Basis Set Limit Research Articles

Approximating large-basis coupled-cluster theory vibrational frequencies using focal-point approximations.

The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller-Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. The focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm-1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H2O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules.

On the Intermolecular Interactions in Thiophene-Cored Single-Stacking Junctions.

There have been attempts, both experimental and based on density-functional theory (DFT) modeling, at understanding the factors that govern the electronic conductance behavior of single-stacking junctions formed by pi-conjugated materials in nanogaps. Here, a reliable description of relevant stacked configurations of some thiophene-cored systems is provided by means of high-level quantum chemical approaches. The minimal structures of these configurations, which are found using the dispersion-corrected DFT approach, are employed in calculations that apply the coupled cluster method with singles, doubles and perturbative triples [CCSD(T)] and extrapolations to the complete basis set (CBS) limit in order to reliably quantify the strength of intermolecular binding, while their physical origin is investigated using the DFT-based symmetry-adapted perturbation theory (SAPT) of intermolecular interactions. In particular, for symmetrized S-Tn dimers (where "S" and "T" denote a thiomethyl-containing anchor group and a thiophene segment comprising "n" units, respectively), the CCSD(T)/CBS interaction energies are found to increase linearly with n ≤ 6, and significant conformational differences between the flanking 2-thiophene group in S-T1 and S-T2 are described by the CCSD(T)/CBS and SAPT/CBS computations. These results are put into the context of previous work on charge transport properties of S-Tn and other types of supramolecular junctions.

High-level ab initio composites: thermochemical bond dissociation energies for vanadium species

Bond dissociation energies (BDE) are among the most sought-after properties in chemistry. Accurate prediction of BDE’s for transition metal species can be daunting for both experiment and computation. Experimental data has been limited and often has large error bars, making the identification of suitable computational methods difficult. Recent advancements in the experimental determination of BDE’s with techniques such as Velocity Map Imaging and 2 Photon Ionisation now provide useful gauges for computational strategies and new methodologies. The vanadium diatomics have been challenging for computational chemistry methods, and, thus, a new experimental gauge enables methods to be reevaluated and developed for these species. Herein, the super-correlation consistent Composite (s-ccCA), a thermochemical scheme centered around CCSD(T)/complete basis set (CBS) limit computations with additional contributions that account for scalar-relativistic effects, and coupled cluster contributions up to quintuple excitations has been considered. The agreement between the s-ccCA scheme and by recent experiments is excellent, demonstrating the utility of the new approach in addressing challenging systems, even those of multireference nature. The longstanding correlation consistent composite approach (ccCA) is also reevaluated for the vanadium species and find that the mean absolute deviation (MAD) is greatly reduced compared to previously used experimental values.

Even Faster Exact Exchange for Solids via Tensor Hypercontraction.

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals.

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

Accurate Calculation of Isomerization and Conformational Energies of Larger Molecules Using Explicitly Correlated Local Coupled Cluster Methods in Molpro and ORCA.

An overview of the approximations in the explicitly correlated local coupled cluster methods PNO-LCCSD(T)-F12 in Molpro and DLPNO-CCSD(T)F12 in ORCA is given. Options to select the domains of projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and triples natural orbitals (TNOs) in both programs are described and compared in detail. The two programs are applied to compute isomerization and conformational energies of the ISOL24 and ACONFL test sets, where the former is part of the GMTKN55 benchmark suite. Thorough studies of basis set effects are presented for selected systems. These revealed large intramolecular basis set superposition effects that make it practically impossible to reliably determine the complete basis set (CBS) limits without including explicitly correlated terms. The latter strongly reduce the basis set dependence and at the same time also errors caused by the local domain approximations. On the basis of these studies, the PNO-LCCSD(T)-F12 method is applied to determine new reference energies for the above-mentioned benchmark sets. We are confident that our results should agree within a few tenths of a kcal mol-1 with the (unknown) CCSD(T)/CBS values, which therefore allowed us to define computational settings for accurate explicitly correlated local coupled cluster methods with moderate computational effort. With these protocols, especially PNO-LCCSD(T)-F12b/AVTZ', reliable reference values for comprehensive benchmark sets can be generated efficiently. This can significantly advance the development and evaluation of the performance of approximate electronic structure methods, especially improved density functional approximations or machine learning approaches.

Structural, Spectroscopic, and Dynamic Properties of Li2+(X2∑g+) in Interaction with Krypton Atom.

We report a computational study of the potential energy surface (PES) and vibrational bound states for the ground electronic state of Li2+Kr. The PES was calculated in Jacobi coordinates at the Restricted Coupled Cluster method RCCSD(T) level of calculation and using aug-cc-pVnZ (n = 4 and 5) basis sets. Afterward, this PES is extrapolated to the complete basis set (CBS) limit for correction. The obtained interaction energies were, then, interpolated numerically using the reproducing kernel Hilbert space polynomial (RKHS) approach to produce analytic expressions for the 2D-PES. The analytical PES is used to solve the nuclear Schrodinger equation to determine the bound states' eigenvalues of Li2+Kr for a J = 0 total angular momentum configuration and to understand the effects of orientational anisotropy of the forces and the interplay between the repulsive and attractive interaction within the potential surface. In addition, the radial and angular distributions of some selected bound state levels, which lie below, around, and above the T-shaped 90° barrier well, are calculated and discussed. We note that the radial distributions clearly acquire a more complicated nodal structure and correspond to bending and stretching vibrational motions "mode" of the Kr atom along the radial coordinate, and the situation becomes very different at the highest bound states levels with energies higher than the T-shaped 90° barrier well. The shape of the distributions becomes even more complicated, with extended angular distributions and prominent differences between even and odd states.

Highly accurate potential energy surface and dipole moment surface for nitrous oxide and 296K infrared line lists for 14N2 16O and minor isotopologues

To facilitate the data analysis of current and future high-resolution space telescope missions, we adopt ‘Best Theory + Reliable High-resolution Experiment’ (BTRHE) strategy to develop highly accurate infrared line lists for nitrous oxide (N2O). The ‘Ames-1’ potential energy surface (PES) is a CCSD(T)/aug-cc-pVQZ PES refined using selected HITRAN experimental data, with σ rms = 0.02–0.03 cm-1 for five isotopologues. The ‘Ames-1’ dipole moment surface (DMS) is fitted from CCSD(T)/aug-cc-pV(T,Q,5)Z dipoles extrapolated to one electron basis set limit. Using the Ames-1 PES and DMS, Ames-296K line lists are computed in the full range of 0–15,000 cm-1 for 12 N2O isotopologues, with S 296K ≥ 10−31 cm-1/molecule.cm-2. The reliability and consistency of Ames-296K intensity predictions (S Ames) are demonstrated through comparisons with HITRAN (S HITRAN), NOSL-296 (S NOSL), recent observed intensities (S obs) and Effective Dipole Model (EDM) intensities (S EDM). Agreements and discrepancies are discussed, along with preliminary uncertainty estimate for S Ames. The S Ames provides a good constraint to prevent substantial errors in intensity predictions (e.g. for weak bands and minor isotopologues) and can be further improved. Ames-296K and NOSL-296 may complement each other to provide improved input for future database updates, combining the strengths of EH/EDM and BTRHE approaches. Data available at https://doi.org/10.5281/zenodo.7888194 and https://doi.org/10.48667/9kmk-0334.

Accurate thermochemistry at affordable cost by means of an improved version of the JunChS-F12 model chemistry.

The junChS-F12 composite method has been improved by means of the latest implementation of the CCSD(F12*)(T+) ansatz and validated for the thermochemistry of molecules containing atoms of the first three rows of the periodic table. A thorough benchmark showed that this model, in conjunction with cost-effective revDSD-PBEP86-D3(BJ) reference geometries, offers an optimal compromise between accuracy and computational cost. If improved geometries are sought, the most effective option is to add MP2-F12 core-valence correlation corrections to CCSD(T)-F12b/jun-cc-pVTZ geometries without the need of performing any extrapolation to the complete basis set limit. In the same vein, CCSD(T)-F12b/jun-cc-pVTZ harmonic frequencies are remarkably accurate without any additional contribution. Pilot applications to noncovalent intermolecular interactions, conformational landscapes, and tautomeric equilibria confirm the effectiveness and reliability of the model.

PO+−He collision: ab initio potential energy surface and inelastic rotational rate coefficients

ABSTRACT Computations involving quantum dynamics are performed to attain cross-sections corresponding to rotational de-excitation and excitation rates of the PO+ species including four rotational lines recently detected in the interstellar molecular clouds. New ab initio potential energy surface (PES) for PO+−He collision is constructed by using CCSD(T) method and basis set extrapolated to complete basis set limit (CBS) considering a rigid rotor approximation. The PES is then trained to create neural network (NN) model to construct an augmented surface with angular coordinates at 1° intervals. The PES has a global minimum located at $\theta =110{}^{\circ }$ and R = 3.1 Å. An analytical fitting is performed on the NN surface to obtain the first 41 radial coefficients needed to solve the equations of the coupled-channel method. The essentially precise close coupling approach is used to compute the rotational (de-)excitation cross-sections till 1400 cm−1 with rotational states converged up to 26. Further, these cross-sections are thermally averaged to get the rate coefficients for various rotational transitions till 200 K. The propensity rule favours the odd transitions (Δj = 1) for the current study. The rate for the transition 5 → 4 is found to be higher than transition 1→ 0 by a factor of 3.1 at T = 20 K that decreases to 2.1 at T = 100 K.

Benchmark coupled-cluster lattice energy of crystalline benzene and assessment of multi-level approximations in the many-body expansion.

The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller-Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod-Teller-Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol-1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol-1. Our CCSD(T)/CBS best estimate of the 0K lattice energy is -54.01 kJ mol-1, compared to an estimated experimental value of -55.3 ± 2.2 kJ mol-1.

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.

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.

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.