Open accessJournal Article

# A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation.

02 Mar 2021-Journal of Chemical Physics (AIP Publishing LLCAIP Publishing)-Vol. 154, Iss: 9, pp 094111
Abstract: A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrodinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 1013 W/cm2 to 5 × 1014 W/cm2. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

Topics: Gaussian (56%), ,  ... read more
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Open accessJournal Article
J. W. Gao1, Tsveta Miteva2, Yang-Le Wu, J. G. Wang  +2 moreInstitutions (2)
22 Mar 2021-Physical Review A
Abstract: We present a simple and efficient method for computing single and double ionization cross sections in ion-atom and ion-molecule collisions using ${L}^{2}$ Gaussian basis sets. Gaussian functions are widely employed to compute bound states of ions, atoms, and molecules. However, the description of continuum states, and therefore ionization phenomena, remains a theoretical challenge. Our approach is tested on the benchmark system antiproton-helium collisions in the so-called intermediate energy range. A good agreement with numerically exact calculations is observed. The proposed method is general and can thus be employed in any collisional systems in the challenging nonperturbative regime. Our work opens the way to investigate multiple ionization processes by ion impact in multicenter polyelectronic systems.

Topics: Double ionization (66%), Ionization (62%), Gaussian (54%) ... read more

1 Citations

Journal Article
Abstract: With recent experimental advances in laser-driven electron dynamics in polyatomic molecules, the need arises for their reliable theoretical modelling. Among efficient, yet fairly accurate methods for many-electron dynamics are Time-Dependent Configuration Interaction Singles (TD-CIS) (a Wave Function Theory (WFT) method), and Real-Time Time-Dependent Density Functional Theory (RT-TD-DFT), respectively. Here we compare TD-CIS combined with extended Atomic Orbital (AO) bases, TD-CIS/AO, with RT-TD-DFT in a grid representation of the Kohn–Sham orbitals, RT-TD-DFT/Grid. Possible ionization losses are treated by complex absorbing potentials in energy space (for TD-CIS/AO) or real space (for RT-TD-DFT), respectively. The comparison is made for two test cases: (i) state-to-state transitions using resonant lasers (π-pulses), i.e., bound electron motion, and (ii) large-amplitude electron motion leading to High Harmonic Generation (HHG). Test systems are a H2 molecule and cis- and trans-1,2-dichlorethene, C2H2Cl2, (DCE). From time-dependent electronic energies, dipole moments and from HHG spectra, the following observations are made: first, for bound state-to-state transitions enforced by π-pulses, TD-CIS nicely accounts for the expected population inversion in contrast to RT-TD-DFT, in agreement with earlier findings. Secondly, when using laser pulses under non-resonant conditions, dipole moments and lower harmonics in HHG spectra are obtained by TD-CIS/AO which are in good agreement with those obtained with RT-TD-DFT/Grid. Deviations become larger for higher harmonics and at low laser intensities, i.e., for low-intensity HHG signals. We also carefully test effects of basis sets for TD-CIS/AO and grid size for RT-TD-DFT/Grid, different exchange–correlation functionals in RT-TD-DFT, and absorbing boundaries. Finally, for the present examples, TD-CIS/AO is observed to be at least an order of magnitude more computationally efficient than RT-TD-DFT/Grid.

Topics: , Dipole (52%), Atomic orbital (52%) ... read more

1 Citations

Open accessPosted Content
Abstract: Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity; however, existing quantum algorithms based on the split-operator techniques require large-scale fault-tolerant quantum computers that remain elusive in the near future. Here we present variational simulations of real-space quantum dynamics suitable for implementation in Noisy Intermediate-Scale Quantum (NISQ) devices. The Hamiltonian is first encoded onto qubits using a discrete variable representation (DVR) and binary encoding scheme. We show that direct application of real-time variational quantum algorithm based on the McLachlan's principle is inefficient as the measurement cost grows exponentially with the qubit number for general potential energy and extremely small time-step size is required to achieve accurate results. Motivated by the insights that most chemical dynamics occur in the low energy subspace, we propose a subspace expansion method by projecting the total Hamiltonian, including the time-dependent driving field, onto the system low-energy eigenstate subspace using quantum computers, the exact quantum dynamics within the subspace can then be solved classically. We show that the measurement cost of the subspace approach grows polynomially with dimensionality for general potential energy. Our numerical examples demonstrate the capability of our approach, even under intense laser fields. Our work opens the possibility of simulating chemical dynamics with NISQ hardware.

Topics: Quantum algorithm (72%), Quantum dynamics (71%), Quantum computer (70%) ... read more

Open accessJournal Article
Emanuele Coccia1, Eleonora Luppi2Institutions (2)
Abstract: High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrodinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.

Open accessJournal Article
Abstract: The response of the hydrogen molecular ion, H2+, to few-cycle laser pulses of different intensities is simulated. To treat the coupled electron-nuclear motion, we use adiabatic potentials computed with Gaussian-type basis sets together with a heuristic ionization model for the electron and a grid representation for the nuclei. Using this mixed-basis approach, the time-dependent Schrodinger equation is solved, either within the Born-Oppenheimer approximation or with nonadiabatic couplings included. The dipole response spectra are compared to all-grid-based solutions for the three-body problem, which we take as a reference to benchmark the Gaussian-type basis set approaches. Also, calculations employing the fixed-nuclei approximation are performed, to quantify effects due to nuclear motion. For low intensities and small ionization probabilities, we get excellent agreement of the dynamics using Gaussian-type basis sets with the all-grid solutions. Our investigations suggest that high harmonic generation (HHG) and high-frequency response, in general, can be reliably modeled using Gaussian-type basis sets for the electrons for not too high harmonics. Further, nuclear motion destroys electronic coherences in the response spectra even on the time scale of about 30 fs and affects HHG intensities, which reflect the electron dynamics occurring on the attosecond time scale. For the present system, non-Born-Oppenheimer effects are small. The Gaussian-based, nonadiabatically coupled, time-dependent multisurface approach to treat quantum electron-nuclear motion beyond the non-Born-Oppenheimer approximation can be easily extended to approximate wavefunction methods, such as time-dependent configuration interaction singles (TD-CIS), for systems where no benchmarks are available.

Topics: , Dihydrogen cation (53%),  ... read more
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155 results found

Journal ArticleDOI: 10.1063/1.456153
Abstract: In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Almlof, Taylor, and co‐workers have found that basis sets of natural orbitals derived from correlated atomic calculations (ANOs) provide an excellent description of molecular correlation effects. We report here a careful study of correlation effects in the oxygen atom, establishing that compact sets of primitive Gaussian functions effectively and efficiently describe correlation effects i f the exponents of the functions are optimized in atomic correlated calculations, although the primitive (s p) functions for describing correlation effects can be taken from atomic Hartree–Fock calculations i f the appropriate primitive set is used. Test calculations on oxygen‐containing molecules indicate that these primitive basis sets describe molecular correlation effects as well as the ANO sets of Almlof and Taylor. Guided by the calculations on oxygen, basis sets for use in correlated atomic and molecular calculations were developed for all of the first row atoms from boron through neon and for hydrogen. As in the oxygen atom calculations, it was found that the incremental energy lowerings due to the addition of correlating functions fall into distinct groups. This leads to the concept of c o r r e l a t i o n c o n s i s t e n t b a s i s s e t s, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation consistent sets are given for all of the atoms considered. The most accurate sets determined in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding ANO sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estimated that this set yields 94%–97% of the total (HF+1+2) correlation energy for the atoms neon through boron.

Topics: STO-nG basis sets (65%), Basis set (57%),  ... read more

24,491 Citations

Open accessJournal Article
Paul B. Corkum1Institutions (1)
Abstract: During strong-field multiphoton ionization, a wave packet is formed each time the laser field passes its maximum value Within the first laser period after ionization there is a significant probability that the electron will return to the vicinity of the ion with very high kinetic energy High-harmonic generation, multiphoton two-electron ejection, and very high energy above-threshold-ionization electrons are all conssequences of this electron-ion interaction One important parameter which determines the strength of these effects is the rate at which the wave packet spreads in the direction perpendicular to the laser electric field; another is the polarization of the laser It will be essential for experimentalists to be aware of these crucial parameters in future experiments

Topics: Double ionization (61%), Ionization (61%), Photoionization (60%) ... read more

4,891 Citations

Journal Article
Maciej Lewenstein1, Ph. Balcou, Misha Ivanov2, Anne L'Huillier3  +1 moreInstitutions (3)
01 Mar 1994-Physical Review A
Abstract: We present a simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields. The theory recovers the classical interpretation of Kulander et al. in Proceedings of the SILAP III Works hop, edited by B. Piraux (Plenum, New York, 1993) and Corkum [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the single-atom harmonic-generation spectra fall off at an energy approximately equal to the ionization energy plus about three times the oscillation energy of a free electron in the field. The theory is valid for arbitrary atomic potentials and can be generalized to describe laser fields of arbitrary ellipticity and spectrum. We discuss the role of atomic dipole matrix elements, electron rescattering processes, and of depletion of the ground state. We present the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law Ip+3.17Up, where Ip is the atomic ionization potential and Up is the ponderomotive energy, due to the account for quantum tunneling and diffusion effects.

Topics: Ponderomotive energy (63%), ,  ... read more

2,710 Citations

Journal Article
Thomas Brabec1, Ferenc Krausz1Institutions (1)
Abstract: The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Topics: Nonlinear optics (54%), Ponderomotive energy (54%), Photon (52%) ... read more

2,414 Citations

Journal Article
J. Crank, P. Nicolson1, D. R. HartreeInstitutions (1)
01 Jan 1947-
Abstract: This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equationwheresubject to the boundary conditionsA, k, q are known constants.Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).