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.

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.

Exploring spin symmetry-breaking effects for static field ionization of atoms: Is there an analog to the Coulson-Fischer point in bond dissociation?

Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree-Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single Ms (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree-Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis.

Ultrafast photodissociation dynamics and nonadiabatic coupling between excited electronic states of methanol probed by time-resolved photoelectron spectroscopy.

The electronic and nuclear dynamics in methanol, following 156 nm photoexcitation, are investigated by combining a detailed analysis of time-resolved photoelectron spectroscopy experiments with electronic structure calculations. The photoexcitation pump pulse is followed by a delayed 260 nm photoionization probe pulse to produce photoelectrons that are analyzed by velocity map imaging. The yields of mass-resolved ions, measured with similar experimental conditions, are found to exhibit the same time-dependence as specific photoelectron spectral features. Energy-resolved signal onset and decay times are extracted from the measured photoelectron spectra to achieve high temporal resolution, beyond the 20 fs pump and probe pulse durations. When combined with ab initio calculations of selected cuts through the excited state potential energy surfaces, this information allows the dynamics of the transient excited molecule, which exhibits multiple nuclear and electronic degrees of freedom, to be tracked on its intrinsic few-femtosecond time scale. Within 15 fs of photoexcitation, we observe nuclear motion on the initially bound photoexcited 21A″ (S2) electronic state, through a conical intersection with the 11A' (S3) state, which reveals paths to photodissociation following C-O stretch and C-O-H angle opening.

Second order Møller-Plesset and coupled cluster singles and doubles methods with complex basis functions for resonances in electron-molecule scattering.

The method of complex basis functions is applied to molecular resonances at correlated levels of theory. Møller-Plesset perturbation theory at second order and equation-of-motion electron attachment coupled-cluster singles and doubles (EOM-EA-CCSD) methods based on a non-Hermitian self-consistent-field reference are used to compute accurate Siegert energies for shape resonances in small molecules including N2-, CO-, CO2-, and CH2O-. Analytic continuation of complex 𝜃-trajectories is used to compute Siegert energies, and the 𝜃-trajectories of energy differences are found to yield more consistent results than those of total energies. The ability of such methods to accurately compute complex potential energy surfaces is investigated, and the possibility of using EOM-EA-CCSD for Feshbach resonances is explored in the context of e-helium scattering.

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules.

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. We critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the Πg2 shape resonance of N2- which has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.

Complex basis functions revisited: implementation with applications to carbon tetrafluoride and aromatic N-containing heterocycles within the static-exchange approximation.

The method of complex basis functions for computing positions and widths of molecular resonances is revisited. An open-ended and efficient implementation is described. The basis set requirements of the complex basis are investigated within the computationally inexpensive static-exchange approximation, and the results of this investigation lead to a hierarchy of basis sets for complex basis function calculations on small molecules. These basis sets are then applied in static-exchange calculations on some larger molecules with multiple low energy shape resonances: carbon tetrafluoride, benzene, pyridine, pyrimidine, pyrazine, and s-triazine. The results indicate that more sophisticated methods using complex basis functions are worth pursuing in the search for accurate and computationally feasible methods for computing resonance energies in molecular systems.

Restricted and unrestricted non-Hermitian Hartree-Fock: Theory, practical considerations, and applications to metastable molecular anions.

This work describes the implementation and applications of non-Hermitian self-consistent field (NH-SCF) theory with complex basis functions for the ab initio computation of positions and widths of shape resonances in molecules. We utilize both the restricted open-shell and the previously unexplored spin-unrestricted variants to compute Siegert energies of several anionic shape resonances in small diatomic and polyatomic molecules including carbon tetrafluoride which has been the subject of several recent experimental studies. The computation of general molecular properties from a non-Hermitian wavefunction is discussed, and a density-based analysis is applied to the (2)B1 shape resonance in formaldehyde. Spin-unrestricted NH-SCF is used to compute a complex potential energy surface for the carbon monoxide anion which correctly describes dissociation.

An Orbital Basis Set for Double Photoionization of Atoms and Molecules.

The ab initio theoretical treatment of one-photon double photoionization processes has been limited to atoms and diatomic molecules by the challenges posed by large grid-based representations of the double ionized continuum wave function. To provide a path for extensions to polyatomics, an energy-adapted orbital basis approach is demonstrated that reduces the dimensions of such representations and simultaneously allows larger time steps in time-dependent computational descriptions of double ionization. Additionally, an algorithm that exploits the diagonal nature of the two-electron integrals in the grid basis and dramatically accelerates the transformation between grid and orbital representations is presented. Excellent agreement between the present results and benchmark theoretical calculations is found for H- and Be atoms, as well as the hydrogen molecule, including for the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the molecular frame.

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.

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.

A kinetic energy fitting metric for resolution of the identity second-order Møller-Plesset perturbation theory.

A kinetic-energy-based fitting metric for application in the context of resolution of the identity second-order Møller-Plesset perturbation theory is presented, which is derived from the Poisson equation. Preliminary tests of the applicability include the evaluation of the error in the correlation energy, compared to standard Møller-Plesset perturbation theory, with respect to the auxiliary basis set employed. We comment on the potential merits of this fitting metric, compared to standard resolution of the identity second-order Møller-Plesset perturbation theory, and discuss its scaling behavior in the limit of large molecules.

A semiclassical correction for quantum mechanical energy levels.

We propose a semiclassical method for correcting molecular energy levels obtained from a quantum mechanical variational calculation. A variational calculation gives the energy level (i.e., eigenvalue) as the expectation value of the molecular Hamiltonian , where /phi> is the trial wave function. The true (i.e., exact) eigenvalue E can thus be expressed as this variational result plus a correction, i.e., E=+DeltaE, the correction being due to the lack of exactness of the trial wave function. A formally exact expression for DeltaE is usually given (via Löwdin partitioning methodology) in terms of the Greens function of the Hamiltonian projected onto the orthogonal complement of /phi>. Formal treatment of this expression (using Brillouin-Wigner perturbation theory to infinite order) leads to an expression for DeltaE that involves matrix elements of the Greens function for the unprojected, i.e., full molecular Hamiltonian, which can then be approximated semiclassically. (Specifically, the Greens function is expressed as the Fourier transform of the quantum mechanical time evolution operator, e(-iHt/variant Planck's over 2pi), which in turn is approximated by using an initial value representation of semiclassical theory.) Calculations for several test problems (a one dimensional quartic potential, and vibrational energy levels of H(2)O and H(2)CO) clearly support our proposition that the error in the total eigenvalue E arises solely due to the semiclassical error in approximating DeltaE, which is usually a small fraction of the total energy E itself.

Complete photo-induced breakup of the H2 molecule as a probe of molecular electron correlation.

Despite decades of progress in quantum mechanics, electron correlation effects are still only partially understood. Experiments in which both electrons are ejected from an oriented hydrogen molecule by absorption of a single photon have recently demonstrated a puzzling phenomenon: The ejection pattern of the electrons depends sensitively on the bond distance between the two nuclei as they vibrate in their ground state. Here, we report a complete numerical solution of the Schrödinger equation for the double photoionization of H2. The results suggest that the distribution of photoelectrons emitted from aligned molecules reflects electron correlation effects that are purely molecular in origin.