Abstract
Valence molecular orbitals play a crucial role in chemical reactions. Here, we reveal that an intense laser field deforms an inner valence orbital (10a′) in the ethanol molecule. We measure the recoil-frame photoelectron angular distribution (RFPAD), which corresponds to the orientation dependence of the ionization probability of the orbital, using photoelectron-photoion coincidence momentum imaging with a circularly polarized laser pulse. Ab initio simulations show that the orbital deformation depends strongly on the laser field direction and that the measured RFPAD cannot be reproduced without taking the orbital deformation into account. Our findings suggest that the laser-induced orbital deformation occurs before electron emission on a suboptical cycle time scale.
INTRODUCTION
Molecular orbital (MO) shape plays a crucial role in chemical reaction dynamics and is described by theories such as the frontier orbital (1) and Woodward-Hoffmann rules (2). Similarly, in intense laser–induced molecular dynamics, MO shape is known to be important, particularly in tunnel ionization (3, 4). Tunnel ionization is a crucial initial step of successive dynamical processes, leading to high-harmonic generation, dissociative ionization, and multiple ionization. In the past two decades, orientation dependence of tunnel ionization probabilities has been studied mainly for small molecules composed of two or three atoms (5–7). These studies have shown that the shape of an MO from which an electron tunnels strongly affects the orientation dependence of the ionization probability. Hence, the ionization probability as a function of molecular orientation is measured to image the MO shape. This molecular scanning tunnel microscopy (STM) (8) has revealed that laser-induced tunneling occurs not only from the highest-occupied MO (HOMO) but also from inner valence orbitals (9). Inner valence orbitals play a crucial role in intense-field chemistry.
In addition to the contribution of multiple MOs (9–11), laser-induced deformation of HOMOs has been studied in tunnel ionization. Simulations including HOMO deformation agree well with the measured angular dependence of ionization probability for CO2 (12) and with high-harmonic spectra from N2 (13). Experimentally, high-harmonic spectroscopy with the aid of ab initio simulation has revealed that degenerate HOMOs in spatially oriented CH3F are deformed by intense laser fields, which remove the degeneracy (14). The contribution of unoccupied MOs such as Rydberg orbitals was also suggested for dissociative ionization of hydrocarbon molecules (15). There is also evidence that intense laser fields modify the electronic structure of ionized molecules (16, 17). In this study, we demonstrate laser-induced MO deformation of an inner valence orbital in a neutral molecule. Photoionization from an inner valence orbital is essential to creating electronically excited ions, which is necessary for many molecules to dissociate (18–21). For efficient control of laser-driven dissociative ionization, it is important to deepen our understanding of electronic dynamics of inner valence orbitals.
Ethanol is an ideal molecule for exhibiting MO deformation in a strong laser field. Ethanol has rather low symmetry (the point group Cs) with its symmetry plane including an O atom and two C atoms as shown in Fig. 1A. Hence, all MOs of ethanol are classified in two irreducible representations: a′ and a″. The energy levels of the four inner valence MOs, 10a′ (HOMO-1), 2a″ (HOMO-2), 9a′ (HOMO-3), and 8a′ (HOMO-4), lie within 3 eV of each other in the field-free situation (22), and three of the four MOs have a′ symmetry, as illustrated in the inset of Fig. 1A. In our experiment, we used a circularly polarized laser field with an intensity of I0 = 8 × 1013 W/cm2. The electric field of E = 1.7 × 1010 V/m creates a slope with an energy difference of about 6 eV for a distance of ~3.5 Å, which corresponds to the size of ethanol (Fig. 1A). This difference is larger than the energy range of the three a′ MOs in the field-free situation. Therefore, the laser field should induce strong mixing of these MOs. In addition, a previous photoelectron-photoion coincidence (PEPICO) measurement with a He lamp (He I at 21.2 eV) showed that electron emission from the inner valence MOs results in the formation of different fragment ions (23). This means that identifying fragment ion species allows us to identify the MO that has an electron hole just before the ethanol cation dissociates (18, 19, 21).
(A) Density functional theory (DFT)–calculated 10a′ (HOMO-1) structures of ethanol in an electric field with strength of 1.7 × 1010 V/m (corresponding to a circularly polarized laser field at an intensity of 8 × 1013 W/cm2) as a function of field direction. The electric field direction is set parallel to the Cs symmetry plane and defined by the angle Φ from the C─C axis of ethanol. Isosurface plots of the MOs 𝚼10a′(Φ) in the electric field with cutoff values of 0.025 (blue) and –0.025 (red) are drawn around that of the field-free MO (Ψ10a′). Inset: Energy level diagram of the field-free MOs in ethanol. The red and black levels have a′ and a″ symmetries, respectively. (B) Overlap populations ∣〈Ψi ∣ ϒ10a′(Φ)〉∣2 of 𝚼10a′(Φ) with the field-free MOs Ψ8a′, Ψ9a′, and Ψ10a′ as functions of angle Φ.
RESULTS AND DISCUSSION
First, we show theoretically that 10a′ (HOMO-1) in ethanol is deformed by a circularly polarized intense laser field (I0 = 8 × 1013 W/cm2 and E = 1.7 × 1010 V/m) during one cycle of the electric (E) field (Fig. 1A). The field-free MO 10a′ (Ψ10a′), shown at the center of Fig. 1A, is composed mainly of the lone pair on the O atom and the C─C σ bond. We calculate the 10a′ orbitals in the E-field with density functional theory (DFT). The deformed orbital shapes 𝚼10a′(Φ) are drawn around field-free Ψ10a′ in Fig. 1A, where the E-field is parallel to the Cs symmetry plane with the angle Φ between the E-field direction and the C—C axis. As described later, our DFT calculation shows that the ionization occurs dominantly when the E-field is parallel to the Cs symmetry plane. Thus, we focus on the E-field being parallel to the symmetry plane. In the direction Φ = −22.5° (the CH3 side), 𝚼10a′(Ф = −22.5°) is similar to field-free 9a′ (Ψ9a′) shown in Fig. 1B. In the other directions, the deformed MO 𝚼10a′(Φ) exhibits only slight differences from field-free Ψ10a′. Nevertheless, 𝚼10a′(Φ) expands in the direction opposite to the E-field. These deformations of 10a′ occur on a suboptical cycle time scale of the circularly polarized laser pulse, as illustrated in Fig. 1A. The field-deformed MO 𝚼10a′(Φ) can be described as a linear combination of the neighboring a′ MOs, Ψ10a′ (HOMO-1), Ψ9a′ (HOMO-3), and Ψ8a′ (HOMO-4), as shown in Fig. 1B. When the E-field is not parallel to the CS symmetry plane, 10a′ can be mixed with 3a″ (HOMO) and 2a″ (HOMO-2), as well as 9a′ and 8a′, and the mixing between a′ and a″ orbitals is included in our calculation.
The deformation from Ψ10a′ to 𝚼10a′(Φ) in the E-field affects angular dependence of the ionization probability. In our experiment, we applied molecular STM to ethanol in a circularly polarized laser field (λ ~ 795 nm, Δτ ~ 60 fs, and I0 ~ 8 × 1013 W/cm2) (9, 24). We used a partially deuterated ethanol sample, CH3CD2OH, to avoid ambiguity in the mass assignment caused by producing different fragment ions with the same mass. An unaligned ethanol molecule was singly ionized in the circularly polarized intense laser field, and three-dimensional momentum vectors of the electron (
(A) Sketch of relations between the electron tunneling direction (
To understand the experimental RFPAD, we simulated the angular dependence of the tunnel ionization probability using DFT (4). Figure 3A is the simulated ionization probability W10a′(Φ, Θ) of 𝚼10a′(Φ, Θ) as a function of the E-field direction (Φ, Θ) defined in the inset of Fig. 3A. The two-dimensional map of W10a′(Φ, Θ) shows the maximum at (Φ, Θ) = (157.5°, 90°). In other words, an electron in 10a′ tunnels preferentially from the CH3 moiety as illustrated in Fig. 3D; thus, it is somewhat similar to the RFPAD measured for the CD2OH+ channel (Fig. 2B).
(A) DFT-calculated angular-dependent ionization probability of the 10a′ MO [𝚼10a′(Φ, Θ)] in the electric field with E = 1.7 × 1010 V/m. Inset: Defined electric field direction represented with Euler angles (Φ, Θ). (B) Same as (A) but simulated for the field-free 10a′ MO (Ψ10a′). arb. units., arbitrary units. (C and D) Field-deformed MOs 𝚼10a′(Φ, Θ) represented by linear combinations of the field-free MOs Ψ10a′ and Ψ8a′ at (Φ, Θ) = (−112.5°, 90°) and (157.5°, 90°), respectively.
To evaluate the effect of MO deformation on tunnel ionization, we simulated the ionization probability
The experimental RFPAD for the CD2OH+ channel (Fig. 2B) gives evidence of MO deformation. To compare the experimental and simulated results, we derived the theoretical RFPADs from the two-dimensional maps of W10a′(Φ, Θ) and
(A) Theoretical RFPADs Ω3a″(ϕRFPAD) and Ω10a′(ϕRFPAD) from field-deformed 𝚼3a″(Φ, Θ) and 𝚼10a′(Φ, Θ), respectively, in the electric field with E = 1.7 × 1010 V/m. The experimental (exp.) RFPAD is also shown with its vertical error bars. DFT calc., DFT calculations. (B) Same as (A) but simulated for the field-free MOs. (C) Schematic for the tunnel ionization and subsequent processes of CH3CD2OH in the circularly polarized laser field. (D) Comparison of the experimental RFPAD with the linear combination of the theoretical (theo.) RFPADs from the field-deformed MOs (Eq. 1 with
To describe electronic excitation in intense laser fields, perturbative photoabsorption is not appropriate. As illustrated in Fig. 1A, the MO in neutral ethanol varies adiabatically as the E-field rotates. In nonresonant ionization, the adiabaticity in neutral ethanol is maintained until an electron is emitted. Structural deformation, which causes nonadiabatic transition at a specific structure, is also small in neutral ethanol. After electron emission, electronic excitation in intense laser fields can be described as nonadiabatic transition between the laser-driven adiabatic electronic states (26), in which the molecular structure can be deformed substantially because the Franck-Condon geometry is different from the equilibrium geometry in the ionic state (27). Thus, nonadiabatic excitation following electron tunneling plays a key role. Because of the two different pathways producing CD2OH+, the experimental RFPAD should be expressed as a linear combination of two pathways from 10a′ and 3a″
We calculated the fraction
An observed orientation dependence of the ionization probability has been well described by the tunnel ionization of an inner valence MO (10a′) deformed by an intense laser electric field. The MO deformation is not unique to ethanol but should occur in general, especially for polyatomic molecules with a high density of inner valence levels. The orientation dependence of the MO deformation presented in this study will open the door to direct control of electronic dynamics leading to selective bond breaking. Combining molecular orientation and a subcycle probe would serve this end.
MATERIALS AND METHODS
Experimental and analytical details
A linearly polarized Ti:Sapphire laser pulse (~60 fs, ~800 nm, and ~140 μJ) was converted into a circularly polarized pulse by passing through an achromatic quarter wave plate and was focused on an effusive ethanol beam with an off-axis parabolic mirror (f = 200 mm). The effusive beam of deuterated ethanol CH3CD2OH vapor was continuously supplied into a vacuum chamber through a microsyringe (70-μm inner diameter) and a skimmer (0.2-mm orifice diameter; Beam Dynamics model 2). The base pressure of the chamber without the sample was below 1 × 10−8 Pa.
The three-dimensional momentum vectors of an electron and an ion from an identical molecule were measured in coincidence (18, 21). Ions and electrons created in the focal region were accelerated by an electrostatic lens (28) toward two microchannel plate detectors with delay line position encoding (RoentDek HEX80) on opposite ends of the vacuum chamber. Two-dimensional positions and time of flights were recorded using time-to-digital converters with a resolution of 25 ps (RoentDek TDC8HP). The laser repetition rate was 1 kHz, and the detection count rate was set to be less than 0.3 counts per laser shot.
The measured ion and electron momentum vectors (
The laboratory frame momentum distributions of the CD2OH+ and CH3CD2+ fragment ions are almost isotropic and have a peak at the center (pion = 0) (fig. S2, A and B). The orientation of the parent molecule was determined from the direction of the fragment recoil based on the axial recoil approximation. In the present analysis, we selectively analyzed the coincidence events for the fragment ions satisfying the following two conditions. The first condition was that the out-of-plane angle of the ion emission with respect to the polarization plane was smaller than 10° (
Simulation method of tunnel ionization probability in laser electric field
The simulation procedure of the tunnel ionization probability [W10a′(Φ, Θ)] is similar to the previous one (4). Briefly, we used the Kohn-Sham formalism in the DFT to calculate the tunnel ionization probability. Here, we considered a case in which the external field changes very slowly in time. More precisely, we assumed that the tunneling occurs much faster than one cycle of the external field. We also assumed that tunnel or above barrier processes are dominant and that the multiphoton process is negligible. Under these circumstances, the time-dependent Kohn-Sham equation (30) yields the static Kohn-Sham equation with an external dipole field, Vext(
Here, the electrons in the molecule are continuously emitted so that the static Kohn-Sham orbitals φi(
The imaginary part of the eigenvalue, Γi, is related to the ionization probability. To see it, we multiplied
Then, we found
Integrating both sides over the volume V, which includes the molecule inside and using the Gauss theorem, we had
The electrons emitted to the continuum, in principle, should contribute to the self-consistent potential. However, if the ionization probability is very small, then the contribution of emitted electrons to the potential is negligible. Under the condition that the ionization probability is sufficiently small, we calculated ionization probability through the following two steps: First, we solved the static Kohn-Sham equation under the static external field, eEz. In this step, the tunnel ionization was forced to be prohibited by placing infinite wall potential outside the barrier. The problem becomes a usual static Kohn-Sham problem except the appearance of the external dipole field and infinite wall potential. In the second step, we calculated the Gamow state solution (31) for each Kohn-Sham orbital using the Hamiltonian obtained at the first step with the outgoing boundary condition.
The ionization probability is sensitive to the asymptotic behavior of the potential and the binding energies of the occupied orbitals. To appropriately incorporate the asymptotic behavior, we used the exchange-correlation potential, which takes account of the self-interaction correction. We adopted an approximate construction of the optimized effective potential including the self-interaction correction, which was proposed by Krieger, Li, and Iafrate (KLI) (32, 33). In this treatment, it has been shown that the ionization potentials of atoms and molecules approximately coincide with the energies of the highest occupied orbitals. The potential in this model also has a correct asymptotic behavior, −e2/r, for neutral molecules, where r is the radial distance from the center of the molecule.
To calculate the Gamow states, we needed to solve the static Kohn-Sham equation (Eq. 3) with the outgoing boundary condition. For systems without spherical symmetry, the treatment of the outgoing boundary condition is not simple. Instead of imposing the outgoing boundary condition explicitly, we used the absorbing boundary condition (ABC). The absorbing potential was placed in the spatial region outside a certain radius r = R with a thickness of ΔR. Outside the region of the absorbing potential, r > R + ΔR, the wave functions were set to vanish. If the absorbing potential works ideally, then there exist only the outgoing waves just inside the absorbing potential.
In the present calculation, we used the following spherical absorbing potential with a linear radial dependence
Using the absorbing potential, the Gamow state was obtained by solving the following Kohn-Sham equation
We also derived an expression for the ionization probability with the absorbing potential, W(
We assumed that the denominator of Eq. 13 is equal to a normalization constant, unity, so long as the ionization probability is sufficiently small. Then, the ionization probability of the orbital i is expressed as the following integral form using the absorbing potential W(
We checked whether the ionization probabilities calculated with Eq. 14 coincide with those obtained from the imaginary part of the eigenvalue within the numerical error.
To express the orbital wave functions, we used the real-space grid method. This is a convenient representation in the Kohn-Sham theory, since the potential is almost local in the coordinate representation. To impose the ABC, one must treat large spatial region far outside the molecule. The number of grid points becomes substantially large. To save the computational effort, we reduced the number of grid points using the adaptive grid.
The adaptive grid was generated as follows. We introduced the following coordinate transformation from (x, y, z) to (u, v, w) for each Cartesian coordinate
Simulation method of tunnel ionization probability for field-free MO
The numerical method described in the previous section cannot be applied to the ionization probability from the undeformed MOs in the field-free condition. Instead, we evaluated the ionization probability from the number of electrons outside the potential barrier formed by the external field. We defined the potential barrier based on the Kohn-Sham potential, VKS = VH + Vxc, where VH is the Hartree potential and Vxc is the exchange-correlation potential, together with the potential by the electric field, Vext = −e
The present DFT calculation of the field-free MO was based on the same procedure used for the calculation of the molecule in the E-field. We used the static Kohn-Sham formalism in the DFT without an external dipole field, which is expressed in Eq. 3 with Vext(
Derivation of theoretical RFPAD and integrated probability from angular-dependent ionization probability
We considered three vectors of the laser electric field
The ionization probability σ10a′(ΦLR, β, γ) was obtained from the ionization probability W10a′(Φ, Θ) in the molecular frame (X, Y, Z) (fig. S4D) by two successive rotational transformations. We prepared three-dimensional grid points (ΦLR, β, γ) with equal intervals for the respective coordinates. The laboratory recoil frame was transformed to the molecular frame (fig. S4D) by the coordinate rotation represented with the two direct cosine matrices A(0°, β, γ) (fig. S4, B and C) and A(−90°, −90°, −ηCD2OH+) (fig. S4, C′ and D), in which ηCD2OH+ (=158.6°) is the angle between the recoil direction of CD2OH+ and the C─C (X) axis. The ionization probability σ10a′(ΦLR, β, γ) at each grid point was equal to the probability W10a′(Φ, Θ) at the transformed point in the molecular frame. We interpolated discrete data points of W10a′(Φ, Θ) calculated by the DFT to obtain the probability at the transformed point. Thus, the theoretical RFPAD Ω10a′(φRFPAD) was obtained by calculating the integral of Eq. 18.
To compare the theoretical RFPAD with the experimental one, the solid angle of the photoelectron emission was taken into account. We approximated the solid angle of photoelectron emission on the polarization plane to be the same as the out-of-plane distribution (fig. S3). The calculated RFPAD was convoluted with the Gaussian curve with its width of 31° (FWHM).
When we calculated the excitation fraction
Note that the analytical procedure mentioned in this section is valid not only for the 10a′ but also for all other orbitals.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaaw1885/DC1
Section S1. Yields of fragment ions produced from CH3CD2OH in the circularly polarized laser field
Section S2. Comparison of measured RFPAD for the CH3CD2+ production with theoretical RFPADs
Fig. S1. Electron momentum distributions in the laboratory frame.
Fig. S2. Ion momentum distributions in the laboratory frame.
Fig. S3. Out-of-plane angular distributions of electrons with respect to the polarization plane.
Fig. S4. Scheme of the rotational transformations for derivation of theoretical RFPAD.
Fig. S5. Time-of-flight mass spectrum of CH3CD2OH.
Fig. S6. Results for the CH3CD2+ production channel.
Table S1. The spatial parameters used in the calculations of ethanol.
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REFERENCES AND NOTES
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