Modelling Time-Resolved Two-Dimensional Electronic Spectroscopy of the Primary Photoisomerization Event in Rhodopsin

Abstract

Time-resolved two-dimensional (2D) electronic spectra (ES) tracking the evolution of the excited state manifolds of the retinal chromophore have been simulated along the photoisomerization pathway in bovine rhodopsin, using a state-of-the-art hybrid QM/MM approach based on multiconfigurational methods. Simulations of broadband 2D spectra provide a useful picture of the overall detectable 2D signals from the near-infrared (NIR) to the near-ultraviolet (UV). Evolution of the stimulated emission (SE) and excited state absorption (ESA) 2D signals indicates that the S₁ → S_N (with N ≥ 2) ESAs feature a substantial blue-shift only after bond inversion and partial rotation along the cis → trans isomerization angle, while the SE rapidly red-shifts during the photoinduced skeletal relaxation of the polyene chain. Different combinations of pulse frequencies are proposed in order to follow the evolution of specific ESA signals. These include a two-color 2DVis/NIR setup especially suited for tracking the evolution of the S₁ → S₂ transitions that can be used to discriminate between different photochemical mechanisms of retinal photoisomerization as a function of the environment. The reported results are consistent with the available time-resolved pump–probe experimental data, and may be used for the design of more elaborate transient 2D electronic spectroscopy techniques.

Introduction

Rhodopsin (Rh) is a type II opsin found in the photoreceptor rod cells of the retina, where it is used for night and peripheral vision. The chromophore responsible for light reception in Rh is the polyene 11-cis-retinal, which covalently binds the opsin apoprotein through a Schiff base (SB) linkage to the lysine residue Lys296, forming the 11-cis-retinal protonated Schiff base (PSB11) shown in Figure 1. Rh is the only type II opsin for which the X-ray structure has been resolved,¹⁻⁷ representing a paradigm system for fundamental studies of the primary event in vision and a reference model for the design of biomimetic photochromic devices.⁸⁻¹⁰ Upon absorption of visible light (with an absorption maximum at ∼500 nm, i.e., at a frequency of ν_max = ∼20 000 cm^–1), PSB11 undergoes ultrafast (200 fs) 11-cis → all-trans isomerization (see Figure 1a), triggering protein conformational changes that initiate the signal transduction processes in vision.¹¹ Fundamental understanding of retinal chromophore photochemistry and disentanglement of environmental effects, such as the electrostatic effects of the embedding proteins or the surrounding solvent molecules, are crucial for the design of biomimetic photosensitive devices.

Figure 1.

Schematic representation of the cis → trans photoisomerization reaction of PSB11 in rhodopsin (panel a) and the MEP calculated at the CASPT2/CASSCF level (panel b) describing the photoisomerization process from the FC point to the twisted CI funnel, through a point (FC_REL) where only skeletal bond stretchings have been relaxed (FC_REL) and subsequent structures with increasing (absolute) twisting angles.

Extensive computational studies aimed to unravel environmental effects which tune the photophysical and photochemical properties of retinals have been recently reviewed,¹² indicating possible molecular mechanisms explaining the different behaviors of retinal photoisomerization in various surroundings. Different environmental conditions could, in fact, alter the intrinsic properties of the chromophore by modulating the interplay between the covalent excited states and the ionic “photoactive” S₁ state. It has been proposed that, according to the so-called three-state model, the covalent S₂ excited state is directly involved in slowing down the photoisomerization reaction in bacteriorhodopsin,^13,14 and likely also in solvated retinals, with an avoided crossing between the S₁ and S₂ surfaces giving rise to a transition state (TS) along the S₁ state photoisomerization pathway. Indeed, the presence of an energy barrier on the S₁ energy surface before reaching the conical intersection (CI) with the ground state (GS, or S₀) would slow down the photoreaction rate and make the photoisomerization itself less efficient. In Rh on the other hand, the retinal photoisomerization occurs on a steep and barrierless reaction path involving only the ionic S₁ state and directly leading to a peaked CI, which has the form of a twisted intramolecular charge transfer (TICT) state and provides an efficient and fast (<100 fs) route for radiationless decay. According to the so-called two-state two-mode model,¹⁵ skeletal deformations (namely, a bond order inversion) followed by a torsional motion of the central double bond characterize the excited state branch of the photoisomerization path.

Experimental evidence of two distinct mechanisms for retinal photoisomerization in solution and in Rh is lacking, and the available ultrafast pump–probe experiments, which are intrinsically one-dimensional (1D), do not provide sufficient data to describe the interplay between ionic and covalent states during photoisomerization. Ad hoc designed ultrafast nonlinear optical spectroscopy experiments are therefore needed to shed light on the retinal photoisomerization mechanisms in different environments. In order to guide the design of new time-resolved optical spectroscopy experiments, in this work, we report full characterization of the excited state manifolds of PSB11 in Rh along the retinal photoisomerization pathway. We have characterized the electronic structures of selected critical points along the minimum energy path (MEP) of the S₁ energy surface, see Figure 1b, by means of a state-of-the-art hybrid quantum mechanics (QM)/molecular mechanics (MM) approach based on wave function methods, including complete active space self-consistent field (CASSCF)¹⁶ and second-order multireference perturbation theory (CASPT2).¹⁷ This methodology has shown to provide consistent photophysical and photochemical data for retinals in different environments, including vacuo,¹⁸ protein,¹⁹ and solution,¹⁹ in excellent agreement with chiroptical data,²⁰ absorption spectroscopy,¹⁸ resonance Raman,²¹ and ultrafast optical spectroscopy experiments.²²⁻²⁴ A set of data collected from first-principles calculations has been used to simulate time-resolved two-dimensional (2D) electronic spectroscopy experiments of photoactivated rhodopsin. 2D electronic spectroscopy (2DES) is the ultimate third-order nonlinear optical experiment, combining high spectral and temporal resolution and providing a wealth of information which usually remains hidden in conventional pump–probe experiments, such as intra- and intermolecular electronic couplings (that are resolved as off-diagonal cross-peaks in a 2D map), pathway specific signals, homogeneous and inhomogeneous broadening, etc.²⁵⁻³⁰ In 2DES, a sequence of three ultrashort laser pulses interacts with the sample, and the emitted signal field is detected as a function of the three time delays (t₁, t₂, and t₃); see Figure S1 in the Supporting Information. The 2D rephasing (KI) and nonrephasing (KII) signals can be obtained by double Fourier transformation (FT) with respect to times t₁ and t₃, providing 2D signals as a function of two frequencies, the “pump frequency” Ω(t₁), i.e., Ω₁, and the “probe frequency” Ω(t₃), i.e., Ω₃, given a fixed value of the “population time” t₂. For each value of the population time t₂, the 2DES spectrum can be interpreted, to a first approximation, by associating to the Ω₁ axis the absorption spectrum sensed by the excitation pulses and to the Ω₃ axis the transient absorption spectrum sensed by the probe pulse. A complete description of excited state relaxation is obtained by collecting a sequence of 2D maps as a function of population time t₂. Thus, with 2DES, the photoisomerization process of retinals can be monitored in proteins and in solution with the best possible combination of spectral and temporal resolution. Such types of experiments should be designed by setting the pump frequency resonant with ν_max, i.e., populating the spectroscopic state S₁, and probing the absorptions and/or the emission of the wave packet evolving on the S₁ surface with different probe frequencies and at various probe delays.

In this scenario, the unique advantage of using 2DES instead of conventional pump–probe spectroscopy is the possibility of resolving inhomogeneous broadening of the different signals along the Ω₁ axis, since there is only one diagonal peak present in the 2D map due to the (GS)S₀ → S₁ transition, and off-diagonal cross-peaks are absent. Unfortunately, computational modeling of the inhomogeneous broadening of the electronic transitions requires a complete sampling of the configurational space of the ground state and the characterization of a very large number of electronic structures along the photoisomerization dynamics, which is challenging, highly computationally demanding, and beyond the scope of the present work. Nevertheless, the simulated 2DES spectra along the “static” MEP of the retinal photoisomerization can provide information on the spectral regions where signals with opposite signs, e.g., excited state absorption (ESA) versus stimulated emission (SE), overlap. In these regions, the inhomogeneous broadening of each electronic transition could significantly affect the shape of the 2D overall signal. Such an effect could be observed experimentally, providing information on the time evolution of the 2D signals, which in conjunction with the simulated 2DES spectra reported here could give “time-resolved” atomistic details of the retinal photoisomerization reaction in Rh. Reliable characterization of temporal evolution of the electronic levels during the photoisomerization reaction requires first-principles simulations. Therefore, accurate simulations of 2DES spectra will be performed using the sum-over-states (SOS) approach,³¹ as implemented in our SOS//QM/MM method,^32,33 following the evolution of the 2DES map along the photoisomerization path, otherwise not achievable with a more simple parametrized approach based on Frenkel exciton models.^32,33 Accurate simulations of the 2DES spectra have the advantage of predicting the detectable 2D signals, allowing the design of tailored experiments suited for observation of specific signals. Despite the accuracy of electronic structure calculations of the MEP points, the simulated 2DES spectra still represent a coarse picture of the experimental spectra, since here we assume that during time intervals t₁ and t₃ the electronic energy levels remain fixed, i.e., a “static” snapshot of the photoisomerizing chromophore can be recorded in an experimental 2D spectrum. To follow more precisely the evolution of the electronic excited state manifold during a real measurement, a nonadiabatic propagation of the eigenstates should be performed, but such a level of complexity is beyond the scope of this work.

Here, we focus on the detection of ESA involving low-lying covalent states of PSB11, because of their relevance in the mechanism of retinal photoisomerization. In particular, with the proposed 2DES experiments, it could be possible to detect the S₁ → S₂ transitions during the photoisomerization and determine the fluctuations of the S₁/S₂ energy gap separation, elucidating the role of the low energy ionic and covalent excited states on retinal photoisomerization in Rh. A comparison between analogous 2DES experiments carried out in other proteins and in solution could finally discriminate between different photochemical mechanisms of retinal photoisomerization as a function of the (bio)chemical environment. Finally, it has been proposed that more elaborate multipulse two-dimensional techniques measuring the fifth-order nonlinear response, i.e., “transient” 2DES, could also be very informative for determining the retinal photoisomerization mechanism in different environments.¹² The electronic structure calculations and the simulations of time-resolved 2DES spectra reported here represent the groundwork for the design of such elaborate multipulse spectroscopy experiments.

Theoretical Methods

Electronic Structure Calculations

Constrained geometry optimizations were performed along the C₁₀—C₁₁=C₁₂—C₁₃ torsion coordinate of the PSB11 ranging from −13° at FC to ca. −90° at the CI (absolute values of the twisting angle in degrees are used hereafter) were performed using a combined CASSCF(12,12)/6-31G*//Amber (QM/MM) approach and the G09 Berny-algorithm³⁴ through COBRAMM.³⁵ The QM region was described using Molpro’s CASSCF routines.³⁶ The whole π-system of retinal and the N-terminal methylene group were considered. The β-ionone ring and its methyl groups were described by Amber99ff parameters.^22,37 QM and MM regions were connected through hydrogen link-atoms,³⁸ the β-ionone moiety and the two water molecules near the Schiff-base terminus were free to move during optimization, and the rest of the protein pocket was kept fixed at their crystal structure positions.³⁹ The ground state equilibrium structure was optimized with single state CASSCF considering only S₀, and the torsion path was obtained through state-averaging (SA) involving the S₀ and S₁ states with equal weight. SA gradients were computed using Molpro’s CPMCSCF routine. As initial structures, we used optimized geometries obtained in previous work.⁴⁰ On top of the newly optimized structures, QM/MM excited state calculations were performed with Molcas 7.7⁴¹ using the SA-CASSCF(12,12)/6-31G* method followed by energy refinement at the single-state CASPT2 level (hereafter named CASPT2/CASSCF), including all valence π-electrons and π-orbitals of the chromophore in the active space, with the MM part of the system treated as external point charges in both CASSCF and CASPT2 calculations. In the CASSCF state-averaging procedure, 70 states were included to ensure that enough roots are comprised in the CASSCF and CASPT2 calculations in order to describe the energy ranges reported for the 2D spectra. An imaginary shift⁴² of 0.2 and a zero-order Hamiltonian IPEA shift of 0.0 were used. Transition dipole moments were calculated at the CASSCF level using the RASSI module of Molcas 7.7.⁴³

Two-Dimensional Spectroscopy Simulations

The temporal evolution of the nonlinear response reveals electronic and geometrical changes in the system. While the recovery of the ground state bleach (B, blue arrow in Figure 2) depends on the excited state decay rates, the stimulated emission (E, cyan arrow in Figure 2) and excited state absorption (ESA, red arrows in Figure 2) exhibit characteristic shifts along the excited state deactivation pathways. In this work, we employ minimum energy path (MEP) calculations on the first excited state S₁ and probe the higher excited manifold and the ground state at selected geometries along the MEP, following the S₁ → S_N (with N ≥ 2) and S₁ → S₀ transitions at a given MEP point, respectively, while keeping the pump pulse pair in resonance with the GS → S₁ transition at the Franck–Condon (FC) point. Evolution in the ground state is neglected; thus, the B signal arises by probing the ground state equilibrium geometry. We mainly assume that during time intervals t₁ and t₃ the electronic energy levels remain fixed, i.e., their propagation is slow with respect to the ultrafast measurement, which allows associating the electronic structure of a static MEP point with its corresponding 2D spectrum. Additional approximations are adopted: the system evolves coherently along S₁ following closely the MEP; no population transfer between states occurs before the CI (i.e., signal intensities depend only on the transition dipole moments). It should be noted that MEP calculations do not contain dynamical and temporal information; therefore, we cannot directly extract time delays. For simulation of the 2DES spectra, we have combined the QM/MM methodology, which provides the transition dipole moments at the CASSCF level and CASPT2 corrected transition energies, with the SOS approach,³¹ as implemented in our SOS//QM/MM approach documented elsewhere.^32,33 SOS calculations were performed with Spectron 2.7,¹⁴ readapting the energy levels calculated at each MEP point in order to include the GS bleaching (GSB), i.e., by maintaining the FC S₀–S₁ energy gap and rigidly shifting all of the S_N energies calculated at the MEP point in order to align the S₁ energy with the FC S₁ energy. A constant dephasing of 200 cm^–1 has been employed, with finite transform-limited Gaussian pulse envelopes corresponding to a bandwidth of 5000 cm^–1. Infinite bandwidth pulses have also been used when specified. We report the combined rephasing and nonrephasing (KI + KII) signals (hereafter named 2D signals), which have absorptive features and can be collected experimentally with either partially collinear pump–probe geometry^44,45 or heterodyne detected three-pulse photon echo configuration;^46,47 see Figure S1 in the Supporting Information. Spectra are plotted on a logarithmic scale.

Figure 2.

Evolution of the excited state manifold along the MEP of retinal photoisomerization. Selected critical points along the MEP are reported. Ground state (GS) (cyan lines), S₂ state (green lines), and high-lying excited state (bright states in red or orange and dark states in black) energies are reported using the spectroscopic S₁ state (blue lines) as zero-energy for each MEP point. Bright excited states appearing exclusively in the FC_REL–30° and 60–90° structures are reported with magenta and brown lines, respectively. Stimulated emission (E), GS bleaching (B), and S₁ → S₂ (D and D′) transitions and excited state absorptions to higher-lying states are also depicted as arrows, only in the FC region (for simplicity).

Results

Excited State Manifolds along the Photoisomerization Pathway

Figure 2 shows the energy levels of PSB11 along the S₁ photoisomerization MEP for energies up to 34 000 cm^–1 (4.2 eV) from the spectroscopic state. The electronic structures calculated at the CASPT2//CASSCF level are reported from the FC region to the CI (at ∼90° twisting angle), considering a structure where only skeletal bonds have been relaxed (FC_REL), and two other structures with intermediate cis → trans isomerization angles, i.e., 30 and 60°. In the FC region, the first excited state accessible from the spectroscopic S₁ state is the double excitation H ⇒ L (hereafter D), i.e., the above-mentioned covalent S₂ state (see green bar in Figure 2), located at ∼8000 cm^–1 from S₁, in agreement with previous calculations.¹⁵ The molecular orbital labels, from H – 5 to L + 5, refer to the 12 active space orbitals in the CASSCF(12,12) calculations reported in Figure S2 in the Supporting Information. Above 10 000 cm^–1 from S₁, the first two excited states encountered are the covalent S₃ state, characterized predominantly by double (H, H – 1 ⇒ L) and single H – 3 → L excitations, see Table 1, and the ionic S₄ state, corresponding to a single H – 1 → L excitation. The S₁ → S₂ and S₁ → S_3,4 transitions are bright (i.e., with an oscillator strength larger than 0.02, see transitions D, 3, and 4 in Figure 2) and are expected to appear in the near-infrared (NIR) and the visible (red) spectral regions, respectively. At higher energies, in the range 20 000–30 000 cm^–1 from S₁, several excited states are found, generally characterized by single excitations into the lowest virtual orbitals (L and L + 1). In particular, the S₁ → S₇ transition (see transition 7 in Figure 2) has a transition energy close to the fundamental S₀ → S₁ transition frequency in the blue-green region of the visible spectrum, while higher-lying excited states, i.e., S_9–12 and S₁₄, give rise to a series of ESA bands in the violet and near-UV spectral regions (see transitions 9–12 and 14 in Figure 2).

Table 1. Excited States of the FC, FC_REL, 30°, 60°, and 90°(CI) Structures^a.

FC					FCREL
root	type	coeff	f	label	root	type	coeff	f	label
S1	H → L	–0.75	0.73	B	S1	H → L	–0.59	0.81	B
S2	D(H ⇒ L)	0.47	0.06	D	S2	H → L + 1	–0.40	0.27	D
						D(H ⇒ L)	–0.37
S3	D(H, H – 1 ⇒ L)	0.37	0.11	3	S3	D(H, H – 1 ⇒ L)	0.40	0.07	3
	H – 3 → L	0.37				H – 2 → L	0.39
S4	H – 1 → L	–0.51	0.68	4	S4	D(H, H – 2 ⇒ L)	0.39	0.05	i
						H – 3 → L	0.37
S7	H – 5 → L	0.45	0.13	7	S5	H – 1 → L	0.54	0.59	4
S9	H → L + 1	–0.52	0.44	9	S6	D(H – 1 ⇒ L)	–0.38	0.08	8
S10	H – 2 → L	0.39	0.07	10	S7	H – 5 → L	–0.38	0.07	7
	H – 2 → L + 1	–0.36				D(H, H – 3 ⇒ L)	0.33
S11	H – 2 → L	0.29	0.07	11	S8	D(H, H ⇒ L + 1)	0.26	0.24	i
	H – 3 → L + 1	0.24				H – 1 → L + 1	–0.25
S12	H → L + 1	0.32	0.36	12	S9	H → L + 1	0.48	0.28	12
						D(H ⇒ L)	–0.34
S14	H – 3 → L	0.33	0.14	14	S11	H – 4 → L	–0.61	0.04	13
					S12	H – 2 → L	0.35	0.08	ii
						D(H, H – 1 ⇒ L)	–0.31
						H – 1 → L + 1	–0.31
					S13	H – 5 → L	0.25	0.08	iii
						H → L + 3	0.21
					S14	H → L + 2	0.35	0.08	iv
					S15	D(H – 1, H – 3 ⇒ L)	0.25	0.03	v
						H – 5 → L + 1	–0.19

30°					60°
root	type	coeff	f	label	root	type	coeff	f	label
S1	H → L	–0.59	0.73	B	S1	H → L	0.42	0.19	B
S2	H → L + 1	–0.42	0.32	D	S2	D(H, H – 1 ⇒ L)	0.54	0.13	D′
	D(H ⇒ L)	–0.33				H → L + 1	0.42
S3	H – 2 → L	0.40	0.13	3	S3	H – 3 → L	0.40	0.11	3′
	D(H, H – 1 ⇒ L)	0.37				D(H, H – 1 ⇒ L)	0.36
S4	H – 1 → L	0.55	0.65	4	S4	D(H, H – 3 ⇒ L)	–0.47	0.06	l
						H → L + 3	0.37
S6	D(H – 1 ⇒ L)	–0.38	0.07	8	S5	H – 1 → L	0.66	0.62	4
	H – 2 → L	–0.35
S8	H – 1 → L	0.25	0.17	i	S6	D(H, H – 5 ⇒ L)	0.48	0.22	ll
	D(H → L and H → L + 1)	0.25				H → L + 4	0.33
S9	H – 1 → L + 1	–0.35	0.05	ii	S8	H – 4 → L	–0.52	0.07	13
	D(H, H – 1 ⇒ L)	–0.33				D(H ⇒ L, L + 1)	–0.31
S10	H – 4 → L	0.63	0.05	13	S9	D(H – 1 ⇒ L)	–0.46	0.03	8
						H – 2 → L	–0.46
S12	H → L + 1	–0.47	0.18	12	S10	H → L + 1	–0.48	0.29	12
S13	H – 5 → L	–0.23	0.13	iii
	H – 2 → L	0.22

90° (CI)
root	type	coeff	f	label	root	type	coeff	f	label
S3	H – 3 → L	–0.71	0.07	3′	S9	H – 4 → L	–0.46	0.12	13′
	D(H, H ⇒ L + 2)	–0.39				D(H, H – 5 ⇒ L)	–0.42
S6	D(H, H – 5 ⇒ L)	0.48	0.83	ll	S10	H → L + 1	–0.57	0.50	D′
	H – 4 → L	0.33				D(H, H – 1 ⇒ L)	0.57

^aOnly excited states having S₁ → S_N transitions (with N = 0, >2) with oscillator strength (f) larger than 0.02 are reported. Electron excitations refer to active space orbitals in Figure S2 of the Supporting Information. Labels of S₁ → S_N transitions are reported for assignment of 2D peaks in Figures 2–4.

Upon photoexcitation to the spectroscopic S₁ state, the retinal chromophore undergoes skeletal relaxation¹⁵ inducing bond order inversion and formation of a (transient) relaxed state (FC_REL), which is characterized by an elongated C₁₁–C₁₂ (“originally double”) bond which allows barrier-less rotation driving the 11-cis → all-trans isomerization. As shown in Figure 2, the photoinduced skeletal relaxation induces some significant changes in the electronic structure of the chromophore. As expected, the S₀/S₁ energy gap is reduced due to the relaxation along the S₁ surface, with consequent red-shift of the S₁ → S₀ SE (hereafter E, see cyan line in Figure 2). The relative positions of the covalent S₂ and S₃ states with respect to S₁ are not significantly affected by the bond relaxation, and the corresponding transitions from S₁ result in being just slightly red-shifted with respect to FC. It is worth noting, however, that upon bond relaxation the single H → L + 1 excitation provides a significant contribution to the covalent S₂ state and the H – 2 → L excitation contributes to the S₃ state. In contrast, the skeletal relaxation induces a blue-shift of transition 4 by ∼2000 cm^–1. Interestingly, above 20 000 cm^–1, the double H – 1 ⇒ L excitation, corresponding to the S₈ state in the FC manifold (and the S₆ state in FC_REL), gives rise to a bright transition (transition 8) which falls in the same spectral region of transition 7 and close to the fundamental S₀ → S₁ transition frequency. Analogously, the single H – 4 → L excitation (the S₁₃ state in the FC manifold and the S₁₁ state in FC_REL) gives rise to a bright transition just below 30 000 cm^–1 (see transition 13 in Figure 2), which, in return, is dark (i.e., with an oscillator strength smaller than 0.02) in the FC region. It is worth noting that skeletal relaxation also induces stabilization of some high-lying excited states that were not present in the FC region between 25 000 and 34 000 cm^–1 from S₁ (see magenta lines in Figure 2, i.e., transitions i–v).

Starting from the relaxed FC_REL structure, the chromophore undergoes rotation about the C₁₁–C₁₂ bond until reaching the twisted CI, at a torsional angle of ∼90°. Here, we analyze the variations of the excited state manifold induced by this torsional motion. At 30°, we find the electronic structure of the chromophore almost unchanged with respect to the FC_REL structure, with a slightly less rich excited state manifold due to the disappearance of the transition 7 ESA band. All the conserved ESA bands, including transitions D, 3–4, 8, 12–13, and i–iii, are slightly blue-shifted with respect to the FC_REL structure, while, as expected, the SE keeps red-shifting. In contrast to the first 30° rotation, a subsequent torsion of 30° induces significant changes in the excited state manifold of the chromophore. In fact, at 60° from the FC_REL structure, most of the ESA bands are significantly blue-shifted (>2700 cm^–1) with respect to the 30° structure. Interestingly, at 60°, we observe a significant localization of the CASSCF active orbitals which significantly affects some of the ESAs. In particular, the first excited state above S₁ is now characterized mainly by the single H → L + 1 and double (H, H – 1 ⇒ L) excitations; see Table 1. The S₂ state still maintains its covalent character, but the transition from S₁ (hereafter named transition D′) blue-shifts by ∼6000 cm^–1 with respect to the 30° structure. At 60°, the S₃ state is mainly characterized by the H – 3 → L excitation (in contrast to H – 2 → L at 30°) and the transition from S₁ (hereafter named transition 3′) is blue-shifted by ∼2750 cm^–1 with respect to its energy at 30°, now falling nearby the D′ transition, in the red region of the visible spectrum (at ∼15 000 cm^–1). At energies above 20 000 cm^–1 from S₁, excited states with mainly double excitation nature are found, see Table 1, with corresponding bright transitions (named l and ll, see brown lines in Figure 2) lying at ∼23 500 and ∼27 200 cm^–1 and transitions 4 and 8 being blue-shifted to ∼24 300 and ∼30 000 cm^–1, respectively, while transition 13 remains unaffected. It should be noted that also the SE is significantly affected at 60°, red-shifting to the near-IR, well below 10 000 cm^–1 (i.e., 1 μm). Finally, at the CI structure with a twisting angle of 90°, only a few bright transitions survive, including transitions 3′, ll, 13, and D′. All the surviving ESA bands substantially blue-shift with respect to the 60° structure, in particular transition D′, which now lies in the near-UV at ∼33 800 cm^–1. Particularly at the CI, transition 3′ falls nearby the fundamental S₀ → S₁ transition frequency and is expected to overlap with the GSB.

Two-Dimensional Electronic Spectra

In the above section, we have shown the changes of the electronic structure of retinal embedded in the Rh protein along the S₁ isomerization pathway, resulting in several ESA bands from S₁ to higher states, as well as an SE band from S₁ to S₀, which peak at frequencies that change very rapidly in time. Such dramatic spectral evolution of the photoinduced signals can be followed in real time using several advanced ultrafast spectroscopy techniques, such as broadband pump–probe spectroscopy or 2DES. The advantage of 2DES over pump–probe is that the nonlinear response can be resolved along the pump frequency (Ω₁), allowing characterization of cross-peaks and inhomogeneous broadenings of each electronic transition. In retinal photoisomerization there is a unique spectroscopic state (S₁) on which the photochemical reaction is known to take place. In the present work, thus, we are not interested in cross-peaks that arise from electronic coupling between different excited states (e.g., S₁–S₂, S₁–S₃ off-diagonal peaks, etc.), since their characterization requires population of higher excited states (S₂, S₃, etc.) that have unknown photophysical or photochemical pathways. We thus focus on the ESA and SE signals of the wave packet evolving only along the S₁ photoisomerization pathway. In this work, we report 2D spectra that can be experimentally collected with either the partially collinear pump–probe geometry^44,45 or the heterodyne detected three-pulse photon echo experimental setups,^46,47 using the simplest nonchiral xxxx polarization scheme.

Broadband 2D Spectra

In the previous section, we have described the evolution of the excited state manifold along the MEP of the photoisomerization, considering those excited states located below 34 000 cm^–1 from S₁. In order to visualize the energy positions of these electronic transitions, the possible overlaps between signals and the energy shifting trends of some important transitions, we report in Figure 3 the broadband 2DES spectra calculated using all three laser pulses centered at the absorption maximum frequency of the chromophore (ν_max, calculated to be at 20 875 cm^–1 at the CASPT2/CASSCF level) with infinitely broad bandwidth. Infinitely broad pulses reveal all signals that are “ideally” detectable, helping in the selection of experimental parameters (i.e., central probe frequencies and pulse bandwidths) to be used in tailored experiments for the detection of desired electronic transitions.

Figure 3.

Broadband 2DES spectra obtained with infinitely broad laser pulses, using the xxxx nonchiral polarization scheme. 2D spectra are reported for the selected MEP point from the FC to the CI (at ∼90°). The complex part of the signal is plotted on a logarithmic scale. The transitions are labeled according to the Figure 2 assignment, with green and light green boxes highlighting the D and D′ (S₁ → S₂) transitions, respectively.

Figure 3 shows the broadband 2DES spectra at the FC region, i.e., at t₂ = 0, with the negative signals of both GSS (peak B) and SE (peak E) overlapping at Ω₃ = 20 875 cm^–1, i.e., the absorption maximum frequency ν_max, and several positive signals associated with ESA bands in the Ω₃ range from 8000 to 33 000 cm^–1. Following the evolution of the excited state manifolds described in the previous section, all of the 2D signals but the GSB are expected to shift along the MEP during the photoisomerization process. The simulations of 2D spectra at t₂ > 0 are performed on selected geometries of the “static” MEP that cannot be directly associated with effective values of the excited state evolution time t₂. However, comparison of the reported 2DES spectra with experimental data could allow association of probe delay times with PSB11 structures, providing unprecedented atomistic details of the retinal photoisomerization.

The transition from S₁ to the covalent S₂ state (see green boxes in Figure 3, peak D) appears as a positive signal at ∼8000 cm^–1 in the NIR at the FC region. Its transition energy does not change significantly upon skeletal relaxation (small red-shift of 1100 cm^–1) and 30° C₁₁–C₁₂ bond rotation (blue-shift of 1000 cm^–1 with respect to FC). A strong blue-shift of the S₁ → S₂ transition is, instead, observed at a twisted angle of 60°, where the electronic excitation contributing to the covalent S₂ state changes and the corresponding ESA (peak D′) appears in the visible at ∼15 160 cm^–1. At the twisted CI, the S₂ state is highly destabilized and the peak D′ lies at very high energies (>30 000 cm^–1), in the near-UV.

The S₁ → S₃ transition (peak 3) behaves similarly to the S₁ → S₂ transition along the photoisomerization path. In fact, up to 30°, its transition energy is almost unchanged (between 13 100 and 13 900 cm^–1) with respect to its value in the FC region (i.e., 13 820 cm^–1), while a pronounced blue-shift of ∼2500 cm^–1 is observed at 60°, with corresponding changes in the electronic excitations contributing to the S₃ state. Here, peak 3′ is found close to peak D′ in the red of the visible spectrum. At the CI, the S₁ → S₃ transition is further blue-shifted but it lies at much lower energies than the S₁ → S₂ transition, being located at ∼18 000 cm^–1, in proximity to the GSB (B). Indeed, the broadband 2DES spectrum at the CI reported in Figure 3 indicates that the positive peak 3′ is canceled by overlap with the strong negative B signal. It is worth noting that peak 3 disappears in the FC_REL broadband spectrum. This is due to the progressive red-shift of the SE which bumps into low-lying ESA bands that concurrently red-shift during the photoisomerization reaction. Such a signal quenching effect is observed for the S₁ → S₃ transition at the FC_REL structure, and it is expected for the S₁ → S₂ transition at twisting angles slightly larger than 30°, i.e., ∼35°.

The S₁ → S₄ transition (peak 4) is found as a positive signal at Ω₃ ≈ 16 000 cm^–1 in the FC region, and differently from peaks D and 3, it blue-shifts by ∼2100 cm^–1 upon bond relaxations. Therefore, the overlap of (positive) peak 4 with the red-shifted (negative) SE is expected to happen at the earliest stages of the photoisomerization, i.e., during the skeletal relaxation and before the bond inversion is completed, corresponding to an energy range of 16 000–18 000 cm^–1. This result is fully consistent with broadband pump–probe experiments that show the absence of signals in the 16 000–18 000 cm^–1 range (555–625 nm, in wavelength) at early probe delays, where actually the initial SE was expected to show up.²²⁻²⁴ Moreover, at energies >18 000 cm^–1, in the spectral region of the absorption maximum ν_max, the experimental data at probe delays <75 fs shows the presence of a broad ESA band and its overlap with the GSB signal. Our results also indicate that, in this region of the spectra and at early probe delays (for twisting angles <60°), the negative B signal overlaps with the blue-shifting peak 4 and other two ESAs. Remarkably, at 60°, the calculated 2DES spectrum shows an almost unperturbed negative B signal and the positive peaks D′ and 3 at ∼15 200 and ∼16 500 cm^–1, respectively, in very nice agreement with ultrafast pump–probe spectroscopy data at around 75 fs probe delay, showing the recovery of the GSB and the appearance of positive signals at energies below 17 400 cm^–1 (wavelengths >575 nm), with two small spots appearing at ∼16 000 and ∼16 900 cm^–1. Finally, our 2D spectrum at the twisted CI suggests that the only surviving bright ESA band is the S₁ → S₃ transition (peak 3′), whose positive intensity is vanishing due to overlap with the negative B signal. No signals are observed below 19 000 cm^–1, and the first detectable ESA is in the near-UV, above 30 000 cm^–1, in agreement with pump–probe experiments revealing the presence of just GSB negative signal and the formation of the photoinduced ground state absorption band of the rhodopsin photoproduct in the CI region.

In summary, we showed that the broadband 2DES spectra, obtained using the excited state manifolds calculated at the CASPT2/CASSCF level along the MEP of the retinal photoisomerization, provide useful information on the evolution of ESA signals and their overlap with the SE and GSB signals with opposite sign, in good agreement with the available broadband pump–probe spectroscopy data. In the following section, we consider realistic 2DES combinations of pulse frequencies and bandwidths that can provide useful information on the evolution of specific ESA bands during retinal photoisomerization, including excitations from S₁ to low-lying covalent states that have been proposed to interplay with the spectroscopic state in the photoisomerization of retinal in solution.

One- and Two-Color 2D Spectra

The simplest 2DES combination of pulses that can be considered involves identical pump and probe pulses (one-color setup), with all frequencies centered at the absorption maximum of the chromophore, ν_max. Figure 4a shows the calculated 2DES spectra simulating such one-color experiment with the pulses’ bandwidth of 5000 cm^–1. The major contribution to all one-color spectra is, as expected, the negative GSB signal at Ω₃ = ν_max = 20 875 cm^–1, peak B. At the FC region, the GSB is accompanied by the SE (at identical frequency) but the simulated 2D spectrum indicates that the expected strong negative peak is partially overlapping with a positive ESA band, peak 7 at ∼22 000 cm^–1, inducing depletion of the signal and a tiny asymmetry along the Ω₃ frequency axis. At very early probe delays, the wave packet leaves the FC region and the simulated 2DES spectra at the FC_REL and 30° structures indicate that the negative GSB signal will be significantly depleted by a concomitant red-shift of the negative peak E, blue-shift of the positive peak 4 that is approaching ν_max, and lasting positive peaks 7 (at FC_REL) and 8 (at FC_REL and 30°). At twisting angles ≥60°, the GSB signal is almost unperturbed due to the further blue-shift of the ESA band 4, which at 60° lies already at energies >24 000 cm^–1. At the CI, peak B almost recovers the shape of the 2D isolated signal with a tiny perturbation at energies below ν_max due to the presence of the blue-shifted S₁ → S₃ transition. The simulated 2DES spectra along the MEP reported in Figure 4a suggest that with a one-color setup it is possible to observe modulation of the GSB signal at early stages of the photoisomerization, as affected by the evolution of high-lying ESA bands (i.e., the transitions S₁ → S_4, 7–8 in the FC). Probe frequencies lower than ν_max are necessary in order to track the energy gaps between the S₁ state and low-lying covalent excited states (such as S₂ and S₃), and a two-color setup is required.

Figure 4.

2D (xxxx) spectra obtained with the one-color 2DVis (panel a) and the two-color 2DVis (panel b) setups. 2D spectra are reported for the selected MEP point from the FC to the CI (at ∼90°). The complex part of the signal is plotted on a logarithmic scale. The transitions are labeled according to the Figure 2 assignment. Black boxes indicate the 5000 cm^–1 bandwidth that was used.

Figure 4b shows the calculated 2D spectra from the FC to the CI region, simulating a time-resolved two-color 2DES experiment with pump pulses centered at ν_max (Ω₁ = 20 875 cm^–1) and probe pulses centered at Ω₃ = 15 000 cm^–1, in the red region of the visible spectrum. In the FC region, the S₁ → S₃ and S₁ → S₄ transitions, i.e., peaks 3 and 4, are clearly resolved at ∼13 800 and ∼16 000 cm^–1, respectively, but upon bond relaxation, the red-shifted SE burns the positive peak 3, while peak 4 blue-shifts to the green, at ∼18 100 cm^–1, and remains detectable. The positive S₁ → S₃ signal will recover in the two-color spectrum upon torsional motion that further red-shifts the negative E signal. Before reaching the CI region, where the two-color 2D spectrum is essentially signal-free, the D′ transition rapidly shifts to the red and both peaks 3′ and D′ are clearly resolved at 60°. The reported two-color 2DES spectrum at 90° suggests that peak 3′ should also be resolved at the CI structure when using a probe pulse centered at 15 000 cm^–1 with a bandwidth of 5000 cm^–1. The proposed two-color 2DES combination of pulse frequencies allows, indeed, to track the energy gaps between the S₁ state and the low-lying excited states S_2–4 along the retinal photoisomerization pathway. However, the important S₁ → S₂ transition (peak D′) appears in this detection spectral window only for twisting angles close to 60°, where the covalent S₂ state partially changes its double excitation nature (see previous section), and this transition is expected to move from ∼9000 to ∼33 000 cm^–1 while going from 30 to 90°. Thus, the D′ signal is expected to blue-shift very rapidly from the near-IR to the UV, suggesting that it could be difficult to really track the S₁ → S₂ transition with a two-color 2DES setup and detection in the visible. On the other hand, CASPT2/CASSCF calculations suggest that the position of the covalent S₂ state relative to the spectroscopic S₁ state remains almost invariant up to 30° twisting angle, with S₁ → S₂ transition energies varying from 6900 to 9000 cm^–1 in the NIR. Therefore, here we propose an alternative two-color 2D setup especially suited to track the S₁ → S₂ transition during the early stage of the photoisomerization reaction, with pump pulses centered at ν_max and probe pulses in the NIR.

Figure 5 shows the simulated 2DES spectra for MEP structures from the FC to 60°, with NIR probe pulses centered at Ω₃ = 10 000 cm^–1 (i.e., 1 μm in wavelength) and a bandwidth of 5000 cm^–1, corresponding to a transform-limited pulse duration of ∼3 fs. Such tunable broadband pulses can be generated from optical parametric amplifiers.⁴⁸ With this two-color setup, peak D is clearly resolved at ∼8000, ∼6900, and ∼9000 cm^–1, for the FC, FC_REL, and 30° structures, respectively. In particular, both peaks E and D are near the probe central frequency at 30°, indicating that the probe frequency maximum is set very close to the region where the overlap between SE and S₁ → S₂ ESA transition will occur. Unfortunately, the available pump–probe data do not cover energy values below 10 000 cm^–1, and direct observation of the S₁ → S₂ transition at early probe delays has not been achieved yet. In the computed 2DES spectra, the evolution of the S₁ → S₃ transition can also be detected from the FC to 60° structure, including its overlap with the E signal. The two-color 2DES setup with NIR probing, thus, appears to be best suited for providing a clear picture of the evolution of the S₁ → S₂ and S₁ → S₃ transitions, including their overlap with SE, along the retinal photoisomerization in rhodopsin.

Figure 5.

2D (xxxx) spectra obtained with the two-color 2DVis/NIR setup. 2D spectra are reported for the selected MEP point from the FC to the 60° structure. The complex part of the signal is plotted on a logarithmic scale. The transitions are labeled according to the Figure 2 assignment. Black boxes indicate the 5000 cm^–1 bandwidth used.

Conclusions

In this work, we analyze the electronic structure changes of the retinal chromophore in bovine rhodopsin along its photoisomerization pathway by characterizing the manifolds of the excited states at critical points of the MEP along the S₁ energy surface, from the FC region to the twisted CI. The electronic structure calculations based on multiconfigurational ab initio techniques within a hybrid QM/MM scheme reveal that the S₁/S₀ energy gap rapidly decreases during the photoinduced skeletal relaxation of the polyene chain, while the evolution of excited state S₁ → S_N (with N ≥ 2) absorption energies features a remarkable blue-shift only after bond inversion and partial rotation along the cis → trans isomerization angle, i.e., for twisting angles larger than 30°. We report simulated time-resolved 2DES spectra to track the evolution of the S₁ → S₀ SE red-shift and ESA blue-shifts along the MEP. A set of broadband 2DES spectra are reported considering laser pulses with infinite bandwidth, providing a useful picture of the overall detectable 2D signals from the NIR to the near-UV frequency domains. Three different 2D combinations of pulse frequencies have been considered in order to follow the evolution of specific signals: a one-color setup with all pulses centered at the absorption maximum frequency of the chromophore in the blue-green region of the visible (one-color 2DES), a two-color setup with probe pulse centered in the red (two-color 2DVis), and a two-color setup with probe pulses centered in the NIR (two-color 2DVis/NIR). We show that a modulation of the GSB signal due to the overlap with high-lying ESA bands, i.e., transitions S₁ → S_4,7–8, can be observed at early stages of the retinal photoisomerization using a one-color 2DVis setup. To track, instead, the energy gaps between the S₁ state and the low-lying covalent excited states (such as S₂ and S₃), a two-color setup is required. The simulated 2D spectra for the two-color 2DVis setup reveal that the signal quenching of the S₁ → S₃ ESA, due to overlap with the red-shifted SE, can be detected in the red spectral window at early probe delays, while the S₁ → S₂ transition is unlikely to be observed due to the large and rapid blue-shift of this signal at twisting angles larger than 30°. The S₁ → S₂ transition is particularly relevant because it provides direct measurement of the S₁/S₂ energy gap separation along the photoisomerization path, a parameter that could play a crucial role in slowing down the photoreactivity, determining the photoisomerization mechanism of retinal in solution. Finally, we show that the two-color 2DVis/NIR setup is best suited for tracking the evolution of the S₁ → S₂ and S₁ → S₃ transitions along the retinal photoisomerization pathway, and we encourage performing such type of experiments for elucidation of the molecular mechanisms that drive different behaviors of retinal photoisomerization in various environments. The reported results are consistent with the available time-resolved 1D pump–probe experimental data, providing fundamental information for the design of new time-resolved 2D experiments and laying the groundwork for simulation of more elaborate multipulse sequences, such as in transient 2D electronic spectroscopy.

Supporting Information Available

Schematic representations of different 2DES experimental setups, CASSCF(12,12) active space orbitals, and Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors declare no competing financial interest.

Funding Statement

National Institutes of Health, United States