Basis Set Extrapolation Research Articles

Automatic Orbital Pair Selection for Multilevel Local Coupled-Cluster Based on Orbital Maps.

We present an automatic, orbital-map based orbital-pair selection scheme for multilevel local coupled-cluster approaches that exploits the locality of chemical reactions by focusing on the part of the molecule directly involved in the reaction. The previously introduced pair-selected multilevel extension to domain-based local pair natural orbital coupled-cluster with singles, doubles, and semicanonical perturbative triples [DLPNO-CCSD(T0)] partitions the orbital pairs according to relative changes in pair correlation energies [Bensberg, M.; Neugebauer, J. Orbital pair selection for relative energies in the domain-based local pair natural orbital coupled-cluster method. J. Chem. Phys. 2022, 157, 064102. 10.1063/5.0100010]. To this end, maps between localized orbitals are required which in turn require maps between the atoms of structures along reaction paths. So far, these atom maps have been manually determined, which can be a (human) time-consuming procedure. Here, we present an automatic atom mapping algorithm based on the principle of minimum chemical distance that incorporates orientation dependence through dihedral angles. A similar strategy is then introduced to obtain orbital maps, which proves advantageous over the previously used direct orbital selection. Along with a modified orbital pair prescreening, this results in an improved variant of the pair-selected multilevel DLPNO-CCSD(T0) method. The performance of this approach is demonstrated for various reaction types showing a significant efficiency gain and accurate results due to beneficial, systematic error cancellation. The presented method operates in a black-box manner due to its fully automatized algorithms with only the need to specify a single target-accuracy parameter. Additionally, we demonstrate that basis set extrapolation techniques can be applied. In this context, the approach shows deficiencies for the use of large basis sets, especially with diffuse basis functions, which can be traced back to the semicanonical triples correction.

Theoretical study on the spectroscopic and transition properties of phosphorus dimer cation

The potential energy curves of 18 Λ-S states of the P2 + cation have been constructed using the internally contracted multi-reference configuration interaction approach combined with the Davidson correction. The basis-set extrapolation to the complete basis set limit is performed. The relativistic effect is considered in calculations. Treatment of scalar relativistic effect at the third-order Dkroll-Hess approximate and spin-orbit coupling with the state-average Breit-Pauli operator is made. Based on the obtained potential energy curves, the spectroscopic parameters for all bound Λ-S and Ω states are determined. These results are in agreement with experiment where the spectroscopic data are available. The transition dipole moments are calculated. The properties of the dipole-allowed transitions among doublet or quartet Λ-S states are evaluated, from which Einstein coefficients, Franck-Condon factors and radiative lifetimes are estimated. The spin-orbit coupling effect on the transition properties of the 12Πg→X2Πu system is also studied. The spectroscopic and transition properties reported in this study can be used to guide the detection of phosphorus dimer cation in spectroscopy experiments.

Anion photoelectron spectroscopy and chemical bonding of ThS2- and ThSO.

Anion photoelectron spectra of ThSO- and ThS2- were recorded using the third (355nm) harmonic of an Nd-YAG laser; these provided the measured vertical detachment energies of each anion. The experiments are supported by extensive coupled cluster calculations on ThSO, ThSO-, ThS2, and ThS2-, as well as the oxygen congeners ThO2 and ThO2-. The abinitio calculations, which included complete basis set extrapolations, spin-orbit effects using four-component coupled cluster, and higher-order correlation contributions through CCSDT(Q), yielded an adiabatic electron affinity for ThO2 that was within 0.02eV of the previously determined experimental value. The singly occupied molecular orbital (SOMO) in all three anions corresponds primarily to the 7s orbital on Th. Successive substitution of S for each O in ThO2 leads to larger electron affinities and smaller bond angles in the neutral molecules, but larger angles in the anions. As demonstrated by Franck-Condon simulations of the spectra using the CCSD(T) spectroscopic constants, substitution of O by S significantly complicates the resulting detachment spectra due to the lower vibrational frequencies in the sulfur species. Overall the calculated vertical detachment energies are in very good agreement with the experiment. In addition to the adiabatic electron affinities of each species, atomization energies and heats of formation have also been determined via the FPD approach with expected uncertainties of 1-2 kcal/mol.

Basis Set Extrapolation from the Vanishing Counterpoise Correction Condition.

Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems or from fitting extrapolation parameters to reference energetics for a small(ish) training set. Seeking to avoid both, we explore a third alternative: extracting extrapolation parameters from the requirement that the BSSE (basis set superposition error) should vanish at the complete basis set limit. We find this to be a viable approach provided that the underlying basis sets are not too small and reasonably well balanced. For basis sets not augmented by diffuse functions, BSSE minimization and energy fitting yield quite similar parameters.

Molecular structure and spectra of ytterbium dihalides from first principles

The molecular structure, vibrational frequencies, infrared intensities and electric dipole moments of ytterbium dihalides YbX2 (X = F, Cl, Br, I) in their ground electronic state are studied at the coupled-cluster singles, doubles and perturbative triples CCSD(T) level using a series of large all-electron basis sets together with the complete basis set (CBS) extrapolation procedure, and with both scalar-relativistic and spin–orbit coupling effects taken into account. Excitation energies of low-lying electronic states are calculated at the multireference configuration interaction, equation-of-motion CCSD and single-reference CCSD(T) levels of theory. For all of the molecules under study, the CCSD(T)/CBS equilibrium geometries are found to be non-linear (C2v symmetry). There is a rapid decrease in heights of the barriers to linearity on passing through the YbX2 molecular series from fluoride to iodide: 1587 → 261 → 110 → 7 (all in cm−1) for YbF2 → YbCl2 → YbBr2 → YbI2, respectively. The uncertainties in the molecular structure data published to date are discussed and resolved in the light of the present results.

Calculated Aqueous Reduction Potentials of Neutral and Anionic Halogen Diatomic Molecules.

The free energy of hydration, aqueous, and gas phase electron affinity and aqueous reduction potentials of F2, Cl2, Br2, I2, ClF, BrF, IF, BrCl, ICl, IBr, and their corresponding anions were calculated using an electronic structure approach previously developed for these properties for X• and XO•, where X is a halogen which yielded excellent results. The gas phase electron affinities were calculated at the Feller-Peterson-Dixon level based on complete basis set extrapolation of CCSD(T) results with additional corrections. The agreement with the available experimental data is excellent, and the calculations provide a complete set of reliable electron affinities for these diatomic halogens. The hybrid solvation approach uses single point implicit solvation calculations on gas phase optimized clusters with explicit solvent molecules. The gas phase energy calculations were performed using MP2 and CCSD(T)-F12b for tetramer clusters (four explicit waters) and MP2 for octamer clusters (eight explicit waters). The final redox potentials were obtained at the MP2/aug-cc-pVTZ (aT) with a self-consistent reaction field (SMD) level using the octamer clusters. The aqueous reduction potentials of the neutral diatomic halogens are predicted within 0.06 V of the experiment for diatomic neutrals. The same agreement of 0.06 V is predicted for the redox potential resulting from dissociation electron attachment of the diatomic halogen anions. The current work extends reduction potentials for multiple redox couples for which no experimental data is available, for example, those containing iodine and the interhalogen anions. F2•- is predicted to dissociate for its lowest energy structure in both the tetramer and octamer clusters to form solvated F-, HF, and OH•.

Toward Accurate Quantum Chemical Methods for Molecules of Increasing Dimension: The New Family of Pisa Composite Schemes.

The new versions of the Pisa composite scheme introduced in the present paper are based on the careful selection of different quantum chemical models for energies, geometries, and vibrational frequencies, with the aim of maximizing the accuracy of the overall description while retaining a reasonable cost for all the steps. In particular, the computation of accurate electronic energies has been further improved introducing more reliable complete basis set extrapolations and estimation of core-valence correlation, together with improved basis sets for third-row atoms. Furthermore, the reduced-cost frozen natural orbital (FNO) model has been introduced and validated for large molecules. Accurate molecular structures can be obtained avoiding complete basis set extrapolation and evaluating core-valence correlation at the MP2 level. Unfortunately, analytical gradients are not available for the FNO version of the model. Therefore, for large molecules, an accurate reduced-cost alternative is offered by evaluation of valence contributions with a double-hybrid functional in conjunction with the same MP2 contribution for core-valence correlation or by means of a one-parameter approximation. The same double-hybrid functional and basis set are employed to evaluate zero-point energies and partition functions. After the validation of the new models for small systems, a panel of molecular bricks of life has been used to analyze their performances for problems of current fundamental or technological interest. The fully black-box implementation of the computational workflow paves the way toward the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by experimentally oriented researchers.

Building a New Platform for Significantly Improving Performance of Hartree-Fock and CCSD(T) Correlation Energy Based on Two-Point Complete Basis Set Extrapolation Schemes.

The leading cause of high expense in gold standard coupled cluster theory is that calculations of electronic energies converge exceedingly slowly with an increased basis set size. Extrapolation principally allows for achieving higher-quality outcomes at reduced costs. Numerous extrapolation formulas have been developed, with attempts to predict energies up to the complete basis set limit. Unfortunately, since the intricate shape of the function hinges on the molecular properties with the highest angular momentum of the basis set, the accuracy of the extrapolated energies highly depends on the fitted empirical parameters, which rely on the quality of the data sets for fitting. In this work, to overcome the extrapolation deficiency caused by the very limited data sets and smaller basis sets in the early stages, we constructed a new benchmark platform that includes a broader data set of 183 species (containing open-shell, closed-shell, ionic, and neutral species) and a larger basis set up to aug-cc-pV6Z. The newly optimized parameters can significantly improve the energy-predictive abilities of ten published formulas. Notably, all ten formulas perform quite similarly under the new platform with the reoptimized parameters. Finally, we built an online calculator for researchers to use for these extrapolation schemes. Our work would reignite the interest and applications of the underestimated formulas.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene).

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

Fulminic acid: a quasibent spectacle.

Fulminic acid (HCNO) played a critical role in the early development of organic chemistry, and chemists have sought to discern the structure and characteristics of this molecule and its isomers for over 200 years. The mercurial nature of the extremely flat H-C-N bending potential of fulminic acid, with a nearly vanishing harmonic vibrational frequency at linearity, remains enigmatic and refractory to electronic structure theory, as dramatic variation with both orbital basis set and electron correlation method is witnessed. To solve this problem using rigorous electronic wavefunction methods, we have employed focal point analyses (FPA) to ascertain the ab initio limit of optimized linear and bent geometries, corresponding vibrational frequencies, and the HCN + O(3P) → HCNO reaction energy. Electron correlation treatments as extensive as CCSDT(Q), CCSDTQ(P), and even CCSDTQP(H) were employed, and complete basis set (CBS) extrapolations were performed using the cc-pCVXZ (X = 4-6) basis sets. Core electron correlation, scalar relativistic effects (MVD1), and diagonal Born-Oppenheimer corrections (DBOC) were all included and found to contribute significantly in determining whether vibrationless HCNO is linear or bent. At the all-electron (AE) CCSD(T)/CBS level, HCNO is a linear molecule with ω5(H-C-N bend) = 120 cm-1. However, composite AE-CCSDT(Q)/CBS computations give an imaginary frequency (51i cm-1) at the linear optimized geometry, leading to an equilibrium structure with an H-C-N angle of 173.9°. Finally, at the AE-CCSDTQ(P)/CBS level, HCNO is once again linear with ω5 = 45 cm-1, and inclusion of both MVD1 and DBOC effects yields ω5 = 32 cm-1. A host of other topics has also been investigated for fulminic acid, including the dependence of re and ωi predictions on a variety of CBS extrapolation formulas, the question of multireference character, the N-O bond energy and enthalpy of formation, and issues that give rise to the quasibent appellation.

New-Generation Electron-Propagator Methods for Calculations of Electron Affinities and Ionization Energies: Tests on Organic Photovoltaic Molecules.

A new generation of ab initio electron-propagator self-energies recently superseded its antecedents' accuracy and computational efficiency in calculating vertical ionization energies (VIEs) of closed-shell molecules. (See J. Chem. Phys. 2021, 155, 204107, J. Chem. Theory Comput. 2022, 18, 4927, J. Chem. Phys. 2023, 159, 124109.) No adjustable parameters were introduced in the generation of reference orbitals or in the construction of self-energies. The same approach has been extended in this work to vertical electron affinities (VEAs). Calculations were performed on 24 conjugated, organic photovoltaic molecules with diverse functional groups. These molecules are considerably larger than those studied in previous tests on VIEs. Several new-generation self-energies produce mean absolute errors (MAEs) below 0.1 eV versus ΔCCSD(T) (i.e., total energy differences from the coupled-cluster singles, doubles, and perturbative triples method) VIEs and VEAs obtained with identical basis sets. A composite model employs cubically and quintically scaling algorithms and power-law basis-set extrapolations based on augmented double-triple or triple-quadruple ζ data. Its MAEs are near 0.05 eV versus benchmark values, with 0.03 eV error bars for the lowest VIE and the highest VEA of each molecule. A more efficient and equally accurate composite model for calculating VIEs avoids full transformations of electron repulsion integrals to the molecular orbital basis. High probability factors support the diagonal self-energy approximation, wherein Dyson orbitals are proportional to canonical, Hartree-Fock orbitals.

Reactions of Ethynyloxy Radical with Hydroperoxyl Radical: Bridging Theoretical Reaction Dynamics and Chemical Modeling of Combustion.

A detailed and accurate combustion reaction mechanism is crucial for understanding the nature of fuel combustion. In this work, a theoretical study of reaction HCCO+HO2 using M06-2X/6-311++G(d,p) for geometry optimization and combined methods based on spin-unrestricted CCSD(T)/CBS level of theory with basis set extrapolation from MP2/aug-cc-pVnZ (n=T and Q) for energy calculations were performed. The temperature- and pressure-dependent rate coefficients at 300-2000 K and 0.01-100 atm, suitable for combustion conditions, were derived using the Rice-Ramsberger-Kassel-Marcus/Master-Equation approach. Furthermore, temperature-dependent thermochemistry data of key species for the HCCO+HO2 system has also been studied. Finally, an updated ketene model is developed by supplementing the most recent theoretical work and the theoretical work in this paper. This updated model was tested to simulate the speciation of ketene oxidation in available experimental research. It is shown that the updated model for predicting ketene oxidation exhibits a high level of agreement with experimental data across a wide range of species profiles. An analysis was conducted to identify the crucial reactions that influence ketene ignition. This paper's research findings are essential for enhancing the combustion mechanism of ketene and other hydrocarbons and oxygenated hydrocarbon fuels.

Chemical Investigation on the Mechanism and Kinetics of the Atmospheric Degradation Reaction of Trichlorofluoroethene by OH⋅ and Its Subsequent Fate in the Presence of O2 /NOx.

The M06-2X/6-311++G(d,p) level of theory was used to examine the degradation of Trichlorofluoroethene (TCFE) initiated by OH⋅ radicals. Additionally, the coupled-cluster single-double with triple perturbative [CCSD(T)] method was employed to refine the single-point energies using the complete basis set extrapolation approach. The results indicated that OH-addition is the dominant pathway. OH⋅ adds to both the C1 and C2 carbons, resulting in the formation of the C(OH)Cl2 -⋅CClF and ⋅CCl2 -C(OH)ClF species. The associated barrier heights were determined to be 1.11 and -0.99 kcal mol-1 , respectively. Furthermore, the energetic and thermodynamic parameters show that pathway 1 exhibits greater exothermicity and exergonicity compared to pathway 2, with differences of 8.11 and 8.21 kcal mol-1 , correspondingly. The primary pathway involves OH addition to the C2 position, with a rate constant of 6.2×10-13 cm3 molecule-1 sec-1 at 298 K. This analysis served to estimate the atmospheric lifetime, along with the photochemical ozone creation potential (POCP) and ozone depletion potential (ODP). It yielded an atmospheric lifetime of 8.49 days, an ODP of 4.8×10-4 , and a POCP value of 2.99, respectively. Radiative forcing efficiencies were also estimated at the M06-2X/6-311++G(d,p) level. Global warming potentials (GWPs) were calculated for 20, 100, and 500 years, resulting in values of 9.61, 2.61, and 0.74, respectively. TCFE is not expected to make a significant contribution to the radiative forcing of climate change. The results obtained from the time-dependent density functional theory (TDDFT) indicated that TCFE and its energized adducts are unable to photolysis under sunlight in the UV and visible spectrum. Secondary reactions involve the [TCFE-OH-O2 ]⋅ peroxy radical, leading subsequently to the [TCFE-OH-O]⋅ alkoxy radical. It was found that the alkoxy radical resulting from the peroxy radical can lead to the formation of phosgene (COCl2 ) and carbonyl chloride fluoride (CClFO), with phosgene being the primary product.

A systematic study on spectroscopic and transition properties of the phosphorus mononitride cation

The potential energy curves (PECs) of 28 Λ–S states of the phosphors mononitride cation have been constructed by using the internally contracted multireference configuration interaction (icMRCI) method plus Davidson correction (+Q). The effect of core correlation and scalar relativistic treatment of electron, and the basis-set extrapolation to the complete basis set limit are considered. The spin–orbit coupling is computed via the full Breit-Pauli Hamiltonian. The transition dipole moments (TDMs) for the dipole-allowed and spin-forbidden transitions are calculated. Utilizing the PECs and TDMs, the spectroscopic and transition properties of bound states are then evaluated. The current spectroscopic parameters, vibrational band origins, Einstein coefficients, and Franck-Condon factors well match the available measured values. And the radiative lifetimes for most excited states are estimated for the first time. These results can be useful in the analysis and assignment of molecular spectra or as guidelines for detecting these states spectroscopically.

Treating Semiempirical Hamiltonians as Flexible Machine Learning Models Yields Accurate and Interpretable Results.

Quantum chemistry provides chemists with invaluable information, but the high computational cost limits the size and type of systems that can be studied. Machine learning (ML) has emerged as a means to dramatically lower the cost while maintaining high accuracy. However, ML models often sacrifice interpretability by using components such as the artificial neural networks of deep learning that function as black boxes. These components impart the flexibility needed to learn from large volumes of data but make it difficult to gain insight into the physical or chemical basis for the predictions. Here, we demonstrate that semiempirical quantum chemical (SEQC) models can learn from large volumes of data without sacrificing interpretability. The SEQC model is that of density-functional-based tight binding (DFTB) with fixed atomic orbital energies and interactions that are one-dimensional functions of the interatomic distance. This model is trained to ab initio data in a manner that is analogous to that used to train deep learning models. Using benchmarks that reflect the accuracy of the training data, we show that the resulting model maintains a physically reasonable functional form while achieving an accuracy, relative to coupled cluster energies with a complete basis set extrapolation (CCSD(T)*/CBS), that is comparable to that of density functional theory (DFT). This suggests that trained SEQC models can achieve a low computational cost and high accuracy without sacrificing interpretability. Use of a physically motivated model form also substantially reduces the amount of ab initio data needed to train the model compared to that required for deep learning models.

Basis Set Effects on the Stabilities and Interaction Energies of Small Amide Molecules Adsorbed on Kaolinite Surface

Adsorptions of small amide molecules, acetamide (AA) and N-methyl-acetamide (NMA) on the surface of kaolinite are investigated in this study. The focus is on the basis set effects towards the stabilities and the interaction energies of the molecules on the Al–O surface. With a fixed B3LYP functional, we increased the size of the basis sets for the single-point calculations, to find the converged interaction energies and obtain the relative stabilities. We found that, under the direct usage of Pople-type and Dunning’s correlation consistent basis sets, it is not possible to achieve the pattern of convergence for the interaction energies and the relative stabilities. Compared to the complete basis set (CBS) extrapolation scheme, the double zeta basis sets deviated the most, in the range of 21 to 27%, while it is from 1 to 7% for the triple zeta basis sets. Based on the results, we suggest using 6-311++G(2df,2pd) or cc-pVQZ for energy-related quantities. Compared to AA, NMA attached more strongly by 0.5 eV on the surface of Al–O.

DFT Meets Wave-Function Composite Methods for Characterizing Cytosine Tautomers in the Gas Phase.

A general strategy for the accurate computation of structural and spectroscopic properties of biomolecule building blocks in the gas phase has been further improved and validated with a special reference to tautomeric equilibria. The main improvements concern the use of the cc-pVTZ-F12 basis set in both DFT and CCSD(T)-F12 computations, the inclusion of core-valence correlation in geometry optimizations by double hybrid functionals, and the use of the cc-pVQZ-F12 basis set for complete basis set extrapolation at the MP2-F12 level. The resulting model chemistry is applied to the challenging problem of cytosine tautomers in the gas phase. The results are in remarkable agreement with experiment concerning both rotational and vibrational spectroscopic parameters and permit their unbiased interpretation in terms of structural and thermochemical features. Together with the intrinsic interest of the studied molecule, the accuracy of the results obtained at reasonable cost without any empirical parameter suggests that the proposed composite method can be profitably employed for accurate investigations of other molecular bricks of life.

Optimizing Jastrow factors for the transcorrelated method.

We investigate the optimization of flexible tailored real-space Jastrow factors for use in the transcorrelated (TC) method in combination with highly accurate quantum chemistry methods, such as initiator full configuration interaction quantum Monte Carlo (FCIQMC). Jastrow factors obtained by minimizing the variance of the TC reference energy are found to yield better, more consistent results than those obtained by minimizing the variational energy. We compute all-electron atomization energies for the challenging first-row molecules C2, CN, N2, and O2 and find that the TC method yields chemically accurate results using only the cc-pVTZ basis set, roughly matching the accuracy of non-TC calculations with the much larger cc-pV5Z basis set. We also investigate an approximation in which pure three-body excitations are neglected from the TC-FCIQMC dynamics, saving storage and computational costs, and show that it affects relative energies negligibly. Our results demonstrate that the combination of tailored real-space Jastrow factors with the multi-configurational TC-FCIQMC method provides a route to obtaining chemical accuracy using modest basis sets, obviating the need for basis-set extrapolation and composite techniques.

Computation of CCSD(T)-Quality NMR Chemical Shifts via Δ-Machine Learning from DFT.

NMR spectroscopy undoubtedly plays a central role in determining molecular structures across different chemical disciplines, and the accurate computational prediction of NMR parameters is highly desirable. In this work, a new Δ-machine learning approach is presented to correct DFT-computed NMR chemical shifts using input features from the calculation and in addition highly accurate reference data at the CCSD(T)/pcSseg-2 level of theory with a basis set extrapolation scheme. The model is trained on a data set containing 1000 optimized and geometrically distorted structures of small organic molecules comprising most elements of the first three periods and containing data for 7090 1H and 4230 13C NMR chemical shifts. Applied to the PBE0/pcSseg-2 method, the mean absolute deviation (MAD) on the internal NMR shift test set is reduced by 81% for 1H and 92% for 13C at virtually no additional computational cost. For 12 different DFT functional and basis set combinations, the MAD of the ML-corrected NMR shifts ranges from 0.021 to 0.039 ppm (1H) and from 0.38 to 1.07 ppm (13C). Importantly, the new method consistently outperforms the simple and widely used linear regression correction technique. This behavior is reproduced on three different external benchmark sets, confirming the generality and robustness of the correction scheme, which can easily be applied in DFT-based spectral simulations.

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.