Choice Of Basis Set Research Articles

On the use of DFT+U to describe the electronic structure of TiO2 nanoparticles: (TiO2)35 as a case study.

One of the main drawbacks in the density functional theory (DFT) formalism is the underestimation of the energy gaps in semiconducting materials. The combination of DFT with an explicit treatment of the electronic correlation with a Hubbard-like model, known as the DFT+U method, has been extensively applied to open up the energy gap in materials. Here, we introduce a systematic study where the selection of the U parameter is analyzed considering two different basis sets: plane-waves and numerical atomic orbitals (NAOs), together with different implementations for including U, to investigate the structural and electronic properties of a well-defined bipyramidal (TiO2)35 nanoparticle. This study reveals, as expected, that a certain U value can reproduce the experimental value for the energy gap. However, there is a high dependence on the choice of basis set and on the U parameter employed. The present study shows that the linear combination of the NAO basis functions, as implemented in Fritz Haber Institute ab initio molecular simulation (FHI-aims), requires, requires a lower U value than the simplified rotationally invariant approach, as implemented in the Vienna ab initio simulation package (VASP). Therefore, the transfer of U values between codes is unfeasible and not recommended, demanding initial benchmark studies for the property of interest as a reference to determine the appropriate value of U.

Benchmarking Correlated Methods for Frequency-Dependent Polarizabilities: Aromatic Molecules with the CC3, CCSD, CC2, SOPPA, SOPPA(CC2), and SOPPA(CCSD) Methods.

A benchmark study of several correlated second-order methods for frequency-dependent polarizabilities has been carried out. For the benchmark, a set of 14 (hetero)aromatic medium-sized molecules has been chosen. For the first time, CC3 polarizabilities are reported for these molecules using Sadlej's polarized triple-ζ basis set, and for a subset of these molecules the polarizabilities were obtained at the CC3 level also with the larger aug-cc-pVTZ basis set. These CC3 values are used as the reference values for benchmarking the second-order methods: SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, as well as CCSD. The influence of different basis sets, aug-cc-pVDZ, aug-cc-pVTZ, aug-cc-pVQZ, d-aug-cc-pVTZ, and Sadlej's polarized triple-ζ basis set, on static and frequency-dependent polarizabilities was investigated for the full set of molecules at the SOPPA level. It was found that the choice of basis set had a somewhat greater influence on the frequency-dependent polarizabilities than on the static polarizabilities, but all effects were small. The aug-cc-pVTZ basis set performed adequately for both static and frequency-dependent polarizabilities, having an insignificant offset from the values obtained with the larger d-aug-cc-pVTZ and aug-cc-pVQZ basis sets. Comparing the second-order methods, SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, as well as CCSD, to the CC3 reference values, it was found that the best performing method was CCSD, as expected. The SOPPA method, on the contrary, outperformed the CC2 method, suggesting the use of SOPPA rather than CC2 for polarizabilities, at least for these kinds of molecules. The SOPPA results were found to improve further when the Møller-Plesset correlation coefficients in the wave function were replaced by coupled-cluster amplitudes in the SOPPA(CC2) and SOPPA(CCSD) methods. Finally, a comparison was made for a small subset of the molecules between experimental data and calculated polarizabilities. It shows that, for this set of molecules, the trend in the performance of the different second-order methods does not depend on whether the reference values are calculated CC3 values or experimental values.

Al27 NMR chemical shift of Al(OH)4 - calculated from first principles: Assessment of error cancellation in chemically distinct reference and target systems.

Predicting accurate nuclear magnetic resonance chemical shieldings relies upon cancellation of different types of errors between the theoretically calculated shielding constant of the analyte of interest and the reference. Often, the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral trivalent cation Al(H2O)6 3+, accounting for ab initio intrinsic errors. However, the use of this species as a reference for the chemically distinct tetrahedral anion Al(OH)4 - requires an understanding of how these errors cancel in order to define the limits of accurately predicting Al27 chemical shielding in Al(OH)4 -. In this work, we estimate the absolute shielding of the Al27 nucleus in Al(OH)4 - at the coupled cluster level (515.1 ± 5.3 ppm). Shielding sensitivity to the choice of method approximation and atomic basis sets used has been evaluated. Solvent and thermal effects are assessed through ensemble averaging techniques using ab initio molecular dynamics. The contribution of each type of intrinsic error is assessed for the Al(H2O)6 3+ and Al(OH)4 - ions, revealing significant differences that fundamentally hamper the ability to accurately calculate the Al27 chemical shift of Al(OH)4 - from first principles.

Gaussian Basis Sets for Crystalline Solids: All-Purpose Basis Set Libraries vs System-Specific Optimizations.

It is customary in molecular quantum chemistry to adopt basis set libraries in which the basis sets are classified according to either their size (triple-ζ, quadruple-ζ, ...) and the method/property they are optimal for (correlation-consistent, linear-response, ...) but not according to the chemistry of the system to be studied. In fact the vast majority of molecules is quite homogeneous in terms of density (i.e., atomic distances) and types of bond involved (covalent or dispersive). The situation is not the same for solids, in which the same chemical element can be found having metallic, ionic, covalent, or dispersively bound character in different crystalline forms or compounds, with different packings. This situation calls for a different approach to the choice of basis sets, namely a system-specific optimization of the basis set that requires a practical algorithm that could be used on a routine basis. In this work we develop a basis set optimization method based on an algorithm–similar to the direct inversion in the iterative subspace–that we name BDIIS. The total energy of the system is minimized together with the condition number of the overlap matrix as proposed by VandeVondele et al. [VandeVondele et al. J. Chem. Phys.2007, 227, 114105]. The details of the method are here presented, and its performance in optimizing valence orbitals is shown. As demonstrative systems we consider simple prototypical solids such as diamond, graphene sodium chloride, and LiH, and we show how basis set optimizations have certain advantages also toward the use of large (quadruple-ζ) basis sets in solids, both at the DFT and Hartree–Fock level.

The performance of Dunning, Jensen, and Karlsruhe basis sets on computing relative energies and geometries

ABSTRACT In an effort to assist researchers in choosing basis sets for quantum mechanical modeling of molecules (i.e. balancing calculation cost versus desired accuracy), we present a systematic study on the accuracy of computed conformational relative energies and their geometries in comparison to MP2/CBS and MP2/AV5Z data, respectively. In order to do so, we introduce a new nomenclature to unambiguously indicate how a CBS extrapolation was computed. Nineteen minima and transition states of buta-1,3-diene, propan-2-ol and the water dimer were optimized using 45 different basis sets. Specifically, this includes one Pople (i.e. 6-31G(d)), 8 Dunning (i.e. VXZ and AVXZ, X = 2–5), 25 Jensen (i.e. pc-n, pcseg-n, aug-pcseg-n, pcSseg-n, and aug-pcSseg-n, n = 0–4), and 9 Karlsruhe (e.g. def2-SV(P), def2-QZVPPD) basis sets. The molecules were chosen to represent both common and electronically diverse molecular systems. In comparison to MP2/CBS relative energies computed using the largest Jensen basis sets (i.e. n = 2,3,4), the use of smaller sizes (n = 0,1,2 and n = 1,2,3) provides results that are within 0.11–0.24 and 0.09–0.16 kcalmol. To practically guide researchers in their basis set choice, an equation is introduced that ranks basis sets based on a user-defined balance between their accuracy and calculation cost. Furthermore, we explain why the aug-pcseg-2, def2-TZVPPD and def2-TZVP basis sets are very suitable choices to balance speed and accuracy.

Photoionization of H2 using the molecular R-matrix with time approach

SynopsisWe present results of the first calculations using the variational ab initio molecular R-matrix with time approach. We have calculated two and four-photon ionization cross sections for H2 and studied the effects of electron correlation and choice of the Gaussian atomic basis sets. Our results are compared with earlier calculations.

Hylleraas' variational method with orthogonality restrictions.

In this paper, we suggest a new computational technique for the minimization of Hylleraas' functional with additional orthogonality restrictions imposed on the desired vectors. It is shown how Hylleraas' constrained problem can be reduced to an unconstrained one by minimal computational efforts. The asymptotic projection (AP) method proposed earlier to minimize Rayleigh's quotient subject to some orthogonality restrictions is applied to construct a modified Hylleraas' functional whose solution fulfills the required constraints automatically. Specifically, equivalence between the original problem and the one for the modified Hamilton operator is derived. It is shown that the AP methodology allows additional restrictions to be treated in a unified approach for both Rayleigh's quotient and Hylleraas' functional. Specific features of the method are demonstrated on the electronic parallel polarizability of H2+. Some emphasis is put on the choice of specific distributed basis set adapted for polarizability computation. A comparison with other methods, considered exact or extremely accurate, is also given.

Large Amplitude Motions in Fruit Flavors: The Case of Alkyl Butyrates.

To accurately characterize the large amplitude motions and soft degrees of freedom of isolated molecules, sampling their conformational landscape by molecular mechanics and quantum chemical calculations may provide a valuable insight into the structure and dynamics. However, the resulting models need to be validated by a reliable experimental counterpart. For ethyl pentanoates, which belong to the family of fruit esters, benchmark calculations at different levels of theory showed that the C-C bond in proximity to the ester carbonyl group exhibits a large amplitude motion that is extremely sensitive to the choice of quantum chemical method and basis set. In such cases, insights from high-resolution molecular jet techniques are ideal to accurately identify and characterize soft degrees of freedom. Here, we report on the most abundant conformer of ethyl 2-ethyl butyrate using Fourier-transform microwave spectroscopy. We show that - unlike other structurally related pentanoates for which gas-phase and crystallographic data is available - ethyl 2-ethyl butyrate possesses a Cs symmetry plane under molecular jet conditions.

Prediction of pKa s of Late Transition-Metal Hydrides via a QM/QM Approach.

Three implicit solvation models, the conductor-like polarizable continuum model (C-PCM), the conductor-like screening model (COSMO), and universal implicit solvent model (SMD), combined with a hybrid two layer QM/QM approach (ONIOM), were utilized to calculate the pKa values, using a direct thermodynamic scheme, of a set of Group 10 transition metal (TM) hydrides in acetonitrile. To obtain the optimal combination of quantum methods for ONIOM calculations with implicit solvation models, the influence of factors, such as the choice of density functional and basis set, the atomic radii used to build a cavity in the solvent, and the size of the model system in an ONIOM scheme, was examined. Additionally, the impact of Grimme's empirical dispersion correction and exact exchange was also investigated. The results were calibrated by experimental data. This investigation provides insight about effective models for the prediction of thermodynamic properties of TM-containing complexes with bulky ligands. © 2019 Wiley Periodicals, Inc.

Evaluation of DFT methods to calculate structure and partial atomic charges for zeolite N

Zeolite N is a synthetic zeolite of the EDI framework type with chemical formula K12Al10Si10O40Cl2·8H2O Experimental and computational investigations verify the valuable ion-exchange capability of zeolite N. In this study, we assess the effects of Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) DFT models on zeolite structural parameters and on partial atomic charges of framework atoms. We applied these functionals with different quality of convergence and SCF tolerances, numerical basis sets and dispersion correction schemes. Optimized zeolite N structures are evaluated by comparing the atom positions and framework TO bond lengths with experimental data. The obtained SiO and AlO bond lengths of optimized structures in this study are in agreement with previous experimental and computational studies on zeolite N and other zeolites. The values of Mulliken partial atomic charges are sensitive to the choice of numerical basis sets. Results show that the GGA-PBE functional with DNP-4.4 basis set and TS dispersion correction scheme is a reliable DFT model in order to optimize and establish the structural parameters of zeolite N for further MD simulations.

Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)2] and dicyanomercury(II) [Hg(CN)2]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)2 and Hg(CN)2, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

Non-trivial band gaps and charge transfer in Janus-like functionalized bilayer boron arsenide

Herein, we predict the stability, structural and electronic properties of Janus-like boron arsenide (BAs) bilayer with the help of DFT calculations. We combine one hydrogenated and one fluorinated BAs layers in different stacking and arrangements. The interlayer charge transfer is also calculated and discussed with the help of various charge population mechanism. In addition to this, the choice of basis set is critical in determining the interlayer distances and consequently, the energy gaps. Additionally, the layer-resolved PDOS, at vdW-DF level, revealed that these bilayers are type-II semiconductors as the valence and conduction bands are composed of different layers. Furthermore, the band gap of these bilayers can efficiently be engineered from 0 to 0.54 eV by controlling the arrangement of the layers. That being said, the electronic properties can optionally be tuned from semiconducting to semimetallic. Additionally, the shape of the conduction band minima and the heavy-, light-hole bands provides the opportunity of utilization of these bilayers in ultrafast nanoelectronics.

Optimizing many-body atomic descriptors for enhanced computational performance of machine learning based interatomic potentials

We explore different ways to simplify the evaluation of the smooth overlap of atomic positions (SOAP) many-body atomic descriptor [Bart\'{o}k et al., Phys. Rev. B 87, 184115 (2013)]. Our aim is to improve the computational efficiency of SOAP-based similarity kernel construction. While these improved atomic descriptors can be used for general characterization and interpolation of atomic properties, their main target application is accelerated evaluation of machine-learning-based interatomic potentials within the Gaussian approximation potential (GAP) framework [Bart\'{o}k et al., Phys. Rev. Lett. 104, 136403 (2010)]. We achieve this objective by expressing the atomic densities in an approximate separable form, which decouples the radial and angular channels. We then express the elements of the SOAP descriptor (i.e., the expansion coefficients for the atomic densities) in analytical form given a particular choice of radial basis set. Finally, we derive recursion formulas for the expansion coefficients. This new SOAP-based descriptor allows for tenfold speedups compared to previous implementations, while improving the stability of the radial expansion for distant atomic neighbors, without degradation of the interpolation power of GAP models.

Calculations of neon nuclear-spin optical rotation, Verdet and hyperfine constants with configuration-interaction many-body perturbation theory

The nuclear-spin optical rotation (NSOR) effect can enable correlated optical-NMR spectroscopy and imaging. The calculation of NSOR constants is very challenging owing to the high sensitivity to various interactions and neon arguably is a relatively simple atom for calculations. While the neon NSOR effect was not observed and characterized, it can be measured similarly to xenon NSOR to provide data for testing theories. One goal of this paper is to give an estimate of the effect for future experiments in neon. We have calculated the neon NSOR constant using relativistic configuration-interaction many-body perturbation (CI-MBPT). In order to evaluate the accuracy of the CI-MBPT, it was tested on neon energies, oscillator strengths, hyperfine constants and Verdet constants to show a good agreement with experiment. However, the NSOR constant calculations turned out to be more sensitive to the basis set choice, correlation corrections and relativistic effects, which were studied using the CI-MBPT framework. Apart from providing data for future neon NSOR experiments, the CI-MBPT results can be useful for comparison with molecular-structure calculations, as we illustrated on the example of Dalton calculations.The neon atom NSOR is similar to the NSOR of fluorine-containing molecules, to which DALTON calculations can be applied, unlike the atomic CI-MBPT method, so the performance of DALTON calculations in neon can be a good testing ground for F-containing molecules as well.

Galerkin approximation of dynamical quantities using trajectory data.

Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion. A specific choice of basis set in the expansion corresponds to the estimation of dynamical quantities using a Markov state model. More generally, the boundary conditions impose restrictions on the choice of basis sets. We demonstrate how an alternative basis can be constructed using ideas from diffusion maps. In our numerical experiments, this basis gives results of comparable or better accuracy to Markov state models. Additionally, we show that delay embedding can reduce the information lost when projecting the system's dynamics for model construction; this improves estimates of dynamical statistics considerably over the standard practice of increasing the lag time.

Modeling L2,3-edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory.

X-ray absorption spectroscopy (XAS) is a powerful tool that can provide physical insights into element-specific chemical processes and reactivities. Although relativistic time-dependent density functional theory (TDDFT) has been previously applied to model the L-edge region in XAS, there has not been a more comprehensive study of the choices of basis sets and density functional kernels available for variational relativistic excited state methods. In this work, we introduce the implementation of the generalized preconditioned locally harmonic residual algorithm to solve the complex-valued relativistic TDDFT for modeling the L-edge X-ray absorption spectra. We investigate the L2,3-edge spectra of a series of molecular complexes using relativistic linear response TDDFT with a hybrid iterative diagonalization algorithm. A systematic error analysis was carried out with a focus on the energetics, intensities, and magnitude of L2-L3 splitting compared to experiments. Additionally, the results from relativistic TDDFT calculations are compared to those computed using other theoretical methods, and the multideterminantal effects on the L-edge XAS were investigated.

Investigation of the sensitivity-specificity of canonical- and deconvolution-based linear models in evoked functional near-infrared spectroscopy.

Functional near-infrared spectroscopy (fNIRS) is a noninvasive brain imaging technique to measure evoked changes in cerebral blood oxygenation. In many evoked-task studies, the analysis of fNIRS experiments is based on a temporal linear regression model, which includes block-averaging, deconvolution, and canonical analysis models. The statistical parameters of this model are then spatially mapped across fNIRS measurement channels to infer brain activity. The trade-offs in sensitivity and specificity of using variations of canonical or deconvolution/block-average models are unclear. We quantitatively investigate how the choice of basis set for the regression linear model affects the sensitivity and specificity of fNIRS analysis in the presence of variability or systematic bias in underlying evoked response. For statistical parametric mapping of amplitude-based hypotheses, we conclude that these models are fairly insensitive to the parameters of the regression basis for task durations and we report the highest sensitivity-specificity results using a low degree-of-freedom canonical model under these conditions. For shorter duration task ( ), the signal-to-noise ratio of the data is also important in this decision and we find that deconvolution or block-averaging models outperform the canonical models at high signal-to-noise ratio but not at lower levels.

Multicomponent density functional theory with density fitting.

Multicomponent Density Functional Theory (MDFT) is a promising methodology to incorporate nuclear quantum effects, such as zero-point energy or tunneling, or to simulate other types of particles such as muons or positrons using particle densities as basic quantities. As for standard electronic DFT, a still ongoing challenge is to achieve the most efficient implementations. We introduce a multicomponent DFT implementation within the framework of auxiliary DFT, focusing on molecular systems comprising electrons and quantum protons. We introduce a dual variational procedure to determine auxiliary electron and proton densities which leads to a succession of approximate energy expressions. Electronic and protonic fitted densities are employed in (i) electron-electron, proton-proton, and electron-proton classical Coulomb interactions and (ii) electron exchange-correlation, proton-proton exchange, and electron-proton correlation (EPC) potentials. If needed, exact exchange among electrons or among protons is computed by the variational fitting of the corresponding Fock potential. The implementation is carried out in deMon2k. We test various electron proton correlation functionals on proton affinities. We find that auxiliary densities can be safely used in electron-electron, proton-proton, and electron-proton classical Coulomb interactions, as well as in EPC, albeit with some precautions related to the choice of the electronic auxiliary basis set that must be flexible enough. Computational tests reported indicate that introduction of density fitting in MDFT is clearly advantageous in terms of computational effort with good scaling properties with respect to the number of electrons and protons treated at the DFT level.

Determination of the best functional and basis sets for optimization of the structure of hypervalent iodines and calculation of their first and second bond dissociation enthalpies

AbstractHypervalent iodines are widely used in organic chemistry, and their most important feature is the three‐center four‐electron bond. However, there have been few reports on the measurement of their bond dissociation enthalpy (BDE). Therefore, in many cases, BDE is estimated by computational calculations. However, the value of a calculated BDE usually varies depending on the choice of functional and basis set, and the best method for making an accurate evaluation of the three‐center four‐electron bond has not been determined. We succeeded in determining the best functional and basis set to calculate the three‐center four‐electron bond to within 0.79% error and 0.53 standard deviation. Using the optimal functional and basis set, the first and second BDEs of several hypervalent iodines are calculated, and as the effect of benzene substituents was investigated, negative correlation was observed in the Hammett plot. In addition, the effect of ortho‐substituent in cyclic hypervalent iodine was found to be significant. Furthermore, the decomposition route of hypervalent iodine is calculated. The value of a calculated BDE usually varies depending on the choice of functional and basis set. We succeeded in determining the best functional and basis sets to calculate the three‐center four‐electron bond of hypervalent iodine to within 0.79% error and 0.53 standard deviation. Using the optimal functional and basis sets, the first and second BDEs of several hypervalent iodines are calculated, and additionally, the decomposition route of hypervalent iodine is calculated.

Single-center approach for photodetachment and radiative electron attachment: Comparison with other theoretical approaches and with experimental photodetachment data

A single-center method for calculating photodetachment cross section for anions and radiative electron attachment cross section for neutral molecules by microreversibility is presented. It uses the integral equation method to calculate the ejected electron's continuum wave function while the single-electron bound function of the anion is described by the Dyson orbital. It is compared with related theoretical approaches and benchmarked to the experimental photodetachment cross sections of ${{\mathrm{O}}_{2}}^{\ensuremath{-}}$, ${\mathrm{OH}}^{\ensuremath{-}}$, and ${\mathrm{CN}}^{\ensuremath{-}}$. The use of the plane-wave approximation of the ejected electron wave function combined with the Hartree-Fock frozen-core approximation of the Dyson orbital is also considered and its results are compared with those of our methods and with experiment. A good agreement between the calculated photodetachment cross sections and the experimental data is obtained for ${{\mathrm{O}}_{2}}^{\ensuremath{-}}$ and ${\mathrm{CN}}^{\ensuremath{-}}$ when using the three methods. For ${\mathrm{OH}}^{\ensuremath{-}}$, the calculated scattering-wave electron photodetachment cross sections agree well with two most recent sets of experimental data among the three available while the plane-wave results disagree with all the experimental and theoretical data. The different approaches to calculate the Dyson orbital are also discussed as well as the convergence of the calculations with respect to the choice of the one-electron basis set. The approximation of Dyson orbitals by Kohn-Sham orbitals appears to overestimate the photodetachment cross section.