An official website of the United States government
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 cut-off 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 cut-off 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 and 5% - 10% for cations. 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%.
more »
« less
This content will become publicly available on April 10, 2026
Evaluation of Diffuse Basis Sets for Simulations of Strong Field Ionization Using Time-Dependent Configuration Interaction with a Complex Absorbing Potential
For simulations of strong field ionization using time-dependent configuration with a complex absorbing potential (TDCI-CAP), standard molecular basis set must be augmented by several sets of diffuse functions to support the wavefunction as it is distorted by the strong field and interacts with the absorbing potential. Various sets of diffuse functions used in previous studies have been extended and evaluated for their ability to model the angular dependence of strong field ionization. These sets include diffuse s, p, d and f gaussian functions with selected even-tempered exponents of the form 0.0001×2n placed on each atom. For single-centered test cases, the largest contribution to the ionization rate is from functions with a maximum in the radial distribution close to the onset of the complex absorbing potential, while functions with smaller exponents also contributed to the rate. For molecules, diffuse functions on adjacent centers overlap strongly, leading to linear dependencies. The transformation to remove these linear dependencies mixes functions of different angular momenta making it difficult to assess the importance of individual s, p, d and f functions in simulating the rate for molecules. As an alternative, a hierarchy of diffuse basis sets was constructed starting with a small set and adding one or two functions at a time. These basis sets were evaluated for their ability to reproduce the rate and the shape of the angular dependence of strong field ionization. When combined with the aug-cc-pVTZ molecular basis set and an absorbing potential starting at 3.5 times the van der Waals radius for each atom, the most diffuse s, p, d and f functions need to have exponents of 0.0032, 0.0032, 0.0064 and 0.0064, respectively, or smaller. Strong field ionization from electronegative atoms such as oxygen required additional f functions with tight exponents of 0.0512 and 0.1024. Diffuse basis sets that perform well for the angular dependence of the ionization rate with a static field are equally effective for strong field ionization with a linearly polarized 7 cycle 800 nm pulse.
more »
« less
- Award ID(s):
- 1856437
- PAR ID:
- 10612972
- Publisher / Repository:
- American Chemical Society
- Date Published:
- Journal Name:
- The Journal of Physical Chemistry A
- Volume:
- 129
- Issue:
- 14
- ISSN:
- 1089-5639
- Page Range / eLocation ID:
- 3353 to 3367
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga–Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn–Sham limit is improved relative to other basis sets where convergence to the Kohn–Sham limit is typically not observed.more » « less
-
High harmonic spectra for H 2 and [Formula: see text] 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.more » « less
-
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.more » « less
-
Attosecond photoionization time delays reveal information about the potential energy landscape that an outgoing electron wavepacket probes upon ionization. In this study, we experimentally quantify the dependence of the time delay on the angular momentum of the liberated photoelectrons. For this purpose, we resolved electron quantum-path interference spectra in energy and angle using a two-color attosecond pump–probe photoionization experiment in helium. A fitting procedure of the angle-dependent interference pattern allows us to disentangle the relative phase of all four quantum pathways that are known to contribute to the final photoelectron signal. In particular, we resolve the dependence on angular momentum of the delay of one-photon transitions between continuum states, which is an essential and universal contribution to the total photoionization delay observed in attosecond pump–probe measurements. For such continuum–continuum transitions, we measure a delay between outgoing and electrons as large as 12 attoseconds, close to the ionization threshold in helium. Both single-active-electron and first-principlesab initiosimulations confirm this observation for helium and hydrogen, demonstrating the universality of the observed delays.more » « less
