Atomic Orbital Basis Sets Research Articles

Finite-order method to calculate approximate density matrices in the Fock-space multireference coupled cluster theory

An efficient approach to calculate approximate pure-state and transition reduced density matrices in the framework of the multireference relativistic Fock-space coupled cluster (FS CC) theory is proposed. The method is based on the effective operator formalism and consists of the direct substitution of the FS CC Ansatz for a wave operator into the effective operator expression with the subsequent truncation of expansion at the terms quadratic in cluster amplitudes. The final density matrix is defined by active-space density matrices of different ranks ‘dressed’ with contributions from cluster operators. The method gives a connected expression for pure-state density matrices, provided that the intermediate normalisation condition is fulfilled. Moreover, under some additional assumptions, the connectivity can also be ensured for calculated transition property matrix elements and natural transition spinors. The developed technique allows for fast and accurate calculations of one-particle reduced density matrices for a wide range of electronic states. A pilot application of the new technique to construct averaged atomic natural orbital (ANO) basis sets for fully relativistic electronic structure calculations is presented.

Machine-Learning-Based Interatomic Potentials for Group IIB to VIA Semiconductors: Toward a Universal Model.

Rapid advancements in machine-learning methods have led to the emergence of machine-learning-based interatomic potentials as a new cutting-edge tool for simulating large systems with ab initio accuracy. Still, the community awaits universal interatomic models that can be applied to a wide range of materials without tuning neural network parameters. We develop a unified deep-learning interatomic potential (the DPA-Semi model) for 19 semiconductors ranging from group IIB to VIA, including Si, Ge, SiC, BAs, BN, AlN, AlP, AlAs, InP, InAs, InSb, GaN, GaP, GaAs, CdTe, InTe, CdSe, ZnS, and CdS. In addition, independent deep potential models for each semiconductor are prepared for detailed comparison. The training data are obtained by performing density functional theory calculations with numerical atomic orbitals basis sets to reduce the computational costs. We systematically compare various properties of the solid and liquid phases of semiconductors between different machine-learning models. We conclude that the DPA-Semi model achieves GGA exchange-correlation functional quality accuracy and can be regarded as a pretrained model toward a universal model to study group IIB to VIA semiconductors.

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive.

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

Importance profiles. Visualization of atomic basis set requirements

Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function |α⟩ centered on some nucleus can be visualized by projecting |α⟩ on the set of numerically represented occupied orbitals |ψi⟩ as I0(α)=∑i⟨α|ψi⟩⟨ψi|α⟩ . Choosing α to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visualization I0(α) has the important property 0⩽I0(α)⩽1 which allows unambiguous interpretation. We also propose a straightforward generalization of the importance profile for polyatomic applications I(α) , in which the importance of a test function |α⟩ is measured as the increase in projection from the atomic minimal basis. We exemplify the methods with importance profiles computed for atoms from the first three rows, and for a set of chemically diverse diatomic molecules. We find that the importance profile offers a way to visualize the atomic basis set requirements for a given system in an a priori manner, provided that a fully numerical reference wave function is available.

Basis Set Calculations of Heavy Atoms

Most modern calculations of many-electron atoms use basis sets of atomic orbitals. An accurate account for electronic correlations in heavy atoms is a very difficult computational problem, and an optimization of the basis sets can reduce computational costs and increase final accuracy. Here, we propose a simple differential ansatz to form virtual orbitals from the Dirac–Fock orbitals of the core and valence electrons. We use basis sets with such orbitals to calculate different properties in Cs including hyperfine structure constants and QED corrections to the valence energies and to the E1 transition amplitudes.

Valence-to-core X-ray emission spectroscopy of transition metal tetrahalides: mechanisms governing intensities.

Valence-to-core (VtC) X-ray emission spectroscopy offers the opportunity to probe the valence electronic structure of a system filtered by selection rules. From this, the nature of its ligands can be inferred. While a preceding 1s ionization creates a core hole, in VtC XES this core hole is filled with electrons from mainly ligand based orbitals. In this work, we investigated the trends in the observed VtC intensities for a series of transition metal halides, which spans the first row transition metals from manganese to copper. Further, with the aid of computational studies, we corroborated these trends and identified the mechanisms and factors that dictate the observed intensity trends. Small amounts of metal p contribution to the ligand orbitals are known to give rise to intensity of a VtC transition. By employing an LCAO (linear combination of atomic orbitals) approach, we were able to assess the amount of metal p contribution to the ligand molecular orbitals, as well as the role of the transition dipole moment and correlate these factors to the experimentally observed intensities. Finally, by employing an ano (atomic natural orbital) basis set within the calculations, the nature of the metal p contribution (3p vs. 4p) was qualitatively assessed and their trends discussed within the same transition metal halide series.

An atom-in-molecule adaptive polarized valence single-ζ atomic orbital basis for electronic structure calculations.

Many low-cost or semiempirical quantum mechanical-based electronic structure methods suffer from the use of unpolarized minimal atomic orbital (AO) basis sets. In this work, we overcome this limitation by a fully DFT variationally optimized, adaptive minimal basis set consistently available for the elements up to radon (Z = 86). The new key feature is to make the linear coefficients of the primitive Gaussians in a contracted AO dependent on the effective atomic charge of the atom in the molecule, i.e., each symmetry-unique atom obtains its "own" specifically adapted basis functions. In this way, the physically important "breathing" of the AOs in a molecule with (a) atomic charge (expansion/contraction for anionic/cationic states) and (b) the number of close-lying bonded neighbor atoms is accounted for. The required atomic charges are obtained from a specially developed extended Hückel type Hamiltonian and the coordination numbers from the molecule geometry. Proper analytical derivatives of the resulting adaptive basis functions can easily be derived. Moreover, the basis functions are electric field-dependent, thus improving the description of, e.g., dipole moments and polarizabilities. The new basis set termed q-vSZP (charge dependent valence single-ζ, polarized) is thoroughly benchmarked for atomic/molecular and thermochemical properties compared to standard minimal and double-ζ basis sets at the DFT level with the accurate ωB97X-D4 functional. It is shown that q-vSZP is clearly superior to existing minimal basis sets, often reaching double-ζ quality or even better results. We expect it to be the optimal choice in future semiempirical quantum mechanical methods.

DFT Study of WS2-Based Nanotubes Electronic Properties under Torsion Deformations.

In this study, the influence of torsional deformations on the properties of chiral WS2-based nanotubes was investigated. All calculations presented in this study were performed using the density functional theory (DFT) and atomic gaussian type orbitals basis set. Nanotubes with chirality indices (8, 2), (12, 3), (24, 6) and (36, 9) corresponding to diameters of 10.68 Å, 14.90 Å, 28.26 Å and 41.90 Å, respectively, are examined. Our results reveal that for nanotubes with smaller diameters, the structure obtained through rolling from a slab is not optimal and undergoes spontaneous deformation. Furthermore, this study demonstrates that the nanotube torsion deformation leads to a reduction in the band gap. This observation suggests the potential for utilizing such torsional deformations to enhance the photocatalytic activity of the nanotubes.

Water Solvated Zn(II)-Guanine Complex: Structural Aspects and Luminescence Properties.

Understanding the role of metal ions in living organisms and their interactions with biological compounds is fundamental for our health and for developing technological devices for bioinorganic applications. In this work, structural aspects and photophysical mechanisms involved in the luminescence of the Zn(II)-guanine complex in water were studied by using computational quantum chemical methods, providing molecular-level explanations for reported experimental findings. Structural aspects were investigated with def2-SVP basis sets, Density Functional Theory, Resolution of Identity Algebraic Diagrammatic Construction in Second-Order (RI-ADC(2)), Polarizable Continuum Model (PCM), and Conductor-like Screening Model (COSMO) methods. Spectroscopic properties and photophysical deactivation mechanisms were explored with the atomic natural orbital basis sets including relativistic and semicore correlation (ANO-RCC-VDZP) basis sets, Multistate Complete-Active-Space Second-Order Perturbation Theory (MS-CASPT2), and Polarizable Continuum Model (PCM) methods. Our results indicate that Zn(II) ions bind preferentially to the N7 position, and three water molecules in its coordination sphere are sufficient for describing the photophysical properties. The complexation with Zn(II) ions and solvation effects favor fluorescence because the minimum energy region of the S1 (La) (1ππ*) ((La)min) potential energy hypersurface is stabilized, the (La/GS) crossing region is destabilized, and a high energetic barrier along the pathway from the (La)min and (La/GS) regions hampers fast nonradiative return of the electronic population to the ground state, as observed for isolated 9H-guanine.

Ab initio electronic structure calculations based on numerical atomic orbitals: Basic fomalisms and recent progresses

AbstractThe numerical atomic orbital (NAO) basis sets offer a computationally efficient option for electronic structure calculations, as they require fewer basis functions compared with other types of basis sets. Moreover, their strict localization allows for easy combination with current linear scaling methods, enabling efficient calculation of large physical systems. In recent years, NAO bases have become increasingly popular in modern electronic structure codes. This article provides a review of the ab initio electronic structure calculations using NAO bases. We begin by introducing basic formalisms of the NAO‐based electronic structure method, including NAO base set generation, self‐consistent calculations, force, and stress calculations. We will then discuss some recent advances in the methods based on the NAO bases, such as real‐time dependent density functional theory (rt‐TDDFT), efficient implementation of hybrid functionals, and other advanced electronic structure methods. Finally, we introduce the ab initio tight‐binding model, which can be generated directly after the self‐consistent calculations. The model allows for efficient calculation of electronic structures, and the associated topological, and optical properties of the systems.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory Structure and Mechanism > Computational Materials Science

Semiempirical Methods for Molecular Systems in Strong Magnetic Fields.

A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, || ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, || > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.

Automatic Generation of Accurate and Cost-Efficient Auxiliary Basis Sets.

We have recently discussed an algorithm to automatically generate auxiliary basis sets (ABSs) of the standard form for density fitting (DF) or resolution-of-the-identity (RI) calculations in a given atomic orbital basis set (OBS) of any form, such as Gaussian-type orbitals, Slater-type orbitals, or numerical atomic orbitals [J. Chem. Theory Comput. 2021, 17, 6886]. In this work, we study two ways to reduce the cost of such automatically generated ABSs without sacrificing their accuracy. We contract the ABS with a singular value decomposition proposed by Kállay [J. Chem. Phys. 2014, 141, 244113], used here in a somewhat different setting. We also drop the high-angular momentum functions from the ABS, as they are unnecessary for global fitting methods. Studying the effect of these two types of truncations on Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) calculations on a chemically diverse set of first- and second-row molecules within the RI/DF approach, we show that accurate total and atomization energies can be achieved by a combination of the two approaches with significant reductions in the size of the ABS. While the original approach yields ABSs whose number of functions NbfABS scales with the number of functions in the OBS, NOBSbf, as NABSbf = γNOBSbf with the prefactor , the reduction schemes of this work afford results of essentially the same quality as the original unpruned and uncontracted ABS with γ ≈ 5-6, while an accuracy that may suffice for routine applications is achievable with a further reduced ABS with γ ≈ 3-4. The observed errors are similar at HF and MP2 levels of theory, suggesting that the generated ABSs are highly transferable and can also be applied to model challenging properties with high-level methods.

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments.

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

Hyper-Rayleigh scattering optical activity: Theory, symmetry considerations, and quantum chemistry applications.

This work reports on the first computational quantum-chemistry implementation of the hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. First, from the basics of the theory, which is based on quantum electrodynamics, and focusing on the electric dipole, magnetic-dipole, and electric-quadrupole interactions, the equations for the simulation of the differential scattering ratios of HRS-OA are re-derived. Then, for the first time, computations of HRS-OA quantities are presented and analyzed. They have been enacted on a prototypical chiral organic molecule (methyloxirane) at the time-dependent density functional theory level using a broad range of atomic orbital basis sets. In particular, (i) we analyze the basis set convergence, demonstrating that converged results require basis sets with both diffuse and polarization functions, (ii) we discuss the relative amplitudes of the five contributions to the differential scattering ratios, and (iii) we study the effects of origin-dependence and derived the expression of the tensor shifts and we prove the origin-independence of the theory for exact wavefunctions. Our computations show the ability of HRS-OA as a nonlinear chiroptical method, able to distinguish between the enantiomers of the same chiral molecule.

Atomic Electronic Structure Calculations with Hermite Interpolating Polynomials.

We have recently described the implementation of atomic electronic structure calculations within the finite element method with numerical radial basis functions of the form χμ(r) = r-1Bμ(r), where high-order Lagrange interpolating polynomials (LIPs) were used as the shape functions Bμ(r). In this work, we discuss how χμ(r) can be evaluated in a stable manner at small r and also revisit the choice of the shape functions Bμ(r). Three kinds of shape functions are considered: in addition to the continuous LIPs, we consider the analytical implementation of first-order Hermite interpolating polynomials (HIPs) that are continuous, as well as numerical implementations of n-th order ( continuous) HIPs that are expressed in terms of an underlying high-order LIP basis. Furnished with the new implementation, we demonstrate that the first-order HIPs are reliable even with large numbers of nodes and that they also work with nonuniform element grids, affording even better results in atomic electronic structure calculations than LIPs with the same total number of basis functions. We demonstrate that discontinuities can be observed in the spin-σ local kinetic energy τσ in small LIP basis sets, while HIP basis sets do not suffer from such issues; however, either set can be used to reach the complete basis set limit with smooth τσ. Moreover, we discuss the implications of HIPs on calculations with meta-GGA functionals with a number of recent meta-GGA functionals, and we find most Minnesota functionals to be ill-behaved. We also examine the potential usefulness of the explicit control over the derivative in HIPs for forming numerical atomic orbital basis sets, but we find that confining potentials are still likely a better option.

Meta-GGA Density Functional Calculations on Atoms with Spherically Symmetric Densities in the Finite Element Formalism.

Density functional calculations on atoms are often used for determining accurate initial guesses as well as generating various types of pseudopotential approximations and efficient atomic-orbital basis sets for polyatomic calculations. To reach the best accuracy for these purposes, the atomic calculations should employ the same density functional as the polyatomic calculation. Atomic density functional calculations are typically carried out employing spherically symmetric densities, corresponding to the use of fractional orbital occupations. We have described their implementation for density functional approximations (DFAs) belonging to the local density approximation (LDA) and generalized gradient approximation (GGA) levels of theory as well as Hartree-Fock (HF) and range-separated exact exchange [Lehtola, S. Phys. Rev. A 2020, 101, 012516]. In this work, we describe the extension to meta-GGA functionals using the generalized Kohn-Sham scheme, in which the energy is minimized with respect to the orbitals, which in turn are expanded in the finite element formalism with high-order numerical basis functions. Furnished with the new implementation, we continue our recent work on the numerical well-behavedness of recent meta-GGA functionals [Lehtola, S.; Marques, M. A. L. J. Chem. Phys. 2022, 157, 174114]. We pursue complete basis set (CBS) limit energies for recent density functionals and find many to be ill-behaved for the Li and Na atoms. We report basis set truncation errors (BSTEs) of some commonly used Gaussian basis sets for these density functionals and find the BSTEs to be strongly functional dependent. We also discuss the importance of density thresholding in DFAs and find that all of the functionals studied in this work yield total energies converged to 0.1 μEh when densities smaller than 10-11a0-3 are screened out.

A non-self-consistent tight-binding electronic structure potential in a polarized double-ζ basis set for all spd-block elements up to Z = 86.

Existing semiempirical molecular orbital methods suffer from the usually minimal atomic-orbital (AO) basis set used to simplify the calculations. Here, a completely new and consistently parameterized tight-binding electronic structure Hamiltonian evaluated in a deeply contracted, properly polarized valence double-zeta basis set (vDZP) is described. The inner-shell electrons are accounted for by standard, large-core effective potentials and approximations to them. The primary target of this so-called density matrix tight-binding method is to reproduce the one-particle density matrix P of a molecular ωB97X-V range-separated hybrid density functional theory (DFT) calculation in exactly the same basis set. Additional properties considered are orbital energies, dipole polarizabilities and dipole moments, and dipole polarizability derivatives. The key features of the method are as follows: (a) it is non-self-consistent with an overall fixed number of only three required matrix diagonalizations; (b) only AO overlap integrals are needed to construct the effective Hamiltonian matrix; (c) new P-dependent terms emulating non-local exchange are included; and (d) only element-specific empirical parameters (about 50 per element) need to be determined. The method globally achieves a high accuracy for the target properties at a speedup compared to the ωB97X-V/vDZP reference of about 3-4 orders of magnitude. It performs robustly for difficult transition metal complexes, for highly charged or zwitterionic systems, and for chemically unusual bonding situations, indicating a generally robust approximation of the (self-consistent) Kohn-Sham potential. As an example application, the vibrational Raman spectrum of an entire protein with 327 atoms with respect to the DFT reference calculation is shown. This method may be used out-of-the-box to generate molecular/atomic features for machine learning applications or as the basis for accurate high-speed DFT methods.

Further investigations into a Laplace MP2 method using range separated Coulomb potential and orbital selective virtuals: Multipole correction, OSV extrapolation, and critical assessment.

We report further investigations to aid the development of a Laplace MP2 (second-order Møller Plesset) method with a range separated Coulomb potential partitioned into short- and long-range parts. The implementation of the method extensively uses sparse matrix algebra, density fitting techniques for the short-range part, and a Fourier transformation in spherical coordinates for the long-range part of the potential. Localized molecular orbitals are employed for the occupied space, whereas virtual space is described by orbital specific virtual orbitals (OSVs) associated with localized molecular orbitals. The Fourier transform is deficient for very large distances between localized occupied orbitals, and a multipole expansion for widely separated pairs is introduced for the direct MP2 contribution, which is applicable also to non-Coulombic potentials that do not satisfy the Laplace equation. For the exchange contribution, an efficient screening of contributing localized occupied pairs is employed, which is discussed more completely here. To mitigate errors due to the truncation of OSVs, a simple and efficient extrapolation procedure is used to obtain results close to MP2 for the full basis set of atomic orbitals Using a suitable set of default parameters, the accuracy of the approach is demonstrated. The current implementation of the approach is not very efficient, and the aim of this paper is to introduce and critically discuss ideas that can have more general applicability beyond MP2 calculations for large molecules.

Why Is Quantum Chemistry So Complicated?

The myriad tools of quantum chemistry are now widely used by a diverse community of chemists, biologists, physicists, and material scientists. The large number of methods (e.g., Hartree-Fock, density functional theory, configuration interaction, perturbation theory, coupled-clusters, equations of motion, Green's functions, and more) and the multitude of atomic orbital basis sets often give rise to consternation and confusion. In this Perspective, I explain why quantum chemistry has so many different methods and why researchers should understand their relative strengths and weaknesses. I explain how chemistry's use of orbitals and the need for wave functions to be antisymmetric causes computational-effort scaling proportional to the cube or higher power of the number of orbitals. I also illustrate how the fact that the Schrödinger equation's energies are extensive makes it difficult to extract intensive properties such as bond and excitation energies, ionization potentials, and electron affinities.

Automatic purpose-driven basis set truncation for time-dependent Hartree–Fock and density-functional theory

Real-time time-dependent density-functional theory (RT-TDDFT) and linear response time-dependent density-functional theory (LR-TDDFT) are two important approaches to simulate electronic spectra. However, the basis sets used in such calculations are usually the ones designed mainly for electronic ground state calculations. In this work, we propose a systematic and robust scheme to truncate the atomic orbital (AO) basis set employed in TDDFT and TD Hartree–Fock (TDHF) calculations. The truncated bases are tested for both LR- and RT-TDDFT as well as RT-TDHF approaches, and provide an acceleration up to an order of magnitude while the shifts of excitation energies of interest are generally within 0.2 eV. The procedure only requires one extra RT calculation with 1% of the total propagation time and a simple modification on basis set file, which allows an instant application in any quantum chemistry package supporting RT-/LR-TDDFT calculations. Aside from the reduced computational effort, this approach also offers valuable insight into the effect of different basis functions on computed electronic excitations and further ideas on the design of basis sets for special purposes.