Polarization Consistent Basis Sets Research Articles

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization.

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.

On the impact of side methyl groups on the structure and vibrational properties of β-carotenoids. The case of butadiene and isoprene

Theoretical consideration about the impact of methyl groups on the structure and vibrational properties of β-carotenoids, using medium size molecules of trans-butadiene and trans-isoprene, are reported. Density functional theory (DFT) calculations with correlation-consistent and polarization-consistent basis sets were applied to trans-1,3-butadiene and trans-isoprene as the smallest building bricks of β-carotenoids. Their structure and harmonic vibrations were estimated in the complete basis set limit (CBS) using the non-linear least square fit. Optimized geometries and harmonic frequencies, obtained with B3LYP and BLYP density functionals and large basis sets, were favorably reproduced by a significantly faster approach, using a recently modified STO(1M)-3G Slater-type basis set. Selected density functionals with STO(1M)-3G and 6-311++G** basis sets were also successful in predicting β-carotene structures and harmonic vibrations. This work demonstrates the potential applicability of the proposed level of theory for larger molecules, including β-carotenoids, present in numerous natural food sources. The proposed scheme of molecular modeling, applied to biologically active compounds in food, could provide a deeper insight into their function in vivo, which is directly related to their structure and spectroscopic properties. It could also support the experimental qualitative analysis, based on peak assignment of β-carotenoids in various food sources.

DFT meets the segmented polarization consistent basis sets: Performances in the computation of molecular structures, rotational and vibrational spectroscopic properties

Quantum-chemical calculations assist the analysis of laboratory spectra, and often provide the only means to determine spectroscopic data that cannot be accessed experimentally. For the purpose, reliable predictions of structural and spectroscopic parameters are required. Although coupled cluster theory in conjunction with to large basis sets and composite schemes can reach impressive accuracies for structural, thermochemical and spectroscopic properties, it is still limited to small sized molecules. DFT represents the working option for medium to large molecular systems. In this context, systematic investigations are required aimed at characterizing the performances of the different DFT model chemistries. In this work, the accuracy of the popular hybrid B3LYP and the double hybrid B2PLYP functionals coupled to the segmented polarization consistent (aug-)pcs-n basis sets in the prediction of molecular structures and rotational- and vibrational spectroscopic parameters are investigated using a benchmark set of molecules of both atmospheric and astrochemical relevance. For comparison purposes, different flavors of Dunning’s triple-ζ basis sets and the SNSD basis set, are also employed. The convergence behavior of the pcs-n hierarchy with n = 1–4 is also addressed to some extent. The results indicate the B3LYP-D3 functional in conjunction with the aug-pcs-1 or SNSD basis sets as a cost-effective model chemistry for applications in the field of rotational and vibrational spectroscopies. Improved accuracy is obtained by coupling the B2PLYP-D3 functional with the aug-pcs-2 or aug-cc-pVTZ triple-ζ basis sets that show an accuracy around 0.003 Å and 0.3° for bond lengths and angles, 1% and 3% for rotational and quartic centrifugal distortion constants, respectively, 12 cm−1 for fundamental frequencies and 3 km mol−1 for IR intensities. The B2PLYP-D3/maug-cc-pVTZ-dH level keeps the same accuracy, with slightly larger deviations for intensities.

Polarization consistent basis sets using the projector augmented wave method: a renovation brought by PAW into Gaussian basis sets.

A recently introduced framework incorporating the Projector Augmented Wave method and Gauss-type function (GTF-PAW) [X.-G. Xiong and T. Yanai, J. Chem. Theory Comput., 2017, 13, 3236-3249] opens alternative possibilities for performing low-cost molecular computational chemistry calculations. In this work, we present our first attempt to expand the applicability of this method by developing a family of compact general contracted polarization consistent basis sets (PAW-Ln) as an optimized GTF basis in combination with PAW. The results show that PAW-Ln, despite having small numbers of primitives, can provide not only better performance than effective core potential (ECP) but also good accuracy and desirable systematic convergence compared to larger all-electron basis sets. This demonstrates that GTF-PAW using the PAW-Ln basis sets could be a better alternative to both conventional all-electron- and ECP-based approaches for routine DFT calculations.

Probing basis set requirements for calculating hyperfine coupling constants.

A series of basis sets optimized for the calculation of the hyperfine coupling constant is proposed. The pcH-n basis sets are defined in qualities from double-ζ to pentuple-ζ for the elements H to Ar. They are derived from the polarization consistent basis sets by addition of two tight s-functions and one tight p-, d-, and f-function and are shown to provide an exponential convergence toward the complete basis set limit, and they have significantly lower basis set errors than other commonly used basis sets for a given ζ quality. The pcH basis sets display very similar basis set convergence with a range of density functional theory methods and may also be suitable for wave function based methods.

Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Δ Self-Consistent-Field Approach.

We investigate the basis set requirements for calculating properties corresponding to removing core electrons by the Δ self-consistent-field approach using Hartree-Fock and density functional theory. Standard contracted basis sets are shown to produce large errors and the improved performance of core-augmented basis sets is traced to the fact that the core-augmenting functions effectively create an auxiliary set of uncontracted functions in the core region. We propose two specific basis sets of double and triple-ζ quality based on exponent interpolation of the polarization consistent basis sets, denoted pcX-1 and pcX-2, that display significantly lower basis set errors compared to other alternatives. These are suitable for both nonrelativistic and relativistic calculations of the Douglas-Kroll-Hess type, with typical basis set errors of 0.1 and 0.01 eV, respectively, and they can be used in a mixed basis set approach with only a minor degradation in performance. The versions augmented with diffuse functions (aug-pcX-1 and aug-pcX-2) are shown to perform better than other alternatives for X-ray absorption spectroscopy. When used in connection with range-separated hybrid density functional methods and relativistic corrections, the pcX -n basis sets can in favorable cases reproduce experimental results to within a few tenths of an eV.

Development of polarization consistent basis sets for spin-spin coupling constant calculations for the atoms Li, Be, Na, and Mg.

The pcJ-n basis set, optimized for spin-spin coupling constant calculations using density functional theory methods, are expanded to also include the s-block elements Li, Be, Na, and Mg, by studying several small molecules containing these elements. This is done by decontracting the underlying pc-n basis sets, followed by augmentation with additional tight functions. As was the case for the p-block elements, the convergence of the results can be significantly improved by augmentation with tight s-functions. For the p-block elements, additional tight functions of higher angular momentum were also needed, but this is not the case for the s-block elements. A search for the optimum contraction scheme is carried out using the criterion that the contraction error should be lower than the inherent error of the uncontracted pcJ-n relative to the uncontracted pcJ-4 basis set. A large search over possible contraction schemes is done for the Li2 and Na2 molecules, and based on this search contracted pcJ-n basis sets for the four atoms are recommended. This work shows that it is more difficult to contract the pcJ-n basis sets, than the underlying pc-n basis sets. However, it also shows that the pcJ-n basis sets for Li and Be can be more strongly contracted than the pcJ-n basis sets for the p-block elements. For Na and Mg, the contractions are to the same degree as for the p-block elements.

Convergence of nuclear magnetic shieldings and one-bond 1 J(11 B1 H) indirect spin-spin coupling constants in small boron molecules.

Self-consistent field Hartree-Fock, density functional theory, and coupled-cluster calculations of the nuclear magnetic shielding constants of BH and BH3 molecules have been conducted to characterize the convergence of individual results obtained with correlation-consistent and polarization-consistent basis sets. The individual 11 B and 1 H NMR parameters were estimated in the complete basis set limit and compared with benchmark results. Only the KT3 density functional accurately reproduced 11 B shielding in BH molecule.

Density functional theory basis set convergence of sulfuric acid-containing molecular clusters

We investigate the basis set convergence of three density functionals (M06-2X, PW91, and ωB97X-D) with respect to the binding energy, thermal contribution to the Gibbs free energy, and optimized geometry. We apply correlation consistent, Pople-type, and polarization consistent basis sets with different amount of diffuse and polarization functions. Our test set contains six molecular cluster formation reactions which represent key noncovalent interactions in the atmosphere. In most cases partially augmented basis sets yield as accurate results as the fully augmented basis sets, with significant gain in computational efficiency. Relatively small basis sets are found to be sufficient to optimize geometries and to calculate thermal contributions to the Gibbs free energy. For binding energies, slightly bigger basis sets are needed to reach the complete basis set limit. The PW91 functional with the 6-311++G(3df,3pd) basis set gives a mean absolute error of 0.9kcal/mol in the binding energy, indicating that it has not reached the complete basis set limit. We estimate the effect of anharmonicity and derive scale factors to correct for it. When the lowest vibrational frequencies are treated separately, the errors arising from the anharmonicity of the remaining frequencies are small regardless of system size. We treated the low frequencies as free rotors and calculate thermal contributions to the Gibbs free energy using the quasi-harmonic approximation. We identify an error of a few percent of the total harmonic thermal contributions, which is larger than the error arising from vibrational anharmonicity.

Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn-Sham complete basis set limit.

In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested.The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated harmonic frequencies to the experimentally derived values, while the calculated anharmonic frequencies consistently underestimated the observed wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were consistently significantly higher than those obtained with the pc-3 basis set; applying the aug-pcseg-n basis set family alleviated this problem. Utilization of B3LYP/aug-pcseg-n basis sets instead of B3LYP/aug-cc-pVXZ, which is computationally less expensive, is suggested for medium-sized molecules. Harmonic BLYP/pc-2 calculations produced fairly accurate ethylene frequencies.Graphical In this study, the performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, and 6) was tested. For the first time, we demonstrated regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limitElectronic supplementary materialThe online version of this article (doi:10.1007/s00894-015-2902-z) contains supplementary material, which is available to authorized users.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed.

Sensitivity of 3He NMR Parameters to the Proximity of Heterocyclic Rings. The Helium–Furan Dimer

The potential of the NMR technique in probing the interaction between a noble gas atom (used as a spectroscopic probe) and five-membered heterocyclic systems was theoretically studied. Selected 3He NMR parameters of the free noble gas atom and its dimer were calculated using density functional theory with three functionals (M06-2X, CAM-B3LYP, and APFD), combined with dedicated polarization-consistent basis sets, and critically compared with theoretical high level calculations from the literature. The change of isotropic nuclear magnetic shielding of the free noble gas atom in the presence of furan (3He placed above the middle of the ring and used as NMR probe) increased with its proximity to the heterocyclic ring.

Application of the weak-field asymptotic theory to tunneling ionization ofH2O

The weak-field asymptotic theory of tunneling ionization in a static electric field is applied to ${\mathrm{H}}_{2}\mathrm{O}$. The orientation dependence of the ionization rate is studied. The use of polarization-consistent basis sets with up to heptuble-zeta accuracy and variationally optimized exponents improves the asymptotic form of the wave function and allows for an accurate extraction of the structure factor defining the ionization rate. The results are presented based on Hartree-Fock wave functions and density functional theory. The density functional theory reproduces closely the experimental vertical ionization potential. We find that the rate peaks at an angle of ${81}^{\ensuremath{\circ}}$ between the field and molecular principal inertial axis through the O atom. The predictions for the orientation dependence of the rate are compared to available theoretical results.

Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent Basis Sets.

We propose a method, denoted P-orthogonalization, for converting a general contracted basis set to a computationally more efficient segmented contracted basis set, while inheriting the full accuracy of the general contracted basis set. The procedure can be used for any general contracted basis set to remove the redundancies between general contracted functions in terms of primitive functions. The P-orthogonalization procedure is used to construct a segmented contracted version of the polarization consistent basis sets, which are optimized for density functional theory calculations. Benchmark calculations show that the new pcs-n basis sets provide uniform error control of the basis set incompleteness for molecular systems composed of atoms from the first three rows in the periodic table (H-Kr) and for different exchange-correlation functionals. The basis set errors at a given zeta quality level are lower than other existing basis sets, and the pcs-n basis sets are furthermore shown to be among the computationally most efficient. The pcs-n basis sets are available in qualities ranging from (unpolarized) double-zeta to pentuple zeta quality and should therefore be well suited for both routine and benchmark calculations using density functional theory methods in general.

Efficient Modeling of NMR Parameters in Carbon Nanosystems.

Rapid growth of nanoscience and nanotechnology requires new and more powerful modeling tools. Efficient theoretical modeling of large molecular systems at the ab initio and Density Functional Theory (DFT) levels of theory depends critically on the size and completeness of the basis set used. The recently designed variants of STO-3G basis set (STO-3Gel, STO-3Gmag), modified to correctly predict electronic and magnetic properties were tested on simple models of pristine and functionalized carbon nanotube (CNT) systems and fullerenes using the B3LYP and VSXC density functionals. Predicted geometries, vibrational properties, and HOMO/LUMO gaps of the model systems, calculated with typical 6-31G* and modified STO-3G basis sets, were comparable. The (13)C nuclear isotropic shieldings, calculated with STO-3Gmag and Jensen's polarization consistent pcS-2 basis sets, were also identical. The STO-3Gmag basis sets, being half the size of the latter one, are promising alternative for studying (13)C nuclear magnetic shieldings in larger size CNTs and fullerenes.

3He NMR: from free gas to its encapsulation in fullerene

The (3)He nuclear magnetic shieldings were calculated for single helium atom, its dimer, simple models of fullerene cages (He@Cn), and single wall carbon nanotubes. The performances of several levels of theory (HF, MP2, DFT-VSXC, CCSD, CCSD(T), and CCSDT) were tested. Two sets of polarization-consistent basis sets were used (pcS-n and aug-pcS-n), and an estimate of (3)He nuclear magnetic shieldings in the complete basis set limit using a two-parameter fit was established. Theoretical (3)He results reproduced accurately previously reported theoretical values for helium gas, dimer, and helium probe inside several fullerene cages. Excellent agreement with experimental values was achieved. (3)He nuclear magnetic shieldings of single helium atom approaching various points of benzene ring were tested, and an impact of (3)He confinement within fullerene cages of different size on the (3)He chemical shift was determined.

Structure factors for tunneling ionization rates of molecules

Within the weak-field asymptotic theory, the dependence of the tunneling ionization rate of a molecule in a static electric field on its orientation with respect to the field is determined by the structure factor for the highest occupied molecular orbital (HOMO). An accurate determination of this factor, and hence the ionization rate, requires accurate values of the HOMO in the asymptotic region. Techniques for calculating the structure factors for molecules in the Hartree-Fock approximation are discussed. For diatomics, grid-based numerical Hartree-Fock calculations which reproduce the correct asymptotic tail of the HOMO are possible. However, for larger molecules, to solve the Hartree-Fock equations one should resort to basis-based approaches with too rapidly decaying Gaussian basis functions. A systematic study of the possibility to reproduce the asymptotic tail of the HOMO in calculations with Gaussian basis sets is presented. We find that polarization-consistent basis sets with quadruple or pentuple-zeta quality greatly improve the tail of the HOMO, but only when used with variationally optimized exponents. This methodology is validated by considering the CO molecule for which reliable grid-based calculations can be performed. The optimized Gaussian basis sets are used to calculate the structure factors for the triatomic molecules CO${}_{2}$ and OCS. The results are compared with available experimental and theoretical results.

Polarization consistent basis sets. VIII. The transition metals Sc-Zn

Polarization consistent basis sets, optimized for density functional calculations, are proposed for the transition metals Sc-Zn. The basis set composition in terms of number of primitive functions and the contraction is defined based on energetic analyses of atoms and molecules along the lines used in previous work and on the performance for molecular systems. The performance for atomization energies and dipole moments is compared to other widely used basis sets, and it is shown that the new basis sets allow a systematic reduction of basis set errors and, in general, have basis set errors lower than or at par with existing ones.

Anharmonic vibrational frequency calculations for solvated molecules in the B3LYP Kohn–Sham basis set limit

The solvent dependence of harmonic and anharmonic vibrational wavenumbers of water, formaldehyde and formamide was studied using the B3LYP method. The results obtained with the hierarchy of Jensen's polarization-consistent basis sets were fitted with two-parameter formula toward the B3LYP Kohn–Sham complete basis set (CBS) limit. Anharmonic corrections have been obtained by a second order perturbation treatment (VPT2) and vibrational configuration interaction (VCI) method. The solvent environment was treated according to the self-consistent reaction field polarizable continuum model (SCRF PCM) approach.

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm(-1)) and high (>1000 cm(-1))], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero-point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc-n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree-Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05-2X, M06-2X), a double hybrid functional with Møller-Plesset correlation (B2GP-PLYP), and a dispersion corrected functional (B97-D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc-n, n = 1,2,3,4). A separate scale factor is recommended when the un-polarized basis set, pc-0, is used in combination with the density functionals.