Complete Basis Set Limit Research Articles

Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method.

Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.

Building a New Platform for Significantly Improving Performance of Hartree-Fock and CCSD(T) Correlation Energy Based on Two-Point Complete Basis Set Extrapolation Schemes.

The leading cause of high expense in gold standard coupled cluster theory is that calculations of electronic energies converge exceedingly slowly with an increased basis set size. Extrapolation principally allows for achieving higher-quality outcomes at reduced costs. Numerous extrapolation formulas have been developed, with attempts to predict energies up to the complete basis set limit. Unfortunately, since the intricate shape of the function hinges on the molecular properties with the highest angular momentum of the basis set, the accuracy of the extrapolated energies highly depends on the fitted empirical parameters, which rely on the quality of the data sets for fitting. In this work, to overcome the extrapolation deficiency caused by the very limited data sets and smaller basis sets in the early stages, we constructed a new benchmark platform that includes a broader data set of 183 species (containing open-shell, closed-shell, ionic, and neutral species) and a larger basis set up to aug-cc-pV6Z. The newly optimized parameters can significantly improve the energy-predictive abilities of ten published formulas. Notably, all ten formulas perform quite similarly under the new platform with the reoptimized parameters. Finally, we built an online calculator for researchers to use for these extrapolation schemes. Our work would reignite the interest and applications of the underestimated formulas.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes.

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Probing Antioxidant-Related Properties for Phenolic Compounds.

In this work, properties related to antioxidant-potential mechanisms (such as the bond dissociation enthalpy, BDE, for the homolytic cleavage of the O-H bond and ionization energies, IEs) were determined for phenol, pyrocatechol, and gallic acid (GA). Both the protonated and deprotonated forms of GA were investigated. The Feller-Peterson-Dixon (FPD) composite method was employed with a variety of computational approaches, i.e., density functional theory, Möller-Plesset perturbation theory, and coupled-cluster-based methods, in combination with large correlation consistent basis sets with extrapolation to the complete basis set limit and consideration of core electron correlation effects. FPD results were compared to experimental and computational data available in the literature, presenting good agreement. For example, the FPD BDE (298 K) obtained for phenol, which was based on valence-correlated MP2/CBS calculations with contributions from correlating all electrons, was determined to be 87.56 kcal/mol, a value that is 0.42 kcal/mol lower than the result obtained in the most recent experiments, 87.98 ± 0.62. Calibration against coupled-cluster calculations was also carried out for phenol. We expect that the outcomes gathered here may help in establishing a general protocol for computational chemists that are interested in determining antioxidant-related properties for phenolic compounds with considerable accuracy as well as to motivate future IE measurements (particularly for GA) to be accomplished in the near future.

Diffuse basis functions for explicitly correlated calculations on the heavy p-block: aug-cc-pVnZ-PP-F12 sets for Ga-Kr, In-Xe, and Tl-Rn.

New aug-cc-pVnZ-PP-F12 basis sets (n = D, T, Q) for the heavy p-block elements, Ga-Kr, In-Xe, and Tl-Rn, have been developed by augmenting the cc-pVnZ-PP-F12 sets with additional higher angular momentum diffuse functions. These basis sets have been optimized for use in explicitly correlated F12 calculations, and matching auxiliary basis sets for density fitting of conventional and F12 integrals have also been developed. The new sets have been validated with benchmark CCSD(T)-F12b calculations of electron affinities, where an accelerated convergence to the complete basis set limit is evident. The effect of the additional diffuse functions on electron affinities is shown to be comparable to the effect of correlating the outer-core d electrons.

The formation of nickelalactone in CO2/C2H4 coupling reaction: A benchmark, dispersion correction, and energy decomposition analysis

The oxidative coupling of CO2 and ethylene for synthesizing acrylic acid and its derivatives is considered one of the “dream reactions” in catalysis. The formation of acrylic acid by CO2/C2H4 coupling is hardly possible due to the endothermic nature of the reaction. This work reports a comprehensive study of the nickelalactone formation from CO2/C2H4 coupling over Ni-catalysts. We have evaluated the accuracy of the DLPNO-CCSD(T) method in determining the barrier heights and the reaction energetics for the nickelalactone formation. Extrapolation to the complete basis set limit was performed using two-point extrapolation methods. It was found that the DLPNO-CCSD(T) method, in combination with the complete basis set cc-pVTZ/cc-pVQZ extrapolation, gives the error within 1.0 kcal/mol. To gain a molecular understanding of the formation of acrylic acid by CO2/C2H4 coupling, the distortion-interaction model was used as an energy decomposition method to analyze the inner- and outer-sphere reaction transition states, considering two competing pathways. It was found that i) the inner-sphere reaction is superior to the outer-sphere reaction owing to the lower distortion energy and stronger interactions, ii) three prominent pairs of orbital interactions exist between the Ni-C2H4 complex and the CO2 molecule, and iii) the dispersion correction is crucial to obtaining reliable non-covalent interaction energies.

Production of positronium chloride: A study of the charge exchange reaction between Ps and Cl.

We present cross sections for the formation of positronium chloride (PsCl) in its ground state from the charge exchange between positronium (Ps) and chloride (Cl-) in the range of 10 meV-100eV Ps energy. We have used theoretical models based on the first Born approximation in its three-body formulation. We simulated the collisions between Ps and Cl- using abinitio binding energies and positronic wave functions at both the mean-field and correlated levels extrapolated to the complete basis set limit. The accuracy of these abinitio data was benchmarked on the PsF system with the existing highly accurate results, including the very recent quantum Monte Carlo results. We have investigated Ps excited states up to n = 4. The results suggest that the channel Ps(n = 2) is of particular interest for the production of PsCl in the ground state and shows that an accurate treatment of correlation effects (i.e., electron-electron and electron-positron correlations) leads to a significant change in the magnitude of the PsCl production cross section with respect to the mean-field level.

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.

Adiabatic ionization energies of RuC, RhC, OsC, IrC, and PtC.

The ionization energies (IEs) of RuC, RhC, OsC, IrC, and PtC are assigned by the measurement of their two-photon ionization thresholds. Although late transition metal-carbon bonds are of major importance in organometallic chemistry and catalysis, accurate and precise fundamental thermochemical data on these chemical bonds are mainly lacking in the literature. Based on their two-photon ionization thresholds, in this work, we assign IE(RuC) = 7.439(40) eV, IE(RhC) = 7.458(32) eV, IE(OsC) = 8.647(25) eV, IE(IrC) = 8.933(74) eV, and IE(PtC) = 9.397(32) eV. These experimentally derived IEs are further confirmed through quantum chemical calculations using coupled-cluster single double perturbative triple methods that are extrapolated to the complete basis set limit using a three-parameter mixed Gaussian/exponential extrapolation scheme and corrected for spin-orbit effects using a semiempirical method. The electronic structure and chemical bonding of these MC species are discussed in the context of these ionization energy measurements. The IEs of RuC, RhC, OsC, and IrC closely mirror the IEs of the corresponding transition metal atoms, suggesting that for these species, the (n + 1)s electrons of the transition metals are not significantly involved in chemical bonding.

Theoretical Study on the Mechanisms and Kinetics of Atmospheric Oxidation of Tetrafluoropropyne and Its Analogues.

Tetrafluoropropyne (C3F4) is a potential dielectric in various electrical insulating equipment to replace the most potent industrial greenhouse gas, sulfur hexafluoride. Atmospheric oxidation of C3F4 by OH radicals in the presence of molecular O2 has been investigated theoretically in order to clarify the lifetime and degradation products at mechanistic and kinetic aspects. Energetic minimum-energy pathways for the C3F4 + OH/O2 reactions were calculated in detail using various theoretical methods including density functional M06-2X and CCSD for geometries, CBS-QB3, CCSD(T), and multireference RS2 with extrapolation to the complete basis-set limit for energies. It has been demonstrated that the C3F4 + OH reaction takes place via the bifurcated C-O addition/elimination routes leading to CF3C(OH)═CF and CF3C═C(OH)F radical adducts, where the latter is more preferable in view of the difference in barrier heights (1.3 vs 0.3 kcal/mol), followed by H-migration, HF-elimination, and C-C and C-F bond fission. The atmospheric lifetime of C3F4 was estimated to be about 13 days, which is indicative of a very short-lived substance in the atmosphere. Further degradation of the energy-rich C3F4OH* intermediates by O2 takes place spontaneously in view of the successive barrier-free and highly exothermic pathways, producing a variety of fluorinated acids, anhydrides, biacetyls, and regenerating OH radicals. For comparison, the reactions of C3H4, CF3CCH, and CH3CCF with OH radicals were examined to clarify the F-substitution effect. It is revealed that the reactivity of fluoropropynes could be either reduced by CF3 or enhanced by atomic F attached to the acetylenic carbon. The present work provides a fundamental understanding of the reactions of fluoroalkynes with OH/O2. The use of C3F4 as a promising eco-friendly gaseous dielectric alternative to SF6 has been supported.

High Accuracy Ab Initio Potential Energy Curves and Dipole Moment Functions for the X1Σ+ and a3Π Spin States of the CF+ Diatomic Molecule.

Potential energy curves and dipole moment functions constructed using high-accuracy ab initio methods allow for an in-depth examination of the electronic structure of diatomic molecules. Ab initio computations serve as a valuable complement to experimental data, offering insights into the nature of short-lived molecules such as those encountered within the interstellar medium (ISM). While laboratory experiments provide critical groundwork, the ISM's conditions often permit longer lifetimes for lower stability molecules, enabling unique observations. The CF+ diatomic molecule is one such molecule that has been observed spectroscopically in the ISM. Previous experimental and theoretical work have examined different spectroscopic aspects of the CF+ molecule, but the development of newer, more complete potential energy curves and dipole moment functions allows for even greater insight. We constructed both potential energy curves and dipole moment functions for the ground X1Σ+ and first excited a3Π states of CF+ for both the 12C and 13C isotopologues. The potential energy curves were constructed using coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set limit with corrections from full triple, quadruple, quintuple, and hextuple excitations within a finite-basis coupled cluster wave function as well as corrections from full configuration interaction and relativistic effects. Rovibrational wave functions were calculated using a vibrational Hamiltonian matrix, which moves beyond the harmonic oscillator approximation. The equilibrium bond length, vibrational constant, and rotational constant were reproduced to within 0.00013 Å, 0.28 cm-1, and 0.00045 cm-1, respectively, of experimental values. Experimental transition energies from rovibrational spectra were reproduced with an error of no larger than 0.63 cm-1. The triplet excited state (a3Π) was found to have a longer equilibrium bond length at 1.21069 Å, a vibrational constant of 1611.29 cm-1, and a rotational constant of 1.56376 cm-1. Rovibrational line lists for the 12C and 13C isotopologues for both the X1Σ+ and the excited a3Π states were generated.

Exploring the Tl H potential energy surface: A comparative analysis with group 13 systems and experiment.

Thallium chemistry is experiencing unprecedented importance. Therefore, it is valuable to characterize some of the simplest thallium compounds. Stationary points along the singlet and triplet Tl H potential energy surface have been characterized. Stationary point geometries were optimized with the CCSD(T)/aug-cc-pwCVQZ-PP method. Harmonic vibrational frequencies were computed at the same level of theory while anharmonic vibrational frequencies were computed at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory. Final energetics were obtained with the CCSDT(Q) method. Basis sets up to augmented quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) were employed to obtain energetics in order to extrapolate to the complete basis set limits using the focal point approach. Zero-point vibrational energy corrections were appended to the extrapolated energies in order to determine relative energies at 0 K. It was found that the planar dibridged isomer lies lowest in energy while the linear structure lies highest in energy. The results were compared to other group 13 M H (M = B, Al, Ga, In, and Tl) theoretical studies and some interesting variations are found. With respect to experiment, incompatibilities exist.

Developing correlation-consistent numeric atom-centered orbital basis sets for krypton: Applications in RPA-based correlated calculations.

Localized atomic orbitals are the preferred basis set choice for large-scale explicit correlated calculations, and high-quality hierarchical correlation-consistent basis sets are a prerequisite for correlated methods to deliver numerically reliable results. At present, numeric atom-centered orbital (NAO) basis sets with valence correlation consistency (VCC), designated as NAO-VCC-nZ, are only available for light elements from hydrogen (H) to argon (Ar) [Zhang et al., New J. Phys. 15, 123033 (2013)]. In this work, we extend this series by developing NAO-VCC-nZ basis sets for krypton (Kr), a prototypical element in the fourth row of the periodic table. We demonstrate that NAO-VCC-nZ basis sets facilitate the convergence of electronic total-energy calculations using the Random Phase Approximation (RPA), which can be used together with a two-point extrapolation scheme to approach the complete basis set limit. Notably, the Basis Set Superposition Error (BSSE) associated with the newly generated NAO basis sets is minimal, making them suitable for applications where BSSE correction is either cumbersome or impractical to do. After confirming the reliability of NAO basis sets for Kr, we proceed to calculate the Helmholtz free energy for Kr crystal at the theoretical level of RPA plus renormalized single excitation correction. From this, we derive the pressure-volume (P-V) diagram, which shows excellent agreement with the latest experimental data. Our work demonstrates the capability of correlation-consistent NAO basis sets for heavy elements, paving the way toward numerically reliable correlated calculations for bulk materials.

Capturing the electron-electron cusp with the coupling-constant averaged exchange-correlation hole: A case study for Hooke's atoms.

In density-functional theory, the exchange-correlation (XC) energy can be defined exactly through the coupling-constant (λ) averaged XC hole n̄xc(r,r'), representing the probability depletion of finding an electron at r' due to an electron at r. Accurate knowledge of n̄xc(r,r') has been crucial for developing XC energy density-functional approximations and understanding their performance for molecules and materials. However, there are very few systems for which accurate XC holes have been calculated since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of λ while the electron density remains fixed at the physical (λ = 1) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron-electron cusp using finite basis sets. Focusing on Hooke's atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the λ-integrated XC hole. Our results indicate that, for Hooke's atoms, the error introduced by the description of the electron-electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle-, and coupling-constant-averaged XC holes are also calculated and provide a benchmark against which the Perdew-Burke-Ernzerhof and local density approximation XC hole models are assessed.

Reliable Dimerization Energies for Modeling of Supramolecular Junctions.

Accurate estimates of intermolecular interaction energy, ΔE, are crucial for modeling the properties of organic electronic materials and many other systems. For a diverse set of 50 dimers comprising up to 50 atoms (Set50-50, with 7 of its members being models of single-stacking junctions), benchmark ΔE data were compiled. They were obtained by the focal-point strategy, which involves computations using the canonical variant of the coupled cluster theory with singles, doubles, and perturbative triples [CCSD(T)] performed while applying a large basis set, along with extrapolations of the respective energy components to the complete basis set (CBS) limit. The resulting ΔE data were used to gauge the performance for the Set50-50 of several density-functional theory (DFT)-based approaches, and of one of the localized variants of the CCSD(T) method. This evaluation revealed that (1) the proposed "silver standard" approach, which employs the localized CCSD(T) method and CBS extrapolations, can be expected to provide accuracy better than two kJ/mol for absolute values of ΔE, and (2) from among the DFT techniques, computationally by far the cheapest approach (termed "ωB97X-3c/vDZP" by its authors) performed remarkably well. These findings are directly applicable in cost-effective yet reliable searches of the potential energy surfaces of noncovalent complexes.

Theoretical investigation on isomerization and decomposition reactions of pentanol radicals-part II: linear pentanol isomers.

High-level ab initio calculations are conducted for studying the kinetics of three linear pentanol radicals generated through H-atom abstraction reactions. The species involved are optimized using the M06-2X/6-311++G(d,p) level of theory, while a relaxed scan at the M06-2X/6-31g level of theory with 10° increments is used for the hindrance potential for low-frequency torsional modes. Single-point energies for all stationary points are obtained through the QCISD(T) and MP2 methods in combination with cc-pVDZ, cc-pVTZ, and cc-pVQZ basis sets, which can be extrapolated to the complete basis set (CBS) limit. The rate constants and branching ratios for isomerization and decomposition reactions are computed over a temperature range of 250-2000 K and a pressure range of 0.01-100 atm. Isomerization reactions are dominant at low temperatures, while decomposition reactions are more dominant at high temperatures. The branching ratio of the isomerization reaction exhibits a slight decrease with increasing pressure, while the trend for decomposition reactions depends on the type of the breaking bond. Based on the calculations for five branched pentanol radicals in part I, kinetics of linear and branched pentanol radicals are compared in this work and the results reveal that, for the same kind of β-scission reaction at similar positions of linear and branched pentanol radicals, the rate constants of branched ones are faster than those of linear ones at low temperatures. The hydroxyl group adjacent to the breaking bond can increase the β-scission reaction rate constants, while the effect can be ignored when the hydroxyl group is not adjacent to the breaking bond. Moreover, compared to when the hydroxyl group is located in the middle of the carbon chain, its positioning at the chain's end yields a more noticeable impact on the products and rate constants of C-O bond and O-H bond β-scission reactions. Besides, when incorporating calculated rate constants into the CRECK model, the updated mechanism shows a better performance for ignition delay times of 1-pentanol in the NTC range but exhibits lower reactivity at higher temperatures. The simulation of speciation profiles also shows better agreement with the experimental data obtained using a flow reactor.

Benchmarking Swaths of Intermolecular Interaction Components with Symmetry-Adapted Perturbation Theory.

A benchmark database for interaction energy components of various noncovalent interactions (NCIs) along their dissociation curve is one of the essential needs in theoretical chemistry, especially for the development of force fields and machine-learning methods. We utilize DFT-SAPT or SAPT(DFT) as one of the most accurate methods to generate an extensive stock of the energy components, including dispersion energies extrapolated to the complete basis set limit (CBS). Precise analyses of the created data, and benchmarking the total interaction energies against the best available CCSD(T)/CBS values, reveal different aspects of the methodology and the nature of NCIs. For example, error cancellation effects between the S2 approximation and nonexact xc-potentials occur, and large charge transfer energies in some systems, including heavy atoms, can explain the lower accuracy of DFT-SAPT. This method is perfect for neutral complexes containing light nonmetals, while other systems with heavier atoms should be treated carefully. In the last part, a representative data set for all NCIs is extracted from the original data.

Isomerism of : Accurate structural, energetic, and spectroscopic characterization.

A recent work [Ye et al. Mon. Not. R. Astron. Soc. 2023, 525, 1158] on the gas-phase formation of t-HC(O)SH, already detected in the interstellar medium, pointed out that the trans form of HC(S)OH is a potential candidate for astronomical observations. Prompted by these results, the family of isomers has been investigated from an energetic point of view using a double-hybrid density functional in combination with a partially augmented triple-zeta basis set. This preliminary study showed that the most stable species of the family are the cis and trans forms of HC(O)SH and HC(S)OH. For their structural and spectroscopic characterization, a composite scheme based on coupled cluster (CC) calculations that incorporates up to the quadruple excitations and accounts for the extrapolation to the complete basis set limit and core correlation effects has been employed. This approach opens to the prediction of rotational constants with an accuracy of 0.1%. A hybrid scheme, based on harmonic frequencies computed using the CC singles, doubles and a perturbative treatment of triples method (CCSD(T)) in conjunction with a quadruple-zeta basis set, allowed us to obtain fundamental vibrational frequencies with a mean absolute error of about 1%.

Nested gausslet basis sets

We introduce nested gausslet bases, an improvement on previous gausslet bases that can treat systems containing atoms with much larger atomic numbers. We also introduce pure Gaussian distorted gausslet bases, which allow the Hamiltonian integrals to be performed analytically, as well as hybrid bases in which the gausslets are combined with standard Gaussian-type bases. All these bases feature the diagonal approximation for the electron–electron interactions so that the Hamiltonian is completely defined by two Nb × Nb matrices, where Nb ≈ 104 is small enough to permit fast calculations at the Hartree–Fock level. In constructing these bases, we have gained new mathematical insight into the construction of one-dimensional diagonal bases. In particular, we have proved an important theorem relating four key basis set properties: completeness, orthogonality, zero-moment conditions, and diagonalization of the coordinate operator matrix. We test our basis sets on small systems with a focus on high accuracy, obtaining, for example, an accuracy of 2 × 10−5 Ha for the total Hartree–Fock energy of the neon atom in the complete basis set limit.

Insight on Gaussian Basis Set Truncation Errors in Weak to Intermediate Magnetic Fields with an Approximate Hamiltonian.

Strong magnetic fields such as those found on white dwarfs have significant effects on the electronic structures of atoms and molecules. However, the vast majority of molecular studies in the literature in such fields are carried out with Gaussian basis sets designed for zero field, leading to large basis set truncation errors [Lehtola et al., Mol. Phys. 2020, 118, e1597989]. In this work, we aim to identify the failures of the Gaussian basis sets in atomic calculations to guide the design of new basis sets for strong magnetic fields. We achieve this by performing fully numerical electronic structure calculations at the complete basis set (CBS) limit for the ground state and low lying excited states of the atoms 1 ≤ Z ≤ 18 in weak to intermediate magnetic fields. We also carry out finite-field calculations for a variety of Gaussian basis sets, introducing a real-orbital approximation for the magnetic-field Hamiltonian. Our primary focus is on the aug-cc-pVTZ basis set, which has been used in many works in the literature. A study of the differences in total energies of the fully numerical CBS limit calculations and the approximate Gaussian basis calculations is carried out to provide insight into basis set truncation errors. Examining a variety of states over the range of magnetic field strengths from B = 0 to B = 0.6B0, we observe significant differences for the aug-cc-pVTZ basis set, while much smaller errors are afforded by the benchmark-quality AHGBSP3-9 basis set [Lehtola, J. Chem. Phys. 2020, 152, 134108]. This suggests that there is considerable room to improve Gaussian basis sets for calculations at finite magnetic fields.