Ab initio calculations of the high-order harmonic enhancement in small noble-gas clusters

Modeling of High-Harmonic Generation in the C60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods

“…Second, as HHG involves rapid sequences of electronic transitions and absorption of multiple photons, augmenting the basis set to include functions with higher angular quantum numbers helps capture processes with large changes in the total angular momentum. Besides appending diffuse orbitals to the existing atomic centers, another effective strategy for enhancing the basis set completeness involves adding more functions in the form of ghost atoms. ,, …”

“…Similarly to our previous works ,,, and to the works of other authors utilizing real-time time-dependent methods to simulate strong-field electron dynamics, − ,,,,− we employ the heuristic finite lifetime model of Klinkusch et al to compensate for the incompleteness of the atomic orbital basis sets. The electronic energies E k of excited states beyond the ionization threshold are modified by adding imaginary ionization rates E k → E̅ k = E k − i Γ k / 2 goodbreak0em2em⁣ for .25em E k ≥ E 0 + I p The finite lifetime model was originally developed for RT-TDCIS and later extended to RT-TDCI with higher excitations. , The ionization rates of CIS states are defined as Γ k = ∑ i normalo normalc normalc ∑ a normalv normali normalr | X i a k | 2 θ false( ϵ a false) 2 ϵ a / d where θ( x ) is the Heaviside step function and the empirical parameter d represents a maximum distance from the molecule that a (semiclassical) electron can travel before undergoing ionization.…”

“…Besides appending diffuse orbitals to the existing atomic centers, another effective strategy for enhancing the basis set completeness involves adding more functions in the form of ghost atoms. 60,71,75 It should be emphasized, however, that the aforementioned studies focused on simulating electron dynamics in small systems where HHG is confirmed to occur, at least to some extent, in accordance with the three-step model. On the other hand, in our case, even the addition of the standard Dunning diffuse functions has very little effect on the obtained HHG spectra.…”

“…In the past decade, there has been a significant rise in the popularity of employing quantum chemistry methods extended to the real-time domain for this purpose. − These approaches are characterized by moderate computational costs typical of their time-independent counterparts, as well as a reasonable level of accuracy, allowing, for example, the consideration of multielectron effects. One of the most popular methods of this kind is the real-time time-dependent configuration interaction singles (RT-TDCIS), in which the time-dependent electronic wave function is represented as a linear combination of time-independent ground and singly excited electronic eigenstates of the examined system. − Thanks to its highly favorable scaling with the number of electrons, it can be routinely applied not only to atoms − and simple molecules − but also to complex organic and biological − compounds, often yielding results qualitatively or even quantitatively consistent with the experimental data. ,, This raises the question of whether it can perform equally well for even larger systems such as nanostructured materials.…”

“… 52 − 57 Thanks to its highly favorable scaling with the number of electrons, it can be routinely applied not only to atoms 58 − 65 and simple molecules 66 − 70 but also to complex organic 71 and biological 72 − 74 compounds, often yielding results qualitatively or even quantitatively consistent with the experimental data. 71 , 72 , 75 This raises the question of whether it can perform equally well for even larger systems such as nanostructured materials.…”