Ultrafast terahertz Stark spectroscopy reveals the excited-state dipole moments of retinal in bacteriorhodopsin

Significance

The membrane protein bacteriorhodopsin, a prototypical light-driven proton pump, contains a retinal protonated Schiff base chromophore. Upon photoexcitation, the chromophore undergoes a femtosecond double-bond isomerization that initiates proton pumping. The specific character of the chromophore excited state impacts its isomerization dynamics but has remained controversial. We show that ultrafast terahertz Stark spectroscopy and electronic structure calculations allow for mapping the chromophore transient electric dipole moment and electronic character, providing a direct view on the early time excited state dynamics. The moderate dipole change of 5 $\pm$ 1 Debye observed upon photoexcitation reveals a mixing of the first and second excited states of the chromophore, due to electronic correlations and site interactions. The excited state mixing affects ultrafast reaction dynamics directly.

Abstract

The photoinduced all-trans to 13-cis isomerization of the retinal Schiff base represents the ultrafast first step in the reaction cycle of bacteriorhodopsin (BR). Extensive experimental and theoretical work has addressed excited-state dynamics and isomerization via a conical intersection with the ground state. In conflicting molecular pictures, the excited state potential energy surface has been modeled as a pure S₁ state that intersects with the ground state, or in a 3-state picture involving the S₁ and S₂ states. Here, the photoexcited system passes two crossing regions to return to the ground state. The electric dipole moment of the Schiff base in the S₁ and S₂ state differs strongly and, thus, its measurement allows for assessing the character of the excited-state potential. We apply the method of ultrafast terahertz (THz) Stark spectroscopy to measure electric dipole changes of wild-type BR and a BR D85T mutant upon electronic excitation. A fully reversible transient broadening and spectral shift of electronic absorption is induced by a picosecond THz field of several megavolts/cm and mapped by a 120-fs optical probe pulse. For both BR variants, we derive a moderate electric dipole change of 5 $\pm$ 1 Debye, which is markedly smaller than predicted for a neat S₁-character of the excited state. In contrast, S₂-admixture and temporal averaging of excited-state dynamics over the probe pulse duration gives a dipole change in line with experiment. Our results support a picture of electronic and nuclear dynamics governed by the interaction of S₁ and S₂ states in a 3-state model.

The prototypical reaction cycle of the proton pump bacteriorhodopsin (BR) is triggered by a photoinduced all-trans to 13-cis isomerization of the protonated retinal Schiff base (RSBH⁺, Fig. 1A), located within a trans-membrane protein containing seven $\alpha$-helices (1). Upon electronic excitation of the all-trans retinal chromophore, a vibronic wavepacket propagates within 200 fs from the Franck–Condon coupled region to a shallow minimum of the excited-state potential, the I state, which is characterized by a bond order inversion in the RSBH⁺. This step is followed by propagation to a conical intersection (CI) of the excited- and ground-state potential, where isomerization to a 13-cis geometry generates the vibronically excited ground-state photoproduct J with a 500-fs rise time. The J state transforms within a few picoseconds into the K ground state with a vibrationally relaxed 13-cis Schiff base.

Fig. 1.

(A) Schematic of the protonated retinal Schiff base (RSBH⁺) and its binding pocket in wild-type BR (pdb: 1c3w). The blue arrow symbolizes the electric dipole moment $\mu$ of RSBH⁺. (B) Schematic potential energy surfaces of the S₀, S₁, and S₂ states along the reaction coordinate of retinal isomerization (adopted from refs. Goz20 and Gon00). The 2-state model (lhs) invokes an S₁ excited state potential that intersects with the electronic ground state at the conical intersection CI, whereas the 3-state model (rhs) considers the interaction of S₁ and S₂ states with avoided crossings and shallow potential barriers along the reaction coordinate. (C) Time-dependent electric field $E_{\text{THz}}$ of a picosecond THz pulse as used in the experiments. (D) Electric-field spectrum of the pulse.

Femtosecond pump–probe and two-dimensional (2D) spectroscopy (2–7) and femtosecond X-ray diffraction (8) have given detailed insight into the early BR dynamics. A combination of low-frequency out-of-plane and twisting modes together with high-frequency C$=$C stretching motions represents the relevant reaction coordinate of trans–cis isomerization. Compared to RSBH⁺ in the gas phase (9), interactions in the active site of BR accelerate the excited state dynamics and increase selectivity of the all-trans to 13-cis isomerization. On the other hand, compared to other rhodopsins, the particular shape of the excited-state potential slows down the initial wavepacket propagation in BR.

Extensive theoretical work on isomerization dynamics has led to two partly conflicting pictures. In the so-called 2-state scenario (Fig. 1B), wavepacket propagation occurs on an excited-state potential of S₁ character, which forms a CI with the S₀ ground-state potential (3, 10, 11). The S₂ state of the retinal Schiff base is not part of such dynamics. In contrast, the 3-state scenario involves the interaction of S₁ and S₂ potential surfaces with S₁ being a singly excited state (SES) with charge-transfer (CT) character and a doubly excited state (DES) character for S₂ (7, 12–15). The avoided crossings of the two excited states slow down the initial wavepacket propagation and change the wavefunction character between CT and diradical character along the reaction coordinate. At the CI, the original three-state picture predicts an intersection of the DES with the S₀ state (4), whereas in the refined 3-state model of ref. Goz20 (rhs of Fig. 1B), the CI is characterized by a crossing of the SES and the S₀ state. Moreover, there is a strong modulation of the S₁-S₂ energy gap during the first 100 fs after excitation (7). Recent computational results suggest that the degree of S₁/S₂ mixing affects the photoisomerization quantum efficiency of animal rhodopsins (16) and fluorescence emission in microbial rhodopsins (17, 18). While results from femtosecond pump–probe and 2D experiments have been interpreted in terms of the 3-state model (4, 5, 7), there is a need for more direct experimental characterization of the excited state properties and dynamics.

The electronic charge distributions of the S₀, S₁, and S₂ states of the RSBH⁺ are different, giving rise to electric dipole moments of ${\mu }_{S0}\approx -24$ Debye, ${\mu }_{S1}\approx -7.2$ D, and ${\mu }_{S2}\approx -20$ D (14, 19). As a consequence, the excited-state dipole moment ${\mu }_{\mathit{ex}}$ is expected to be substantially larger for a mixed S₁/S₂ than for a pure S₁ state. An ultrafast measurement of the dipole change $\mathrm{\Delta }\mu =|{\mathit{\mu }}_{\mathit{ex}}-{\mathit{\mu }}_{S0}|$ upon electronic excitation, thus, provides insight into the early excited-state dynamics and the electronic character of the excited state. Stark spectroscopy, i.e., a measurement of changes of electronic absorption upon application of an external electric field (20, 21), gives access to dipole changes, but has exclusively been applied under steady-state conditions, averaging over slow structural dynamics during the millisecond BR reaction cycle (22, 23). Here, we apply the method of ultrafast terahertz (THz) Stark spectroscopy (24) to monitor dipole changes upon electronic excitation of wild-type BR (BR wt) and the BR D85T mutant (BR D85T) (25). Our results provide support for the 3-state scenario of the initial excited-state dynamics of BR.

Experimental Results

The experiments employ a pump–probe approach, in which the picosecond THz pump pulse with an electric field $E_{\text{THz}}$ (Fig. 1C) interacts nonresonantly with a BR film sample and induces a change of electronic absorption of the RSBH⁺. Upon THz pumping, the RSBH⁺ remains in its S₀ ground state. In the spectral range of the THz transient (Fig. 1D), the BR samples display a negligible absorbance on the order of 0.02. The THz field acting on the sample is enhanced with the help of a metallic antenna structure on top of the BR films (26), generating a peak field of $E_{\text{THz}}^p=3.0$ MV/cm or 0.3 V/nm (BR wt, peak intensity 12 GW/cm²) and $E_{\text{THz}}^p=2.1$ MV/cm or 0.21 V/nm (BR D85T). The resulting change of electronic absorption is measured with a 120-fs probe pulse tunable throughout the absorption band $A_0(\nu )$ of BR wt and BR D85T (blue lines in Figs. 2A and 3A). Absorbance changes $\mathrm{\Delta }A(\nu ,t_D)=A(\nu ,t_D)-A_0(\nu )=-log(T(\nu ,t_D)/T_0)$ are recorded as a function of probe frequency $\nu$ and pump–probe delay $t_D$ ($T,T_0$: sample transmission with and without THz electric field). The zero delay is set at the maximum of the THz electric field. Details on samples and experimental methods are given in Materials and Methods and SI Appendix.

Fig. 2.

THz Stark effect in BR wt. (A) Transient absorption spectra (symbols) for two delay times $t_D$ between the maximum of the THz electric field at 0 fs and the optical probe pulse. The change of absorbance $\mathrm{\Delta }A$ in mOD is plotted as a function of probe frequency in THz. A wavelength scale is given on the top abscissa. The THz field induces a spectral broadening of the stationary absorption band (blue line). (B and C) Normalized absorption changes $\mathrm{\Delta }A$ (symbols) at probe frequencies of (B) 476 THz (wavelength $\lambda$$=$ 630 nm) and (C) 526 THz [$\lambda$$=$ 570 nm, c.f. arrows in panel (A)] as a function of $t_D$. The solid lines represent the time-dependent intensity of the THz pulse.

Fig. 3.

THz Stark effect in the D85T mutant of bacteriorhodopsin (BR D85T). (A) Transient absorption spectra of BR D85T (symbols) for two different delay times between the maximum of the THz pulse at 0 fs and the optical probe pulse. Blue solid line: Stationary absorption spectrum. (B and C) Normalized time-resolved absorption changes (symbols) at probe frequencies of (B) 435 THz ($\lambda$$=$ 690 nm) and (C) 500 THz ($\lambda =600$ nm). Solid lines: time-dependent intensity of the THz pulse.

Results for BR wt are summarized in Fig. 2. Panel (A) shows the absorbance change $\mathrm{\Delta }A$ for delay times of $t_D=0$ and 500fs (symbols) as a function of probe frequency. Both spectra display an enhanced spectral width compared to the stationary absorption band $A_0(\nu )$ (blue line) with an absorbance decrease around the maximum $A_0$ and absorbance increases on the low- and high-frequency wings of $A_0$. As a function of delay time, the amplitude of $\mathrm{\Delta }A$ decreases, while the positions of the two zero crossings are essentially maintained.

In Fig. 2 B and C, we present the normalized absorbance change $\mathrm{\Delta }A$ at fixed probe frequencies of (B) 476 THz (wavelength $\lambda$$=$ 630 nm) and (C) 526 THz [$\lambda$$=$ 570 nm, cf. arrows in panel (A)] as a function of pump–probe delay (symbols). The response of BR wt follows in time the THz intensity $I_{\text{THz}}\propto {|E_{\text{THz}}|}^2$ (lines). The absence of absorbance changes at delay times after the THz pulse points to a negligible role of (slower) reorientation processes of the RSBH⁺ in the external THz field and/or THz-induced changes of protein structure with an impact on the absorption line shape. The linear dependence of $\mathrm{\Delta }A$ on THz intensity is confirmed by measurements with different maximum THz amplitudes (SI Appendix).

In a second series of measurements, we studied the BR mutant BR D85T, in which the aspartic acid (D) at position 85 is replaced by a threonine (T) (25). This change modifies electrostatic interactions in the binding pocket of the RSBH⁺ and the arrangement of bound water molecules. As a result, the maximum of the absorption band is red-shifted from 568 nm in BR wt to 595 nm in BR D85T (solid blue line in Fig. 3A). The experimental results (Fig. 3) exhibit a transient behavior of BR D85T similar to BR wt. The THz peak field of 2.1 MV/cm (0.21 V/nm) and the absorbance of the BR D85T sample are smaller than in the BR wt measurements, resulting in smaller absorbance changes $\mathrm{\Delta }A$ [panel (A)].

Data Analysis

Resonant low-frequency excitations of BR and BR D85T by the THz pump pulse are negligible because of the very small THz absorbance of the thin-film samples. In contrast, the THz electric field interacts nonresonantly with the RSBH⁺, which displays substantial electric dipole moments ${\mathit{\mu }}_{\mathit{Si}}$ in the electronic ground state S₀ and the excited S₁ and S₂ states. The interaction strength between the THz field and the dipoles ${\mathit{\mu }}_{\mathit{Si}}$ (i $=$ 0...2) is proportional to $-{\mathit{\mu }}_{\mathit{Si}}·{\mathbf{E}}_{\text{loc}}=-{\mu }_{\mathit{Si}}{E}_{\text{loc}}\text{cos}({\theta }^{\prime })$, where ${\mathbf{E}}_{\text{loc}}$ is the local THz field acting on the RSBH⁺ and ${\theta }^{\prime }$ the angle between ${\mathit{\mu }}_{\mathit{Si}}$ and ${\mathbf{E}}_{\text{loc}}$. This interaction modifies the energies of electronic states and, thus, shifts the spectral positions of electronic transitions. Moreover, the polarizability of the RSBH⁺ in the different electronic states leads to a field-induced change of the dipole moments, which, if strong enough, leads to spectral shifts as well.

Polarization of the RSBH⁺ by the external THz field could induce a change of the electronic transition dipole ${\mu }_{0ex}$, leading to a change of absorption strength. The absolute square $|{\mu }_{0ex}{|}^2$ of the transition moment is proportional to the integral of $A_0(\nu )/\nu$ over the absorption band $A_0$ (21). Correspondingly, the integral of $\mathrm{\Delta }A(\nu )/\nu$ of the THz induced absorbance change $\mathrm{\Delta }A(\nu$) gives the difference of $|{\mu }_{0ex}^{\ast }{|}^2$ and $|{\mu }_{0ex}{|}^2$ with the transition dipole ${\mu }_{0ex}^{\ast }$ in presence of the THz field:

$$\begin{array}{c}\hfill {\int }_{\text{abs.band}}\frac{\mathrm{\Delta }A(\nu )}{\nu }\text{d}\nu =C(|{\mu }_{0ex}^{\ast }{|}^2-|{\mu }_{0ex}{|}^2)\end{array}$$ [1]

Here, $C=108.87·c·l$ is a constant with the RSBH⁺ concentration $c$ (in M) and the sample thickness $l$ (in cm; ${\mu }_{0ex}^{\ast }$, ${\mu }_{0ex}$ in D). For both BR wt and BR D85T, Eq. 1 gives a value of $(|{\mu }_{0ex}^{\ast }{|}^2-|{\mu }_{0ex}{|}^2)/|{\mu }_{0ex}{|}^2\approx {10}^{-3}$, corresponding to a negligible change of the electronic transition moment upon application of the external THz field.

For an individual RSBH⁺, the frequency shift of an electronic S₀-S_ex transition in the time-dependent THz field ${\mathbf{E}}_{\text{loc}}(t)$ is given by

$$\begin{array}{c}\hfill \mathrm{\Delta }\nu (t)=\frac{1}{h}[-\mathrm{\Delta }\mathit{\mu }·{\mathbf{E}}_{\text{loc}}(t)-\frac{1}{2}{\mathbf{E}}_{\text{loc}}(t)·\mathrm{\Delta }\mathit{\alpha }·{\mathbf{E}}_{\text{loc}}(t)],\end{array}$$ [2]

where $h$ is Planck’s constant, $\mathrm{\Delta }\mathit{\mu }={\mathit{\mu }}_{\mathit{ex}}-{\mathit{\mu }}_{S0}$ the difference between the excited and ground state dipole moment, and $\mathrm{\Delta }\mathit{\alpha }={\mathit{\alpha }}_{\mathit{ex}}-{\mathit{\alpha }}_{S0}$ the difference in electronic polarizability between the excited and the S₀ state. In a randomly oriented ensemble of Schiff bases such as in our BR samples, the projection of the dipole change $\mathrm{\Delta }\mathit{\mu }$ onto ${\mathbf{E}}_{\text{loc}}$ (first term in Eq. 2) determines the sign and amount of the individual frequency shift (Fig. 4A). The experiment averages over all orientations and provides the ensemble average of $\mathrm{\Delta }\nu$. As a result, the first term leads to a spectral broadening of the transient relative to the stationary absorption band. In contrast, the second term in Eq. 2 introduces a net red- or blue-shift depending on the sign of polarizability difference $\mathrm{\Delta }\mathit{\alpha }$.

Fig. 4.

Simulations of transient Stark spectra. (A) Schematic of the electronic Stark shift induced by a directed external electric field E_loc. The change in dipole energy of the ground state S₀ and excited state S_ex of an individual molecule in the electric field induces a frequency shift of the electronic S₀-S_ex transition (lhs) $\mathrm{\Delta }\nu \propto \mathrm{\Delta }\mathit{\mu }·{\mathbf{E}}_{\text{loc}}$ (dipole difference $\mathrm{\Delta }\mathit{\mu }={\mathit{\mu }}_{\mathit{ex}}-{\mathit{\mu }}_0$). The overall absorption spectrum of a random molecular ensemble represents an average over all orientations. (B) Absorption change of BR wt calculated from a normalized sum of spectrally shifted stationary absorption spectra with a maximum symmetric shift $\mathrm{\Delta }{\nu }_{\text{max}}=\pm 12.0$ THz and an overall red-shift $\delta \nu =-0.23$ THz, from which the unshifted steady-state spectrum was subtracted (solid line). The symbols represent the experimental spectrum recorded at zero delay. (C) Same for the BR D85T mutant. Solid line: calculation with $\mathrm{\Delta }{\nu }_{\text{max}}=\pm 9.0$ THz and $\delta \nu =0.1$ THz.

The transient absorption spectrum $A(\nu )$ represents the response of the ensemble of randomly oriented RSBH⁺ chromophores to the THz field ${\mathbf{E}}_{\text{loc}}$. This spectrum is simulated by a normalized sum of stationary absorption bands $A_0(\nu \pm \mathrm{\Delta }\nu )$, shifted relative to the maximum of $A_0(\nu )$ in steps of 0.5 THz to higher and lower frequencies up to a maximum symmetric shift of $\pm \mathrm{\Delta }{\nu }_{\text{max}}$, thus accounting for the first term in Eq. 2. Each shifted term stands for a subset of retinal Schiff bases with a different projection of $\mathrm{\Delta }\mathit{\mu }$ onto ${\mathbf{E}}_{\text{loc}}$, i.e., a different (polar) angle $\theta$ between $\mathrm{\Delta }\mathit{\mu }$ and ${\mathbf{E}}_{\text{loc}}$. In addition, we introduce a global shift $\delta \nu$ of the broadened spectrum to account for the second term in Eq. 2. From $A(\nu )$, we subtract the stationary unshifted $A_0(\nu )$ to calculate the electronic absorbance changes $\mathrm{\Delta }A(\nu )$ for a direct comparison with experiment. Details are given in Materials and Methods and SI Appendix. This model neglects changes of the line shape of $A_0(\nu )$ induced by the THz field.

Results of such simulations are presented in Fig. 4 B and C (lines) for BR wt and BR D85T, together with the experimental spectra taken at zero delay (symbols). The solid line in Fig. 4B was calculated with a transient spectrum $A(\nu )$ symmetrically broadened up to a maximum frequency shift $\mathrm{\Delta }{\nu }_{\text{max}}=\pm$12.0 THz and a small red-shift $\delta \nu =$$-$0.23 THz on top ($|\delta \nu |\ll |\mathrm{\Delta }{\nu }_{\text{max}}|$). This simulation reproduces the line shape and amplitudes of the experimental $\mathrm{\Delta }A$ spectrum in a quantitative way. Fig. 4C shows simulation results for the BR D85T mutant for $\mathrm{\Delta }{\nu }_{\text{max}}=\pm$9.0 THz with an additional frequency shift $\delta \nu =$ 0.1 THz. There is good agreement with the experimental line shape and amplitudes at frequencies up to some 560 THz, while the broadening calculated at higher frequencies is stronger than in experiment. We tentatively assign this discrepancy to retinal absorption bands to higher singlet states S_n (n $>$ 2) with a low-frequency tail overlapping with A₀(ν) but displaying a different Stark shift.

The absolute value of the maximum symmetric frequency shift $\mathrm{\Delta }{\nu }_{\text{max}}=\mathrm{\Delta }\mu ·E_{\text{loc}}^p$ is given by the product of the dipole difference $\mathrm{\Delta }\mu =|{\mathit{\mu }}_{\mathit{ex}}-{\mathit{\mu }}_{S0}|$ and peak local field $E_{\text{loc}}^p$ ($\theta =0$, cf. Eq. 2). Applying a Clausius–Mossotti approach (27), the local field is related to the external THz field $E_{\text{THz}}$ by $E_{\text{loc}}=[({ϵ}_{\text{THz}}+2)/3]·E_{\text{THz}}=1.72E_{\text{THz}}$ with the THz dielectric constant ${ϵ}_{\text{THz}}\approx 3.15$ (28). The resulting peak local THz fields are $E_{\text{loc}}^p=5.1$ MV/cm (0.51 V/nm) for BR wt and 3.6 MV/cm (0.36 V/nm) for BR D85T, corresponding to some 10 to 20% of the electric field originating from the protein environment (6, 29, 30). With such numbers, one derives a dipole change $\mathrm{\Delta }\mu =4.8\pm 1$ D for BR wt and $\mathrm{\Delta }\mu =5.0\pm 1$ D for BR D85T. The value for BR wt is consistent with results reported in refs. 6 and 31 (SI Appendix). The small frequency shifts $\delta \nu$ allow for estimating an upper limit of the change in electronic polarizability of $|\mathrm{\Delta }{\alpha }_{\text{iso}}|=|(1/3)\text{Tr}(\mathbf{\Delta }\mathit{\alpha })|\le 15$ ų.

A comment should be made on the polarization of the protein by the external THz field. The Clausius–Mossotti approach relating the local to the external electric field neglects any specific local interactions of the RSBH⁺ such as hydrogen bonds to embedded water molecules and changes in amino acid electrostatics. At the molecular level, specific hydrogen bond interactions with the active site water molecule (H₂O⁴⁰²) affect the RSBH⁺ charge density (see below). The electric dipole moments of the amino acid residues in the RSBH⁺ binding pocket and the related local field components are moderately changed by up to some 15%, as is estimated from their polarizabilities and the local THz field of $E_{\text{loc}}^p=5.1$ MV/cm (0.51 V/nm) (32). A quantitative treatment of such local interactions requires a molecular picture of the binding pocket, which is beyond our present scope. However, the absence of a pronounced spectral shift of the absorption bands of BR wt and BR D85T upon application of the THz field points to limited changes of the relevant local interactions. It should be noted that even without any local field correction, i.e., for ${ϵ}_{\text{THz}}=1$, one derives values of $\mathrm{\Delta }\mu <10$ D.

Theory Results and Discussion

Quantitative simulations of excited state dipole moments of BR are challenging due to the DES character of the S₂ state and pronounced state mixing induced in the vicinity of avoided crossings or conical intersections, requiring a multiconfiguration ansatz and dynamic electron correlations for an accurate description. To investigate the change of dipole moment $\mathrm{\Delta }\mu =|{\mathit{\mu }}_{\mathit{ex}}-{\mathit{\mu }}_{S0}|$ upon electronic excitation we performed high-level ab initio simulations on the XMS-CASPT2 level of theory employing a multiconfiguration reference wavefunction for which all bonding $\pi$ and antibonding ${\pi }^{\ast }$ orbitals of the RSBH⁺ were considered in the active space [CASSCF(12/12); see Materials and Methods]. The approach yields excellent excitation energies of the bright S₁ excited state for RSBH⁺ in the gas phase [simulation: 2.10 eV (589 nm), experiment: 2.03 eV; see SI Appendix] (9, 33).

We now address the various effects influencing the dipole moment of RSBH⁺ and respective changes upon photoexcitation. We consider the RSBH⁺ chromophore bound to K216 in the geometry of the BR active site [cf. Fig. 5A, pdb: 1c3w (34)] and compare the dipole moment changes upon electronic excitation of RSBH⁺ in the gas phase and RSBH⁺ hydrogen bound to crystal water H₂O⁴⁰² (see Materials and Methods for model details and simulation methods). The S₀ state of RSBH⁺ in the geometry of the active site has a dipole moment ${\mu }_{S0}$$=$$-$19.75 Debye on the CASSCF(12/12) level of theory (cf. Table 1), that is largely diminished upon excitation of the optically accessible S₁ state (${\mu }_{S1}$$=$ 0.69 Debye). The dark S₂ state with DES character has a dipole moment ${\mu }_{S2}=-8.46$ Debye and state mixing between S₂ and S₁ states is minor in the multiconfiguration CASSCF(12/12) wavefunction. The large dipole change $|{\mathit{\mu }}_{S1}-{\mathit{\mu }}_{S0}|$$=$ 20.44 Debye on the CASSCF(12/12) level compares well to values reported in the literature (14, 19).

Fig. 5.

(A) BR active site simulation models of RSBH⁺ (with and without crystal water H₂O⁴⁰²) bound to the carbon atoms of K216 [pdb: 1c3w (34)]: Shown is an overlay of the S₁ relaxed (solid) and ground state minimum structure (transparent), bond length changes (in Å) in isolated RSBH⁺ and ${\text{RSBH}}^{+}+{\text{H}}_2{\text{O}}^{402}$ are indicated in blue and red, respectively. The reaction coordinate (RC) toward the I state is characterized by bond inversion at the 13 trans position for RSBH⁺ and the interaction with H₂O⁴⁰² induces a contraction of the adjacent C$=$N bond in the excited state. (B) Potential energy profile of the RC leading to the S₁ minimum of isolated RSBH⁺, the S₁ potential (SES) is governed by a pure CT state character. (C) Potential energy profile of the RC leading to the S₁ minimum of RSBH⁺ interacting with H₂O⁴⁰² in the BR active site geometry. The S₁ potential acquires successively mixed character of SES and DES states, leading to an avoided crossing and state character inversion indicated with the dashed vertical line. Onward, the RC progresses toward the $S_0$-S₁ conical intersection of RSBH⁺ isomerization.

Table 1.

Dipole moments (z-component, in Debye, evaluated on the XMS-CASPT2 level of theory, CASSCF (12/12) dipole moments in parenthesis) and state-mixing of RSBH⁺, RSBH⁺+H₂O (including interaction with H₂O⁴⁰²), and RSBH^+,rlx+H₂O (including H₂O⁴⁰² interaction and reaction coordinate modification)

	RSBH +	RSBH++H2O	RSBH+,rlx+H2O
${\mu }_{S0}$	$-$16.79 ($-$19.75)	$-$12.76 ($-$16.91)	$-$7.79 ($-$14.15)
${\mu }_{S1}$	$-$0.45 (0.69)	0.87 (1.56)	0.12 ($-$3.18)
${\mu }_{S2}$	$-$7.45 ($-$8.46)	$-$10.80 ($-$8.82)	$-$12.55 ($-$3.18)
$c_{S1}^{\mathit{HF}}$	$-$0.05	$-$0.20	0.35
$c_{S1}^{\mathit{SE}}$	0.55(α) −0.55(β)	−0.46(α) + 0.46(β)	0.30(α) −0.3(β)
$c_{S1}^{\mathit{DE}}$	0.13	0.31	0.46
$c_{S1}^{ss-S0}$	$-$0.20	$-$0.34	$-$0.35
$c_{S1}^{ss-S1}$	0.98	0.93	0.93
$c_{S1}^{ss-S2}$	0.02	$-$0.11	$-$0.12

Mixing coefficients ${\mathit{c}}_{\mathit{S}\mathbf{1}}^{\mathit{X}}$ denote the contribution of reference (HF), singly excited (SE), and doubly excited (DE) configurations to the $S_1$ state in the CASSCF(12/12) wavefunction. Mixing coefficients ${\mathit{c}}_{\mathit{S}\mathbf{1}}^{\mathit{s}\mathit{s}\mathbf{-}\mathit{S}\mathit{i}}$ quantify the respective single state contribution to $S_1$ in the XMS-CASPT2 simulation (see SI Appendix for mixing coefficients of $S_0$ and $S_2$).

Distinct mechanisms can alter the dipole moments evaluated on the CASSCF(12/12) level. Dipole moments are particularly sensitive to electron correlation, reflected in differences between the CASSCF and the XMS-CASPT2 level of theory. On the XMS-CASPT2 level, dipole moment differences are reduced ($|{\mathit{\mu }}_{S1}-{\mathit{\mu }}_{S0}|$$=$ 16.34 Debye) by the correlation of S₀ and S₁ states in the multistate correlation treatment while the effect on ${\mu }_{S2}$$=$$-$7.45 Debye is minor. It is important to note that the calculated dipole changes upon S₁ excitation are much larger than and clearly inconsistent with the 5-Debye dipole changes from experiment, ruling out a 2-state description of the early excited state dynamics of BR.

In an alternative scenario, interactions in the active site of BR can induce a mixing of $S_2$ and $S_1$ with a direct impact on dipole moments. Similarly, vibronic wavepacket propagation toward the excited-state potential minimum (I state) during the probe pulse duration can induce a mixing of states. Recent femtosecond X-ray diffraction experiments (8) have shown the strong coupling of the RSBH⁺ charge density changes with an active site water molecule (H₂O⁴⁰²) upon propagation to the I state. To quantify the interactions in the active site, we have included the effect of H₂O⁴⁰² on the RSBH⁺ excited states fully on the XMS-CASPT2 level of theory.

The interaction with H₂O⁴⁰² affects the excitation energies of RSBH⁺ and is found to induce a solvatochromic blue shift of 0.18 eV of the S₀ - S₁ excitation energy. Additionally, the interaction with H₂O⁴⁰² causes a mixing of S₀, S₁, and S₂ states at the active site Franck–Condon geometry, both in the CASSCF multiconfiguration reference wavefunction and in the multistate dynamic electron correlation treatment of the XMS-CASPT2 method. Accordingly, the dipole difference between S₀ and S₁ states is further reduced due to the H₂O⁴⁰² induced mixing of state character ($|{\mathit{\mu }}_{S1}-{\mathit{\mu }}_{S0}|$$=$ 13.63 Debye).

Moreover, we find that H₂O⁴⁰² modifies the reaction coordinate toward the I state and has a strong influence on the concomitant state character (Fig. 5 and Table 1, RSBH^+,rlx+H₂O; see Materials and Methods for details of the constrained excited state relaxation in S₁). For the isolated RSBH⁺, the excited system progresses to a S₁ minimum of pure CT character (Fig. 5B). In contrast, upon interaction with H₂O⁴⁰², the S₁ minimum acquires character of a mixed state due to the vicinity of the S₁/S₂ avoided crossing (Fig. 5C). Respective dipole moment changes are $|{\mathit{\mu }}_{S1}-{\mathit{\mu }}_{S0}|$$=$ 7.91 Debye and $|{\mathit{\mu }}_{S2}-{\mathit{\mu }}_{S0}|$$=$$-$4.75 Debye. Due to the strong state mixing of S₁ and S₂ at the geometry of the I state, S₁ and S₂ both have substantial transition strength with the ground state $S_0$, the RSBH⁺ Stokes shift is simulated on the order of 0.2 eV, i.e., well within the width of the absorption band.

We recall that the THz Stark shift data give dipole changes of $\mathrm{\Delta }\mu =|{\mathit{\mu }}_{S1}-{\mathit{\mu }}_{S0}|\approx$ 5 D. The experiments probe the dipole change in the Franck–Condon coupled region of the excited-state potential, averaging in time the initial wavepacket dynamics over the probe pulse duration of some 120 fs. A comparison to the simulations suggests that the experimental dipole changes are the result of a complex interplay of electron correlation effects, mixing of state character of SES and DES S₁ and S₂ states due to active site interactions, and the progression toward the I state minimum, associated with an increased state mixing in vicinity of the S₁/S₂ avoided crossing in the 3 state model. We note that the calculations presented in refs. 7 and 15 predict a strong S₁/S₂ mixing within the first 100 fs after photoexcitation, in qualitative agreement with our results. The dipole changes are induced via the directed hydrogen bond interaction with H₂O⁴⁰² which polarizes the $\pi$ orbitals of RSBH⁺ and thus directly affects the charge density, while the counterion residues D85 and D212 are expected to be less relevant (SI Appendix). Our simulations reveal the key interactions with H₂O⁴⁰² for tuning the excited state properties in the BR active site, giving rise to dipole moment changes between S₀ and S₁ states of 7.91 Debye and $-$4.75 Debye between S₀ and S₂ states, and a strong mixing of states in the multiconfigurational wavefunction induced by the avoided crossing.

Materials and Methods

Samples.

Film samples of BR wt were prepared from aqueous solutions, while BR D85T films were made from a phosphate buffer solution with a pH value of 7.2, as described in SI Appendix. The film thickness was 6.5 $\mathrm{\mu }$m for BR wt and 15 $\mathrm{\mu }$m for BR D85T. The peak optical densities of the samples are 0.8 OD at 568 nm for BR wt and 0.4 OD at 595 nm for BR D85T. The film samples were integrated in a humidity cell to maintain a relative humidity (r. h.) of 97%. To keep BR wt in the light adapted form, the sample was illuminated during the time-resolved measurements by a light-emitting diode working at 595 nm. The experiments on BR D85T were performed without external illumination.

Ultrafast THz Stark Spectroscopy.

The experiments employ a pump–probe scheme in which a THz pulse provides an external electric field and the resulting absorption changes of the BR samples are probed by a femtosecond optical pulse tunable throughout the absorption bands of BR wt and BR D85T in the visible (24). The THz electric field $E_{\text{THz}}$ acting on the sample is enhanced with the help of a bow-tie antenna made from gold (thickness 150 nm) with a central gap of 12 $\mathrm{\mu }$m width (26). The electric field enhancement in the antenna gap is characterized by electrooptic sampling in a nonlinear ZnTe crystal with an identical antenna structure on its front facet. The probe pulses travel through the antenna gap and are detected in transmission. The THz pump and visible probe pulses a linearly polarized along the long axis of the antenna. Details of antenna and sample geometries and of pulse generation are given in SI Appendix.

Analysis of Transient THz Stark Spectra.

The broadened absorption spectrum in presence of the THz field ${\mathbf{E}}_{\text{loc}}$ represents the average over an ensemble of molecular chromophores with a random orientation relative to the direction of ${\mathbf{E}}_{\text{loc}}$, i.e., a different projection of the dipole change $\mathrm{\Delta }\mathit{\mu }$ on ${\mathbf{E}}_{\text{loc}}$. In our analysis, the broadened spectrum is calculated as the normalized sum $A(\nu )$ of spectrally shifted linear absorption spectra $A_0(\nu )$ ($\nu$: optical frequency), each term representing a subgroup of RSBH⁺ chromophores with a fixed orientation relative to the THz field. The field-induced absorbance change $\mathrm{\Delta }A(\nu )$ is then given by

$$\begin{array}{c}\hfill \mathrm{\Delta }A(\nu )=A(\nu )-A_0(\nu )=[\frac{1}{Z}{\displaystyle \sum _{i=-N}^N}{A}_0(\nu +i·\mathrm{\Delta }\nu +\delta \nu )]-A_0(\nu )\end{array}$$ [3]

The sum is composed of $(2N+1)$ terms with a constant mutual frequency spacing $\mathrm{\Delta }\nu$ up to the maximum frequency shift $\mathrm{\Delta }{\nu }_{\text{max}}=\pm N\mathrm{\Delta }\nu$ relative to the maximum of $A_0(\nu )$.

The underlying dipole change $\mathrm{\Delta }\mu$ between ground and excited state of the RSBH⁺ is given by $\mathrm{\Delta }\mu =h\mathrm{\Delta }{\nu }_{\text{max}}/E_{\text{loc}}^p$ [cf. Eq. 2]. The normalization factor Z is chosen in a way that the overall electronic transition moment is preserved. On top, the broadened spectrum is shifted in frequency by $\delta \nu$ to account for changes of electronic polarizability (cf. Eq. 2). Calculations were performed with up to $(2N+1)=53$ components of the sum, i.e., up to $\mathrm{\Delta }{\nu }_{\text{max}}=\pm 13$ THz. A detailed discussion of this approach and its application to the experimental spectra is given in SI Appendix.

Ab Initio Simulations.

Simulation models RSBH⁺ + H₂O⁴⁰² and RSBH⁺ (Fig. 5A) consider the retinal protonated Schiff base chromophore bound to the carbon atoms of K216, with or without crystal water H₂O⁴⁰², respectively. Heavy atom positions were taken from pdb: 1c3w (34) that served as starting structure in ab initio simulations and reflect the chromophore geometry in the BR active site. All ab initio simulations were performed with the Molpro program package (35, 36). For both model systems RSBH⁺ and RSBH⁺+H₂O⁴⁰², hydrogen atoms were initially added manually and the position of hydrogen atoms was relaxed on the DFT(B3LYP-D3/cc-pvdz) level of theory subject to the restraining of all heavy atom positions during optimization. Constrained geometry optimization was performed with the SLAPAF program in Molpro by Lindh and Galvan using cartesian positional constraints. Excitation energies and dipole moments were evaluated on the XMS-CASPT2 level of theory (basis: cc-pvdz, the influence of diffuse basis functions was explored with the aug-cc-pvdz basis set; see SI Appendix) using a CASSCF(12/12) wave function with all bonding $\pi$ and antibonding $\pi \ast$ orbitals of the RSBH⁺ considered in the active space (see SI Appendix for the influence of active space on excitation energies and dipole moments). The S₁ excited state gradient for the relaxed potential energy profile of RSBH⁺ with and without H₂O⁴⁰² (Fig. 5 B and C) was evaluated on the CASSCF(12/12) level of theory, subject to the restraining of carbon atom positions of K216 and oxygen position of H₂O⁴⁰² (cartesian positional constraints in SLAPAF; see above), accounting for the geometric relaxation of the RSBH⁺ chromophore in the $S_1$ excited state and allowing to assess the influence of crystal water H₂O⁴⁰² on the reaction coordinate. See SI Appendix for benchmark simulations for the protonated Schiff base of all-trans retinal in the gas phase.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All study data are included in the article and/or SI Appendix.