Optimized Basis Sets Research Articles

A fast, convenient and stable fluorescent probe for detecting Fe3+/2+ and its applications

A turn-on benzimidazole-based fluorescent probe (E)-2-((4-(5-bromo-1H-benzo[d]imidazole-2-yl)benzylidene)amino)phenol (BRAP) for the detection of Fe3+/2+ was developed. The probe BRAP was designed and synthesized using 2-hydroxyaniline as the recognition site and benzimidazole as the fluorophore. It was highly selective and sensitive with a detection limit as low as 2.1 × 10−8 mol/L and didn't interfere with other analytes. Using EtOH: H2O (v:v = 9:1) as the detection system, BRAP had non-fluorescence at 466 nm, which was mainly due to isomerization and rotation of the CN bond. The dihedral angle rotation hindered the charge transfer between benzimidazole and 2-hydroxyaniline. However, upon the addition of Fe3+/2+, the CN bond in probe BRAP was cleaved to form compound 3, whose electrons were transferred from the benzimidazole ring to the benzaldehyde portion upon excitation and showed blue fluorescence. In addition, the optimized structure and orbital energies of probe BRAP and its products were calculated by comparing three functional combinations with time-dependent density functional theory (TD-DFT) and the optimal functional and basis set [B3LYP/6-311 + G(d,p)]. In addition, the probe BRAP combined with a smartphone was explored for the rapid detection of Fe3+/2+ in wine.

Electronic structure of ground and low-lying excited states of BaLi+ molecular ion: spin-orbit effect, radiative lifetimes and Franck-Condon factor

The study of BaLi+ and its reactivity plays a crucial role in advancing our understanding of chemical bonding or reaction mechanisms. The aim of this work is to represent a complete and extended theoretical study of BaLi+ molecular ion including ground and highly excited electronic states of 1,3Σ, 1,3Π and 1,3Δ symmetries, dissociated to the first seven dissociation limits. The corresponding potential energy curves (PECs), permanent and transition dipole moments have been investigated. These calculations were performed using the multireference configuration interaction (MRCI) method in combination with optimized basis sets and non-empirical pseudopotentials (ECP) for both Ba and Li atoms. Afterwards, the spin–orbit (SO) operator is incorporated in valence MRCI calculation using optimized relativistic spin–orbit pseudopotentials and 16 Ω states are generated and splitted into Λ-S states. The SO effect gives rise to a more complicated structure of electronic states presented in PEC and permanent and transition dipole moments. Nonadiabatic coupling matrix elements between the five lowest 1Σ+ states are also presented for the nonrelativistic results. Based on the vibrational radiative lifetime and Franck–Condon calculation, the possibilities of laser cooling of this system have been also discussed.

BasisOpt: A Python package for quantum chemistry basis set optimization.

The accuracy and efficiency of molecular quantum chemical calculations depend critically on the basis set used. However, the development of novel basis sets is hindered because much of the literature relies on the use of opaque processes and tools that are not publicly available. We present here BasisOpt, a tool for the automated optimization of basis sets with an easy-to-use framework. It features an open and accessible workflow for basis set optimization that can be easily adapted to almost any quantum chemistry program, a standardized approach to testing basis sets, and visualization of both the optimized basis sets and the optimization process. We provide examples of usage in realistic basis set optimization scenarios where: (i) a density fitting basis set is optimized for He, Ne, and Ar; (ii) the exponents of the def2-SVP basis are re-optimized for a set of molecules rather than atoms; and (iii) a large, almost saturated basis of sp primitives is automatically reduced to (10s5p) while achieving the lowest energy for such a basis set composition.

Theoretical Investigation on Highly Efficient Quinacridone Derivatives for Green Dopant OLEDs: A DFT Simulation

The present computational work deals with the Quinacridone green dopant theoretical organic light emitting diode molecule has been carried out with density functional theory by using Gaussian09 package. All the quantum chemical calculations have been performed with HF, B3LYP and B3PW91 functional methods. The structural parameter, bond topological analysis and the corresponding electrostatic and transport properties of the OLED molecule has been calculated. The laplacian of electron density and bond ellipticity of molecule have been studied for various optimized methods. The atomic charges of the molecule for different optimized methods has been analysed with AIM, MPA and NPA charges. The HLG of the molecule are calculated from different optimized basis sets. The HF method value is 8.49 eV. The B3LYP and B3PW91 methods energy values are 3.13 eV and 3.12 eV respectively. These values are most equal to the energy gap obtained from density of states (DOS) spectrum. Hence, the ESP shows that expend of O-atoms and the charge accumulated through Quinacridone OLED molecule. The grateful Quinacridone green dopant derivative molecule is high quantum efficiency, longer lifetime and very useful to industrial organic pigment of these molecules.

Optimal Small Basis Set and Geometric Counterpoise Correction for DFT Computations.

In the present study, we have examined the performance of the various small basis sets and their geometric counterpoise (gCP) corrections for DFT computations. The original gCP correction scheme includes four adjustable parameters tailored for each method and basis set, but we find that the use of a single scaling parameter also yields fair results. We term this simplified scheme unity-gCP, which can be straightforwardly applied for devising a reasonable correction for an arbitrary basis set. With the use of unity-gCP, we have examined a systematic set of medium-sized basis sets, and we find 6-31+G(2d) to be the optimal balance between accuracy and computational efficiency. On the other hand, less balanced basis sets, even larger ones, can show significantly worse accuracy; the inclusion of gCP may even lead to severe overcorrections. Thus, sufficient validations would be imperative before the general application of gCP for a particular basis set. For 6-31+G(2d), a welcoming finding is that its gCP has small magnitudes, and thus, it also yields adequate results without gCP corrections. This observation echoes that for the ωB97X-3c method, which uses an optimized double-ζ basis set (vDZP) without the inclusion of gCP. In an attempt to improve vDZP by mimicking the somewhat better-performing 6-31+G(2d), we partially decontract the outer functions of vDZP. The resulting basis set, which we termed vDZ+(2d), generally yields improved results. Overall, the vDZP and the new vDZ+(2d) basis sets pave a way for obtaining reasonable results more efficiently for a wide range of systems than the practice of using a triple- or quadruple-ζ basis set in DFT calculations.

Optimized basis sets for DMRG calculations of quantum chains of rotating water molecules.

In this contribution, we employ a density matrix-based optimization procedure to obtain customized basis functions to describe chains of rotating water molecules in interaction regimes associated with different intermolecular distances. This procedure is shown to yield a very compact basis with a clear truncation criterion based on the population of the single particle basis functions. For the water trimer, we discuss the convergence behavior of several properties and show it to be superior when compared to an energy-based truncated basis. It is demonstrated that the optimized basis reduces the necessary number of basis functions by at least an order of magnitude. Finally, the optimization procedure is employed to study larger chains of up to ten water molecules. The formation of hydrogen bonds as well as its impact on the net polarization of the chain is discussed.

EEG-LLAMAS: A low-latency neurofeedback platform for artifact reduction in EEG-fMRI

Simultaneous EEG-fMRI is a powerful multimodal technique for imaging the brain, but its use in neurofeedback experiments has been limited by EEG noise caused by the MRI environment. Neurofeedback studies typically require analysis of EEG in real time, but EEG acquired inside the scanner is heavily contaminated with ballistocardiogram (BCG) artifact, a high-amplitude artifact locked to the cardiac cycle. Although techniques for removing BCG artifacts do exist, they are either not suited to real-time, low-latency applications, such as neurofeedback, or have limited efficacy. We propose and validate a new open-source artifact removal software called EEG-LLAMAS (Low Latency Artifact Mitigation Acquisition Software), which adapts and advances existing artifact removal techniques for low-latency experiments. We first used simulations to validate LLAMAS in data with known ground truth. We found that LLAMAS performed better than the best publicly-available real-time BCG removal technique, optimal basis sets (OBS), in terms of its ability to recover EEG waveforms, power spectra, and slow wave phase. To determine whether LLAMAS would be effective in practice, we then used it to conduct real-time EEG-fMRI recordings in healthy adults, using a steady state visual evoked potential (SSVEP) task. We found that LLAMAS was able to recover the SSVEP in real time, and recovered the power spectra collected outside the scanner better than OBS. We also measured the latency of LLAMAS during live recordings, and found that it introduced a lag of less than 50 ms on average. The low latency of LLAMAS, coupled with its improved artifact reduction, can thus be effectively used for EEG-fMRI neurofeedback. A limitation of the method is its use of a reference layer, a piece of EEG equipment which is not commercially available, but can be assembled in-house. This platform enables closed-loop experiments which previously would have been prohibitively difficult, such as those that target short-duration EEG events, and is shared openly with the neuroscience community.

On basis set optimisation in quantum chemistry

In this article, we propose general criteria to construct optimal atomic centered basis sets in quantum chemistry. We focus in particular on two criteria, one based on the ground-state one-body density matrix of the system and the other based on the ground-state energy. The performance of these two criteria are then numerically tested and compared on a parametrized eigenvalue problem, which corresponds to a one-dimensional toy version of the ground-state dissociation of a diatomic molecule.

Preservation of EEG spectral power features during simultaneous EEG-fMRI.

Electroencephalographic (EEG) data quality is severely compromised when recorded inside the magnetic resonance (MR) environment. Here we characterized the impact of the ballistocardiographic (BCG) artifact on resting-state EEG spectral properties and compared the effectiveness of seven common BCG correction methods to preserve EEG spectral features. We also assessed if these methods retained posterior alpha power reactivity to an eyes closure-opening (EC-EO) task and compared the results from EEG-informed fMRI analysis using different BCG correction approaches. Electroencephalographic data from 20 healthy young adults were recorded outside the MR environment and during simultaneous fMRI acquisition. The gradient artifact was effectively removed from EEG-fMRI acquisitions using Average Artifact Subtraction (AAS). The BCG artifact was corrected with seven methods: AAS, Optimal Basis Set (OBS), Independent Component Analysis (ICA), OBS followed by ICA, AAS followed by ICA, PROJIC-AAS and PROJIC-OBS. EEG signal preservation was assessed by comparing the spectral power of traditional frequency bands from the corrected rs-EEG-fMRI data with the data recorded outside the scanner. We then assessed the preservation of posterior alpha functional reactivity by computing the ratio between the EC and EO conditions during the EC-EO task. EEG-informed fMRI analysis of the EC-EO task was performed using alpha power-derived BOLD signal predictors obtained from the EEG signals corrected with different methods. The BCG artifact caused significant distortions (increased absolute power, altered relative power) across all frequency bands. Artifact residuals/signal losses were present after applying all correction methods. The EEG reactivity to the EC-EO task was better preserved with ICA-based correction approaches, particularly when using ICA feature extraction to isolate alpha power fluctuations, which allowed to accurately predict hemodynamic signal fluctuations during the EEG-informed fMRI analysis. Current software solutions for the BCG artifact problem offer limited efficiency to preserve the EEG spectral power properties using this particular EEG setup. The state-of-the-art approaches tested here can be further refined and should be combined with hardware implementations to better preserve EEG signal properties during simultaneous EEG-fMRI. Existing and novel BCG artifact correction methods should be validated by evaluating signal preservation of both ERPs and spontaneous EEG spectral power.

Optimal pupil basis set for telescope-coronagraph design and perturbation analysis based on the method of moments.

This paper concerns optimization and analysis of telescope-coronagraph systems for direct imaging of exoplanets. In this paper, the coronagraph system, with arbitrary pupil geometry, is theoretically considered, and the governing equation for the pupil design is derived. The method of moments is applied to solve the generalized energy-concentration eigenvalue problem to obtain the optimal pupil apodization and complete sets of orthonormal basis functions for arbitrary pupil geometries. The method yields eigenvalues indicating the fraction of starlight energy encircled in the area of the focal-plane mask (FPM), where starlight can be occulted and/or nulled. In other words, a higher eigenvalue implies less leakage/spillover of light outside of the FPM region and into the planet-discovery zone. Thus, a higher eigenvalue supports better starlight suppression for a given type of coronagraph. This methodology is useful for semi-quantitatively ranking different modes of perturbation with respect to energy spillage in the focal plane independent of coronagraph design details. A model-order-reduction-based sensitivity analysis is conducted to investigate the coupling between different pupil modes induced by aberrations. A pupil mode recovery scheme is presented to offer a theoretically rigorous and computationally efficient approach to reconstruct the optimal pupil mode under an arbitrary phase perturbation. The reconstruction coefficients and recovery-effectiveness factors are derived theoretically and demonstrated numerically. Several numerical examples, including the LUVOIR A and B pupils, are provided to validate and demonstrate the applicability of the proposed methods. The reported methodology enables model-order reduction based on degree of focal-plane energy concentration and reconstruction of optimal pupil apodization vis-á-vis phase aberrations using a precomputed basis set. These features should enhance computational efficiency for coronagraph design and sensitivity analysis.

Ballistocardiogram suppression in concurrent EEG-MRI by dynamic modeling of heartbeats.

The ballistocardiogram (BCG), the induced electric potentials by the head motion originating from heartbeats, is a prominent source of noise in electroencephalography (EEG) data during magnetic resonance imaging (MRI). Although methods have been proposed to suppress the BCG artifact, more work considering the variability of cardiac cycles and head motion across time and subjects is needed to provide highly robust correction. Here, a method called “dynamic modeling of heartbeats” (DMH) is proposed to reduce BCG artifacts in EEG data recorded inside an MRI system. The DMH method models BCG artifacts by combining EEG points at time instants with similar dynamics. The modeled BCG artifact is then subtracted from the EEG recording to suppress the BCG artifact. Performance of DMH was tested and specifically compared with the Optimal Basis Set (OBS) method on EEG data recorded inside a 3T MRI system with either no MRI acquisition (Inside‐MRI), echo‐planar imaging (EPI‐EEG), or fast MRI acquisition using simultaneous multi‐slice and inverse imaging methods (SMS‐InI‐EEG). In a steady‐state visual evoked response (SSVEP) paradigm, the 15‐Hz oscillatory neuronal activity at the visual cortex after DMH processing was about 130% of that achieved by OBS processing for Inside‐MRI, SMS‐InI‐EEG, and EPI‐EEG conditions. The DMH method is computationally efficient for suppressing BCG artifacts and in the future may help to improve the quality of EEG data recorded in high‐field MRI systems for neuroscientific and clinical applications.

Non-Relativistic Electronic-Structure Computation of Neutral and Cationic Systems [Fr2, Fr-AEM+ (AEM= Ca, Sr, Ba)

The experimental field of ultracold ion-atom mixtures including an alkali-metal atom and an alkaline-earth-metal ion as well as of homonuclear alkali dimers has paved the way for creating and manipulating the ultracold molecules. The present paper is focused on a study of molecules such us francium dimer and a comparative spectroscopic investigation of the cationic systems Fr-(Ca+, Sr+, Ba+). We adopt a computational scheme without spin-orbit coupling reposed on the full configuration interaction and semi-empirical pseudo-potential theory of the atomic cores Fr+, Ca2+, Sr2+, and Ba2+ with extended and optimized basis sets. We have determined the adiabatic potentials with their relative spectroscopic constants, the electric dipole moments and the vibrational levels spacings for the 1,3Σu,g+ and 1,3Σ+ electronic states for Fr2 and Fr-AEM+, respectively, correlated toward {Fr(7s) + Fr(7s, 7p, 6d, 8s, 8p)}, {Ca(4s2, 4s4p, 4s3d), Sr(5s2, 5s5p, 5s4d), Ba(6s2, 6s6p, 6s5d) + Fr+}, and {Ca+(4s, 3d), Sr+(5s, 4d), Ba+(6s, 5d) + Fr(7s, 7p)}. The accuracy and reliability of the current results are discussed by comparing with theoretical data available in the literature. The occurrence of some avoided crossings between the neighboring electronic states is leading to a charge or excitation transfer for atom-ion collisions in the diverse charge or excited states. The Σ+-Σ+ transitions are determined in order to evaluate the future radiative lifetimes of vibrational states serving the direct laser cooling.

Complex energies and transition dipoles for shape-type resonances of uracil anion from stabilization curves via Padé.

Absorption of slow moving electrons by neutral ground state nucleobases has been known to produce resonance metastable states. There are indications that such metastable states may play a key role in DNA/RNA damage. Therefore, herein, we present an ab initio non-Hermitian investigation of the resonance positions and decay rates for the low lying shape-type states of the uracil anion. In addition, we calculate the complex transition dipoles between these resonance states. We employ the resonance via Padé (RVP) method to calculate these complex properties from real stabilization curves by analytical dilation into the complex plane. This method has already been successfully applied to many small molecular systems, and herein, we present the first application of RVP to a medium-sized system. The presented resonance energies are optimized with respect to the size of the basis set and compared with previous theoretical studies and experimental findings. Complex transition dipoles between the shape-type resonances are computed using the optimal basis set. The ability to calculate ab initio energies and lifetimes of biologically relevant systems paves the way for studying reactions of such systems in which autoionization takes place, while the ability to also calculate their complex transition dipoles opens the door for studying photo-induced dynamics of such biological molecules.

EEG-fMRI: Ballistocardiogram Artifact Reduction by Surrogate Method for Improved Source Localization.

For the analysis of simultaneous EEG-fMRI recordings, it is vital to use effective artifact removal tools. This applies in particular to the ballistocardiogram (BCG) artifact which is difficult to remove without distorting signals of interest related to brain activity. Here, we documented the use of surrogate source models to separate the artifact-related signals from brain signals with minimal distortion of the brain activity of interest. The artifact topographies used for surrogate separation were created automatically using principal components analysis (PCA-S) or by manual selection of artifact components utilizing independent components analysis (ICA-S). Using real resting-state data from 55 subjects superimposed with simulated auditory evoked potentials (AEP), both approaches were compared with three established BCG artifact removal methods: Blind Source Separation (BSS), Optimal Basis Set (OBS), and a mixture of both (OBS-ICA). Each method was evaluated for its applicability for ERP and source analysis using the following criteria: the number of events surviving artifact threshold scans, signal-to-noise ratio (SNR), error of source localization, and signal variance explained by the dipolar model. Using these criteria, PCA-S and ICA-S fared best overall, with highly significant differences to the established methods, especially in source localization. The PCA-S approach was also applied to a single subject Berger experiment performed in the MRI scanner. Overall, the removal of BCG artifacts by the surrogate methods provides a substantial improvement for the analysis of simultaneous EEG-fMRI data compared to the established methods.

Photoemission Spectra from the Extended Koopman's Theorem, Revisited.

The Extended Koopman’s Theorem (EKT) provides a straightforward way to compute charged excitations from any level of theory. In this work we make the link with the many-body effective energy theory (MEET) that we derived to calculate the spectral function, which is directly related to photoemission spectra. In particular, we show that at its lowest level of approximation the MEET removal and addition energies correspond to the so-called diagonal approximation of the EKT. Thanks to this link, the EKT and the MEET can benefit from mutual insight. In particular, one can readily extend the EKT to calculate the full spectral function, and choose a more optimal basis set for the MEET by solving the EKT secular equation. We illustrate these findings with the examples of the Hubbard dimer and bulk silicon.

Property-oriented basis sets for computation of atomization energies.

The SBO4-DZ(d,p)-3G basis sets introduced in a previous paper have been modified to improve their performance in the calculation of the atomization energies of organic molecules (pure or substituted hydrocarbons). The first step was to explore the possibility of improving those basis sets by adding a second D shell. The scale factor for an additional "D-3G" shell was first studied by minimizing the total energies. In a second step, the scale factor was calculated by optimizing atomization energies directly (instead total energies). This way the results obtained were very similar to those of the cc-pV5Z basis sets. Finally, we optimized simplified box orbital (SBO) basis sets for different methods obtaining optimal SBO basis sets for HF, DFTs, and MP2.

SpectrumSDT: A program for parallel calculation of coupled rotational-vibrational energies and lifetimes of bound states and scattering resonances in triatomic systems

We present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over the user-defined regions of potential energy surface, which helps to classify these states. In this release of the code, SpectrumSDT is limited to ABA-type molecules with wave functions that do not extend into the regions near Eckart singularities. Program summaryProgram title: SpectrumSDTCPC Library link to program files:https://doi.org/10.17632/9gftxjs4yk.1Developer's repository link:https://github.com/IgorGayday/SpectrumSDTLicensing provisions: GNU General Public License 3 (GPL)Programming language: FortranNature of problem: Calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems.Solution method: A Hamiltonian matrix is built in APH coordinates using an optimal 2D basis set, adjusted for a given problem. A complex absorbing potential (CAP) is added to define a boundary condition for calculation of scattering resonances above the dissociation threshold. The eigenstates of the Hamiltonain matrix are found using a state-of-the-art iterative eigensolver.Restrictions: The present version is restricted to ABA-molecules and wave functions that do not extend into linear and equilateral triangle configurations.Additional comments including restriction and unusual features: Probabilities and lifetimes of the wave functions can be calculated in user-defined regions on the PES, which allows to analyze their localization properties (i.e. automatic isotopomer assignment) and obtain channel-specific lifetimes for scattering resonances.

The structure and stability of faecal pigment-Zinc(II) complexes

This work presents an in-depth study on the nature of the faecal pigment-zinc(II) complexes using spectroscopic, thermodynamic and computational studies towards a molecular level understanding regarding its structure, complexation and stability. The analysis of faecal pigments (FPs), specifically urobilin (UB) and stercobilin (SB), is often carried out using Schlesinger's test, that uses the zinc complexation induced enhancement of FPs fluorescence. It was observed that in addition to the expected 1:1 stoichiometry, FP-Zn(II) complex with 1:2 stoichiometry also form. This was confirmed by the ESI-MS mass spectral fragmentation patterns. A rigorous benchmarking process towards using optimized basis set and functionals for molecular orbital TD-DFT calculations on UB-Zn(II) complex suggested the use of B3LYP hybrid functional and LANL2DZ basis set as the optimized combination. Molecular geometries and transition energies predicted from MO calculations corroborated well with FTIR and mass spectrometric results. FP-Zn(II) complexation equilibria in aqueous media involve disaggregation of higher FPs followed by metal-ligand complexation. The binding constant values of FP-Zn(II) complexes were estimated to be 101 M−1 & 22 M−1 for 1:1 and 1:2 stoichiometries of SB-Zn(II) complexes and 105 M−1 & 11 M−1 for 1:1 and 1:2 stoichiometries of UB-Zn(II) complexes in aqueous media. For the 1:1 complexes, the enthalpy (∆H0) and entropy (∆S0) values for SB-Zn(II) are 65 k J mol−1 and 269 J K−1 mol−1, respectively. Similarly, enthalpy (∆H0) and entropy (∆S0) for UB-Zn(II) complexes are 69 kJ mol−1 and 256 J K−1 mol−1, respectively. This understanding of the structure and thermodynamics of FP-Zn(II) complex is expected to aid in developing aqueous phase analytical strategies towards the fluorescence-based analysis of FPs, an important component of water quality analysis.

Basis Set Selection for Calculation of Structural and Electronic Properties of Systems Incorporating a Superoxide Radical in an Aqueous Medium

In this work, computer simulation has been carried out, and the molecular parameters of oxygen and a superoxide ion have been calculated to select the most optimal basis set of functions for further quantum mechanical calculations that include the presence of reactive oxygen species. For each particle, the equilibrium bond lengths and averaged polarizabilities in a continuous dielectric aqueous medium are obtained with the Conductor-like Polarizable Continuum Model (CPCM) and Solvation Model based on Density (SMD). Calculations for the 16 basic sets are conducted using the Orca software package. The obtained numerical values are compared with experimental data. The electron affinity energy of the oxygen molecule is used as the main selection criterion. The total time of computer calculations for each basis set is considered, and the most optimal basis sets are selected. The basis sets 6-31+G(d), 6-311+G, def2-TZVPD, and aug-cc-pVDZ are recommended for numerical calculations of molecular systems incorporating molecular oxygen and superoxide radical as its reduction product.

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

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 Schrödinger 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.