Bond-length dependence of attosecond ionization delays in O2 arising from electron correlation to a shape resonance.

We experimentally and theoretically demonstrate that electron correlation can cause the bond-length sensitivity of a shape resonance to induce an unexpected vibrational state-dependent ionization delay in a nonresonant channel. This discovery was enabled by a high-resolution attosecond-interferometry experiment based on a 400-nm driving and dressing wavelength. The short-wavelength driver results in a 6.2-electron volt separation between harmonics, markedly reducing the spectral overlap in the measured interferogram. We demonstrate the promise of this method on O2, a system characterized by broad vibrational progressions and a dense photoelectron spectrum. We measure a 40-attosecond variation of the photoionization delays over the X2Πg vibrational progression. Multichannel calculations show that this variation originates from a strong bond-length dependence of the energetic position of a shape resonance in the [Formula: see text] channel, which translates to the observed effects through electron correlation. The unprecedented energy resolution and delay accuracies demonstrate the promise of visible-light-driven molecular attosecond interferometry.

Filming enhanced ionization in an ultrafast triatomic slingshot.

Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e., filmed) by ionizing at an adjustable delay with respect to the start of interatomic motion. Results are distorted, however, by ultrafast motion during the ionizing pulse. We studied this effect in water and filmed the rapid "slingshot" motion that enhances ionization and distorts CEI results. Our investigation uncovered both the geometry and mechanism of the enhancement which may inform CEI experiments in many other polyatomic molecules.

Strongly coupled intermediate electronic states in one-color two-photon single valence ionization of O2.

We present an experimental and theoretical energy- and angle-resolved investigation on the non-dissociative photoionization dynamics of near-resonant, one-color, two-photon, single valence ionization of neutral O2 molecules. Using 9.3 eV femtosecond pulses produced via high harmonic generation and a 3-D momentum imaging spectrometer, we detect the photoelectrons and O2 + cations produced from one-color, two-photon ionization in coincidence. The measured and calculated photoelectron angular distributions show agreement, which indicates that a superposition of two intermediate electronic states is dominantly involved and that wavepacket motion on those near-resonantly populated intermediate states does not play a significant role in the measured two-photon ionization dynamics. Here, we find greater utility in the diabatic representation compared to the adiabatic representation, where invoking a single valence-character diabat is sufficient to describe the underlying two-photon ionization mechanism.

Step-by-step state-selective tracking of fragmentation dynamics of water dications by momentum imaging.

The double photoionization of a molecule by one photon ejects two electrons and typically creates an unstable dication. Observing the subsequent fragmentation products in coincidence can reveal a surprisingly detailed picture of the dynamics. Determining the time evolution and quantum mechanical states involved leads to deeper understanding of molecular dynamics. Here in a combined experimental and theoretical study, we unambiguously separate the sequential breakup via D+ + OD+ intermediates, from other processes leading to the same D+ + D+ + O final products of double ionization of water by a single photon. Moreover, we experimentally identify, separate, and follow step by step, two pathways involving the b 1Σ+ and a 1Δ electronic states of the intermediate OD+ ion. Our classical trajectory calculations on the relevant potential energy surfaces reproduce well the measured data and, combined with the experiment, enable the determination of the internal energy and angular momentum distribution of the OD+ intermediate.

Coupled nuclear-electronic decay dynamics of O2 inner valence excited states revealed by attosecond XUV wave-mixing spectroscopy.

Multiple Rydberg series converging to the O2+c4Σ-u state, accessed by 20-25 eV extreme ultraviolet (XUV) light, serve as important model systems for the competition between nuclear dissociation and electronic autoionization. The dynamics of the lowest member of these series, the 3sσg state around 21 eV, has been challenging to study owing to its ultra-short lifetime (<10 fs). Here, we apply transient wave-mixing spectroscopy with an attosecond XUV pulse to investigate the decay dynamics of this electronic state. Lifetimes of 5.8 ± 0.5 fs and 4.5 ± 0.7 fs at 95% confidence intervals are obtained for v = 0 and v = 1 vibrational levels of the 3s Rydberg state, respectively. A theoretical treatment of predissociation and electronic autoionization finds that these lifetimes are dominated by electronic autoionization. The strong dependence of the electronic autoionization rate on the internuclear distance because of two ionic decay channels that cross the 3s Rydberg state results in the different lifetimes of the two vibrational levels. The calculated lifetimes are highly sensitive to the location of the 3s potential with respect to the decay channels; by slight adjustment of the location, values of 6.2 and 5.0 fs are obtained computationally for the v = 0 and v = 1 levels, respectively, in good agreement with experiment. Overall, an intriguing picture of the coupled nuclear-electronic dynamics is revealed by attosecond XUV wave-mixing spectroscopy, indicating that the decay dynamics are not a simple competition between isolated autoionization and predissociation processes.

Distinguishing resonance symmetries with energy-resolved photoion angular distributions from ion-pair formation in O2 following two-photon absorption of a 9.3 eV femtosecond pulse.

We present a combined experimental and theoretical study on the photodissociation dynamics of ion-pair formation in O2 following resonant two-photon absorption of a 9.3 eV femtosecond pulse, where the resulting O+ ions are detected using 3D momentum imaging. Ion-pair formation states of Σg-3 and 3Πg symmetry are accessed through predissociation of optically dark continuum Rydberg states converging to the B Σg-2 ionic state, which are resonantly populated via a mixture of both parallel-parallel and parallel-perpendicular two-photon transitions. This mixture is evident in the angular distribution of the dissociation relative to the light polarization and varies with the kinetic energy release (KER) of the fragmenting ion pair. The KER-dependent photoion angular distribution reveals the underlying two-photon absorption dynamics involved in the ion-pair production mechanism and indicates the existence of two nearly degenerate continuum resonances possessing different symmetries, which can decay by coupling to ion-pair states of the same total symmetry through internal conversion.

Probing molecular bond-length using molecular-frame photoelectron angular distributions.

The molecular-frame photoelectron angular distributions (MFPADs) in O 1s photoemission from CO2 molecule were measured. Patterns due to photoelectron diffractions were observed in the MFPADs. The polarization-averaged MFPADs were compared with theoretical calculation and were found to be useful in determining the molecular bond-length, which is a component to determine molecular structures.

Canonical Approach To Generate Multidimensional Potential Energy Surfaces.

A new force-based canonical approach for the accurate generation of multidimensional potential energy surfaces is demonstrated. Canonical transformations previously developed for diatomic molecules are used to construct accurate approximations to the 3-dimensional potential energy surface of the water molecule from judiciously chosen (adopting the right coordinate system) 1-dimensional planar slices that are shown to have the same canonical shape as the classical Lennard-Jones potential curve. Spline interpolation is then used to piece together the 1-dimensional canonical potential curves, to obtain the full 3-dimensional potential energy surface of a water molecule with a relative error less than 0.01. This work provides an approach to greatly reduce the computational cost of constructing potential energy surfaces in molecules from ab initio calculations. The canonical transformation techniques developed in this work illuminate a pathway to deepening our understanding of chemical bonding.

Is there any fundamental difference between ionic, covalent, and others types of bond? A canonical perspective on the question.

The concept of chemical bonding is normally presented and simplified through two models: the covalent bond and the ionic bond. Expansion of the ideal covalent and ionic models leads chemists to the concepts of electronegativity and polarizability, and thus to the classification of polar and non-polar bonds. In addition, the intermolecular interactions are normally viewed as physical phenomena without direct correlation to the chemical bond in any simplistic model. Contrary to these traditional concepts of chemical bonding, recently developed canonical approaches demonstrate a unified perspective on the nature of binding in pairwise interatomic interactions. This new canonical model, which is a force-based approach with a basis in fundamental molecular quantum mechanics, confirms much earlier assertions that in fact there are no fundamental distinctions among covalent bonds, ionic bonds, and intermolecular interactions including the hydrogen bond, the halogen bond, and van der Waals interactions.

Morse, Lennard-Jones, and Kratzer Potentials: A Canonical Perspective with Applications.

Canonical approaches are applied to classic Morse, Lennard-Jones, and Kratzer potentials. Using the canonical transformation generated for the Morse potential as a reference, inverse transformations allow the accurate generation of the Born-Oppenheimer potential for the H2+ ion, neutral covalently bound H2, van der Waals bound Ar2, and the hydrogen bonded one-dimensional dissociative coordinate in a water dimer. Similar transformations are also generated using the Lennard-Jones and Kratzer potentials as references. Following application of inverse transformations, vibrational eigenvalues generated from the Born-Oppenheimer potentials give significantly improved quantitative comparison with values determined from the original accurately known potentials. In addition, an algorithmic strategy based upon a canonical transformation to the dimensionless form applied to the force distribution associated with a potential is presented. The resulting canonical force distribution is employed to construct an algorithm for deriving accurate estimates for the dissociation energy, the maximum attractive force, and the internuclear separations corresponding to the maximum attractive force and the potential well.

Canonical Force Distributions in Pairwise Interatomic Interactions from the Perspective of the Hellmann-Feynman Theorem.

Force-based canonical approaches have recently given a unified but different viewpoint on the nature of bonding in pairwise interatomic interactions. Differing molecular categories (covalent, ionic, van der Waals, hydrogen, and halogen bonding) of representative interatomic interactions with binding energies ranging from 1.01 to 1072.03 kJ/mol have been modeled canonically giving a rigorous semiempirical verification to high accuracy. However, the fundamental physical basis expected to provide the inherent characteristics of these canonical transformations has not yet been elucidated. Subsequently, it was shown through direct numerical differentiation of these potentials that their associated force curves have canonical shapes. However, this approach to analyzing force results in inherent loss of accuracy coming from numerical differentiation of the potentials. We now show that this serious obstruction can be avoided by directly demonstrating the canonical nature of force distributions from the perspective of the Hellmann-Feynman theorem. This requires only differentiation of explicitly known Coulombic potentials, and we discuss how this approach to canonical forces can be used to further explain the nature of chemical bonding in pairwise interatomic interactions. All parameter values used in the canonical transformation are determined through explicit physical based algorithms, and it does not require direct consideration of electron correlation effects.

Canonical Approaches to Applications of the Virial Theorem.

Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem.

Canonical Potentials and Spectra within the Born-Oppenheimer Approximation.

A generalized formulation of canonical transformations and spectra are used to investigate the concept of a canonical potential strictly within the Born-Oppenheimer approximation. Data for the most accurate available ground electronic state pairwise intermolecular potentials in H2, HD, D2, HeH(+), and LiH are used to rigorously evaluate such transformations. The corresponding potentials are generated explicitly using parameters calculated with algebraic functions from that of the single canonical potential of the simplest molecule, H2(+). The efficacy of this approach is further tested by direct comparison of the predicted eigenvalues of all vibrational states in the selected molecular systems considered with the corresponding most accurately known Born-Oppenheimer eigenvalues currently available. Deviations are demonstrated to be less than 2 cm(-1) for all vibrational states in H2, HD, D2, HeH(+), and LiH, with an average standard deviation of 0.27 cm(-1) for the 87 states considered. The implications of these results for molecular quantum chemistry are discussed.

A general transformation to canonical form for potentials in pairwise interatomic interactions.

A generalized formulation of explicit force-based transformations is introduced to investigate the concept of a canonical potential in both fundamental chemical and intermolecular bonding. Different classes of representative ground electronic state pairwise interatomic interactions are referenced to a chosen canonical potential illustrating application of such transformations. Specifically, accurately determined potentials of the diatomic molecules H2, H2(+), HF, LiH, argon dimer, and one-dimensional dissociative coordinates in Ar-HBr, OC-HF, and OC-Cl2 are investigated throughout their bound potentials. Advantages of the current formulation for accurately evaluating equilibrium dissociation energies and a fundamentally different unified perspective on nature of intermolecular interactions will be emphasized. In particular, this canonical approach has significance to previous assertions that there is no very fundamental distinction between van der Waals bonding and covalent bonding or for that matter hydrogen and halogen bonds.

Vibrationally specific photoionization cross sections of acrolein leading to the X̃²A' ionic state.

The vibrational branching ratios in the photoionization of acrolein for ionization leading to the X̃²A' ion state were studied. Computed logarithmic derivatives of the cross section and the corresponding experimental data derived from measured vibrational branching ratios for several normal modes (ν9, ν10, ν11, and ν12) were found to be in relatively good agreement, particularly for the lower half of the 11-100 eV photon energy range considered. Two shape resonances have been found near photon energies of 15.5 and 23 eV in the photoionization cross section and have been demonstrated to originate from the partial cross section of the A' scattering symmetry. The wave functions computed at the resonance complex energies are delocalized over the whole molecule. By looking at the dependence of the cross section on the different normal mode displacements together with the wave function at the resonant energy, a qualitative explanation is given for the change of the cross sections with respect to changing geometry.

The Badger-Bauer rule revisited: correlation of proper blue frequency shifts in the OC hydrogen acceptor with morphed hydrogen bond dissociation energies in OC-HX (X = F, Cl, Br, I, CN, CCH).

Potential morphing has been applied to the investigation of proper blue frequency shifts, Δν0 in CO, the hydrogen acceptor complexing in the hydrogen bonded series OC-HX (X= F, Cl, Br, I, CN, CCH). Linear correlations of morphed hydrogen bonded ground dissociation energies D0 with experimentally determined Δν0 free from matrix and solvent effects demonstrate consistency with original tenets of the Badger-Bauer rule (J. Chem. Phys. 1937, 5, 839-51). A model is developed that provides a basis for explaining the observed linear correlations in the range of systems studied. Furthermore, the generated calibration curve enables prediction of dissociation energies for other related but different complexes. The latter include D0 for H2O-CO, H2S-CO, and CH3OH-CO which are predicted by interpolation and found to be 355(13), 171(11), and 377(14) cm(-1) respectively from available experimentally determined proton acceptor shifts. Results from this study will also be discussed in relation to investigations in which CO has been used as a probe of heme protein active sites.

Electron scattering from gas phase cis-diamminedichloroplatinum(II): quantum analysis of resonance dynamics.

We present scattering calculations of electron collisions with the platinum-containing compound cis-diamminedichloroplatinum (CDDP), commonly known as cisplatin, between 0.5 eV and 6 eV, and the corresponding isolated Pt atom from 0.1 eV to 10 eV. We find evidence of resonances in e(-)-CDDP scattering, using an ab initio description of the target. We computed scattering matrix elements from equations incorporating exchange and polarization effects through the use of the static-exchange plus density functional correlation potential. Additionally, we made use of a purely local adiabatic model potential that allows Siegert eigenstates to be calculated, thereby allowing inspection of the possible resonant scattering wave functions. The total cross section for electron scattering from (5d(10)) (1)S Pt displays a large magnitude, monotonic decay from the initial collision energies, with no apparent resonance scattering features in any scattering symmetry. By contrast, the e(-)-CDDP scattering cross section shows a small feature near 3.8 eV, which results from a narrow, well localized resonance of b2 symmetry. These findings are then related to the possible electron-mediated mechanism of the action of CDDP on DNA replication as suggested by recent experiments.

Valence and inner-valence shell dissociative photoionization of CO in the 26-33 eV range. II. Molecular-frame and recoil-frame photoelectron angular distributions.

Experimental and theoretical results for molecular-frame photoemission are presented for inner-valence shell photoionization of the CO molecule induced by linearly and circularly polarized light. The experimental recoil frame photoelectron angular distributions (RFPADs) obtained from dissociative photoionization measurements where the velocities of the ionic fragment and photoelectron were detected in coincidence, are compared to RFPADs computed using the multichannel Schwinger configuration interaction method. The formalism for including a finite lifetime of the predissociative ion state is presented for the case of general elliptically polarized light, to obtain the RFPAD rather than the molecular frame photoelectron angular distribution (MFPAD), which would be obtained with the assumption of instantaneous dissociation. We have considered photoionization of CO for the photon energies of 26.0 eV, 29.5 eV, and 32.5 eV. A comparison of experimental and theoretical RFPADs allows us to identify the ionic states detected in the experimental studies. In addition to previously identified states, we found evidence for the 2 (2)Δ state with an ionization potential of 25.3 eV and (2)Σ(+) states with ionization potentials near 32.5 eV. A comparison of the experimental and theoretical RFPADs permits us to estimate predissociative lifetimes of 0.25-1 ps for some of the ion states. Consideration of the MFPADs of a series of (2)Π ion states indicates the importance of inter-channel coupling at low photoelectron kinetic energy and the limitations of a single-channel analysis based on the corresponding Dyson orbitals.

CMM-RS potential for characterization of the properties of the halogen-bonded OC-Cl2 complex, and a comparison with hydrogen-bonded OC-HCl.

Transitions associated with the vibrations ν1, ν1 + ν(b)¹, ν1 + ν5¹, and ν1 + ν5¹ - ν5¹ of the complex OC···Cl2 have been rovibrationally analyzed for several isotopologues involving isotopic substitutions in Cl2. Spectra were recorded using a recently constructed near-infrared (4.34 to 4.56 µm), quantum-cascade laser spectrometer with cw supersonic slit jet expansion. Spectral analysis allowed precise determination of the ν5¹ intermolecular vibration of OC-³5Cl2 to be 25.977637(80) cm⁻¹. These results were incorporated with other previously determined data into a spectroscopic database for generation of a five-dimensional morphed potential energy surface. This compound-model morphed potential with radial shifting (CMM-RS) was then used to make more accurate predictions of properties of the OC-³5Cl2 complex including D(e) = 544(5) cm⁻¹, D0 = 397(5) cm⁻¹, ν3 = 56.43(4) cm⁻¹, and ν(b)¹ = 85.43(4) cm⁻¹. The CMM-RS potential determined for OC-Cl2 was also used to compare quantitatively many of the inherent properties of this non-covalent halogen bonded complex with those of the closely related hydrogen-bonded complex OC-HCl, which has a similar dissociation energy D0. We found that in the ground state, the CO bending amplitude is larger in OC-Cl2 than in OC-HCl.

Photolysis of methane revisited at 121.6 nm and at 118.2 nm: quantum yields of the primary products, measured by mass spectrometry.

Methane photolysis has been performed at the two Vacuum UltraViolet (VUV) wavelengths, 121.6 nm and 118.2 nm, via a spectrally pure laser pump-probe technique. The first photon is used to dissociate methane (either at 121.6 nm or at 118.2 nm) and the second one is used to ionise the CH(2) and CH(3) fragments. The radical products, CH(3)(X), CH(2)(X), CH(2)(a) and C((1)D), have been selectively probed by mass spectrometry. In order to quantify the fragment quantum yields from the mass spectra, the photoionisation cross sections have been carefully evaluated for the CH(2) and CH(3) radicals, in two steps: first, theoretical ab initio approaches have been used in order to determine the pure electronic photoionisation cross sections of CH(2)(X) and CH(2)(a), and have been rescaled with respect to the measured absolute photoionisation cross section of the CH(3)(X) radical. In a second step, in order to take into account the substantial vibrational energy deposited in the CH(3)(X) and CH(2)(a) radicals, the variation of their cross sections near threshold has been simulated by introducing the pertinent Franck-Condon overlaps between neutral and cation species. By adding the interpolated values of CH quantum yields measured by Rebbert and Ausloos [J. Photochem., 1972, 1, 171-176], a complete set of fragment quantum yields has been derived for the methane photodissociation at 121.6 nm, with carefully evaluated 1σ uncertainties: Φ[CH(3)(X)] = 0.42 ± 0.05, Φ[CH(2)(a)] = 0.48 ± 0.05, Φ[CH(2)(X)] = 0.03 ± 0.08, Φ[CH(X)] = 0.07 ± 0.01. These new data have been measured independently of the H atom fragment quantum yield, subject to many controversies in the literature. From our results, we evaluate Φ(H) = 0.55 ± 0.17 at 121.6 nm. The quantum yields for the photolysis at 118.2 nm differ notably from those measured at 121.6 nm, with a substantial production of the CH(2)(X) fragment: Φ[CH(3)(X)] = 0.26 ± 0.04, Φ[CH(2)(a)] = 0.17 ± 0.05, Φ[CH(2)(X)] = 0.48 ± 0.06, Φ[CH(X)] = 0.09 ± 0.01, Φ(H) = 1.31 ± 0.13. These new data should bring reliable and essential inputs for the photochemical models of the Titan atmosphere.