Angle-Dependent Ionization of Hydrides AHn Calculated by Time-Dependent Configuration Interaction with an Absorbing Potential

Reducing the Cost of TD-CI Simulations of Strong Field Ionization

Strong field ionization of molecules by intense laser pulses can be simulated by time-dependent configuration interaction (TD-CI) with a complex absorbing potential (CAP). Standard molecular basis sets need to be augmented with several sets of diffuse functions for effective interaction with the CAP. This dramatically increases the number of configurations and the cost of the TD-CI simulations as the size of the molecules increases. The cost can be reduced by making use of spin symmetry and by employing an orbital energy cutoff to limit the number of virtual orbitals used to construct the excited configurations. Greater reductions in the number of virtual orbitals can be obtained by examining their interaction with the absorbing potential during simulations and their contributions to the strong field ionization rate. This can be determined from the matrix elements of the absorbing potential and the TD-CI coefficients from test simulations. Compared to a simple 3 hartree cutoff in the orbital energies, these approaches reduce the number of virtual orbitals by 20-35% for neutral molecules and 5-10% for cations. As a result, the cost of simulations is reduced by 35-60% for neutral molecules. The number of virtual orbitals needed can also be estimated by second-order perturbation theory without the need for test simulations. The number of virtual orbitals can be reduced further by adapting orbitals to the laser field using natural orbitals derived from test simulations. This is particularly effective for cations, yielding reductions of more than 20%.

Charge Migration in HCCI Cations Probed by Strong Field Ionization: Time-Dependent Configuration Interaction and Vibrational Wavepacket Simulations

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations and results in charge migration between the CC π orbital and the iodine π-type lone pair. This charge migration causes oscillations in the rate of strong field ionization of the cation to the dication that can be monitored using intense few-cycle probe pulses. The dynamics and strong field ionization of the coherent superposition the X and A states of HCCI⁺ have been modeled by time-dependent configuration interaction (TDCI) simulations. When the nuclei are allowed to move, the electronic wavefunctions need to be multiplied by vibrational wavefunctions. Nuclear motion has been modeled by vibrational packets moving on quadratic approximations to the potential energy surfaces for the X and A states of the cation. The overlap of the vibrational wavepackets decays in about 10-15 fs. Consequently, the oscillations in the strong field ionization decay on the same time scale. A revival of the vibrational overlap and in the oscillations of the strong field ionization is seen at 60-110 fs. TDCI simulations show that the decay and revival of the charge migration can be monitored by strong field ionization with intense 2- and 4-cycle linearly polarized 800 nm pulses. The revival is also seen with 7-cycle pulses.

Attosecond Imaging of Electronic Wave Packets

An electronic wave packet has significant spatial evolution besides its temporal evolution, due to the delocalized nature of composing electronic states. The spatial evolution was not previously accessible to experimental investigations at the attosecond timescale. A phase-resolved two-electron-angular-streaking method is developed to image the shape of the hole density of an ultrafast spin-orbit wave packet in the krypton cation. Furthermore, the motion of an even faster wave packet in the xenon cation is captured for the first time: An electronic hole is refilled 1.2 fs after it is produced, and the hole filling is observed on the opposite side where the hole is born.

High harmonic spectra computed using time-dependent Kohn-Sham theory with Gaussian orbitals and a complex absorbing potential

High harmonic spectra for H₂ and H₂ ⁺ are simulated by solving the time-dependent Kohn-Sham equation in the presence of a strong laser field using an atom-centered Gaussian representation of the density and a complex absorbing potential. The latter serves to mitigate artifacts associated with the finite extent of the basis functions, including spurious reflection of the outgoing electronic wave packet. Interference between the outgoing and reflected waves manifests as peak broadening in the spectrum as well as the appearance of spurious high-energy peaks after the harmonic progression has terminated. We demonstrate that well-resolved spectra can be obtained through the use of an atom-centered absorbing potential. As compared to grid-based algorithms, the present approach is more readily extensible to larger molecules.

Ionization of HCCI Neutral and Cations by Strong Laser Fields Simulated With Time Dependent Configuration Interaction

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations. This superposition results in charge migration between the CC π orbital and the iodine π-type lone pair which can be monitored by strong field ionization with short, intense probe pulses. Strong field ionization of the X and A states of HCCI cation was simulated with time-dependent configuration interaction using singly ionized configurations and singly excited, singly ionized configurations (TD-CISD-IP) and an absorbing boundary. Studies with static fields were used to obtain the 3-dimensional angular dependence of instantaneous ionization rates by strong fields and the orbitals involved in producing the cations and dications. The frequency of charge oscillation is determined by the energy separation of the X and A states; this separation can change depending on the direction and strength of the field. Furthermore, fields along the molecular axis can cause extensive mixing between the field-free X and A configurations. For coherent superpositions of the X and A states, the charge oscillations are characterized by two frequencies-the driving frequency of the laser field of the probe pulse and the intrinsic frequency due to the energy separation between the X and A states. For linear and circularly polarized pulses, the ionization rates show marked differences that depend on the polarization direction of the pulse, the carrier envelope phase and initial phase of the superposition. Varying the initial phase of the superposition at the beginning of the probe pulse is analogous to changing the delay between the pump and probe pulses. The charge oscillation in the coherent superposition of the X and A states results in maxima and minima in the ionization yield as a function of the superposition phase.

Ab Initio Direct Dynamics

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this "on-the-fly" approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. This approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH₂O → H₂ + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

Sequential double ionization of molecules by strong laser fields simulated with time-dependent configuration interaction

A new time-dependent configuration interaction method has been developed for simulating strong field sequential double ionization of molecular systems. Ionization of the neutral is simulated by time-dependent configuration interaction with single excitations (TD-CIS) and an absorbing boundary. At each time step, the ionized part of the wavefunction from the TD-CIS calculation is transferred to a second time-dependent configuration interaction simulation for ionization of the cation to the dication. The second simulation uses a CISD-IP wavefunction that consists of singly ionized configurations and singly excited, singly ionized configurations (TD-CISD-IP). The transfer between the TD-CIS and TD-CISD-IP simulations is accomplished by partitioning the first ionization rate into contributions from individual orbitals or by singular value decomposition of the absorbed wavefunction. Sequential double ionization simulations have been carried out for HBr in five cycle 800 nm linearly polarized pulses and HI (with spin-orbit coupling) in four cycle 800 nm circularly polarized pulses, with intensities chosen so that the population of the neutral was depleted by the mid-pulse. The singular value decomposition of the cation produced by the first ionization is dominated by a single component for the two orientations considered. The population of the cation rises and then falls as it is ionized to the dication. Depending on the pulse shape and field strength, the ionization of the cation to the dication can continue for several half cycles. For HI with circularly polarized light, the rates for both the first and second ionization peak when the electric field is aligned with the p_π orbital.

Effect of spin-orbit coupling on strong field ionization simulated with time-dependent configuration interaction

Time-dependent configuration interaction with a complex absorbing potential has been used to simulate strong field ionization by intense laser fields. Because spin-orbit coupling changes the energies of the ground and excited states, it can affect the strong field ionization rate for molecules containing heavy atoms. Configuration interaction with single excitations (CIS) has been employed for strong field ionization of closed shell systems. Single and double excitation configuration interaction with ionization (CISD-IP) has been used to treat ionization of degenerate states of cations on an equal footing. The CISD-IP wavefunction consists of ionizing single (one hole) and double (two hole/one particle) excitations from the neutral atom. Spin-orbit coupling has been implemented using an effective one electron spin-orbit coupling operator. The effective nuclear charge in the spin-orbit coupling operator has been optimized for Ar⁺, Kr⁺, Xe⁺, HX⁺ (X = Cl, Br, and I). Spin-orbit effects on angular dependence of the strong field ionization have been studied for HX and HX⁺. The effects of spin-orbit coupling are largest for ionization from the π orbitals of HX⁺. In a static field, oscillations are seen between the ²Π_3/2 and ²Π_1/2 states of HX⁺. For ionization of HX⁺ by a two cycle circularly polarized pulse, a single peak is seen when the maximum in the carrier envelope is perpendicular to the molecular axis and two peaks are seen when it is parallel to the axis. This is the result of the greater ionization rate for the π orbitals than for the σ orbitals.

Angular Dependence of Strong Field Ionization of 2-Phenylethyl-N,N-dimethylamine (PENNA) Using Time-Dependent Configuration Interaction with an Absorbing Potential

Ionization of 2-phenylethyl-N,N-dimethylamine (PENNA) may lead to charge migration between the amine group and the phenyl group. The angular dependence of strong field ionization of PENNA has been modeled by time-dependent configuration interaction with an absorbing potential. The total ionization rate can be partitioned into contributions from the amine group and the phenyl group, and these components have very distinct shapes. Ionization from the amine is primarily from the side opposite to the lone pair and is dominated by the CH₂ and CH₃ groups. Similarly, trimethylamine (N(CH₃)₃), dimethyl ether (CH₃OCH₃), and methyl fluoride (CH₃F) are also found to ionize primarily from the methyl groups. The predominance of ionization from the methyl groups can be attributed to the fact that the orbital energies of individual lone pairs of N, O, and F are lower than the CH₃ groups. Because the angular dependence of ionization of the two groups is quite different, alignment of PENNA could be used to control the ratio of the amine and phenyl cations and potentially probe charge migration in PENNA cation.

Angular dependence of strong field sequential double ionization for neon and acetylene simulated with time-dependent configuration interaction using CIS and CISD-IP

Strong field ionization is fundamentally important for attosecond spectroscopy and coherence control. However, the modeling beyond the single active electron approximation is still difficult. Time-dependent configuration interaction with singly excited configurations and a complex absorbing potential (TDCIS-CAP), can be used to simulate single and double ionization by intense laser fields. When the monocation does not have degenerate states, TDCIS-CAP starting from a Hartree-Fock calculation of the cation is suitable for simulating the second ionization step. When the monocation has two or more degenerate states, the simulations should treat these degenerate states equivalently. CISD-IP (single and double excitation configuration interaction with ionization) can be used to treat degenerate states of the cation on an equal footing by representing the cation wavefunctions with ionizing single (1 hole) and double (2 holes/1 particle) excitations from the neutral molecule. Since CISD-IP includes single excitations for each of the monocation states, time dependent CISD-IP with a complex absorbing potential (TDCISDIP-CAP) can also be used to simulate ionization to the dications states. In this work, TDCIS-CAP and TDCISDIP-CAP have been used to simulate the angular dependence of ionization of the neon cation and acetylene cation. In both cases, the second electron is ionized predominantly from an orbital perpendicular to the orbital involved in the first ionization. The TDCISDIP-CAP simulations show some features involving interactions between the monocation states that are not seen in the TDCIS-CAP simulations.

Hovering States of Ammonia in a High-Intensity, High-Frequency Oscillating Field: Trapped into Planarity by Laser-Induced Hybridization

A high-intensity, high-frequency laser can create an oscillating induced dipole moment in a molecule. At high laser frequencies with a long pulse width, a stable non-ionizing state with a laser-induced hybridization of the electrons is formed. For ammonia, aligned with the linear polarization direction of the laser, such stable states can be realized. Electronic hybridization in the presence of the high-frequency field is such that the lone pair propensity is dynamically equalized on either side of ammonia. This leads to a destabilization of pyramidal ammonia and hovering states with the electron density flipping to either side of the geometry. Electronic structure calculations in an oscillating frame of reference anticipate this effect with a predicted classical quiver distance of 0.1 Å. Electronic dynamics at a laser intensity of 1.14 × 10¹³ W/cm² and a frequency of 8.16 eV predicts negligible ionization for the planar geometry. Approximate nuclear wave packet dynamics in the oscillating potential energy generated by the electrons predicts a trapping of ammonia in its planar transition state geometry.

Disentangling Strong-Field Multielectron Dynamics with Angular Streaking

The study into the interaction between a strong laser field and atoms/molecules has led to significant advances in developing spectroscopic tools in the attosecond time-domain and methods for controlling chemical reactions. There has been great interest in understanding the complex electronic and nuclear dynamics of molecules in strong laser fields. However, it is still a formidable challenge to fully model such dynamics. Conventional experimental tools such as photoelectron spectroscopy encounter difficulties in revealing the involved states because the electron spectra are largely dictated by the property of the laser field. Here, with strong field angular streaking technique, we measure the angle-dependent ionization yields that directly reflect the symmetry of the ionizing orbitals of methyl iodide and thus reveal the ionization/dissociation dynamics. Moreover, kinematically complete measurements of momentum vectors of all fragments in dissociative double ionization processes allow access to electron-momentum correlations that reveal correlated multielectron dynamics.

Attosecond Electron Correlation Dynamics in Double Ionization of Benzene Probed with Two-Electron Angular Streaking

With a novel three-dimensional electron-electron coincidence imaging technique and two-electron angular streaking method, we show that the emission time delay between two electrons can be measured from tens of attoseconds to more than 1 fs. Surprisingly, in benzene, the double ionization rate decays as the time delay between the first and second electron emission increases during the first 500 as. This is further supported by the decay of the Coulomb repulsion in the direction perpendicular to the laser polarization. This result reveals that laser-induced electron correlation plays a major role in strong field double ionization of benzene driven by a nearly circularly polarized field.

Angle-dependent strong-field ionization of triple bonded systems calculated by time-dependent configuration interaction with an absorbing potential

The angle dependence of strong field ionization has been studied for a set of molecules containing triple bonds: HCCH, HCN, HCC–CN, H2N–CCH, H2N–CN, and H2N–CC–CN. Time-dependent configuration interaction (TDCI) with a complex absorbing potential was used to model strong field ionization by a linearly polarized seven-cycle 800 nm cosine squared pulse. The ionization yields have been calculated as a function of the laser intensity and polarization direction and plotted as three-dimensional surfaces. At low field strengths, the angular dependence can be understood in terms of ionization from the highest occupied orbitals. At higher laser intensities, ionization occurs from lower lying orbitals as well as from the highest occupied orbitals, as indicated by changes in the angular dependence of the ionization yield and by variations in the population analysis of the TDCI wavefunction with the intensity of the laser field. The ionization yield for directions parallel to the molecular axis increases more rapidly than perpendicular to the axis as the conjugation length is increased. NH2 substitution substantially increases the ionization yield along the molecular axis but has only a small effect for perpendicular directions.

Controlling Chemical Reactions by Short, Intense Mid-Infrared Laser Pulses: Comparison of Linear and Circularly Polarized Light in Simulations of ClCHO(+) Fragmentation

Enhanced mode selective fragmentation of oriented ClCHO(+) → Cl + HCO(+), H + ClCO(+), HCl(+) + CO with linear polarized intense mid-IR pulses was demonstrated in our previous computational study ( J. Phys. Chem. Lett. 2012 , 3 , 2541 ). Simulations of angle-dependent strong field ionization of ClCHO indicate the ionization rate in the molecular plane is nearly twice as large as perpendicular to the plane, suggesting a degree of planar alignment can be obtained experimentally for ClCHO(+), starting from neutral molecules. Classical trajectory calculations with a 4 cycle 7 μm laser pulse (peak intensity of 1.26 × 10(14) W/cm(2)) show that circularly polarized light with the electric field in the plane of the molecule deposits more energy and yields larger branching ratios for higher energy fragmentation channels than linearly polarized light with the same maximum field strength. These results suggest circularly polarized mid-IR pulses can not only achieve control on reactions but also provide an experimentally accessible implementation.