Complete Basis Set Research Articles

Atomic Electronic Structure Calculations with Hermite Interpolating Polynomials.

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

Aiming for high-capacity multi-modal free-space optical transmission leveraging complete modal basis sets

Free-space optical (FSO) communication has gained much interest due to its capability of providing not only a cost-efficient solution where the optical fiber is too expensive or too difficult to deploy but also a much higher system capacity than its radio-frequency competitor. In addition to conventional polarization-division multiplexing and coherent detection, combining with mode-division multiplexing can unlock the full potential of FSO communications and achieve ultra-high spectral efficiency. In this paper, we review the recent progress of multi-modal FSO communication systems leveraging complete modal basis sets. Some practical issues for system design are discussed. We also present two latest demonstrations that achieved the record-high single-wavelength data rate using a commercial transponder and a pair of commercial multiplexer/demultiplexer for multi-modal FSO transmission without turbulence and in atmospheric turbulence, respectively, showing the potential of such a technique.

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

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

Computational studies of HCCCCS isomers

The recent identification of interstellar molecules HCCCHCCC and HCCCCS in TMC-1 has prompted an ab initio investigation of these isomers. The isomers of HCCCHCCC have been studied previously but not so much HCCCCS. In this paper we carry out high-level CCSD(T) calculations to characterise the lowest eleven isomers of HCCCCS. We also apply complete basis set extrapolation including core correlation and relativistic effects to further investigate the key isomers and provide high-precision rotational constants which will hopefully aid astronomers in their assignments. Source: This image has been adapted from http://www.eso.org/public/images/eso1209d/ licensed under CC BY-SA 3.0.

Multicomponent wavefunction-in-DFT embedding for positronium molecules.

This work presents an extension of the projector operator embedding scheme of Manby et al. [J. Chem. Theory Comput. 8, 2564 (2012)] in a multicomponent (MC) framework. Here, a molecular system containing electrons and other types of quantum species is divided into a wavefunction (WF) subsystem of interest and a density functional theory (DFT) environment. The WF-in-DFT partition decreases computational costs by partially truncating the WF subsystem basis set at the cost of introducing a controllable embedding error. To explore the applicability of the MC extension, third-order propagator-in-DFT calculations were performed for positron-anion complexes for alkoxides and carboxylates with carbon chains of different sizes. For these systems, it was found that selecting a WF subsystem with the positron and only the oxygen atoms caused an error of 0.1eV or lower in positron-binding energies, while reducing between 33% and 55% the basis set size. The reduction of computational costs achieved with the embedding scheme allowed us to improve molecular positron-binding energy predictions by performing complete basis set limit extrapolations. Combining the WF-in-DFT embedding and the complete basis set extrapolation, positronium aliphatic alkoxides were predicted to be energetically stable by 0.3eV with respect to Ps emission. Similarly, positronium carboxylates, both aromatic and aliphatic, were predicted to be stable by 1.3eV.

Size-Reduced Basis Set Calculation of Accurate Isotropic Nuclear Magnetic Shieldings Using CTOCD-GRRO and GPRO Methods in Amino Acids and Oligopeptides

The origin-independent magnetically induced CTOCD-GRRO and -GPRO (after continuous transformation of the origin of the current density-gradient of ρ and gradient of a power of ρ) current densities are shown to vary linearly with respect to their own defining α and β parameters. The same is reflected in the connected magnetic properties, in particular the magnetic shielding. This is exploited to find values for α and β that, using small basis sets, provide isotropic nuclear magnetic shieldings matching an accurate prediction, chosen as the complete basis set limit. An application to the 20 naturally occurring amino acids shows that different nuclei require different values of the parameters, which have been determined at the BHandHLYP/6-31+G(d,p) level with or without consideration of diversified chemical environments. Using CTOCD-GRRO and -GPRO methods, equipped with the optimized parameters at this low-cost level of calculation, 1H, 13C, 15N, and 17O magnetic shielding constants in glutathione, ophthalmic acid, and thyrotropin-releasing hormone are predicted with nearly the same accuracy as that of much more expensive calculations.

Basis Set Extrapolation of Vibrational Frequencies

We investigate three different approaches for extrapolating harmonic vibrational frequencies to the complete basis set limit, by direct extrapolation of the frequencies, by calculation of frequencies based on extrapolated Hessians, or based on the Hessian from optimization of the extrapolated energy surface. For regular molecules, the three extrapolation procedures yield essentially identical results, but for loosely bound complexes, the frequencies derived from extrapolated Hessians yield unpredictable behavior. None of the basis set extrapolations, however, provide any significant improvement over the results upon which the extrapolation is based.

Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions

We use the tridiagonal representation approach to solve the radial Schrödinger equation for the continuum scattering states of the Coulomb problem in a complete basis set of discrete Bessel functions. Consequently, we obtain a new representation of the confluent hypergeometric function as an infinite sum of Bessel functions, which is numerically very stable and more rapidly convergent than another well-known formula.

Bond dissociation energies of diatomic transition metal nitrides.

Resonant two-photon ionization (R2PI) spectroscopy has been used to measure the bond dissociation energies (BDEs) of the diatomic transition metal nitrides ScN, TiN, YN, MoN, RuN, RhN, HfN, OsN, and IrN. Of these, the BDEs of only TiN and HfN had been previously measured. Due to the many ways electrons can be distributed among the d orbitals, these molecules possess an extremely high density of electronic states near the ground separated atom limit. Spin-orbit and nonadiabatic interactions couple these states quite effectively, so that the molecules readily find a path to dissociation when excited above the ground separated atom limit. The result is a sharp drop in ion signal in the R2PI spectrum when the molecule is excited above this limit, allowing the BDE to be readily measured. Using this method, the values D0(ScN) = 3.905(29) eV, D0(TiN) = 5.000(19) eV, D0(YN) = 4.125(24) eV, D0(MoN) = 5.220(4) eV, D0(RuN) = 4.905(3) eV, D0(RhN) = 3.659(32) eV, D0(HfN) = 5.374(4) eV, D0(OsN) = 5.732(3) eV, and D0(IrN) = 5.115(4) eV are obtained. To support the experimental findings, ab initio coupled-cluster calculations extrapolated to the complete basis set limit (CBS) were performed. With a semiempirical correction for spin-orbit effects, these coupled-cluster single double triple-CBS calculations give a mean absolute deviation from the experimental BDE values of 0.20eV. A discussion of the periodic trends, summaries of previous work, and comparisons to isoelectronic species is also provided.

Improving the performance of fermionic neural networks with the Slater exponential Ansatz

AbstractIn this work, we propose a technique for the use of fermionic neural networks (FermiNets) with the Slater exponential Ansatz for electron‐nuclear and electron–electron distances, which provides faster convergence of target ground‐state energies due to a better description of the interparticle interaction in the vicinities of the coalescence points, while the accuracies of results, obtained with original and input‐modified FermiNets are similar due to high expressiveness of underlying neural network. Our analysis of learning curves indicates on the possibility to obtain accurate energies with smaller batch sizes using arguments of the bagging approach. In order to obtain even more accurate results for the ground‐state energies, we propose an extrapolation scheme for estimating Monte Carlo integrals in the limit of an infinite number of points. Numerical tests for a set of molecules demonstrate a good agreement with the results of the original FermiNets approach (achieved with larger batch sizes than required by our approach) and with results of the coupled‐cluster singles and doubles with perturbative triples (CCSD(T)) method that are calculated in the complete basis set limit.

Complete, Theoretical Rovibronic Spectral Characterization of the Carbon Monoxide, Water, and Formaldehyde Cations

New high-level ab initio quartic force field (QFF) methods are explored which provide spectroscopic data for the electronically excited states of the carbon monoxide, water, and formaldehyde cations, sentinel species for expanded, recent cometary spectral analysis. QFFs based on equation-of-motion ionization potential (EOM-IP) with a complete basis set extrapolation and core correlation corrections provide assignment for the fundamental vibrational frequencies of the A˜2B1 and B˜2A1 states of the formaldehyde cation; only three of these frequencies have experimental assignment available. Rotational constants corresponding to these vibrational excitations are also provided for the first time for all electronically excited states of both of these molecules. EOM-IP-CCSDT/CcC computations support tentative re-assignment of the ν1 and ν3 frequencies of the B˜2B2 state of the water cation to approximately 2409.3 cm-1 and 1785.7 cm-1, respectively, due to significant disagreement between experimental assignment and all levels of theory computed herein, as well as work by previous authors. The EOM-IP-CCSDT/CcC QFF achieves agreement to within 12 cm-1 for the fundamental vibrational frequencies of the electronic ground state of the water cation compared to experimental values and to the high-level theoretical benchmarks for variationally-accessible states. Less costly EOM-IP based approaches are also explored using approximate triples coupled cluster methods, as well as electronically excited state QFFs based on EOM-CC3 and the previous (T)+EOM approach. The novel data, including vibrationally corrected rotational constants for all states studied herein, provided by these computations should be useful in clarifying comet evolution or other remote sensing applications in addition to fundamental spectroscopy.

Accuracy of Noncovalent Interactions Involving d-Elements by the 1-Determinant Fixed-Node Diffusion Monte Carlo Method with Effective Core Potentials.

A critical assessment of effective core potential (ECP)-based single-determinant (SD) fixed-node diffusion quantum Monte Carlo (FNDMC) accuracy in prototypical noncovalent closed-shell systems involving d-elements is presented. Careful analysis of biases and elimination of possible bias sources leads to two findings of practical importance for SD FNDMC in these systems. First, in some systems (HCu:HCu, HCu:CuH), SD FNDMC reveals large biases of interaction energy differences (significantly exceeding the target 2% relative error) vs a reliable coupled-cluster CCSD(T)/CBS (complete basis set) reference. Second, the leading error of SD FNDMC with ECPs was attributed to a higher nuclear charge Z of d-group (pseudo) atoms, when compared to sp elements, in line with a previously reported finding that aggregate SD FNDMC bias tends to increase in systems with higher electronic densities. Therefore, SD FNDMC should only be used with caution in systems with a large Z.

Benchmarking two-body contributions to crystal lattice energies and a range-dependent assessment of approximate methods.

Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol-1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%.

Characterization of competing halogen-bonding and hydrogen-bonding motifs in the acetonitrile/hydrogen iodide dimer

Three different C3v configurations of the CH3CN/HI dimer have been characterized using MP2 and CCSD(T) methods with large correlation consistent basis sets. All three stationary points are minima. The hydrogen bonded CH3CN⋯HI configuration is the global minimum (GM) with an electronic dissociation energy exceeding 4 kcal mol−1 near the CCSD(T) complete basis set (CBS) limit. A strongly bound halogen-bonded form of the dimer, CH3CN⋯IH, lies within 0.9 kcal mol−1 of the GM according to CCSD(T) electronic energies extrapolated to the CBS limit. The energetic separation between the two minima decreases by approximately 0.1 kcal mol−1 at all levels of theory when the harmonic zero-point vibrational energies are included. A third minimum was identified in which iodine interacts with the hydrogens of the methyl group (HI⋯CH3CN). This minimum is significantly higher in energy than the GM, almost within 1 kcal mol−1 of the dissociation limit. The GM has been previously identified via matrix isolation infrared spectroscopy. The energetics, vibrational frequencies, and infrared intensities computed here corroborate the tentative assignment of a second feature in the HI stretching region of the experimental infrared spectrum to the halogen-bonded configuration.

Investigation of Methylcyclopentadiene Reactivity: Abstraction Reactions and Methylcyclopentadienyl Radical Unimolecular Decomposition.

Understanding the reactivities of methylcyclopentadiene and the methylcyclopentadienyl radical is important in order to improve our comprehension of the chemical kinetics leading to the formation, decomposition, and growth of the first aromatic ring, as it has been shown that five-membered-ring species are important intermediates in the reaction kinetics of aromatic species. In this work, the rate constants of some key H-abstraction reactions from methylcyclopentadiene to produce the methylcyclopentadienyl radical and the formation of fulvene and benzene from the latter are theoretically determined. Rate constants are evaluated using the ab initio transition state theory-based master equation approach, determining structures and Hessians of all stationary points at the ωB97X-D/aug-cc-pVTZ level, energies at the CCSD(T) level extrapolated to the complete basis set limit, RRKM rate constants using conventional and variational transition state theory, and phenomenological rate constants through the solution of the one-dimensional master equation. Variational corrections are determined in both internal and Cartesian coordinates, and it is found that the choice of the coordinate system can impact the accuracy of the calculated rate constants by up to a factor of 4 for H-abstraction reactions and 2 for the unimolecular decomposition of the methylcyclopentadienyl radical. The calculated rate constants are in good agreement with the available literature data. Prompt dissociation of methylcyclopentadienyl radicals accessed following H-abstraction from methylcyclopentadiene was also investigated, and the corresponding rate constants were determined; the results show that prompt dissociation plays a key role under combustion conditions. Finally, lumping of theoretically derived rate constants to account for methylcyclopentadiene ⇄ methylcyclopentadienyl tautomerism allowed the derivation of a simplified set of rate constants suitable to be inserted into kinetic mechanisms.

High-Level Coupled-Cluster Study on Substituent Effects in H2 Activation by Low-Valent Aluminyl Anions.

The synthesis of novel aluminyl anion complexes has been well exploited in recent years. Moreover, the elucidation of the structure and reactivity of these complexes opens the path toward a new understanding of low-valent aluminum complexes and their chemistry. This work computationally treats the substituent effect on aluminyl anions to discover suitable alternatives for H2 activation at a high level of theory utilizing coupled-cluster techniques extrapolated to the complete basis set. The results reveal that the simplest AlH2- system is the most reactive toward the activation of H2, but due to the low steric demand, severe difficulty in the stabilization of this system makes its use nonviable. However, the results indicate that, in principle, aluminyl systems with -C, -CN, -NC, and -N chelating centers would be the best choices of ligand toward the activation of molecular hydrogen by taking care of suitable steric demand to prevent dimerization of the catalysts. Furthermore, computations show that monosubstitution (besides -H) in aluminyl anions is preferred over disubstitution. So our predictions show that bidentate ligands may yield less reactive aluminyl anions to activate H2 than monodentate ones.

Is explicitly correlated double-hybrid density functional theory advantageous for vibrational frequencies?

We have investigated the effect of F12 geminals on the basis set convergence of harmonic frequencies calculated using two representative double-hybrid density functionals, namely, B2GP-PLYP and revDSD-PBEP86-D4. Like previously found for energetics (Mehta N.; Martin J. M. L. J. Chem. Theory Comput. 2022, 18, 5978), one sees an acceleration by two zeta steps, such that even the cc-pVDZ-F12 basis set is quite close to the complete basis set (CBS) limit. However, the basis set convergence problem is not as acute as for energetics, and compared with experimental harmonic frequencies, conventional orbital calculations with augmented triple zeta quality basis set are acceptably close to the CBS limit, and can be carried out using analytical second derivatives. An efficient implementation of double-hybrid F12 analytical derivatives would make the F12 approach attractive in the sense that even an spd orbital basis set would be adequate. For the accurate revDSD-PBEP86-D4 functional, the role of differing local correlation terms (Perdew–Zunger 1981 versus VWN5) in different electronic structure programs has been investigated, while optimal double-hybrid parameters and performance statistics for energetics as well as frequencies differ slightly between the two implementations; these differences are insignificant for practical purposes.

Redox Potentials with COSMO-RS: Systematic Benchmarking with Different Databases.

Recent techniques of computational electrochemistry can yield redox potentials with accuracy as good as 0.1 V. Yet, many such methods are not universal, easy to use, or computationally efficient. Herein, we provide a systematic benchmarking of a relatively cheap and straightforward computational approach for fairly accurate computations of redox potentials. It is based on a combination of the conductor-like screening model for real solvents (COSMO-RS) and the density functional theory (DFT). The benchmarking is done with databases covering diverse redox systems, including transition-metal aquacomplexes and various organic and inorganic compounds. In addition, we also present our own test set aiming at maximum chemical diversity and maximum range of redox potential values. We assess the performance of the fairly efficient computational protocol combining the COSMO-RS with the BP86 DFT functional. This is done by calibrating it against different high-level state-of-the-art techniques, in particular, polarizable continuum model (PCM) connected to composite G3(MP2,CC)(+) method, domain-based pair natural orbital implementation of coupled cluster theory, or complete basis set CBS-QB3 method. We also elaborate on the absolute reduction potential value of standard hydrogen electrode to be used with COSMO-RS, and we propose the value of approx. 4.4 V. The COSMO-RS/BP86-D3(BJ) combination outperforms other methods on a wide range of redox systems. However, we show that its accuracy is based on a balanced error cancelation and, therefore, it cannot be further systematically improved. As a result, the proposed procedure represents a pragmatic choice for large-scale screening, yet it could be combined with more advanced methods for detailed studies.

Mechanistic and Kinetic Investigations on Decomposition of Trifluoromethanesulfonyl Fluoride in the Presence of Water Vapor and Electric Field

As a potential insulation gas to replace sulfur hexafluoride (SF6) due to environmental concerns, trifluoromethanesulonyl fluoride (CF3SO2F) has attracted great interests in various high-voltage electric applications. Thermal stability of CF3SO2F plays an important role in the rational design of the gas-insulated electric equipment. Unimolecular decomposition of CF3SO2F was investigated using high-level ab initio methods including the explicitly correlated RCCSD(T)-F12, the composite ROCBS-QB3, and the multireference RS2 extrapolated to complete basis set limit on the basis of M06-2X-, B2PLYPD3-, and CCSD-optimized geometrical parameters. Rate coefficients and decomposition temperatures were simulated using master equations. CF3SO2F decomposes predominantly via a simple C-S bond cleavage to form CF3 and SO2F, accompanied by a roaming induced F-abstraction detour to release CF4 and SO2, or isomerizes via CF3 migration to the more stable CF3OSFO followed by the production of CF2O and SOF2. Various characteristic decomposition products (e.g., CF4, C2F6, CF2O, SO2, SOF2, SO2F2, CF3H, and so on.) have been identified theoretically through secondary reactions and hydrolysis of CF3SO2F in the presence of water vapor. Electronic structures and stability of CF3SO2F could be affected significantly by the external electric field orientated along the S-C bond. The field-dependent electron-molecule capture rates support that CF3SO2F is superior to SF6 in dielectric strength. The present computational findings shed light on the practical use of CF3SO2F as the replacement gas for SF6.

Canonical Unified Statistical Rate Constants Using a High-Level Composite Coupled Cluster Energy Scheme for the CH4 + CH Reaction

We report an ab initio study on the kinetics and chemical dynamics of the CH4 + CH reaction using a coupled cluster based composite scheme that includes unrestricted coupled cluster singles and doubles with perturbative connected triples method, UCCSD(T), energies extrapolated to the complete basis set limit, in addition to core-valence, higher-order correlation, and relativistic corrections. With this protocol, the reaction enthalpies for the two main reaction channels, C2H4 + H and CH2 + CH3, are reproduced with an absolute deviation of 0.04 kcal mol–1 relative to experimental data. At the UCCSD(T)/complete basis set (CBS) level of theory, the formation of the C2H5 intermediate is barrierless, in contrast with the low submerged barrier (–1.87 kcal -mol–1 relative to the reactants) found at the UCCSD(T)/augmented correlation-consistent polarized double-zeta (aug-cc-pVDZ) level of theory. With the correlation-consistent polarized triple-zeta (cc-pVTZ) basis set, we describe structural variations for the reaction bottleneck along the reaction path, finding at least three canonical variational transition states for the temperature range from 20 to 800 K. The thermal rates were obtained via the canonical unified statistical theory (CUS), using the canonical variational transition state theory (VTST) for the inner-transition state and long-range transition state theory (LRTST) for the outer-transition state. Our calculations agree with literature measurements and show inverse Arrhenius behavior, as observed experimentally. At 298 K, the computed rate constant is 2.65 × 10–10 cm3 molecule–1 s−1 and reported experimental measurements range from 2.5 × 10−12 to 3.0 × 10–10 cm3 molecule–1 s−1. Our theoretical study represents an improvement on previous computational investigations and highlights that even relatively simple gas-phase reactions can require high levels of theory to be modeled accurately.