Complete Basis Set Research Articles

Theoretical Investigation on Atmospheric Chemistry of Nitryl Cyanide: A Novel Fluorine-Free Dielectric Gas.

In view of the significant greenhouse effect of sulfur hexafluoride and the potential biotoxic hazard of perfluorinated substances, we proposed that nitryl cyanide (NCNO2), a nearly nonpolar molecule with a unique combination of two strongly electronegative and polarized functional groups, is a novel fluorine-free replacement to be used as the insulating gas in green electrical grids. Atmospheric chemistry of NCNO2 has been investigated theoretically to assess its environmental impact if emitted into the atmosphere. Potential energy surfaces for the reaction of NCNO2 with OH in the presence of O2 were calculated using the restricted open-shell complete basis set quadratic Becke3 and Gaussian-4 methods on the basis of the density functional (M06-2X) and couple-cluster (CCSD) optimized geometrical parameters. The oxidation of NCNO2 takes place via the nearly zero-barrier association of OH with the cyano-C to form energy-rich adducts NC(OH)NO2, followed by C-N bond rupture to the major HOCN + NO2 and the minor HONO + NCO products. Interception of the adduct by O2 can result in OH-regeneration together with further degradation to CO and NOx. Moreover, photolysis of NCNO2 under tropospheric sunlight conditions might compete with OH-oxidation. The atmospheric lifetime and radiative efficiency of NCNO2 were computed to be far less than those of either nitriles or nitro compounds. The global warming potential of NCNO2 was estimated to be in the range of 0-5 for a 100 year time horizon. However, the secondary chemistry of NCNO2 should be treated with caution in view of the production of NOx in the atmosphere.

Dynamics of C(3P) + OH(X 2Π) reaction on the new global HCO(X2A') potential energy surface.

A precise analytical potential energy surface (PES) of HCO(X2A') is fitted from a great quantity of abinitio energy points computed with the multi-reference configuration interaction method and aug-cc-pV(Q/5)Z basis sets. The whole energy points extrapolated to the complete basis set limit are fitted by the many-body expansion formula. The calculated topographic characteristics are analyzed and compared with the existing work to prove the precision of the present HCO(X2A') PES. By utilizing the time-dependent wave packet and quasi-classical trajectory methods, the reaction probabilities, integral cross sections, and rate constants are computed. The results are compared in detail with the former results carried out on the other PES. Moreover, the provided information on stereodynamics leads to an in-depth understanding of the role of collision energy in product distribution.

An accurate many-body expansion potential energy surface for HO2 (X 2A″) by extrapolation to the complete basis set limit and quantum dynamics of the related reaction O(3P) + OH(2Π)

A new global many-body expansion potential energy surface (PES) for the ground electronic state of HO2 is constructed. All ab initio energy points are employed using aug-cc-pV(Q+ d)Z and aug-cc-pV(5+ d)Z basis sets at the multi-reference conformational interaction level and then extrapolated to the complete basis set limit. The topographic characteristics of the global PES for HO2 (X 2A″) are discussed in detail and compared with experimental results, showing good agreement. We subsequently consider the O(3P) + OH(2Π) → O2(3 ) + H(2S) reaction using the time-dependent wave packet method and calculate dynamics behaviors, including the vibration–rotation distribution and reaction probabilities. The results indicate that the new PES is suitable for dynamics investigations of O(3P) + OH(2Π) → O2(3 ) + H(2S) and can be used as a component for PESs to construct larger oxygen/hydrogen containing systems.

Quantifying the Intrinsic Strength of C-H⋯O Intermolecular Interactions.

It has been recognized that the C-H⋯O structural motif can be present in destabilizing as well as highly stabilizing intermolecular environments. Thus, it should be of interest to describe the strength of the C-H⋯O hydrogen bond for constant structural factors so that this intrinsic strength can be quantified and compared to other types of interactions. This description is provided here for C2h-symmetric dimers of acrylic acid by means of the calculations that employ the coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)] together with an extrapolation to the complete basis set (CBS) limit. Dimers featuring the C-H⋯O and O-H⋯O hydrogens bonds are carefully investigated in a wide range of intermolecular separations by the CCSD(T)/CBS approach, and also by the symmetry-adapted perturbation theory (SAPT) method, which is based on the density-functional theory (DFT) treatment of monomers. While the nature of these two types of hydrogen bonding is very similar according to the SAPT-DFT/CBS calculations and on the basis of a comparison of the intermolecular potential curves, the intrinsic strength of the C-H⋯O interaction is found to be about a quarter of its O-H⋯O counterpart that is less than one might anticipate.

Mechanistic and kinetic study of the oxidation of trifluoroacetonitrile by hydroxyl and oxygen

AbstractTrifluoroacetonitrile (CF3CN) is one of the perfluoronitriles to be used as replacements for electrical insulation, working fluids, and biomedical applications. Potential energy surfaces for the reactions of CF3CN with OH radicals in the presence of molecular O2 have been calculated in details using the second‐order Møller−Plesset perturbation theory (MP2) and coupled‐cluster theory with single and double substitutions (CCSD) for geometrical optimization, and the restricted open‐shell complete basis set quadratic ROCBS‐QB3, multireference second‐order Rayleigh–Schrodinger perturbation theory extrapolated to complete basis set limit (RS2/CBS), and the explicitly‐correlated RS2 theory (RS2‐F12) for energetics. The CF3CN + OH reaction undergoes predominantly via the CO addition/elimination mechanism, leading to CF3C(OH)N radical adduct followed by the formation of CF3 and HOCN. The OH radicals could be recycled through the interception of CF3C(OH)N by O2 to form the orientation‐dependent CF3C(OH)NO2 radicals, leading to CF3C(O)NO + OH via the successive H‐migration and OO bond fission. Under the typical atmospheric conditions, the OH‐recycling mechanism is dominant for the oxidation of CF3CN. The production of CF3 and HOCN can be significant at high temperatures and low pressures. Theoretical rate coefficients are in excellent agreement with the experimental data. The effect of substitution on the reactivity of the perfluoronitriles toward OH was revealed. The present work provides a fundamental understanding on the degradation of CF3CN and serves as a theoretical basis for its secondary chemistry.

Single-Point Extrapolation to the Complete Basis Set Limit through Deep Learning.

Machine learning (ML) offers an attractive method for making predictions about molecular systems while circumventing the need to run expensive electronic structure calculations. Once trained on ab initio data, the promise of ML is to deliver accurate predictions of molecular properties that were previously computationally infeasible. In this work, we develop and train a graph neural network model to correct the basis set incompleteness error (BSIE) between a small and large basis set at the RHF and B3LYP levels of theory. Our results show that, when compared to fitting to the total potential, an ML model fitted to correct the BSIE is better at generalizing to systems not seen during training. We test this ability by training on single molecules while evaluating on molecular complexes. We also show that ensemble models yield better behaved potentials in situations where the training data is insufficient. However, even when only fitting to the BSIE, acceptable performance is only achieved when the training data sufficiently resemble the systems one wants to make predictions on. The test error of the final model trained to predict the difference between the cc-pVDZ and cc-pV5Z potential is 0.184 kcal/mol for the B3LYP density functional, and the ensemble model accurately reproduces the large basis set interaction energy curves on the S66x8 dataset.

Theoretical study of the spectroscopic constants of the ground state of the diatomic Ba-RG (RG = Kr, Xe, Rn) based on the coupled cluster theory with spin–orbit coupling

The spectroscopic constants including equilibrium distance, harmonic frequency and binding energy of the ground state of the diatomic Ba-RG (RG = Kr, Xe, Rn) are studied by using the closed-shell coupled-cluster theory with spin–orbit coupling (SOC) at the singles, doubles, and non-iterative triples level [CCSD(T)] based on the two-component relativistic pseudo-potentials. The advantage of the adopted computational protocol is that the SOC is incorporated in the post-Hartree–Fock part (i.e. the couple-cluster iteration) which makes it possible to significantly improve the computational efficiency. The extrapolation to the complete basis set (CBS) limit is used to provide the most accurate computational values in the framework of the adopted theoretical approach. The computational values to the CBS limit show that the SOC effect decreases the equilibrium distance by 0.067 Å while the binding energy increases by 21.023 cm−1 for the heaviest Ba-Rn, but not significant in the Ba-Kr and Ba-Xe. To date, both experimental and theoretical spectroscopic constants for Ba-Rn are unavailable, the present work thus provides the reliable theoretical results of the ground state of Ba-Rn for the future investigations.

Symmetry-adapted modeling for molecules and crystals

We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the complete symmetry-adapted multipole basis set to describe any of electronic degrees of freedom in isolated cluster systems and periodic crystals. The symmetry-adapted modeling is then achieved by expressing the Hamiltonian in terms of the linear combination of these bases belonging to the identity irreducible representation, and the model parameters (linear coefficients) in the Hamiltonian can be determined so as to reproduce the electronic structures given by the density-functional computation. We demonstrate our method for the modeling of graphene, and emphasize usefulness of the symmetry-adapted basis to analyze and predict physical phenomena and spontaneous symmetry breaking in a phase transition. The present method is complementary to de-facto standard Wannier tight-binding modeling, and it provides us with a fundamental basis to develop a symmetry-based analysis for materials science.

Comprehensive Theoretical Study on Four Typical Intramolecular Hydrogen Shift Reactions of Peroxy Radicals: Multireference Character, Recommended Model Chemistry, and Kinetics.

Intramolecular hydrogen shift reactions in peroxy radicals (RO2• → •QOOH) play key roles in the low-temperature combustion and in the atmospheric chemistry. In the present study, we found that a mild-to-moderate multireference character of a potential energy surface (PES) is widely present in four typical hydrogen shift reactions of peroxy radicals (RO2•, R = ethyl, vinyl, formyl methyl, and acetyl) by a systematic assessment based on the T1 diagnostic, %TAE diagnostic, M diagnostic, and contribution of the dominant configuration of the reference CASSCF wavefunction (C02). To assess the effects of these inherent multireference characters on electronic structure calculations, we compared the PESs of the four reactions calculated by the multireference method CASPT2 in the complete basis set (CBS) limit, single-reference method CCSD(T)-F12, and single-reference-based composite method WMS. The results showed that ignoring the multireference character will introduce a mean unsigned deviation (MUD) of 0.46-1.72 kcal/mol from CASPT2/CBS results by using the CCSD(T)-F12 method or a MUD of 0.49-1.37 kcal/mol by WMS for three RO2• reactions (R = vinyl, formyl methyl, and acetyl) with a stronger multireference character. Further tests by single-reference Kohn-Sham (KS) density functional theory methods showed even larger deviations. Therefore, we specifically developed a new hybrid meta-generalized gradient approximation (GGA) functional M06-HS for the four typical H-shift reactions of peroxy radicals based on the WMS results for the ethyl peroxy radical reaction and on the CASPT2/CBS results for the others. The M06-HS method has an averaged MUD of 0.34 kcal/mol over five tested basis sets against the benchmark PESs, performing best in the tested 38 KS functionals. Last, in a temperature range of 200-3000 K, with the new functional, we calculated the high-pressure-limit rate coefficients of these H-shift reactions by the multi-structural variational transition-state theory with the small-curvature tunneling approximation (MS-CVT/SCT) and the thermochemical properties of all of the involved key radicals by the multi-structural torsional (MS-T) anharmonicity approximation method.

Focal-Point Analysis to Achieve Accurate CCSD(T) Data Set References for Static Polarizabilities.

Static polarizability is an important ingredient for describing optical phenomena, intermolecular interactions, etc. It also offers a way to gauge the accuracy of the electronic structure methods. However, polarizability data sets that include a large variety of species with high-quality reference data are still lacking. In this work, we calibrate the reference data of two existing data sets, HR46 (Hickey and Rowley J. Phys. Chem. A 2014, 118, 3678-3687.) and T145 (Thakkar et al. Chem. Phys. Lett. 2015, 635, 257-261.), consisting of molecules with sizes up to 15 atoms. We apply the focal-point analysis (FPA) to the isotropic and anisotropic polarizability calculations, achieving the MP2 correlation contribution by the complete basis set (CBS) extrapolation of aug-cc-pCV[Q5]Z, augmented by the CCSD(T) correlation contribution from the CBS extrapolation of aug-cc-pV[XY]Z with [XY] = [Q5], [TQ], and [DT], respectively, to accommodate the computation to the system size. We conclude that our reference data are close to the CCSD(T)/aug-cc-pCV[Q5]Z quality, which are beneficial to the future assessment and benchmark studies of other electronic structure methods, in particular, density functional approximations.

High-Order Quantum-Mechanical Analysis of Hydrogen Bonding in Hachimoji and Natural DNA Base Pairs.

High-order quantum chemistry is applied to hydrogen-bonded natural DNA nucleobase pairs [adenine:thymine (A:T) and guanine:cytosine (G:C)] and non-natural Hachimoji nucleobase pairs [isoguanine:1-methylcytosine (B:S) and 2-aminoimidazo[1,2a][1,3,5]triazin-4(1H)-one:6-amino-5-nitropyridin-2-one (P:Z)] to see how the intermolecular interaction energies and their energetic components (electrostatics, exchange-repulsion, induction/polarization, and London dispersion interactions) vary among the base pairs. We examined the Hoogsteen (HG) geometries in addition to the traditional Watson-Crick (WC) geometries. Coupled-cluster theory through perturbative triples [CCSD(T)] extrapolated to the complete basis set (CBS) limit and high-order symmetry-adapted perturbation theory (SAPT) at the SAPT2+(3)(CCD)δMP2/aug-cc-pVTZ level are used to estimate highly accurate noncovalent interaction energies. Electrostatic interactions are the most attractive component of the interaction energies, but the sum of induction/polarization and London dispersion is nearly as large, for all base pairs and geometries considered. Interestingly, the non-natural Hachimoji base pairs interact more strongly than the corresponding natural base pairs, by -21.8 (B:S) and -0.3 (P:Z) kcal mol-1 in the WC geometries, according to CCSD(T)/CBS. This is consistent with the H-bond distances being generally shorter in the non-natural base pairs. The natural base pairs are energetically more stabilized in their Hoogsteen geometries than in their WC geometries. The Hoogsteen geometry makes the A:T base pair slightly more stable, by -0.8 kcal mol-1, and it greatly stabilizes the G:C+ base pair, by -15.3 kcal mol-1. The G:C+ stabilization is mainly due to the fact that C has typically added a proton when found in Hoogsteen geometries. By contrast, Hoogsteen geometries are substantially less favorable than WC geometries for non-natural Hachimoji base pairs, by 17.3 (B:S) and 13.8 (P:Z) kcal mol-1.

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.