Hybrid basis and multi-center grid method for strong-field processes

TL;DR

The paper introduces ATTOMESA's one-electron implementation, combining a hybrid Gaussian–FEDVR basis with a multicenter Becke grid to accurately simulate strong-field and attosecond dynamics in atoms and simple molecules. It details the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, unitary time propagation with a CAP, and the extraction of photoelectron and high-harmonic observables, validating the approach against essentially-exact benchmarks for H, a one-electron He model, and H$_2^+$. Key results include machine-precision bound-state energies, correct static polarizabilities, and excellent agreement of HHG spectra, photoionization cross sections, and photoelectron momentum distributions with reference data. The work provides a solid foundation for integrating quantum-chemistry methods and enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields, with future extensions to multi-electron dynamics.

Abstract

We present a time-dependent framework that combines a hybrid Gaussian-FEDVR basis with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation ($\text{H}_{2}^{+}$) through comparisons with essentially-exact reference resutls for bound-state energies, high-harmonic generation spcetra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which are already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields.

Figures (4)

• Figure 1: (a) ATTOMESA's simulation volume, with a dihydrogen cation in the center; (b) prototypical radial basis functions used in ATTOMESA's hybrid basis: the Gaussian-type orbitals (red) reside only within the molecular region $\Omega_{m}$, while the FEDVRs (blue) reside within both $\Omega_{m}$ and the external region $\Omega_{e}$. For clarity, here we assume that there is only one atom located at the center of the spherical volume and so only one set of Gaussian-type orbitals centered at the origin. The tick marks at the bottom and top of the plot denote the radial grid points used in the computation of the electronic integrals.
• Figure 2: Comparisons between ATTOMESA and TDSE-SAE in atomic hydrogen: (a) HHG with an 800-nm, $2.2 \times 10^{13}\ \text{W}/\text{cm}^{2}$, 3-o.c. laser pulse; (b) photoelectron spectrum and (c) photoelectron momentum distribution for a $2.72$-eV, $7.5\times 10^{11}\ \text{W}/\text{cm}^{2}$, 10-o.c. laser pulse.
• Figure 3: Comparison between ATTOMESA and TDSE-SAE in helium, using the Tong-Lin potential tong2005: (a) photoelectron spectrum and (b) photoelectron momentum distribution using a $\omega+2\omega$ scheme ($\omega = 0.475$ a.u., with an intensity of $8.8 \times 10^{13}$ W/cm$^{2}$; $2\omega = 0.95$ a.u., with an intensity of $3.5 \times 10^{12}$ W/cm$^{2}$). Both pulses have the same duration ($6.4$ fs) and CEP ($-\pi/2$).
• Figure 4: Total photoionization cross section for H$_{2}^{+}$, polarized (a) parallel to and (b) perpendicular to the molecular axis: the blue curve is from ATTOMESA, while the black dots are from Bates and Öpik bates1968; (c) photoelectron momentum distribution for H$_{2}^{+}$ using a 6.8-eV, $1.2 \times 10^{12}\ \text{W}/\text{cm}^{2}$, 10-o.c. laser pulse.