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Journal ArticleDOI

Gaussian continuum basis functions for calculating high-harmonic generation spectra

15 Jul 2016-International Journal of Quantum Chemistry (John Wiley & Sons, Ltd)-Vol. 116, Iss: 14, pp 1120-1131
TL;DR: In this article, the authors investigate the efficiency of Gaussian functions specifically designed for the description of the continuum proposed by Kaufmann et al. and assess the range of applicability of this approach by studying the hydrogen atom, i.e. the simplest atom for which exact calculations on a grid can be performed.
Abstract: We explore the computation of high-harmonic generation spectra by means of Gaussian basis sets in approaches propagating the time-dependent Schrodinger equation. We investigate the efficiency of Gaussian functions specifically designed for the description of the continuum proposed by Kaufmann et al. [J. Phys. B 22, 2223 (1989)]. We assess the range of applicability of this approach by studying the hydrogen atom, i.e. the simplest atom for which "exact" calculations on a grid can be performed. We notably study the effect of increasing the basis set cardinal number, the number of diffuse basis functions, and the number of Gaussian pseudo-continuum basis functions for various laser parameters. Our results show that the latter significantly improve the description of the low-lying continuum states, and provide a satisfactory agreement with grid calculations for laser wavelengths λ0 = 800 and 1064 nm. The Kaufmann continuum functions therefore appear as a promising way of constructing Gaussian basis sets for studying molecular electron dynamics in strong laser fields using time-dependent quantum-chemistry approaches.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a spin-adapted time-dependent coupled-cluster singles and doubles model for the molecular response to a sequence of ultrashort laser pulses is presented.
Abstract: We present a spin-adapted time-dependent coupled-cluster singles and doubles model for the molecular response to a sequence of ultrashort laser pulses. The implementation is used to calculate the electronic response to a valence-exciting pump pulse, and a subsequent core-exciting probe pulse. We assess the accuracy of the integration procedures used in solving the dynamic coupled-cluster equations, in order to find a compromise between computational cost and accuracy. The transient absorption spectrum of lithium fluoride is calculated for various delays of the probe pulse with respect to the pump pulse. We observe that the transient probe absorption oscillates with the pump-probe delay, an effect that is attributed to the interference of states in the pump-induced superposition.

20 citations

Journal ArticleDOI
TL;DR: The lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set, based on a rigorous analysis of the complex-energy solutions of the Schrödinger equation.
Abstract: We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificial confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules. In this method, using a fitting procedure, the lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set. The method is based on a rigorous analysis of the complex-energy solutions of the Schrodinger equation. It gives lifetimes adapted to any given basis set without using any empirical parameters. The method can be considered as an ab initio version of the heuristic lifetime model of Klinkusch et al. [J. Chem. Phys. 131, 114304 (2009)]. The method is validated on H and He atoms using Gaussian-type basis sets for the calculation of high-harmonic-generation spectra.

20 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules.
Abstract: We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules. In this method, using a fitting procedure, the lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set. The method is based on a rigorous analysis of the complex-energy solutions of the Schr{o}dinger equation. It gives lifetimes adapted to any given basis set without using any empirical parameters. The method can be considered as an ab initio version of the heuristic lifetime model of Klinkusch et al. [J. Chem. Phys. 131, 114304 (2009)]. The method is validated on the H and He atoms using Gaussian-type basis sets for calculation of high-harmonic-generation spectra.

18 citations

Journal ArticleDOI
TL;DR: Time-Dependent Configuration Interaction Singles (TD-CIS) theory in combination with extended atomic orbital bases and different models to account for ionization losses is suggested as an economic and at the same time a reasonably accurate method to compute HHG spectra for polyatomic species.
Abstract: High Harmonic Generation (HHG) is a nonlinear optical process that provides a tunable source for high-energy photons and ultrashort laser pulses. Recent experiments demonstrated that HHG spectroscopy may also be used as an analytical tool to discriminate between randomly oriented configurational isomers of polyatomic organic molecules, namely, between the cis- and trans-forms of 1,2-dichloroethene (DCE) [M. C. H. Wong et al., Phys. Rev. A 84, 051403 (2011)]. Here, we suggest as an economic and at the same time a reasonably accurate method to compute HHG spectra for polyatomic species, Time-Dependent Configuration Interaction Singles (TD-CIS) theory in combination with extended atomic orbital bases and different models to account for ionization losses. The HHG spectra are computed for aligned and unaligned cis- and trans-DCE. For the unaligned case, a coherent averaging over possible rotational orientations is introduced. Furthermore, using TD-CIS, possible differences between the HHG spectra of cis- and trans-DCE are studied. For aligned molecules, spectral differences between cis and trans emerge, which can be related to their different point group symmetries. For unaligned, randomly oriented molecules, we also find distinct HHG spectra in partial agreement with experiment. In addition to HHG response in the frequency space, we compute time-frequency HHG spectra to gain insight into which harmonics are emitted at which time. Further differences between the two isomers emerge, suggesting time-frequency HHG as another tool to discriminate configurational isomers.

17 citations

Journal ArticleDOI
TL;DR: A first attempt to evaluate the accuracy of the time-dependent configuration interaction method so that the optimal representation of the electronic wave function for time- dependent studies can be assessed and a quantifier is determined that can aid in finding this optimal representation.
Abstract: With the recent advances in experimental attosecond science, theoretical predictions of electron dynamics can now be validated against experiment. Time-dependent studies of the electron motion in molecules can be used to obtain information about electronic transitions and the interaction of the electrons with electromagnetic fields. Often, these approaches rely on single-excited wave functions. Presented here is a first attempt to evaluate the accuracy of the time-dependent configuration interaction method so that the optimal representation of the electronic wave function for time-dependent studies can be assessed. A quantifier is determined that can aid in finding this optimal representation. The approach is demonstrated on a variety of molecules that include both localized and intramolecular charge transfer electron excitations. Observables including excitation energies, dipole moments, strengths, and static polarizabilities are obtained from time-independent and time-dependent calculations and are compared to experimental data. In this way, a rigorous routine is developed by which the reliability and accuracy of the CI wave function can be assessed and which represents a first step to a more quantitative description of electron dynamics in molecules.

16 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a detailed study of correlation effects in the oxygen atom was conducted, and it was shown that primitive basis sets of primitive Gaussian functions effectively and efficiently describe correlation effects.
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.

26,705 citations

Book ChapterDOI
01 Jan 1957
TL;DR: The theory of atoms with one or two electrons is the simplest and most completely treated field of application of quantum mechanics as mentioned in this paper, and it is one of the simplest fields of application for quantum mechanics.
Abstract: One of the simplest, and most completely treated, fields of application of quantum mechanics is the theory of atoms with one or two electrons For hydrogen and the analcgous ions He+, Li++, etc, the calculations can be performed exactly, both in Schrodinger’s nonrelativistic wave mechanics and in Dirac’s relativistic theory of the electron More specifically, the calculations are exact for a single electron in a fixed Coulomb potential Hydrogen-like atoms thus furnish an excellent way of testing the validity of quantum mechanics For such atoms the correction terms due to the motion and structure of atomic nuclei and due to quantum electrodynamic effects are small and can be calculated with high accuracy Since the energy levels of hydrogen and similar atoms can be investigated experimentally to an astounding degree of accuracy, some accurate tests of the validity of quantum electrodynamics are also possible Finally, the theory of such atoms in an external electric or magnetic field has also been developed in detail and compared with experiment

5,385 citations


"Gaussian continuum basis functions ..." refers methods in this paper

  • ...1162 hartree obtained with the 6-aug-ccpVTZ+8K basis set with the analytical solution of the time-independent Schrödinger equation [46]....

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  • ...5: Comparison between the exact radial wave function R(r) [46] and the radial wave function obtained using the 6-aug-cc-pVTZ+8K basis set for a s continuum state at the energy E = 0....

    [...]

  • ...[46] H....

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Journal ArticleDOI
TL;DR: During strong-field multiphoton ionization, a wave packet is formed each time the laser field passes its maximum value, and 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.
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

5,334 citations

Journal ArticleDOI
TL;DR: A simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields is presented and the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law Ip+3.17Up is presented.
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.

3,007 citations

Journal ArticleDOI
16 Dec 2004-Nature
TL;DR: It is demonstrated that the full three-dimensional structure of a single orbital can be imaged by a seemingly unlikely technique, using high harmonics generated from intense femtosecond laser pulses focused on aligned molecules.
Abstract: Single-electron wavefunctions, or orbitals, are the mathematical constructs used to describe the multi-electron wavefunction of molecules. Because the highest-lying orbitals are responsible for chemical properties, they are of particular interest. To observe these orbitals change as bonds are formed and broken is to observe the essence of chemistry. Yet single orbitals are difficult to observe experimentally, and until now, this has been impossible on the timescale of chemical reactions. Here we demonstrate that the full three-dimensional structure of a single orbital can be imaged by a seemingly unlikely technique, using high harmonics generated from intense femtosecond laser pulses focused on aligned molecules. Applying this approach to a series of molecular alignments, we accomplish a tomographic reconstruction of the highest occupied molecular orbital of N2. The method also allows us to follow the attosecond dynamics of an electron wave packet.

1,713 citations