Optimization of augmentation functions for correlated calculations of spin-spin coupling constants and related properties

On the performance of HRPA(D) for NMR spin-spin coupling constants: Smaller molecules, aromatic and fluoroaromatic compounds

In this study, the performance of the doubles-corrected higher random-phase approximation [HRPA(D)] has been investigated in calculations of nuclear magnetic resonance spin-spin coupling constants (SSCCs) for 58 molecules with the experimental values used as the reference values. HRPA(D) is an approximation to the second-order polarization propagator approximation (SOPPA) and is, therefore, computationally less expensive than SOPPA. HRPA(D) performs comparable and sometimes even better than SOPPA, and therefore, when calculating SSCCs, it should be considered as an alternative to SOPPA. Furthermore, it was investigated whether a coupled-cluster singles, doubles and perturbative triples [CCSD(T)] or Møller-Plesset second order (MP2) geometry optimization was optimal for a SOPPA and a HRPA(D) SSCC calculation for eight smaller molecules. CCSD(T) is the optimal geometry optimization for the SOPPA calculation, and MP2 was optimal for HRPA(D) SSCC calculations.

Exploring Alternate Methods for the Calculation of High-Level Vibrational Corrections of NMR Spin-Spin Coupling Constants

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wave function that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wave function and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarization propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available (i.e., CC3//CCSD(T) + CCSD//CCSD(T)). CCSD//CCSD(T) statistics showed favorable statistics in comparison to experimental values, albeit at an unfavorably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all of the other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational-corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis set or lack of solvation effects for the CC3 equilibrium calculations.

Benchmarking Basis Sets for Density Functional Theory Thermochemistry Calculations: Why Unpolarized Basis Sets and the Polarized 6-311G Family Should Be Avoided

Basis sets are a crucial but often largely overlooked choice in setting up quantum chemistry calculations. The choice of the basis set can be critical in determining the accuracy and calculation time of your quantum chemistry calculations. Clear recommendations based on thorough benchmarking are essential but not readily available currently. This study investigates the relative quality of basis sets for general properties by benchmarking basis set performance for a diverse set of 139 reactions (from the diet-150-GMTKN55 data set). In our analysis, we find the distributions of errors are often significantly non-Gaussian, meaning that the joint consideration of median errors, mean absolute errors, and outlier statistics is helpful to provide a holistic understanding of basis set performance. Our direct comparison of performance between most modern basis sets provides quantitative evidence for basis set recommendations that broadly align with the established understanding of basis set experts and is evident in the design of modern basis sets. For example, while zeta is a good measure of quality, it is not the only determining factor for an accurate calculation with unpolarized double- and triple-ζ basis sets (like 6-31G and 6-311G) having very poor performance. Appropriate use of polarization functions (e.g., 6-31G*) is essential to obtain the accuracy offered by double- or triple-ζ basis sets. In our study, the best performances for double- and triple-ζ basis sets are 6-31++G** and pcseg-2, respectively. However, the performances of singly polarized double-ζ and doubly polarized triple-ζ basis sets are quite similar with one key exception: the polarized 6-311G basis set family has poor parametrization, which means its performance is more like a double-ζ than a triple-ζ basis set. All versions of the 6-311G basis set family should be avoided entirely for valence chemistry calculations moving forward.

New pecJ-n (n = 1, 2) Basis Sets for Selenium Atom Purposed for the Calculations of NMR Spin-Spin Coupling Constants Involving Selenium

We present new compact pecJ-n (n = 1, 2) basis sets for the selenium atom developed for the quantum-chemical calculations of NMR spin-spin coupling constants (SSCCs) involving selenium nuclei. These basis sets were obtained at the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) level with the property-energy consistent (PEC) method, which was introduced in our previous papers. The existing SSCC-oriented selenium basis sets are rather large in size, while the PEC method gives more compact basis sets that are capable of providing accuracy comparable to that reached using the property-oriented basis sets of larger sizes generated with a standard even-tempered technique. This is due to the fact that the PEC method is very different in its essence from the even-tempered approaches. It generates new exponents through the total optimization of angular spaces of trial basis sets with respect to the property under consideration and the total molecular energy. New basis sets were tested on the coupled cluster singles and doubles (CCSD) calculations of SSCCs involving selenium in the representative series of molecules, taking into account relativistic, solvent, and vibrational corrections. The comparison with the experiment showed that the accuracy of the results obtained with the pecJ-2 basis set is almost the same as that provided by a significantly larger basis set, aug-cc-pVTZ-J, while that achieved with a very compact pecJ-1 basis set is only slightly inferior to the accuracy provided by the former.

On the Utmost Importance of the Basis Set Choice for the Calculations of the Relativistic Corrections to NMR Shielding Constants

The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1H and 13C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant (J). In general, it has been shown that the nonrelativistic J-oriented and σ-oriented basis sets, artificially saturated in the tight s-region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Hydrogen-Atom Electronic Basis Sets for Multicomponent Quantum Chemistry

Multicomponent methods are a conceptually simple way to include nuclear quantum effects into quantum chemistry calculations. In multicomponent methods, the electronic molecular orbitals are described using the linear combination of atomic orbitals approximation. This requires the selection of a one-particle electronic basis set which, in practice, is commonly a correlation-consistent basis set. In multicomponent method studies, it has been demonstrated that large electronic basis sets are required for quantum hydrogen nuclei to accurately describe electron-nuclear correlation. However, as we show in this study, much of the need for large electronic basis sets is due to the correlation-consistent electronic basis sets not being optimized to describe nuclear properties and electron-nuclear correlation. Herein, we introduce a series of correlation-consistent electronic basis sets for hydrogen atoms called cc-pVnZ-mc with additional basis functions optimized to reproduce multicomponent density functional theory protonic densities. These new electronic basis sets are shown to yield better protonic densities with fewer electronic basis functions than the standard correlation-consistent basis sets and reproduce other protonic properties such as proton affinities and protonic excitation energies, even though they were not optimized for these purposes. The cc-pVnZ-mc basis sets should enable multicomponent many-body calculations on larger systems due to the improved computational efficiency they provide for a given level of accuracy.

New pecJ-n (n = 1, 2) Basis Sets for High-Quality Calculations of Indirect Nuclear Spin–Spin Coupling Constants Involving 31P and 29Si: The Advanced PEC Method

In this paper, we presented new J-oriented basis sets, pecJ-n (n = 1, 2), for phosphorus and silicon, purposed for the high-quality correlated calculations of the NMR spin–spin coupling constants involving these nuclei. The pecJ-n basis sets were generated using the modified version of the property-energy consistent (PEC) method, which was introduced in our earlier paper. The modifications applied to the original PEC procedure increased the overall accuracy and robustness of the generated basis sets in relation to the diversity of electronic systems. Our new basis sets were successfully tested on a great number of spin–spin coupling constants, involving phosphorus or/and silicon, calculated within the SOPPA(CCSD) method. In general, it was found that our new pecJ-1 and pecJ-2 basis sets are very efficient, providing the overall accuracy that can be characterized by MAEs of about 3.80 and 1.98 Hz, respectively, against the benchmark data obtained with a large dyall.aae4z⁺ basis set of quadruple-ζ quality.

Fluorine spin-spin coupling constants of pentafluorobenzene revisited at the ab initio correlated levels

All possible spin-spin coupling constants, ¹⁹ F-¹⁹ F, ¹⁹ F-¹³ C, and ¹⁹ F-¹ H, of pentafluorobenzene were calculated at five different levels of theory, HF, DFT, SOPPA (CCSD), CCSD, and the SOPPA (CCSD)-based composite scheme with taking into account solvent, vibrational, relativistic, and correlation corrections. Most corrections were next to negligible for the long-range couplings but quite essential for the one-bond carbon-fluorine coupling constants. Hartree-Fock calculations were found to be entirely unreliable, while DFT results were comparable in accuracy with the data obtained using the wave function-based methods.

New pecS-n (n = 1, 2) basis sets for quantum chemical calculations of the NMR chemical shifts of H, C, N, and O nuclei

This paper demonstrates the performance of our previously suggested property-energy consistent method on the example of the generation of effective basis sets, pecS-1 and pecS-2, suited for the calculation of hydrogen, carbon, nitrogen, and oxygen chemical shifts. The new basis sets were successfully approbated in the GIAO-DFT calculations of the chemical shifts of 35 molecules using six different functionals. The pecS-1 basis set demonstrated very good accuracy, which makes this small basis set an effective means for the large-scale computations. At the same time, the pecS-2 basis set also gave very accurate results, thus putting it on a par with the other commensurate basis sets suited for the chemical shifts calculations.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation

We present the first steps to extend the Green's function GW method and the Bethe-Salpeter equation (BSE) to molecular response properties such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants. We discuss both a nonrelativistic one-component and a quasi-relativistic two-component formalism. The latter describes scalar-relativistic and spin-orbit effects and allows us to study heavy-element systems with reasonable accuracy. Efficiency is maintained by the application of the resolution of the identity approximation throughout. The performance is demonstrated using conventional central processing units (CPUs) and modern graphics processing units (GPUs) for molecules involving several thousand basis functions. Our results show that a large amount of Hartree-Fock exchange is vital to provide a sufficient Kohn-Sham starting point to compute the GW quasi-particle energies. As the GW-BSE approach is generally less accurate for triplet excitations or related properties such as the Fermi-contact interaction, the admixture of the Kohn-Sham correlation kernel through the contracted BSE (cBSE) method improves the results for NMR coupling constants. This leads to remarkable results when combined with the eigenvalue-only self-consistent variant (evGW) and Becke's half and half functional (BH&HLYP) or the CAM-QTP family. The developed methodology is used to calculate the Karplus curve of tin molecules, illustrating its applicability to extended chemically relevant molecules. Here, the GW-cBSE method improves upon the chosen BH&HLYP Kohn-Sham starting points.

Hyperfine Coupling Constants in Local Exact Two-Component Theory

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within the one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, that is, the derivatives of the unitary decoupling transformation are considered. This requires the solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened nuclear spin-orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12-17 transition-metal compounds. The error introduced by DLU is negligible, and the DLU-X2C Hamiltonian accurately reproduces its four-component "fully" relativistic parent results. Functionals with a large amount of Hartree-Fock exchange such as CAM-QTP-02 and ωB97X-D are generally favorable. The pure density functional r²SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-ζ bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C₆Cl₅)₄]^- with more than 4700 primitive basis functions and four rare-earth single-molecule magnets: [La(OAr*)₃]^-, [Lu(NR₂)₃]^-, [Lu(OAr*)₃]^-, and [TbPc₂]^-. Here, the results with the spin-orbit DLU-X2C Hamiltonian are in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

We present an efficient implementation of paramagnetic NMR shielding tensors and shifts in a nonrelativistic and scalar-relativistic density functional theory framework. For the latter, we make use of the scalar exact two-component Hamiltonian in its local approximation, and generally we apply the well established (multipole-accelerated) resolution of the identity approximation and the seminumerical exchange approximation. The perturbed density matrix of a paramagnetic NMR shielding calculation is further used to study the magnetically induced current density and ring currents of open-shell systems as illustrated for [U@Bi₁₂]^3-. [U@Bi₁₂]^3- features delocalized highest occupied molecular orbitals and sustains a net diatropic ring current of ca. 18 nA/T through the Bi₁₂ torus similar to the all-metal aromatic heavy-element cluster [Th@Bi₁₂]^4-.

The aug-cc-pVTZ-J basis set for the p-block fourth-row elements Ga, Ge, As, Se, and Br

The aug-cc-pVTZ-J basis set family is extended to include the fourth-row p-block elements Ga, Ge, As, Se, and Br. We use the established approach outlined by Sauer and coworkers (J. Chem. Phys. 115, 1324 [2001], J. Chem. Phys. 133, 054308 [2010], J. Chem. Theory Comput. 7, 4070 [2011], and J. Chem. Theory Comput. 7, 4077 [2011]) where the completely uncontracted aug-cc-pVTZ basis set is saturated with tight s-, p-, d-, and f-functions to form the aug-cc-pVTZ-Juc basis set for the tested elements. The saturation is carried out on the simplest hydrides possible for the tested elements GaH, GeH₄ , AsH₃ , H₂ Se, and HBr until an improvement is less than 0.01% for all s-, p-, and d-functions added. f-Functions are added to an improvement less than or equal to 1.0% due to the computational expense these functions add. The saturated aug-cc-pVTZ-Juc (26s16p12d5f) is then recontracted using the molecular orbital coefficients from self-consistent field calculations on the simple hydrides to improve computational efficiency. During contraction of the basis set, we observe that the linear hydrogen bromide molecule has a slower convergence than the other tested molecules which sets a limit on the accuracy obtained. All calculations with the contracted aug-cc-pVTZ-J [17s10p7d5f] gives results that are within 1.0% of the uncontracted results at considerable computational savings.

Multi-configurational short-range density functional theory can describe spin-spin coupling constants of transition metal complexes

The multi-configurational short-range (sr) density functional theory has been extended to the calculation of indirect spin-spin coupling constants (SSCCs) for nuclear magnetic resonance spectroscopy. The performance of the new method is compared to Kohn-Sham density functional theory and the ab initio complete active space self-consistent field for a selected set of molecules with good reference values. Two density functionals have been considered, the local density approximation srLDA and srPBE from the GGA class of functionals. All srDFT calculations are of Hartree-Fock-type HF-srDFT or complete active space-type CAS-srDFT. In all cases, the calculated SSCC values are of the same quality for srLDA and srPBE functionals, suggesting that one should use the computationally cost-effective srLDA functionals in applications. For all the calculated SSCCs in organic compounds, the best choice is HF-srDFT; the more expensive CAS-srDFT does not provide better values for these single-reference molecules. Fluorine is a challenge; in particular, the FF, FC, and FO couplings have much higher statistical errors than the rest. For SSCCs involving fluorine and a metal atom CAS-srDFT with singlet, generalized Tamm-Dancoff approximation is needed to get good SSCC values although the reference ground state is not a multi-reference case. For VF₆ ^-1, all other considered models fail blatantly.

Introducing Pseudoramps and Mixed Ramp-Gaussian Jensen Basis Sets for Better Nuclear Densities

Gaussian basis sets dominate quantum chemistry but struggle to model near-core electron densities and thus nuclear magnetic resonance (NMR) spectral properties. Mixed ramp-Gaussian (RG) basis sets show significant promise for these core properties due to the inclusion of a ramp-function with a non-zero nuclear-electron cusp. To enable quicker testing of the potential of RG basis sets for core chemistry, here we approximate ramps as a large linear combination of Gaussians called pseudoramps, thus enabling standard quantum chemistry packages to be used to approximate RG basis set results. We produce and test rampified general-purpose segmented Jensen basis sets. These basis sets retain the valence chemistry of their parent all-Gaussian basis sets, as desired, but unfortunately fail to show significantly improved performance in core chemistry. Crucially, for NMR spin-spin couplings (the most promising potential application of RG basis sets), general-purpose basis sets are so poorly performing that results cannot be interpreted. For chemical shifts, P-ramps are likely required for improved performance. We conclude that the use of pseudoramps to test the performance of ramp-Gaussian basis sets is extremely helpful, decoupling methodology development and evaluation from implementation, but that more sophisticated basis set optimisation will be required to identify potential advantages of ramp-Gaussian basis sets over all-Gaussian basis sets.

An efficient method for generating property-energy consistent basis sets. New pecJ-n (n = 1, 2) basis sets for high-quality calculations of indirect nuclear spin-spin coupling constants involving 1H, 13C, 15N, and 19F nuclei

This paper presents a new method of generating property-energy consistent (PEC) basis sets that can be applied to any arbitrary molecular property. The PEC method generates a basis set that is optimized for the molecular property under interest, providing the least possible total molecular energy. The main algorithm of the PEC approach involves Monte Carlo simulations to generate random exponents in the predetermined range. In this work, the PEC method is introduced in the example of generation of new pecJ-n (n = 1, 2) basis sets suited for high-quality correlated calculations of indirect nuclear spin-spin coupling constants involving the most popular NMR-active nuclei: 1H, 13C, 15N, and 19F.

Efficient J-oriented tin basis sets for the correlated calculations of indirect nuclear spin-spin coupling constants

New J-oriented tin basis sets, acvXz-J (X = 2, 3, 4), have been developed at the level of the second-order polarization propagator approximation with the coupled-cluster single and double amplitudes, SOPPA (CCSD), for the purpose of correlated calculations of indirect nuclear spin-spin coupling constants involving tin nucleus. High-quality coupled-cluster calculations of several tin-proton and tin-carbon spin-spin coupling constants, performed with one of the newly developed basis sets, namely, the acv3z-J, taking into account relativistic, solvent, and vibrational corrections showed that the acv3z-J basis set is capable to provide reliable results, as compared with the experimental data.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

Estimating the accuracy of calculated electron paramagnetic resonance hyperfine couplings for a lytic polysaccharide monooxygenase

Lytic polysaccharide monooxygenases (LPMOs) are enzymes that bind polysaccharides followed by an (oxidative) disruption of the polysaccharide surface, thereby boosting depolymerization. The binding process between the LPMO catalytic domain and polysaccharide is key to the mechanism and establishing structure-function relationships for this binding is therefore crucial. The hyperfine coupling constants (HFCs) from EPR spectroscopy have proven useful for this purpose. Unfortunately, EPR does not provide direct structural data and therefore the experimental EPR parameters have to be supported with parameters calculated with density functional theory. Yet, calculated HFCs are extremely sensitive to the employed computational setup. Using the LPMO Ls(AA9)A catalytic domain, we here quantify the importance of several choices in the computational setup, ranging from the use of specialized basis, the underlying structures, and the employed exchange-correlation functional. We show that specialized basis sets are an absolute necessity, and also that care has to be taken in the optimization of the underlying structure: only by allowing large parts of the protein around the active site to structurally relax could we obtain results that uniformly reproduced experimental trends. We compare our results to previously published X-ray structures and experimental HFCs for Ls(AA9)A as well as to recent experimental/theoretical results for another (AA10) family of LPMOs.

NMR parameters of FNNF as a test for coupled-cluster methods: CCSDT shielding and CC3 spin-spin coupling

NMR shielding and spin-spin coupling constants of cis and trans isomers of FNNF have been determined to near-quantitative accuracy from ab initio calculations. The FNNF system, containing multiple N-F bonds and fluorine atoms, provides a severe test of computational methods. Coupled-cluster methods were used with large basis sets and complete basis set (CBS) extrapolations of the equilibrium geometry results, with vibrational and relativistic corrections. Shielding constants were calculated with basis sets as large as aug-cc-pCV7Z, together with coupled-cluster expansions up to CCSDT, at the all-electron CCSD(T)/aug-cc-pCVQZ optimized geometries. Spin-spin coupling constants have been determined with specialized versions of the correlation consistent basis sets ccJ-pVXZ, further augmented with diffuse functions. All-electron coupled-cluster methods up to CC3 were applied in these calculations. The results of this work highlight the application of state-of-the-art theoretical techniques, and provide the most accurate NMR properties of FNNF to date, which can serve to guide and supplement NMR experimentation.

An Internuclear J-Coupling of 3He Induced by Molecular Confinement

The solution-state ¹³C NMR spectrum of the endofullerene ³He@C₆₀ displays a doublet structure due to a J-coupling of magnitude 77.5 ± 0.2 mHz at 340 K between the ³He nucleus and a ¹³C nucleus of the enclosing carbon surface. The J-coupling increases in magnitude with increasing temperature. Quantum chemistry calculations successfully predict the approximate magnitude of the coupling. This observation shows that the mutual proximity of molecular or atomic species is sufficient to induce a finite scalar nuclear spin-spin coupling, providing that translational motion is restricted by confinement. The phenomenon may have applications to the study of surface interactions and to mechanically bound species.

Surprisingly broad applicability of the cc-pVnZ-F12 basis set for ground and excited states

Excellent convergence properties for the (aug-)cc-pVnZ-F12 basis set family, purpose-made for explicitly correlated calculations, are demonstrated with conventional wave function methods and Kohn-Sham density functional theory for various ground and excited-state calculations. Among the ground-state properties studied are dipole moments, covalent bond lengths, and interaction and reaction energies. For excited states, we looked at vertical excitation energies, UV absorption, and excited-state absorption spectra. Convergence is compared against the basis sets cc-pVnZ, def2-nVD, aug-pcseg-n, and nZaPa-NR. It is established that the cc-pVnZ-F12 family consistently yields results of n + 1 quality and better. Especially, the cc-pVDZ-F12 basis set is found to be a basis set of good cost vs performance trade-off.

Probing basis set requirements for calculating hyperfine coupling constants

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

RPA(D) and HRPA(D): Two new models for calculations of NMR indirect nuclear spin-spin coupling constants

In this article, the RPA(D) and HRPA(D) models for the calculation of linear response functions are presented. The performance of the new RPA(D) and HRPA(D) models is compared to the performance of the established RPA, HRPA, and SOPPA models in calculations of indirect nuclear spin-spin coupling constants using the CCSD model as a reference. The doubles correction offers a significant improvement on both the RPA and HRPA models; however, the improvement is more dramatic in the case of the RPA model. For all coupling types investigated in this study, the results obtained using the HRPA(D) model are comparable in accuracy to those given by the SOPPA model, while requiring between 30% and 90% of the calculation time needed for SOPPA. The RPA(D) model, while of slightly lower accuracy compared to the CCSD model than HRPA(D), offered calculation times of only approximately 25% of those required for SOPPA for all the investigated molecules. © 2018 Wiley Periodicals, Inc.

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted ¹³ C and ¹ H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for ¹³ C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.

Theoretical calculations of carbon-hydrogen spin-spin coupling constants

Structural applications of theoretical calculations of carbon-hydrogen spin-spin coupling constants are reviewed covering papers published mainly during the last 10-15 years with a special emphasis on the most notable studies of hybridization, substitution and stereoelectronic effects together with the investigation of hydrogen bonding and intermolecular interactions. The wide scope of different applications of calculated carbon-hydrogen couplings in the structural elucidation of particular classes of organic and bioorganic molecules is reviewed, concentrating mainly on saturated, unsaturated, aromatic and heteroaromatic compounds and their functional derivatives, as well as on natural compounds and carbohydrates. The review is dedicated to Professor Emeritus Michael Barfield in view of his invaluable pioneering contribution to this field.

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

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

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

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

Importance of Triples Contributions to NMR Spin-Spin Coupling Constants Computed at the CC3 and CCSDT Levels

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin-spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1-3%, but much higher corrections were found for ¹J_CN in FCN, 15.7%, and ¹J_OF in OF₂, 6.4%. The changes vary significantly in the case of multibond couplings, with differences of up to 10%, and even 13.6% for ³J_FH in fluoroacetylene. Calculations at the coupled cluster singles, doubles, and triples (CCSDT) level indicate that the most important contributions arising from connected triple excitations in the coupled cluster expansion are accounted for at the CC3 level. Thus, we believe that the CC3 method will become the standard approach for the calculation of reference values of nuclear spin-spin coupling constants.

Nonempirical calculations of the one-bond (29)Si-(13)C spin-spin coupling constants taking into account relativistic and solvent corrections

The computational study of the one-bond (29)Si-(13)C spin-spin coupling constants has been performed at the second-order polarization propagator approximation (SOPPA) level in the series of 60 diverse silanes with a special focus on the main factors affecting the accuracy of the calculation including the level of theory, the quality of the basis set, and the contribution of solvent and relativistic effects. Among three SOPPA-based methods, SOPPA(MP2), SOPPA(CC2), and SOPPA(CCSD), the best result was achieved with SOPPA(CCSD) when used in combination with Sauer's basis set aug-cc-pVTZ-J characterized by the mean absolute error of calculated coupling constants against the experiment of ca 2 Hz in the range of ca 200 Hz. The SOPPA(CCSD)/aug-cc-pVTZ-J method is recommended as the most accurate and effective computational scheme for the calculation of (1)J(Si,C). The slightly less accurate but essentially more economical SOPPA(MP2)/aug-cc-pVTZ-J and/or SOPPA(CC2)/aug-cc-pVTZ-J methods are recommended for larger molecular systems. It was shown that solvent and relativistic corrections do not play a major role in the computation of the total values of (1)J(Si,C); however, taking them into account noticeably improves agreement with the experiment. The rovibrational corrections are estimated to be of about 1 Hz or 1-1.5% of the total value of (1)J(Si,C).

Computational NMR coupling constants: shifting and scaling factors for evaluating 1JCH

Optimized shifting and/or scaling factors for calculating one-bond carbon-hydrogen spin-spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97-2 and M06-L) and basis sets (TZVP, HIII-su3, EPR-III, aug-cc-pVTZ-J, ccJ-pVDZ, ccJ-pVTZ, ccJ-pVQZ, pcJ-2 and pcJ-3) using 68 organic molecular systems with 88 (1)JCH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of (1)JCH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root-mean-square deviations lie between 4.7 and 16.4 Hz and are reduced to 4-6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97-2 functionals in combination with HIII-su3, aug-cc-pVTZ-J and pcJ-2 basis sets.

Improving the calculation of Electron Paramagnetic Resonance hyperfine coupling tensors for d-block metals

Calculation of hyperfine coupling constants (HFCs) of Electron Paramagnetic Resonance from first principles can be a beneficial complement to experimental data in cases where the molecular structure is unknown. We have recently investigated basis set convergence of HFCs in d-block complexes and obtained a set of basis functions for the elements Sc-Zn, which were saturated with respect to both the Fermi contact and spin-dipolar components of the hyperfine coupling tensor [Hedegård et al., J. Chem. Theory Comput., 2011, 7, 4077-4087]. Furthermore, a contraction scheme was proposed leading to very accurate, yet efficient basis sets for the elements Sc-Zn. Here this scheme is tested against a larger test set of molecules and a wider range of DFT functionals. We further investigate the regular aug-cc-pVTZ and core-valence correlation aug-cc-pCVTZ basis sets as well as another core-property basis set, CP(PPP). While aug-cc-pVTZ-J provides hyperfine coupling constants that are almost identical to the converged series (aug-cc-pVTZ-Juc), we observe that not only the regular but also the core-valence correlation basis sets provide results far from the converged results. The usage of specialized core-basis sets leads to a large and highly significant improvement of the calculated hyperfine couplings in comparison with experimental data.