Interference in acetylene intersystem crossing acts as the molecular analog of Young's double-slit experiment

Abstract

We report on an experimental approach that reveals crucial details of the composition of singlet-triplet mixed eigenstates in acetylene. Intersystem crossing in this prototypical polyatomic molecule embodies the mixing of the lowest excited singlet state (S₁) with 3 triplet states (T₁, T₂, and T₃). Using high-energy (157-nm) photons from an F₂ laser to record excited-state photoelectron spectra, we have decomposed the mixed eigenstates into their S₁, T₃, T₂, and T₁ constituent parts. One example of the interpretive power that ensues from the selective sensitivity of the experiment to the individual electronic state characters is the discovery and examination of destructive interference between two doorway-mediated intersystem crossing pathways. This observation of an interference effect in nonradiative decay opens up possibilities for rational coherent control over molecular excited state dynamics.

Singlet-triplet intersystem crossing (ISC) is a fundamental nonradiative decay pathway for molecular electronically excited states. At its basis is the spin-orbit interaction that mixes low-lying vibrational levels of a singlet state with isoenergetic highly excited vibrational levels of lower-lying triplet electronic states (1). Being able to exert control over intersystem crossing or over any nonradiative decay pathway of molecular excited states potentially has important applications. For example, it could lead to control over photochemical reactions (2), more efficient dyes in fluorescence microscopy (3), driving of molecular motors (4), and other photonic applications. However, mixing between the “optically bright” state and the bath of “optically dark” states is generally viewed to be statistical, and as such offers no possibility for the design and application of rational coherent control schemes. Sometimes the interaction between bright and dark states is locally promoted by a “doorway” state* (5–8) that facilitates stronger indirect mixing than would occur in the case of direct interaction between bright and dark states. Nevertheless, even for ISC mediated by a doorway state, control schemes cannot go beyond a simple energy and temporal control based on prior knowledge of specific spectroscopic details, such as the choice to excite close to or far from the doorway state.

It is only after an appropriate experimental approach has been devised to understand the mechanism of ISC that one may hope to exert full external control over ISC. Typically, studies of intersystem crossing focus on its effects in the time domain, i.e., the evolution of the relevant electronic state populations is followed after excitation of the singlet state. However, with this approach details of interaction mechanisms are very difficult to determine when vibrational levels of more than one triplet electronic state lie below the singlet state. Clearly, determining the composition of the mixed wavefunctions in terms of all of their contributing parts is the most direct and complete way to characterize intersystem crossing. However, achieving such a complete description of the wavefunction is an experimental challenge that has rarely has been met for a polyatomic molecule.

In the present study we use intersystem crossing in acetylene to demonstrate that excited-state photoelectron spectroscopy is uniquely suited to perform such a decomposition; it interrogates an eigenstate via the different additive parts of its vibronic wavefunction (9, 10). We show that only by exploiting the selective sensitivity to particular electronic characters in the wavefunction that is made possible by this approach is it possible to observe state-specific changes of their relative contributions to the wavefunction. These excitation energy dependent variations of wavefunction character provide compelling evidence for the occurrence of interference between two doorway mediated coupling pathways in what we call here a “double doorway” mechanism for intersystem crossing.

The resulting picture is very much like a double slit experiment in a molecule, the two doorway states forming the slits that cast an interference pattern. In our experiments this pattern is probed directly by determining the composition of the wavefunction as a function of the energy relative to the energies of the doorway states. Similar quantum mechanical interferences provide the basis for the extensive repertoire of coherent control techniques (11–15). Experimentally, these techniques, however, typically make use of “blind” iterative algorithms to optimize the amplitude and phase of frequency components of laser pulses without detailed knowledge of the underlying interference mechanism that provides a basis for the control. The direct observation of quantum mechanical interference in nonradiative decay in the present study offers the first genuine prospect for rational control over nonradiative decay dynamics in a polyatomic molecule.

Singlet-triplet interaction in acetylene has been extensively studied by a variety of experimental methods (5, 16–21), which showed that the mixing of the lowest excited singlet state S₁ with the manifold of dark T₁ and T₂ triplet states increases monotonically with increasing excitation of the trans-bend mode, ν′₃. The comprehensive picture that has emerged from these experiments is one in which ISC of each S₁ vibrational level into the manifold of T₁ and T₂ states is mediated by a single doorway vibrational level of T₃ (ref. 5 and references therein). The mixed electronic character of the eigenstates that result from the underlying spin-orbit interaction has been illustrated by the diagnostically complementary combination of Laser Induced Fluorescence (LIF), which is sensitive to the singlet character, with Surface Electron Ejection by Laser Excited Metastables (SELEEM), which is sensitive to the triplet character. Combining these techniques, the eigenstates can be sorted according to their lifetime, which then provides a measure of their electronic composition. States with a relatively long lifetime have a large triplet contribution, short-lived states a large singlet contribution. The radiative lifetime based complementary nature of the two techniques, however, does not explicitly capture the electronically “schizophrenic” nature of each eigenstate wavefunction: It detects an averaged property, but not the unique contribution from each underlying electronic state. More importantly, the techniques used so far do not distinguish among contributions from the 3 triplet electronic states that can be involved.

The experimental approach presented here allows both singlet and triplet characters to be extracted in one single measurement via the distinct spectral signatures of the 3 triplet states. Resonance Enhanced MultiPhoton Ionization PhotoElectron Spectroscopy (REMPI-PES) distinguishes S₁, T₁, T₂, and T₃ characters. Ionization does not favor either singlet or triplet character, but instead allows for a direct PES projection of the full wavefunction of each eigenstate. The idea of the experiment is illustrated schematically in Fig. 1. Each eigenstate wavefunction is a linear combination of S₁, T₁, T₂, and T₃ states. The power of the experiment lies in the fact that all of these electronic states have similar ionization probabilities, but yield distinguishable photoelectron spectra because of different patterns of vibrational overlap integrals between the excited-state vibrational wavefunctions and those of the electronic ground state of the ion. In the past, REMPI-PES has already been applied to studies of the S₁ state, but in those experiments the photon energy of the ionization laser was far from sufficient to enable a full projection of the singlet and triplet vibrational characters onto the vibrational wavefunctions of the ionic manifold (22). The crucial improvement made in the present study is that the eigenstates are now ionized via a 1-photon process, using a high-energy F₂ laser (157 nm).

Fig. 1.

Schematic representation of the experiment. The doorway-mediated perturbation of the ùA_u(S₁)V₀³K₀¹ band of acetylene mixes the S₁ and T₁, T₂ and T₃ states. A dye laser is scanned over the mixed eigenstates, which are ionized with a 157 nm beam from an F₂ laser. The dashed line indicates the total photon energy of the two lasers. The arrows labeled a–d and a⁺–d⁺ indicate the vibrational energy in the basis states and in the ion, respectively.

Results and Discussion

Decomposition of the eigenstate wavefunctions.

To efficiently record the data needed for the eigenstate decomposition, we have used the 2-dimensional multiphoton ionization technique presented in ref. 23. Further information on the experimental approach is given in ref. 24 and Materials and Methods. Fig. 2A displays the 1 + 1′ 2D-REMPI-PE spectrum resonant with the 3ν′₃ level in S₁. In these experiments the first laser (ω₁) is scanned over the band, while the second laser (ω₂), at a fixed wavelength of 157 nm, ionizes the ensemble of eigenstates excited by the first laser. The photoelectron spectrum is presented in terms of ion internal energy (IIE) according to IEE = ℏω₁ + ℏω₂ − IP − PKE, where IP is the adiabatic ionization potential of acetylene (91,953.5 cm⁻¹) (25) and PKE the photoelectron kinetic energy. The IIE distribution is largely determined by the squared overlap of the vibrational wavefunctions of the ion with the vibrational wavefunction of the excited state, i.e., the Franck–Condon factors. One can obtain a qualitative idea of the IIE region accessed by each of the relevant excited vibronic states by considering the potential energy surfaces of the S₁, T₃, T₂, and T₁ electronic states recently determined in an ab initio study, using various extended multireference electron correlation techniques (26). Table 1 lists the excitation energies reported for these states at several geometries relevant to the present study. The transition from S₁ to the electronic ground state of the ion is a bent-to-linear transition. Table 1 shows that trans-bent S₁ acetylene is stabilized with respect to the linear conformation by ≈1.2 eV. Accordingly, one expects ionization of this state to lead to a long progression in the trans-bend vibration, ν₄⁺, qualitatively similar to what is observed for the emissive transitions from the trans-bent S₁ state to the linear S₀ ground state of the neutral molecule (29). The T₃ state, in contrast, is considerably less stabilized (relative to the linear conformation) along the bending coordinates, but adopts a nonplanar equilibrium geometry that is ≈0.3 eV lower in energy than the planar one.^† Based on the energies given in Table 1, we expect that ionization of T₁ and T₂ vibrational levels at the energy of the S₁ 3ν′₃ level results in ions with, respectively, ≈1.1–1.4 eV and ≈0.7 eV more internal energy than ions resulting from ionization of S₁.

Fig. 2.

Ion internal energy distributions and state-selected excitation spectra of acetylene. (A) 2D-PE spectrum of acetylene obtained via the ùA_u(S₁)V₀³K₀¹ band. (B–D) extracted excitation spectra (B) S₁ and T₃ (IIE 0.31–0.62 eV). (C) T₁ and T₂ (IIE 2.03–2.20 eV). (D) S₁4ν′_b(K₀¹) (IIE 0.83–1.44 eV).

Table 1.

Calculated excitation energies (eV) of the S₁ and T_1,2,3 states at various geometries taken from ref. 16

nddum	State
Geometry	S1	T1	T2	T3‡
planar trans	5.23 (5.15) 5.23*	4.18	4.46	5.60
planar cis	5.58 (5.48) 5.78†	3.88 (3.81) 3.58†	4.77	5.69
linear	6.48	4.85	5.73	5.73

The reported values concern the energy differences T_e relative to the ground state calculated at the multi-reference averaged quadratic cluster (MR-AQCC) level. For comparison with available experimental values (given in italics), zero-point-energy corrected T₀ values are given in parentheses.

*Ref. 17.

^†Ref. 18.

^‡Optimization under C₂ restriction leads to a local minimum corresponding to a non-planar ³B state with an HCCH torsional angle of 106.1° that has an excitation energy of 5.36 eV.

We thus conclude that the patterns of Franck–Condon factors for ionization from the singlet and triplet parts of the probed eigenstate are considerably different. The S₁ and T₃ characters give rise to signals at relatively low IIE, while the T₁ and T₂ characters result in signals at relatively high IIE. The amplitudes of the electronic states that contribute to each eigenstate may therefore be disentangled from each other by exploiting the characteristic IIE patterns. Figs. 2 and 3 confirm these expectations: We find that the photoelectron spectra obtained via different features in the spectrum show striking differences because of the varying electronic compositions of the eigenstates underlying the features (compare Fig. 3 A with C). We even observe large changes in the photoelectron spectrum while scanning over a single feature (Fig. 3 B and C).

Fig. 3.

High-resolution photoelectron spectra for selected rotational lines of Fig. 2. These spectra have been obtained by using the stepped retardation voltage method described in ref. 23. (A) Excitation at 45,317.65 cm⁻¹, the R branch band head of S₁3ν′₃(K₀¹). (B) Excitation at 45,299.05 cm⁻¹, S₁3ν′₃(K₀¹) Q(3) red edge. (C) Excitation at 45,299.40 cm⁻¹, S₁3ν′₃(K₀¹) Q(3) blue edge. (D) Excitation at 45,301.05 cm⁻¹, S₁4ν′_b(K₀¹) Q(1), Q(2), Q(3). Excitation energies are indicated in Fig. 4 by arrows marked A–D.

If we assume, based on the Franck–Condon arguments discussed above, that the signals at low IIE originate exclusively from S₁ and T₃ contributions and that the signals at high IIE are associated with the T₁ and T₂ contributions, we can extract the (S₁, T₃) vs. (T₁, T₂) relative contributions to the features observed in the REMPI excitation spectrum by integration of different energy regions of the photoelectron spectrum. The result of such an analysis is depicted in Fig. 2 where the contributions from S₁ and T₃ is given in Fig. 2B, and the contributions from T₁ and T₂ in Fig. 2C. Fig. 2D illustrates the sensitivity of the technique to the vibrational composition of the excited state. This spectrum has been obtained by integration of a part of the photoelectron spectrum where the intensity is mostly induced by the so-called “extra” lines assigned to a component of the S₁4ν′_b (where b stands for bend) polyad formed by mixing of the ν′₄ and ν′₆ (torsion and cis-bend) vibrational levels of S₁ (31). Because of their different vibrational wavefunction and their relative lack of local triplet perturbations, these “extra” bands give rise to a different photoelectron spectrum that is easily recognized (Fig. 3D). Selective integration of different parts of the photoelectron spectrum thus has enabled us to disentangle the vibrational characters of the eigenstates, and to obtain the rovibronic dependences of the contributions of the participating electronic states.

The spectra in Fig. 2 B and C allow us to calculate the fractional (T₁, T₂) character at every excitation wavelength. Fig. 4 shows the REMPI excitation spectrum obtained by integration of the full photoelectron spectrum, and the relative contribution of (T₁, T₂) is displayed by the color-coding of the various features in the spectrum. The fully-integrated spectrum closely matches the LIF spectrum of acetylene at room temperature (32). Most features in the spectrum have a width that is broader than the resolution of the experiment, which, based on the observed widths of the relatively unperturbed “extra” lines (marked in Fig. 4 by arrows d and e), is estimated as 0.2 cm⁻¹ FWHM. This broadening reflects the strength of the spin-orbit interaction that results in a splitting of the eigenstates that underlie each spectral feature. The line contours are the convolution of the discrete eigenstates with the Doppler-limited experimental resolution. In a few lines, the splitting of the underlying eigenstates is sufficiently large to permit resolution of part of the underlying eigenstate structure. This is, for example, the case for the Q(3) line at 45,299.4 cm⁻¹, which is observed to contain considerable (T₁, T₂) character on the low-frequency side, but mostly (S₁, T₃) character on the high-frequency side (compare Fig. 3 B with C).

Fig. 4.

(color online) REMPI spectrum of acetylene obtained via the ùA_u(S₁)V₀³K₀¹ band. The spectrum is the sum of the spectra from Figs. 2 B–D. The rotational assignments, taken from ref. 22, are displayed above the spectrum. The color of the spectrum indicates the relative contribution of T₁ and T₂ to the total photoelectron yield. It is clear that the T₁, T₂ character goes through a minimum at low values of J. The color was optimized for the best contrast: fully black corresponds to >80% T₁, T₂ character, fully yellow to <40%. Arrows a–e mark several features referred to in the text and figures.

Double Doorway Interference.

Fig. 4 shows a striking variation of the (T₁, T₂) fraction vs. the level energy: In each of the P, Q, and R branches, the fractional (T₁, T₂) character goes through a minimum near J = 3. Interestingly, it has been shown that the zero-order energies of S₁ and the F₂ spin-component of T₃ cross near this value of J (33). Suppose for the moment that this vibrational level of the T₃ state would act as the only doorway state responsible for the coupling between S₁ and the triplet manifold. In that case, the only possibility is that the T_1,2 character reaches a maximum near the J value of the S₁-T₃ level crossing and is symmetric above and below the crossing J value (34). We thus must conclude that destructive interference occurs between two doorway mediated intersystem crossing pathways from S₁ to (T₁, T₂). This double doorway mechanism for intersystem crossing is illustrated schematically in Fig. 5. One path is mediated by a weak, but local, T₃ doorway state responsible for the fractionation of the locally T₃-perturbed rotational levels in the S₁ level. Importantly, the set of signs of the T_1,2 amplitudes admixed via this pathway reverses when crossing through (as a function of J) degeneracy with the local doorway state. The other path is mediated by a strong, but energetically remote, T₃ doorway state(s) responsible for the monotonic increase of singlet-triplet coupling with increasing excitation of the trans-bend mode, ν′₃. The set of signs of the T_1,2 amplitudes admixed via this remote doorway pathway is not dependent on J. Our experiments show that near J = 3 the amplitudes for the T_1,2 states admixed via one T₃ doorway state destructively interfere with the oppositely-signed amplitudes of the same T_1,2 states admixed via the other T₃ doorway state. Globally destructive interference between the two pathways is surprising and is also the key to being able to exploit this interference in external control schemes for intersystem crossing.

Fig. 5.

Double doorway model for intersystem crossing from S₁ to T₁ and T₂ in acetylene. One path is mediated by a strong, but energetically remote, T₃ doorway state. The other path is mediated by a weak, but local, T₃ doorway state(s). Interference between the two paths causes a systematic suppression of the T₁ and T₂ character of eigenstates close to the energy of the local doorway state.

The same experiment performed in the absence of a local doorway state should thus give rise to photoelectron spectra that are independent of J, that is, with constant contributions of singlet and triplets. This is indeed confirmed in REMPI-PES experiments resonant with the 2ν′₃ level in S₁. The photoelectron spectra of this band show contributions from T₂ and T₁ states as well (consistent with previous experiments (21)), but all lines in the 2D-REMPI-PE spectrum give rise to the same photoelectron spectrum. In agreement with the idea that the strong interaction with the energetically remote T₃ doorway state increases monotonically with increasing excitation of the trans-bend mode ν′₃, we now observe that the S₁ contribution dominates over the triplet contribution. Another important difference between the 2ν′₃ and 3ν′₃ levels is that the resonances in the 2ν′₃ excitation spectrum are significantly narrower (≈0.2 cm⁻¹). These results thus confirm that spin-orbit interactions of the S₁ state with the T₁ and T₂ triplet manifolds is also important at the 2ν′₃ level, but because of the larger energy gap and smaller Franck–Condon overlap with the remote doorway state, the interaction is smaller at these excitation energies.

The rather coarse-grained low-resolution analysis of the excited state photoelectron spectra presented above has made it possible to decompose the vibronic wavefunction of an eigenstate into its different additive parts. This has enabled us to discover an interference effect in acetylene intersystem crossing. A more detailed analysis of the vibrational structure of the spectra in Fig. 3 could possibly help to determine the structure and identity of the doorway states involved.^‡

Conclusions

We have used excited-state photoelectron spectroscopy to project the wavefunctions of singlet-triplet mixed eigenstates of acetylene onto the C₂H₂⁺ ionic manifold, and have determined the fractional (S₁, T₃) and (T₁, T₂) characters of the states. Our experiments have provided direct visualization of how the fractional (T₁, T₂) character of the eigenstates is strongly affected by a local perturbation of the S₁ 3ν′₃ level by a vibrational level of the T₃ state. Significantly, we have found that this (T₁, T₂) character is locally suppressed at the J = 3 value of this S₁, T₃ level crossing, an observation that demonstrates interference between two competing doorway-mediated coupling pathways.

This “double doorway” mechanism could be an exciting starting point for a new class of external control schemes over nonradiative decay pathways, and lead to innovative techniques to rationally manipulate the flow of energy in molecules and influence the fate of photochemical and photophysical processes. However, from the point of view of fundamental studies of the interaction between light and matter, observation of such a molecular version of Young's classic double slit experiment is fascinating in its own right.

Materials and Methods

The experimental setup used has been described in detail elsewhere (35, 36). Briefly, acetylene, introduced into the ionization region of a magnetic bottle spectrometer (37) as an effusive beam, is excited using a XeCl excimer-based laser system, while a second excimer laser (Neweks; PSX-100) operating on F₂ is used to ionize the excited states. The light from both lasers is focused from opposite sides into the ionization chamber with lenses with focal lengths of 175 and 200 mm for the excitation and ionization laser, respectively. The beam path of the 157-nm laser is shielded from the atmosphere by PVC tubing that is continuously flushed with nitrogen.

Because of the large number of states that need to be probed and because of the small differences in the photoelectron spectra for the different states, we have applied in the present studies an approach to measure photoelectron spectra in which we construct a 2-dimensional image by measuring photoelectron time-of-flight spectra as a function of the excitation wavelength (23). The time-of-flight spectra can be converted into real photoelectron spectra that are linear in energy by applying the following formula:

where E is the photoelectron energy in electron volts, m_e the mass of the electron, l the distance from the ionization region to the detector, t the flight time, t₀ the time at which ionization occurs and e the elementary charge. In practice t₀ and l are fitted to a known spectrum (typically that of xenon). Because of the limited time resolution of the measurement, the disadvantage of retrieving photoelectron spectra in this way is that the resolution is not uniform and is worse for faster photoelectrons. By sacrificing resolution we gain, however, access to the full photoelectron spectrum at every excitation wavelength. This makes it possible to extract the contribution from the singlet and triplet characters of the eigenstate wavefunctions to the total, integrated, excitation spectrum.

For selected wavelengths we have also measured high-resolution photoelectron spectra in the traditional way, that is, by using a retarding voltage that decelerates the electrons. The dye laser frequency is held fixed at a certain transition and the signal is obtained as a 2D image, S(x,y), this time by measuring the time-of-flight spectrum as a function of the retarding voltage. A photoelectron spectrum is obtained by conversion of the time-of-flight axis into a linear energy scale, using Eq. 1, and integrating the signal over a chosen energy range ΔE. The photoelectron spectrum is then defined by the integral

The best resolution is obtained by integrating only the low-energy part of S(x,y) (the slow electrons), but sometimes it is necessary to include faster electrons to gain signal, albeit at the expense of resolution. Application of the method to a 2 + 1′ spectrum of xenon enables us to determine the effective retardation voltage and thereby to calibrate the relative energies. Depending on the experimental conditions, a typical resolution of 10–15 meV can be obtained, but, especially when using deep UV as in the present case, the resolution is often closer to 40 meV. This decrease in resolution is most likely caused by spurious photoelectrons that are formed by ionization processes involving scattered light and the inner surfaces of the spectrometer. Because the calibration is sensitive to the exact position between the copper electrodes where ionization takes place and the timing of the ionizing laser, it is essential to calibrate the 2-color measurements, using 2-color signals that in the present experiments derive from 2-color ionization of xenon atoms. This procedure leads to maximum errors of ≈3% in the relative energies. Calibration of the absolute energy is hindered by the fact that the photoelectrons associated with ionization of xenon have a rather large energy (≈5.7 eV). Fortunately, ionization of acetylene leads to photoelectron spectra in which the Franck–Condon envelope extends to energies above the total available photon energy, i.e., the photoelectrons with the lowest kinetic energy [that we can detect by applying an extra voltage (see Materials and Methods)] must have zero energy. This allows us to recalibrate the absolute energy scale with an accuracy of ≈15 meV.