Basis Set Selection Research Articles

First-Principles Linear Combination of Atomic Orbitals Calculations of K2SiF6 Crystal: Structural, Electronic, Elastic, Vibrational and Dielectric Properties.

The results of first-principles calculations of the structural, electronic, elastic, vibrational, dielectric and optical properties, as well as the Raman and infrared (IR) spectra, of potassium hexafluorosilicate (K2SiF6; KSF) crystal are discussed. KSF doped with manganese atoms (KSF:Mn4+) is known for its ability to function as a phosphor in white LED applications due to the efficient red emission from Mn⁴⁺ activator ions. The simulations were performed using the CRYSTAL23 computer code within the linear combination of atomic orbitals (LCAO) approximation of the density functional theory (DFT). For the study of KSF, we have applied and compared several DFT functionals (with emphasis on hybrid functionals) in combination with Gaussian-type basis sets. In order to determine the optimal combination for computation, two types of basis sets and four different functionals (three advanced hybrid-B3LYP, B1WC, and PBE0-and one LDA functional) were used, and the obtained results were compared with available experimental data. For the selected basis set and functional, the above-mentioned properties of KSF were calculated. In particular, the B1WC functional provides us with a band gap of 9.73 eV. The dependencies of structural, electronic and elastic parameters, as well as the Debye temperature, on external pressure (0-20 GPa) were also evaluated and compared with previous calculations. A comprehensive analysis of vibrational properties was performed for the first time, and the influence of isotopic substitution on the vibrational frequencies was analyzed. IR and Raman spectra were simulated, and the calculated Raman spectrum is in excellent agreement with the experimental one.

Semi-empirical supported, Ab initio derived thermodynamic properties for ClO2 and its sub and extended species, applied in water treatment cycles

This paper describes a group of sixty (60) sub and extended chlorine oxide species with the general formulae of ClxOy (with x ≤ 2, y ≤ 8). Their role in water treatment cycles, behaving as key reactive species, is represented by a complex sequence of chemical inter-dependencies, exposed as a cohesive set of chemical reactions to demonstrate their cyclic role in aqueous media. An empirical/semi-empirical computational approach, supported by Ab Initio simulations, in accordance with open-shell character, has been followed to determine their optimum molecular geometries, to obtain their thermochemical properties. Besides a single molecular analysis, Grand Canonical Ensemble simulations, supported by a revised library of force field parameters, constituted a core component of the computational approach and proved to be invaluable in confirming thermochemical properties. This approach also offered finite estimates of optimum model sizes, a benefit with wider modelling application. Extended molecular species of ClO2 display a complex sequence of bonding character, with a variable charge dissipation (reported as partial charges), which complicates selection of basis sets in optimizing molecular geometries, during Ab Initio analyses.Optimum molecular geometries were obtained using Gaussian and MOPAC, which in turn resulted in reliable Heats of Formation. These correlated well with energies extracted from the open literature. Thermodynamic Analysis of the reaction of selected chlorine oxides with water using FactSage, predicted the production of known and two previously undetected chlorine species, [ClO4]- and [ClOH2]+.

Data-driven determination of 1H-MRS basis set composition.

Metabolite amplitude estimates derived from linear combination modeling of MR spectra depend upon the precise list of constituent metabolite basis functions used (the "basis set"). The absence of clear consensus on the "ideal" composition or objective criteria to determine the suitability of a particular basis set contributes to the poor reproducibility of MRS. In this proof-of-concept study, we demonstrate a novel, data-driven approach for deciding the basis-set composition using Bayesian information criteria (BIC). We have developed an algorithm that iteratively adds metabolites to the basis set using iterative modeling, informed by BIC scores. We investigated two quantitative "stopping conditions", referred to as max-BIC and zero-amplitude, and whether to optimize the selection of basis set on a per-spectrum basis or at the group level. The algorithm was tested using two groups of synthetic in-vivo-like spectra representing healthy brain and tumor spectra, respectively, and the derived basis sets (and metabolite amplitude estimates) were compared to the ground truth. All derived basis sets correctly identified high-concentration metabolites and provided reasonable fits of the spectra. At the single-spectrum level, the two stopping conditions derived the underlying basis set with 77-87% accuracy. When optimizing across a group, basis set determination accuracy improved to 84-92%. Data-driven determination of the basis set composition is feasible. With refinement, this approach could provide a valuable data-driven way to derive or refine basis sets, reducing the operator bias of MRS analyses, enhancing the objectivity of quantitative analyses, and increasing the clinical viability of MRS.

MP2-Based Composite Extrapolation Schemes Can Predict Core-Ionization Energies for First-Row Elements with Coupled-Cluster Level Accuracy.

X-ray photoelectron spectroscopy (XPS) measures core-electron binding energies (CEBEs) to reveal element-specific insights into the chemical environment and bonding. Accurate theoretical CEBE prediction aids XPS interpretation but requires proper modeling of orbital relaxation and electron correlation upon core-ionization. This work systematically investigates basis set selection for extrapolation to the complete basis set limit of CEBEs from ΔMP2 and ΔCC energies across 94 K-edges in diverse organic molecules. We demonstrate that an alternative composite scheme using ΔMP2 in a large basis corrected by ΔCC-ΔMP2 difference in a small basis can quantitatively recover optimally extrapolated ΔCC CEBEs within 0.02 eV. Unlike ΔCC, MP2 calculations do not suffer from convergence issues and are computationally cheaper, and thus, the composite ΔMP2/ΔCC scheme balances accuracy and cost, overcoming limitations of solely using either method. We conclude by providing a comprehensive analysis of the choice of small and large basis sets for the composite schemes and provide practical recommendations for highly accurate (within 0.10-0.15 eV MAE) ab initio prediction of XPS data.

The use of constrained methods to analyze the molecular reactivity and to define a new type of pseudo atoms

ContextConstrained methods in electronic structure methodologies add terms to the variational equations and generate solutions that represent distorted electronic distributions. In some cases, the new solutions can be used to study the chemical reactivity of parts of the molecule. Additionally, this contribution presents the use of population constraints to define pseudo atoms in a molecule. The effects of the pseudo atom on the molecular properties are analyzed. The pseudo atoms are used to simulate the inductive effect of the substituent in a group of carbonyl molecules and their effect on the stability of the complexes between these organic species and one molecule of water. A discussion on the assumptions involved in the present definition of pseudo atoms is also included.MethodThe constrained RHF computations are done in a modified Hartree-Fock code for Gaussian basis sets. The selected basis set is STO-6 G.

Potential energy surfaces and dynamic properties via ab initio composite and density functional approaches.

Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction-based ab initio or density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self-consistent field Theory (VSCF) and post-VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode-coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode-mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI-PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post-VSCF methods to generate more accurate representations of computed infrared spectra.

Nuclear spin diffusion under fast magic-angle spinning in solid-state NMR.

Solid-state nuclear spin diffusion is the coherent and reversible process through which spin order is transferred via dipolar couplings. With the recent increases in magic-angle spinning (MAS) frequencies and magnetic fields becoming routinely applied in solid-state nuclear magnetic resonance, understanding how the increased 1H resolution obtained affects spin diffusion is necessary for interpretation of several common experiments. To investigate the coherent contributions to spin diffusion with fast MAS, we have developed a low-order correlation in Liouville space model based on the work of Dumez et al. (J. Chem. Phys. 33, 224501, 2010). Specifically, we introduce a new method for basis set selection, which accounts for the resonance-offset dependence at fast MAS. Furthermore, we consider the necessity of including chemical shift, both isotropic and anisotropic, in the modeling of spin diffusion. Using this model, we explore how different experimental factors change the nature of spin diffusion. Then, we show case studies to exemplify the issues that arise in using spin diffusion techniques at fast spinning. We show that the efficiency of polarization transfer via spin diffusion occurring within a deuterated and 100% back-exchanged protein sample at 60kHz MAS is almost entirely dependent on resonance offset. We additionally identify temperature-dependent magnetization transfer in beta-aspartyl L-alanine, which could be explained by the influence of an incoherent relaxation-based nuclear Overhauser effect.

Realizing the potentials of density functional theory (DFT) and of the materials genome initiative (MGI)

From 1964 and 1965 to present, the wide spread utilization of an incomplete density functional theory (DFT) has led to mixed results: The second theorem of the theory asserts that the energy functional reaches its minimum if the calculation employs the ground state charge density—without providing a mechanism for finding this density. Calculations purporting to employ DFT have mostly assumed that results obtained with a judiciously selected basis set, following self-consistent iterations, are those of the ground state. The state obtained with a single basis set is a stationary one, among an infinite number of such states, with no proven relation to the actual ground state of the material. Most failures or limitations of the incomplete DFT can be traced to this error. We present results from calculations using the completed DFT. They are in excellent agreement with experiment and portend the realization of the Materials Genome Initiative.

Reconstructing Quantum States from Sparse Measurements

Quantum state tomography (QST) is a central technique to fully characterize an unknown quantum state. However, standard QST requires an exponentially growing number of quantum measurements against the system size, which limits its application to smaller systems. Here, we explore the sparsity of underlying quantum state and propose a QST scheme that combines the matrix product states’ representation of the quantum state with a supervised machine learning algorithm. Our method could reconstruct the unknown sparse quantum states with very high precision using only a portion of the measurement data in a randomly selected basis set. In particular, we demonstrate that the Wolfgang states could be faithfully reconstructed using around 25% of the whole basis, and that the randomly generated quantum states, which could be efficiently represented as matrix product states, could be faithfully reconstructed using a number of bases that scales sub-exponentially against the system size.

Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H3PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

Density functional theory and CCSD(T) evaluation of ionization potentials, redox potentials, and bond energies related to zirconocene polymerization catalysts.

Quantum-mechanical-based computational design of molecular catalysts requires accurate and fast electronic structure calculations to determine and predict properties of transition-metal complexes. For Zr-based molecular complexes related to polyethylene catalysis, previous evaluation of density functional theory (DFT) and wavefunction methods only examined oxides and halides or select reaction barrier heights. In this work, we evaluate the performance of DFT against experimental redox potentials and bond dissociation enthalpies (BDEs) for zirconocene complexes directly relevant to ethylene polymerization catalysis. We also examined the ability of DFT to compute the fourth atomic ionization potential of zirconium and the effect the basis set selection has on the ionization potential computed with CCSD(T). Generally, the atomic ionization potential and redox potentials are very well reproduced by DFT, but we discovered relatively large deviations of DFT-calculated BDEs compared to experiment. However, evaluation of BDEs with CCSD(T) suggests that experimental values should be revisited, and our CCSD(T) values should be taken as most accurate.

Benchmarking ANO-R basis set for multiconfigurational calculations

The selection of basis sets is very important for multiconfigurational wave function calculation, due to a balance between a desired accuracy and computational costs. Recently, the atomic natural orbital-relativistic (ANO-R) basis set was published as a suggested replacement for the ANO-RCC basis set for scalar-relativistic correlated calculations Zobel et al (2021 J. Chem. Theory Comput. 16 278–294). Benchmarking ANO-R basis set against ANO-RCC for atoms (from H to Rn) and their compounds is the goal of this study. Many of these compounds (for instance, diatomic molecules containing transition metals) have open shells, for which reason a multiconfigurational approach is necessary and was primarily used throughout this project. Performance of the ANO-R basis set in multiconfigurational calculations is similar to the ANO-RCC basis set for the ionisation potential of atoms, and the bond distance in diatomic molecules. Deficiencies are noted for atomic electron affinities and dissociation energies of fluoride diatomic molecules. ANO-R basis sets are more compact in comparison to the corresponding ANO-RCC basis sets leading to smaller computational costs, which was demonstrated by chloroiron corrole molecule as an example.

Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion.

The balance between cost-effective and sufficiently accurate methods represents the proverbial "promised land" for quantum chemistry calculations. The burden thus falls upon theoretical and computational chemists to provide such alternatives to mitigate the issues that arise from the employ of finite computing resources. In this paper, we attempt to demonstrate the importance of the quality of the initial guess for the self-consistent field (SCF) calculation when considering cost reduction techniques. We broach this challenge by using the many body expansion (MBE) to yield high quality density matrices (DMs) which, in turn, are applied as an SCF initial guess. The MBE-DM approaches combined with purification schemes and distance-based cutoff schemes can serve as initial guesses to reduce the SCF cycles necessary for convergence or derive energy directly through one Fock build. To this end, four unique types of clusters including water clusters, fluoride anion water clusters, sodium cation water clusters, and ammonium-bisulfate salt clusters have been used to test the performance of MBE-DM where its truncation at three-body expansion, MBE(3)-DM, shows vast improvement for those four clusters with reductions in the number of SCF cycles up to 40% as compared with the traditional superposition of atomic densities (SAD) guess. Other types of typical initial guesses, superposition of atomic potentials (SAP) and basis set projection (BSP), perform much worse than MBE-DM and SAD. In addition, the MBE-DM shows consistency across an array of fragment types irrespective of charges, size, level of theory, and basis set selection. Through MBE(3)-DM with the distance cutoff and the average purification scheme, the energy can be obtained directly with a mere 3.2 mH of the mean absolute deviation (MAD) for (H2O)N=6-55 which is at least 73 times better than the energy prediction using the typical initial guesses (SAD, SAP, and BSP). The corresponding MAD per monomer is only 0.14 mH which reaches the threshold of the "dynamical accuracy". The promising results of the methods outlined in this paper not only indicate two direct routes for computational cost reduction but also lay the possible foundation for composite techniques (i.e., ab initio sampling) that make best use of near converged values as their starting point.

A Statistically Supported Antioxidant Activity DFT Benchmark—The Effects of Hartree–Fock Exchange and Basis Set Selection on Accuracy and Resources Uptake

Polyphenolic compounds are now widely studied using computational chemistry approaches, the most popular of which is Density Functional Theory. To ease this process, it is critical to identify the optimal level of theory in terms of both accuracy and resource usage—a challenge we tackle in this study. Eleven DFT functionals with varied Hartree–Fock exchange values, both global and range-separated hybrids, were combined with 14 differently augmented basis sets to calculate the reactivity indices of caffeic acid, a phenolic acid representative, and compare them to experimental data or a high-level of theory outcome. Aside from the main course, a validation of the widely used Janak’s theorem in the establishment of vertical ionization potential and vertical electron affinity was evaluated. To investigate what influences the values of the properties under consideration, linear regression models were developed and thoroughly discussed. The results were utilized to compute the scores, which let us determine the best and worst combinations and make broad suggestions on the final option. The study demonstrates that M06–2X/6–311G(d,p) is the best fit for such research, and, curiously, it is not necessarily essential to include a diffuse function to produce satisfactory results.

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.

Development of nuclear basis sets for multicomponent quantum chemistry methods.

The nuclear-electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born-Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems.

On the basis set selection for calculations of core-level states: different strategies to balance cost and accuracy

We present a study on basis set effects in correlated calculations of core-level states. While it is well recognised that the core-level states require using more extensive basis sets than their valence counterparts, the standard strategy has been to use large contracted basis sets, such as the cc-pVXZ or cc-pCVXZ series. Building upon the ideas of Besley et al. [J. Chem. Phys. 130, 124308 (2009)], we show that a much more effective strategy is to use uncontracted bases, such as core or fully uncontracted Pople's basis. The physical grounds behind this approach are explained and illustrated by numeric results. We also discuss other cost-saving strategies, such as virtual space truncation and mixed precision execution.

PSIXAS: A Psi4 plugin for efficient simulations of X-ray absorption spectra based on the transition-potential and Δ-Kohn-Sham method.

Near edge X-ray absorption fine structure (NEXAFS) spectra and their pump-probe extension (PP-NEXAFS) offer insights into valence- and core-excited states. We present PSIXAS, a recent implementation for simulating NEXAFS and PP-NEXAFS spectra by means of the transition-potential and the Δ-Kohn-Sham method. The approach is implemented in form of a software plugin for the Psi4 code, which provides access to a wide selection of basis sets as well as density functionals. We briefly outline the theoretical foundation and the key aspects of the plugin. Then, we use the plugin to simulate PP-NEXAFS spectra of thymine, a system already investigated by others and us. It is found that larger, extended basis sets are needed to obtain more accurate absolute resonance positions. We further demonstrate that, in contrast to ordinary NEXAFS simulations, where the choice of the density functional plays a minor role for the shape of the spectrum, for PP-NEXAFS simulations the choice of the density functional is important. Especially hybrid functionals (which could not be used straightforwardly before to simulate PP-NEXAFS spectra) and their amount of "Hartree-Fock like" exact exchange affects relative resonance positions in the spectrum.

Calculation of Chemical Reaction Barrier Heights by Multiconfiguration Pair-Density Functional Theory with Correlated Participating Orbitals.

The accurate description of reaction barrier heights is challenging for quantum mechanical methods due to the need for a balanced treatment of dynamic and static correlation energies because their importance varies during the course of a chemical reaction. While some regions of potential energy surfaces are well-described by a single-reference wave function or by Kohn-Sham density functional theory, in other cases a multireference treatment is needed. For systems with many active electrons, most accurate multireference methods have prohibitive computational scalings with system size. Multiconfiguration pair-density functional theory, MC-PDFT, is a more affordable multireference approach that computes the total electron correlation energy in a single step by using the multiconfiguration kinetic energy, density, and on-top pair density and an on-top density functional. In this work, we apply MC-PDFT to a benchmark database (DBH24/18) of 24 diverse reaction barrier heights. We explore the role of active space and basis set selection on the performance of MC-PDFT. We find that MC-PDFT is able to calculate reaction barrier heights with a similar accuracy to complete active space second order perturbation theory, CASPT2, but at a lower computational cost, and we find that MC-PDFT is less dependent on basis set selection than CASPT2.

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts.

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted 13 C and 1 H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for 13 C chemical shifts in DMSO of about 5ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.