Benchmarking density-functional theory calculations of NMR shielding constants and spin-rotation constants using accurate coupled-cluster calculations

31P Chemical Shifts in Ru(II) Phosphine Complexes. A Computational Study of the Influence of the Coordination Sphere

The NMR chemical shift has been the most versatile marker of chemical structures, by reflecting global and local electronic structures, and is very sensitive to any change within the chemical species. In this work, Ru(II) complexes with the same five ligands and a variable sixth ligand L (none, H₂O, H₂S, CH₃SH, H₂, N₂, N₂O, NO⁺, C═CHPh, and CO) are studied by using as the NMR reporter the phosphorus P_A of a coordinated bidentate P_A-N ligand (P_A-N = o-diphenylphosphino-N,N'-dimethylaniline). The chemical shift of P_A in RuCl₂(P_A-N)(PR₃)(L) (R = phenyl, p-tolyl, or p-FC₆H₄) was shown to increase as the Ru-P_A bond distance decreases, an observation that was not rationalized. This work, using density functional theory (DFT) calculations, reproduces reasonably well the observed ³¹P chemical shifts for these complexes and the correlation between the shifts and the Ru-P_A bond distance as L varies. An interpretation of this correlation is proposed by using a natural chemical shift (NCS) analysis based on the natural bonding orbital (NBO) method. This analysis of the principal components of the chemical shift tensors shows how the σ-donating properties of L have a particularly high influence on the phosphine chemical shifts.

Electric field effect on 31P NMR magnetic shielding

Magnetic shielding depends on molecular structure and noncovalent interactions. This study shows that it is also measurably dependent on the electric field generated by surrounding molecules. This effect has been observed explicitly for ³¹P nucleus using the adduct under field approach. The results obtained indicate that the field strength experienced by molecules in crystals consisting of molecules with large dipole moments is similar to that in polar solvents. Therefore, magnetic shielding should explicitly depend on solvent polarity. It is important to note that this effect cannot be reproduced correctly within the polarizable continuum model approach.

Correlated ab initio calculations of one-bond 31 P77 Se and 31 P125 Te spin-spin coupling constants in a series of PSe and PTe systems accounting for relativistic effects (part 2)

Synthetic chalcogen-phosphorus chemistry permanently makes new challenges to computational Nuclear Magnetic Resonance (NMR) spectroscopy, which has proven to be a powerful tool of structural analysis of chalcogen-phosphorus compounds. This paper reports on the calculations of one-bond ³¹ P⁷⁷ Se and ³¹ P¹²⁵ Te NMR spin-spin coupling constants (SSCCs) in the series of phosphine selenides and tellurides. The applicability of the combined computational approach to the one-bond ³¹ P⁷⁷ Se and ³¹ P¹²⁵ Te SSCCs, incorporating the composite nonrelativistic scheme, built of high-accuracy correlated SOPPA (CC2) and Coupled Cluster Single and Double (CCSD) methods and the Density Functional Theory (DFT) relativistic corrections (four-component level), was examined against the experiment and another scheme based on the four-component relativistic DFT method. A special J-oriented basis set (acv3z-J) for selenium and tellurium atoms, developed previously by the authors, was used throughout the NMR calculations in this work at the first time. The proposed computational methodologies (combined and 'pure') provided a reasonable accuracy for ³¹ P⁷⁷ Se and ³¹ P¹²⁵ Te SSCCs against experimental data, characterizing by the mean absolute percentage errors of about 4% and 1%, and 12% and 8% for selenium and tellurium species, respectively. The present study reports typical relativistic corrections to ⁷⁷ Se³¹ P and ¹²⁵ Te³¹ P SSCCs, calculated within the four-component DFT formalism for a broad series of tertiary phosphine selenides and tellurides with different substituents at phosphorus.

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.

Predicting 19 F NMR Chemical Shifts: A Combined Computational and Experimental Study of a Trypanosomal Oxidoreductase-Inhibitor Complex

The absence of fluorine from most biomolecules renders it an excellent probe for NMR spectroscopy to monitor inhibitor-protein interactions. However, predicting the binding mode of a fluorinated ligand from a chemical shift (or vice versa) has been challenging due to the high electron density of the fluorine atom. Nonetheless, reliable 19 F chemical-shift predictions to deduce ligand-binding modes hold great potential for in silico drug design. Herein, we present a systematic QM/MM study to predict the 19 F NMR chemical shifts of a covalently bound fluorinated inhibitor to the essential oxidoreductase tryparedoxin (Tpx) from African trypanosomes, the causative agent of African sleeping sickness. We include many protein-inhibitor conformations as well as monomeric and dimeric inhibitor-protein complexes, thus rendering it the largest computational study on chemical shifts of 19 F nuclei in a biological context to date. Our predicted shifts agree well with those obtained experimentally and pave the way for future work in this area.

GIAO versus GIPAW: Comparison of Methods To Calculate 11B NMR Shifts of Icosahedral Closo-Heteroboranes toward Boron-Rich Borides

In this work, we perform first-principle density functional theory calculations with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional to compare the results of the gauge-including atomic orbital (GIAO) method with the gauge-including projector-augmented wave (GIPAW) approach for isotropic ¹¹B nuclear magnetic resonance shifts. GIPAW had been used successfully for the theoretical calculation of nuclear magnetic parameters of ¹¹B species in strong ionic solid-phase compounds such as borates but had been applied very rarely to structures where boron is mainly involved in complex covalent bonding situations, for example, in icosahedra of boron-rich borides. Thus, we investigate the accuracy of both well-known methods and reliability of the effective treatment of core electrons on a test set containing 16 experimentally known closo-(hetero)dodecaboranes. In general, we find very good agreement between GIAO and GIPAW when compared to experimental observations. However, accidental degeneracies of the shift values are better predicted by GIPAW. The optimized molecular geometries on the PBE level agree well with gaseous electron diffraction data and lead to theoretical isotropic chemical ¹¹B shifts with root-mean-square errors of 2.1 and 1.0 ppm depending on the used model of converting absolute shieldings to chemical shifts. The comparison with results from hybrid functionals (B3LYP, B3LYP-D2, and PBE0) shows a minor improvement in accuracy, which is in agreement with ¹³C shifts of sp³-hybridized species. In order to prove the reliability of the conversion parameters obtained by PBE, we report the calculated ¹¹B shifts of 1,2-, 1,7-, and 1,12-PCB₁₀H₁₁ with GIAO and GIPAW to our knowledge for the first time. Additionally, Bader's analysis is carried out on the converged electron density for all boron species within the molecular test set, yielding no simple direct relation between charge and isotropic shifts.

Weak Intermolecular CH···N Hydrogen Bonding: Determination of 13CH-15N Hydrogen-Bond Mediated J Couplings by Solid-State NMR Spectroscopy and First-Principles Calculations

Weak hydrogen bonds are increasingly hypothesized to play key roles in a wide range of chemistry from catalysis to gelation to polymer structure. Here, ¹⁵N/¹³C spin-echo magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) experiments are applied to "view" intermolecular CH···N hydrogen bonding in two selectively labeled organic compounds, 4-[¹⁵N] cyano-4'-[¹³C₂] ethynylbiphenyl (1) and [¹⁵N₃,¹³C₆]-2,4,6-triethynyl-1,3,5-triazine (2). The synthesis of 2-¹⁵N₃,¹³C₆ is reported here for the first time via a multistep procedure, where the key element is the reaction of [¹⁵N₃]-2,4,6-trichloro-1,3,5-triazine (5) with [¹³C₂]-[(trimethylsilyl)ethynyl]zinc chloride (8) to afford its immediate precursor [¹⁵N₃,¹³C₆]-2,4,6-tris[(trimethylsilyl)ethynyl]-1,3,5-triazine (9). Experimentally determined hydrogen-bond-mediated ^2hJ_CN couplings (4.7 ± 0.4 Hz (1) and 4.1 ± 0.3 Hz (2)) are compared with density functional theory (DFT) gauge-including projector augmented wave (GIPAW) calculations, whereby species-independent coupling values ^2hK_CN (29.0 × 10¹⁹ kg m^-2 s^-2 A^-2 (1) and 27.9 × 10¹⁹ kg m^-2 s^-2 A^-2 (2)) quantitatively demonstrate the J couplings for these "weak" CH···N hydrogen bonds to be of a similar magnitude to those for conventionally observed NH···O hydrogen-bonding interactions in uracil (^2hK_NO: 28.1 and 36.8 × 10¹⁹ kg m^-2 s^-2 A^-2). Moreover, the GIPAW calculations show a clear correlation between increasing ^2hJ_CN (and ^3hJ_CN) coupling and reducing C(H)···N and H···N hydrogen-bonding distances, with the Fermi contact term accounting for at least 98% of the isotropic ^2hJ_CN coupling.

IMPRESSION - prediction of NMR parameters for 3-dimensional chemical structures using machine learning with near quantum chemical accuracy

The IMPRESSION (Intelligent Machine PREdiction of Shift and Scalar information Of Nuclei) machine learning system provides an efficient and accurate method for the prediction of NMR parameters from 3-dimensional molecular structures. Here we demonstrate that machine learning predictions of NMR parameters, trained on quantum chemical computed values, can be as accurate as, but computationally much more efficient (tens of milliseconds per molecular structure) than, quantum chemical calculations (hours/days per molecular structure) starting from the same 3-dimensional structure. Training the machine learning system on quantum chemical predictions, rather than experimental data, circumvents the need for the existence of large, structurally diverse, error-free experimental databases and makes IMPRESSION applicable to solving 3-dimensional problems such as molecular conformation and stereoisomerism.

NMR absolute shielding scales and nuclear magnetic dipole moments of transition metal nuclei

This work reports new, accurate nuclear magnetic dipole moments for transition metal nuclei where the long-standing systematic error due to obsolete diamagnetic correction has been eliminated by ab initio calculations of NMR shielding constants.

Computational protocols for calculating 13C NMR chemical shifts

The most recent results dealing with the computation of ¹³C NMR chemical shifts in chemistry (small molecules, saturated, unsaturated and aromatic compounds, heterocycles, functional derivatives, coordination complexes, carbocations, and natural products) are reviewed, paying special attention to theoretical background and accuracy, the latter involving solvent effects, vibrational corrections, and relativistic effects.

Four-component relativistic 31P NMR calculations for trans-platinum(ii) complexes: importance of the solvent and dynamics in spectral simulations

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

Accurate prediction of nuclear magnetic resonance shielding constants: An extension of the focal-point analysis method for magnetic parameter calculations (FPA-M) with improved efficiency

Previously, we have proposed a method, FPA-M, for focal-point analysis of magnetic parameter calculations [Sun et al., J. Chem. Phys. 138, 124113 (2013)], where the shielding constants at equilibrium geometries σ_e are calculated with the second order Møller-Plesset perturbation (MP2) approach, which are extrapolated to the complete basis set (CBS) limit and then augmented by the [σ_e(CCSD(T)) - σ_e(MP2)] difference at a valence triple-ζ (VTZ) basis set, where CCSD(T) stands for the coupled cluster singles and doubles model with a perturbative correction for triple excitations. This FPA-M(MP2) method provides satisfactory results to approach to the corresponding CCSD(T)/CBS values for elements of the first two rows in the periodic tables. A series of extensions have been explored here, which replace the MP2/CBS with the Hartree-Fock (HF)/CBS for efficiency. In particular, the [σ_e(CCSD(T)) - σ_e(MP2)] VTZ difference is replaced by a step-wise correction from the [σ_e(CCSD(T)) - σ_e(MP2)] difference at a valence double-ζ basis set plus the [σ_e(MP2) - σ_e(HF)] VTZ difference, leading to a new scheme, denoted here as FPA-M(HF'). A systematical comparison has demonstrated that the FPA-M(HF') method provides an excellent balance between accuracy and efficiency, which makes routinely accurate calculations of the shielding constants for medium-sized organic molecules and biomolecules feasible.

An automated framework for NMR chemical shift calculations of small organic molecules

When using nuclear magnetic resonance (NMR) to assist in chemical identification in complex samples, researchers commonly rely on databases for chemical shift spectra. However, authentic standards are typically depended upon to build libraries experimentally. Considering complex biological samples, such as blood and soil, the entirety of NMR spectra required for all possible compounds would be infeasible to ascertain due to limitations of available standards and experimental processing time. As an alternative, we introduce the in silico Chemical Library Engine (ISiCLE) NMR chemical shift module to accurately and automatically calculate NMR chemical shifts of small organic molecules through use of quantum chemical calculations. ISiCLE performs density functional theory (DFT)-based calculations for predicting chemical properties—specifically NMR chemical shifts in this manuscript—via the open source, high-performance computational chemistry software, NWChem. ISiCLE calculates the NMR chemical shifts of sets of molecules using any available combination of DFT method, solvent, and NMR-active nuclei, using both user-selected reference compounds and/or linear regression methods. Calculated NMR chemical shifts are provided to the user for each molecule, along with comparisons with respect to a number of metrics commonly used in the literature. Here, we demonstrate ISiCLE using a set of 312 molecules, ranging in size up to 90 carbon atoms. For each, calculation of NMR chemical shifts have been performed with 8 different levels of DFT theory, and with solvation effects using the implicit solvent Conductor-like Screening Model. The DFT method dependence of the calculated chemical shifts have been systematically investigated through benchmarking and subsequently compared to experimental data available in the literature. Furthermore, ISiCLE has been applied to a set of 80 methylcyclohexane conformers, combined via Boltzmann weighting and compared to experimental values. We demonstrate that our protocol shows promise in the automation of chemical shift calculations and, ultimately, the expansion of chemical shift libraries.

Method Calibration or Data Fitting?

We investigate by explicit parameter optimization to what extent basis sets of polarized double-ζ quality can introduce compensating errors in five different density functional methods. It is shown that minor changes in the contraction coefficients of the valence functions in the basis sets can have a significant impact and allow different density functional methods to achieve very similar performances. This holds for nuclear magnetic shielding constants and for isomerization energies, barrier heights, and noncovalent interactions. It is furthermore shown that errors due to neglect of vibrational and solvent effects can be absorbed in the combined method and basis set errors. These findings hold for data sets consisting of 50-150 data points. This raises the question of whether the common practice of identifying combinations of density functional methods and basis sets that have a good performance against a selected set of reference data should be considered as data fitting in the combined parameter space spanned by the method and basis set.

The influence of substituents and the environment on the NMR shielding constants of supramolecular complexes based on A-T and A-U base pairs

In the present study, we have theoretically analyzed supramolecular complexes based on the Watson-Crick A-T and A-U base pairs using dispersion-corrected density functional theory (DFT). Hydrogen atoms H8 and/or H6 in the natural adenine and thymine/uracil bases were replaced, respectively, by substituents X8, Y6 = NH^-, NH₂, NH₃⁺ (N series), O^-, OH, OH₂⁺ (O series), F, Cl or Br (halogen series). We examined the effect of the substituents on the hydrogen-bond lengths, strength and bonding mechanism, and the NMR shielding constants of the C2-adenine and C2-thymine/uracil atoms in the base pairs. The general belief in the literature that there is a direct connection between changes in the hydrogen-bond strength and the C2-adenine shielding constant is conclusively rejected by our computations.

Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

NMR shielding constants in group 15 trifluorides

By combining large basis and complete basis set (CBS) extrapolations of the coupled-cluster equilibrium geometry results with rovibrational and relativistic corrections, we demonstrate that it is possible to achieve near-quantitative accuracy for the NMR shielding constants in three group 15 trifluorides – NF₃, PF₃ and AsF₃.

Evaluation of the Factors Impacting the Accuracy of 13C NMR Chemical Shift Predictions using Density Functional Theory-The Advantage of Long-Range Corrected Functionals

The various factors influencing the accuracy of ¹³C NMR calculations using density functional theory (DFT), including the basis set, exchange-correlation (XC) functional, and isotropic shielding calculation method, are evaluated. A wide selection of XC functionals (over 70) were considered, and it was found that long-range corrected functionals offer a significant improvement over the other classes of functionals. Based on a thorough study, it is recommended that for calculating NMR chemical shifts (δ) one should use the CSGT method, the COSMO solvation model, and the LC-TPSSTPSS exchange-correlation functional in conjunction with the cc-pVTZ basis set. A selection of problems in natural product identification are considered in light of the newly recommended level of theory.

Fully Automated Quantum-Chemistry-Based Computation of Spin-Spin-Coupled Nuclear Magnetic Resonance Spectra

We present a composite procedure for the quantum‐chemical computation of spin–spin‐coupled ¹H NMR spectra for general, flexible molecules in solution that is based on four main steps, namely conformer/rotamer ensemble (CRE) generation by the fast tight‐binding method GFN‐xTB and a newly developed search algorithm, computation of the relative free energies and NMR parameters, and solving the spin Hamiltonian. In this way the NMR‐specific nuclear permutation problem is solved, and the correct spin symmetries are obtained. Energies, shielding constants, and spin–spin couplings are computed at state‐of‐the‐art DFT levels with continuum solvation. A few (in)organic and transition‐metal complexes are presented, and very good, unprecedented agreement between the theoretical and experimental spectra was achieved. The approach is routinely applicable to systems with up to 100–150 atoms and may open new avenues for the detailed (conformational) structure elucidation of, for example, natural products or drug molecules.

Magnetic-Field Density-Functional Theory (BDFT): Lessons from the Adiabatic Connection

We study the effects of magnetic fields in the context of magnetic field density-functional theory (BDFT), where the energy is a functional of the electron density ρ and the magnetic field B. We show that this approach is a worthwhile alternative to current-density functional theory (CDFT) and may provide a viable route to the study of many magnetic phenomena using density-functional theory (DFT). The relationship between BDFT and CDFT is developed and clarified within the framework of the four-way correspondence of saddle functions and their convex and concave parents in convex analysis. By decomposing the energy into its Kohn-Sham components, we demonstrate that the magnetizability is mainly determined by those energy components that are related to the density. For existing density functional approximations, this implies that, for the magnetizability, improvements of the density will be more beneficial than introducing a magnetic-field dependence in the correlation functional. However, once a good charge density is achieved, we show that high accuracy is likely only obtainable by including magnetic-field dependence. We demonstrate that adiabatic-connection (AC) curves at different field strengths resemble one another closely provided each curve is calculated at the equilibrium geometry of that field strength. In contrast, if all AC curves are calculated at the equilibrium geometry of the field-free system, then the curves change strongly with increasing field strength due to the increasing importance of static correlation. This holds also for density functional approximations, for which we demonstrate that the main error encountered in the presence of a field is already present at zero field strength, indicating that density-functional approximations may be applied to systems in strong fields, without the need to treat additional static correlation.

Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?

Theoreticians and experimentalists should work together more closely to establish reliable rankings and benchmarks for quantum chemical methods. Comparison to carefully designed experimental benchmark data should be a priority. Guidelines to improve the situation for experiments and calculations are proposed.

Effects of the locality of a potential derived from hybrid density functionals on Kohn-Sham orbitals and excited states

Density functional theory (DFT) has been an essential tool for electronic structure calculations in various fields. In particular, its hybrid method including the Hartree-Fock (HF) exchange term remarkably improves the reliability of DFT for chemical applications and computational material design. There are two different types of exchange-correlation potential that can be derived from hybrid functionals. The conventional approach adopts a non-multiplicative potential including the non-local HF exchange operator. Herein, we propose to use a local multiplicative potential as an alternative for accurate excited state calculations. We show that such a local potential can be derived from existing global hybrid functionals using the optimized effective potential method. As a proof-of-concept, we chose PBE0 and investigated its performance for the Caricato benchmark set. Unlike the conventional one, the local potential produced orbital energy gaps with no strong dependence on the mixing ratio as a good approximation for optical excitations. Furthermore, its time-dependent DFT resulted in a surprisingly small mean absolute error even with a local density approximation kernel, surpassing all reported values with various popular functionals. In particular, most excitations were dictated by single orbital transitions due to physically meaningful virtual orbitals, which is beneficial to clear interpretations in the molecular orbital picture.

Prediction of low-field nuclear singlet lifetimes with molecular dynamics and quantum-chemical property surface

Molecular dynamics and quantum chemistry methods are implemented to quantify nuclear spin-1/2 pair singlet-state relaxation rates. Illustrated is the relevant spin-internal-motion mechanism (SIM).

On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework

The implementation of second-order magnetic properties in a frozen density embedding scheme in a four component relativistic framework is outlined and applied to model H₂X–H₂O systems (X = Se, Te, Po).

Finding Our Way in the Dark Proteome

The traditional structure-function paradigm has provided significant insights for well-folded proteins in which structures can be easily and rapidly revealed by X-ray crystallography beamlines. However, approximately one-third of the human proteome is comprised of intrinsically disordered proteins and regions (IDPs/IDRs) that do not adopt a dominant well-folded structure, and therefore remain "unseen" by traditional structural biology methods. This Perspective considers the challenges raised by the "Dark Proteome", in which determining the diverse conformational substates of IDPs in their free states, in encounter complexes of bound states, and in complexes retaining significant disorder requires an unprecedented level of integration of multiple and complementary solution-based experiments that are analyzed with state-of-the art molecular simulation, Bayesian probabilistic models, and high-throughput computation. We envision how these diverse experimental and computational tools can work together through formation of a "computational beamline" that will allow key functional features to be identified in IDP structural ensembles.

Benchmark fragment-based (1)H, (13)C, (15)N and (17)O chemical shift predictions in molecular crystals

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

First principles optimally tuned range-separated density functional theory for prediction of phosphorus–hydrogen spin–spin coupling constants

The novel optimally tuned range-separated approximations for predicting NMR spin–spin coupling constants are proposed and benchmarked numerically.

Theoretical analysis of NMR shieldings in XSe and XTe (X = Si, Ge, Sn and Pb): the spin-rotation constant saga

How the electronic contribution to the spin-rotation constant is close to the paramagnetic contribution of the NMR absolute shielding constant?

Systematic Study of Locally Dense Basis Sets for NMR Shielding Constants

This paper presents a systematic study of partitioning schemes for locally dense basis sets in the context of NMR shielding calculations. The partitionings explored were based exclusively on connectivity and utilized the basis sets from the pcS-n series. Deviations from pcS-4 shieldings were calculated for a set of 28 organic molecules at the HF, B3LYP, and KT3 levels of theory, with the primary goal being the determination of an efficient scheme that achieves maximal deviations of 0.1 ppm for (1)H and 1 ppm for (13)C. Both atom based and group based divisions of basis sets were examined, with the latter providing the most promising results. It is demonstrated that for the systems studied, at least pcS-1 is required for all parts of the molecule. This, coupled with pcS-3 on the group of interest and pcS-2 on the adjacent groups, is sufficient to achieve the desired level of accuracy at a minimal computational expense. In addition, the suitability of the pcS-n basis sets for post-SCF methods was confirmed through a comparison with other standard basis sets at the MP2 level.

Sensitivity of ab Initio vs Empirical Methods in Computing Structural Effects on NMR Chemical Shifts for the Example of Peptides

The structural sensitivity of NMR chemical shifts as computed by quantum chemical methods is compared to a variety of empirical approaches for the example of a prototypical peptide, the 38-residue kaliotoxin KTX comprising 573 atoms. Despite the simplicity of empirical chemical shift prediction programs, the agreement with experimental results is rather good, underlining their usefulness. However, we show in our present work that they are highly insensitive to structural changes, which renders their use for validating predicted structures questionable. In contrast, quantum chemical methods show the expected high sensitivity to structural and electronic changes. This appears to be independent of the quantum chemical approach or the inclusion of solvent effects. For the latter, explicit solvent simulations with increasing number of snapshots were performed for two conformers of an eight amino acid sequence. In conclusion, the empirical approaches neither provide the expected magnitude nor the patterns of NMR chemical shifts determined by the clearly more costly ab initio methods upon structural changes. This restricts the use of empirical prediction programs in studies where peptide and protein structures are utilized for the NMR chemical shift evaluation such as in NMR refinement processes, structural model verifications, or calculations of NMR nuclear spin relaxation rates.

Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals

First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.