Other 5d-Hexahalides. J. Inorg. Nucl. Chem. 1962, 24, 1587–1594. (22) Jørgensen, C. K.; Preetz, W. Interpretation of Electron Transfer Spectra of Iridium (IV) and Osmium(IV) Mixed Chloro-Bromo Complexes. Z. Naturforschg. 1967, 22, 945–954. (23) Matveev, S. M.; Mereshchenko, A. S.; Panov, M. S.; Tarnovsky, A. N. Probing the Fate of Lowest-Energy Near-Infrared Metal-Centered Electronic Excited States: CuCl2− 4 and IrBr2− 6 . J. Phys. Chem. B 2015, 119, 4857–4864. (24) Valiente, R.; Rodriguez, F.; Moreno, M.; Hitchman, M. Effect of Pressure on the Cl− → Cu2+ Charge Transfer in A2 CuCl4 Layer Perovskites (A = Cn H2n+1 NH3 , n = 2, 3) and (3-Chloroanilinium)8 [CuCl6 ]Cl4 : Structural Correlations. Physica B 1999, 265, 176–180. (25) Moritomo, Y.; Tokura, Y. Pressure-Induced Disappearance of the In-Plane Lattice Distortion in Layered Cupric Chloride: (C2 H5 NH3 )2 CuCl4 . J. Chem. Phys. 1994, 101, 1763–1766. (26) Anisimov, V. I.; Aryasetiawan, F.; Lichtenstein, A. I. First-Principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: The LDA + U Method. J. Phys.: Condens. Matter 1997, 9, 767–808. (27) Oilunkaniemi, R.; Pietikäinen,; Laitinen, R. S.; Ahlgrén, Cation–Anion Interactions in Triphenyl Telluronium Salts. The Crystal Structures of (Ph3 Te)2 [MCl6 ] (M=Pt, Ir), 23 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(Ph3 Te)[AuCl4 ], and (Ph3 Te)(NO3 )·HNO3 . J. Organometallic Chemistry 2001, 640, 50–56. (28) Hamaguchi, H.-o. Group-Theoretical Study on the Raman Tensor Patterns in Vibrational Resonance Raman Scattering: Application to the Hexabromoiridate (IV) Ion. J. Chem. Phys. 1977, 66, 5757–5768. (29) Hamaguchi, H.-o. Polarized Resonance Raman Spectra of Hexahalide Complexes of Transition Metals: The Effect of Electronic Degeneracy on the Polarization of Vibrational Raman Scattering. J. Chem. Phys. 1978, 69, 569–578. (30) Clark, R. J. H.; Turtle, P. C. Studies on Vibrational and Electronic Raman Effects. Resonance Raman Spectroscopy of [IrCl6 ]2− , [IrBr6 ]2− and [OsBr6 ]2− Ions. J. Chem. Soc., Faraday Trans. 2 1978, 74, 2063–2076. (31) Harris, D. C.; Bertolucci, M. D. Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy; Dover Publications: New York, 1978. (32) Bosworth, Y. M.; Clark, R. J. H. Intensity Studies on the Raman-Active Fundamentals of Hexahalogenoanions of Second- and Third-Row Transition and Non-Transition Metals. The Calculation of Parallel and Perpendicular Bond Polarisability Derivatives. J. Chem. Soc., Dalton Trans. 1974, 1749–1761. (33) Bizimana, L. A.; Brazard, J.; Carbery, W. P.; Gellen, T.; Turner, D. B. Resolving Molecular Vibronic Structure using High-Sensitivity Two-Dimensional Electronic Spectroscopy. J. Chem. Phys. 2015, 143, 164203. (34) Rubbmark, J. R.; Kash, M. M.; Littman, M. G.; Kleppner, D. Dynamical Effects at Avoided Level Crossings: A Study of the Landau–Zener Effect Using Rydberg Atoms. Phys. Rev. A 1981, 23, 3107–3117.


Page 24 of 26

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(35) Pollard, W. T.; Mathies, R. A. Analysis of Femtosecond Dynamic Absorption Spectra of Nonstationary States. Annu. Rev. Phys. Chem. 1992, 43, 497–523. (36) Jonas, D. M.; Bradforth, S. E.; Passino, S. A.; Fleming, G. R. Femtosecond Wavepacket Spectroscopy: Influence of Temperature, Wavelength, and Pulse Duration. J. Phys. Chem. 1995, 99, 2594–2608. (37) Liebel, M.; Kukura, P. Broad-Band Impulsive Vibrational Spectroscopy of Excited Electronic States in the Time Domain. J. Phys. Chem. Lett. 2013, 4, 1358–1364. (38) Brazard, J.; Bizimana, L. A.; Gellen, T.; Carbery, W. P.; Turner, D. B. Experimental Detection of Branching at a Conical Intersection in a Highly Fluorescent Molecule. J. Phys. Chem. Lett. 2016, 7, 14–19. (39) Manaa, M. R.; Yarkony, D. R. On the Mechanism of the Reaction CH(X 2 Π) + 1 + 4 N2 (X 1 Σ+ g ) → HCN(X Σ ) + N( S). I. A Theoretical Treatment of the Electronic

Structure Aspects of the Intersystem Crossing. J. Chem. Phys. 1991, 95, 1808–1816. (40) Merchán, M.; Andres-Serrano, L.; Robb, M. A.; Blancafort, L. Triplet-State Formation along the Ultrafast Decay of Excited Singlet Cytosine. J. Am. Chem. Soc. 2005, 127, 1820–1825. (41) Courtney, T. L.; Fox, Z. W.; Slenkamp, K. M.; Khalil, M. Two-Dimensional VibrationalElectronic Spectroscopy. J. Chem. Phys. 2015, 143, 154201. (42) Lewis, N. H. C.; Dong, H.; Oliver, T. A. A.; Fleming, G. R. A Method for the Direct Measurement of Electronic Site Populations in a Molecular Aggregate using TwoDimensional Electronic-Vibrational Spectroscopy. J. Chem. Phys. 2015, 143, 124203. (43) Brazard, J.; Bizimana, L. A.; Turner, D. B. Accurate Convergence of TransientAbsorption Spectra using Pulsed Lasers. Rev. Sci. Instr. 2015, 86, 053106.



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(44) Gellen, T.; Bizimana, L. A.; Carbery, W. P.; Breen, I.; Turner, D. B. Ultrabroadband Two-Quantum Two-Dimensional Electronic Spectroscopy. J. Chem. Phys. 2016, 145, 064201.


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