Angle-Dependent Ionization of Small Molecules by Time-Dependent Configuration Interaction and 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%.

Time propagation of electronic wavefunctions using nonorthogonal determinant expansions

The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H2, water, and butadiene.

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.

Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory Using Fourier Contour Deformation

We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain, FCD yields a high-order accurate numerical solution of the time-dependent Schrödinger equation directly in free space, without the need for artificial boundary conditions. Of the many existing artificial boundary condition schemes, FCD is most similar to an exact nonlocal transparent boundary condition, but it works directly on Cartesian grids in any dimension, and runs on top of the fast Fourier transform rather than fast algorithms for the application of nonlocal history integral operators. We adapt FCD to time-dependent density functional theory (TDDFT), and describe a simple algorithm to smoothly and automatically truncate long-range Coulomb-like potentials to a time-dependent constant outside of a bounded domain of interest, so that FCD can be used. This approach eliminates errors originating from the use of artificial boundary conditions, leaving only the error of the potential truncation, which is controlled and can be systematically reduced. The method enables accurate simulations of ultrastrong nonlinear electronic processes in molecular complexes in which the interference between bound and continuum states is of paramount importance. We demonstrate results for many-electron TDDFT calculations of absorption and strong field photoelectron spectra for one and two-dimensional models, and observe a significant reduction in the size of the computational domain required to achieve high quality results, as compared with the popular method of complex absorbing potentials.

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.

Carrier-Envelope Phase Controlling of Ion Momentum Distributions in Strong Field Double Ionization of Methyl Iodide

In strong field ionization of methyl iodide initiated by elliptically polarized few-cycle pulses, a significant correlation was observed between the carrier-envelope phases (CEPs) of the laser and the preferred ejection direction of methyl cation arising from dissociative double ionization. This was attributed to the carrier-envelope phase dependent double ionization yields of methyl iodide. This observation provides a new way for monitoring the absolute CEPs of few-cycle pulses by observing the ion momentum distributions.

Extracting Inelastic Scattering Cross Sections for Finite and Aperiodic Materials from Electronic Dynamics Simulations

Explicit time-dependent electronic structure theory methods are increasingly prevalent in the areas of condensed matter physics and quantum chemistry, with the broad-band optical absorptivity of molecular and small condensed-phase systems nowadays routinely studied with such approaches. In this paper, it is demonstrated that electronic dynamics simulations can similarly be employed to study cross sections for the scattering-induced electronic excitations probed in nonresonant inelastic X-ray scattering and momentum-resolved electron energy loss spectroscopies. A method is put forth for evaluating the electronic dynamic structure factor, which involves the application of a momentum boost-type perturbation and transformation of the resulting reciprocal space density fluctuations into the frequency domain. Good agreement is first demonstrated between the dynamic structure factor extracted from these electronic dynamics simulations and the corresponding transition matrix elements from linear response theory. The method is then applied to some extended (quasi)one-dimensional systems, for which the wave vector becomes a good quantum number in the thermodynamic limit. Finally, the dispersion of many-body excitations in a series of hydrogen-terminated graphene flakes (and twisted bilayers thereof) is investigated to highlight the utility of the presented approach for capturing morphology-dependent effects in the inelastic scattering cross sections of nanostructured and/or noncrystalline materials.

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.

Intruder Peak-Free Transient Inner-Shell Spectra Using Real-Time Simulations

Real-time methods are convenient for simulating core-level absorption spectra but suffer from nonphysical intruder peaks when using atom-centered basis sets. In transient absorption spectra, these peaks exhibit highly nonphysical time-dependent modulations in their energies and oscillator strengths. In this paper, we address the origins of these intruder peaks and propose a straightforward and effective solution based on a filtered dipole operator. In combination with real-time time-dependent density functional theory (RT-TDDFT), we demonstrate how to compute intruder-free attosecond transient X-ray absorption spectra for the aminophenol (C₆H₇NO) oxygen and nitrogen K-edges and the α-quartz (SiO₂) silicon L-edge. Without filtering, the computed spectra are qualitatively wrong. This procedure is suitable for both static and transient inner-shell spectroscopy studies and can easily be implemented in a range of real-time methodologies.

Ellipticity controlled dissociative double ionization of ethane by strong fields

The yields of all dissociation channels of ethane dications produced by strong field double ionization were measured. It was found that the branching ratios can be controlled by varying the ellipticity of laser pulses. The CH₃⁺ formation and H⁺ formation channels show a clear competition, producing the highest and lowest branching ratios at ellipticity of ∼0.6, respectively. With the help of theoretical calculations, such a control was attributed to the ellipticity dependent yields of different sequential ionization pathways.

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.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Short Iterative Lanczos Integration in Time-Dependent Equation-of-Motion Coupled-Cluster Theory

A time-dependent (TD) formulation of equation-of-motion coupled-cluster (EOM-CC) theory can provide excited-state information over an arbitrarily wide energy window with a reduced memory footprint relative to conventional, frequency-domain EOM-CC theory. However, the floating-point costs of the time-integration required by TD-EOM-CC are generally far larger than those of the frequency-domain form of the approach. This work considers the potential of the short iterative Lanczos (SIL) integration scheme [J. Chem. Phys. 1986, 85, 5870-5876] to reduce the floating-point costs of TD-EOM-CC simulations. Low-energy and K-edge absorption features for small molecules are evaluated using TD-EOM-CC with single and double excitations, with the time-integrations carried out via SIL and fourth-order Runge-Kutta (RK4) schemes. Spectra derived from SIL- and RK4-driven simulations are nearly indistinguishable, and with an appropriately chosen subspace dimension, the SIL requires far fewer floating-point operations than are required by RK4. For K-edge spectra, SIL is the more efficient scheme by an average factor of 7.2.

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.

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.

Two-pulse control over double ionization pathways in CO2

We visualize and control molecular dynamics taking place on intermediately populated states during different sequential double ionization pathways of CO2 using a sequence of two delayed laser pulses which exhibit different peak intensities. Measured yields of CO2 (2+) and of fragment pairs CO(+)/O(+) as a function of delay between the two pulses are weakly modulated by various vibronic dynamics taking place in CO2 (+). By Fourier analysis of the modulations we identify the dynamics and show that they can be assigned to merely two double ionization pathways. We demonstrate that by reversing the sequence of the two pulses it becomes possible to control the pathway which is taken across CO2 (+) towards the final state in CO2 (2+). A comparison between the yields of CO2 (2+) and CO(+)/O(+) reveals that the modulating vibronic dynamics oscillate out-of-phase with each other, thus opening up opportunities for strong-field fragmentation control on extended time scales.

Dynamic Exchange in the Strong Field Ionization of Molecules

We show that dynamic exchange is a dominant effect in strong field ionization of molecules. In CO(2) it fixes the peak ionization yield at the experimentally observed angle of 45° between polarization direction and the molecular axis. For O(2) it changes the angle of peak emission and for N(2) the alignment dependence of yields is modified by up to a factor of 2. The effect appears on the Hartree-Fock level as well as in full ab initio solutions of the Schrödinger equation.