Shielding Tensors Research Articles

Theory of Magnetic Properties in Quantum Electrodynamics Environments: Application to Molecular Aromaticity.

In this work, we present ab initio cavity quantum electrodynamics (QED) methods which include interactions with a static magnetic field and nuclear spin degrees of freedom using different treatments of the quantum electromagnetic field. We derive explicit expressions for QED-HF magnetizability, nuclear shielding, and spin-spin coupling tensors. We apply this theory to explore the influence of the cavity field on the magnetizability of saturated, unsaturated, and aromatic hydrocarbons, showing the effects of different polarization orientations and coupling strengths. We also examine how the cavity affects aromaticity descriptors, such as the nucleus-independent chemical shift and magnetizability exaltation. We employ these descriptors to study the trimerization reaction of acetylene to benzene. We show how the optical cavity induces modifications in the aromatic character of the transition state leading to variations in the activation energy of the reaction. Our findings shed light on the effects induced by the cavity on magnetic properties, especially in the context of aromatic molecules, providing valuable insights into understanding the interplay between the quantum electromagnetic field and molecules.

Theoretical investigation of the effects of diverse hydrogen-bonding characteristics on the 17O chemical shielding and electric field gradient tensors within the active sites of MraYAA bound to nucleoside antibiotics capuramycin, carbacaprazamycin, 3′-Hydroxymureidomycin A, and muraymycin D2

This study builds upon our prior researches and seeks to investigate and clarify the influences of various characteristics of hydrogen bonds (H-bonds) and charge transfer (CT) interactions, which were detected within the inhibitor binding pockets (labeled as the QM models I–IV) of MraYAA–capuramycin, MraYAA–carbacaprazamycin, MraYAA–3′-hydroxymureidomycin A, and MraYAA–muraymycin D2 complexes by QTAIM and NBO analyses from DFT QM/MM MD calculations, on the 17O chemical shielding (CS) and electric field gradient (EFG) tensors of carboxylate (Oδ), carbonyl (C═O), and hydroxyl (O–H) oxygens in these models. The 17O CS and EFG tensors of these three types of oxygens in QM models I–IV were calculated at the M06-2X/6-31G** level by including the solvent effects using the polarizable continuum model. From the computed 17O CS and EFG tensors in these models, it was found that the nuclear shielding, σiso, for carboxylate or carbonyl oxygen increases (shielding effect) as the H-bond length decreases and the percentage p-character of nOδ/nC═O lone pair partner in the CT interaction enhances. In contrast, the σiso (17O–H) decreases (deshielding effect) with a reduction in the H-bond length as well as with an enhancement in percentage s-character of the nOH lone pair/σ*O–H antibond. By reducing the H-bond length or by increasing p-character of the nOδ/nC═O lone pair, the 17Oδ/17O═C quadrupole coupling constant smoothly decreases, while the 17Oδ/17O═C asymmetry parameter smoothly increases. Moreover, these calculated parameters are in a good agreement with the experimental values. The information garnered here is valuable particularly for further understanding of empirical correlations between 17O NMR spectroscopic and H-bonding characteristics in the protein–ligand complexes.

Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning.

Theoretical predictions of NMR chemical shifts from first-principles can greatly facilitate experimental interpretation and structure identification of molecules in gas, solution, and solid-state phases. However, accurate prediction of chemical shifts using the gold-standard coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] method with a complete basis set (CBS) can be prohibitively expensive. By contrast, machine learning (ML) methods offer inexpensive alternatives for chemical shift predictions but are hampered by generalization to molecules outside the original training set. Here, we propose several new ideas in ML of the chemical shift prediction for H, C, N, and O that first introduce a novel feature representation, based on the atomic chemical shielding tensors within a molecular environment using an inexpensive quantum mechanics (QM) method, and train it to predict NMR chemical shieldings of a high-level composite theory that approaches the accuracy of CCSD(T)/CBS. In addition, we train the ML model through a new progressive active learning workflow that reduces the total number of expensive high-level composite calculations required while allowing the model to continuously improve on unseen data. Furthermore, the algorithm provides an error estimation, signaling potential unreliability in predictions if the error is large. Finally, we introduce a novel approach to keep the rotational invariance of the features using tensor environment vectors (TEVs) that yields a ML model with the highest accuracy compared to a similar model using data augmentation. We illustrate the predictive capacity of the resulting inexpensive shift machine learning (iShiftML) models across several benchmarks, including unseen molecules in the NS372 data set, gas-phase experimental chemical shifts for small organic molecules, and much larger and more complex natural products in which we can accurately differentiate between subtle diastereomers based on chemical shift assignments.

Carbon-13 chemical shift tensor measurements for nitrogen-dense compounds.

This paper reports the principal values of the 13 C chemical shift tensors for five nitrogen-dense compounds (i.e., cytosine, uracil, imidazole, guanidine hydrochloride, and aminoguanidine hydrochloride). Although these are all fundamentally important compounds, the majority do not have 13 C chemical shift tensors reported in the literature. The chemical shift tensors are obtained from 1 H→13 C cross-polarization magic-angle spinning (CP/MAS) experiments that were conducted at a high field of 18.8T to suppress the effects of 14 N-13 C residual dipolar coupling. Quantum chemical calculations using density functional theory are used to obtain the 13 C magnetic shielding tensors for these compounds. The best agreement with experiment arises from calculations using the hybrid functional PBE0 or the double-hybrid functional PBE0-DH, along with the triple-zeta basis sets TZ2P or pc-3, respectively, and intermolecular effects modeled using large clusters of molecules with electrostatic embedding through the COSMO approach. These measurements are part of an ongoing effort to expand the catalog of accurate 13 C chemical shift tensor measurements, with the aim of creating a database that may be useful for benchmarking the accuracy of quantum chemical calculations, developing nuclear magnetic resonance (NMR) crystallography protocols, or aiding in applications involving machine learning or data mining. This work was conducted at the National High Magnetic Field Laboratory as part of a 2-week school for introducing undergraduate students to practical laboratory experience that will prepare them for scientific careers or postgraduate studies.

Origin of 17O NMR chemical shifts based on molecular orbital theory: paramagnetic terms of the pre-α, α and β effects from orbital-to-orbital transitions, along with the effects from vinyl, carbonyl and carboxyl groups.

17O NMR chemical shifts (δ(O)) were analysed based on the molecular orbital (MO) theory, using the diamagnetic, paramagnetic and total absolute magnetic shielding tensors (σd(O), σp(O) and σt(O), respectively). O2- was selected as the standard for the analysis. An excellent relationship was observed between σd(O) and the charges on O for O6+, O4+, O2+, O0 and O2-. The data from H2O, HO+, HO- and H3O+ were on the correlation line. However, such relationship was not observed for the oxygen species, other than above. The pre-α, α and β effects were evaluated bases on σt(O), where the pre-α effect arises from the protonation to a lone pair orbital on O2-, for an example. The 30-40 ppm and 20-40 ppm (downfield shifts) were predicted for the pre-α and β effects, respectively, whereas the values for the α effect was very small in magnitude, where the effect from the hydrogen bond formation should be considered. Similarly, the carbonyl effect in H2C[double bond, length as m-dash]O and the carboxyl effects in H(HO)C[double bond, length as m-dash]O were evaluated from MeOH, together with H2C[double bond, length as m-dash]CHOH from CH3CH2OH. Very large downfield shifts of 752, 425 and 207 ppm were predicted for H2C[double bond, length as m-dash]O*, H(HO)C[double bond, length as m-dash]O* and H(HO*)C[double bond, length as m-dash]O, respectively, together with the 81 ppm downfield shift for H2C[double bond, length as m-dash]CHO*H. The origin of the effect were visualized based on the occupied-to-unoccupied orbital transitions. As a result, the origin of the 17O NMR chemical shifts (δ(17O)) can be more easily imaged and understand through the image of the effects. The results would help to understand the role of O in the specific position of a compound in question and the mechanisms to arise the shift values also for the experimental scientists. The aim of this study is to establish the plain rules founded in theory for δ(17O), containing the origin, which has been achieved through the treatments.

Predicting 51V nuclear magnetic resonance observables in molecular crystals.

Solid-state nuclear magnetic resonance (NMR) spectroscopy and quantum chemical density functional theory (DFT) calculations are widely used to characterize vanadium centers in biological and pharmaceutically relevant compounds. Several techniques have been recently developed to improve the accuracy of predicted NMR parameters obtained from DFT. Fragment-based and planewave-corrected methods employing hybrid density functionals are particularly effective tools for solid-state applications. A recent benchmark study involving molecular crystal compounds found that fragment-based NMR calculations using hybrid density functionals improve the accuracy of predicted 51V chemical shieldings by 20% relative to traditional planewave methods. This work extends the previous study, including a careful analysis of 51V chemical shift anisotropy, electric field gradient calculations, and a more extensive test set. The accuracy of planewave-corrected techniques and recently developed fragment-based methods using electrostatic embedding based on the polarized continuum model (PCM) are found to be highly competitive with previous methods. Planewave-corrected methods achieve a 34% improvement in the errors of predicted 51V chemical shieldings relative to planewave. Additionally, planewave-corrected and fragment-based calculations were performed using PCM embedding, improving the accuracy of predicted 51V chemical shielding (CS) tensor principal values by 30% and values by 15% relative to traditional planewave methods. The performance of these methods is further examined using a redox-active oxovandium complex and a common 51V NMR reference compound.

Vibrational Spectroscopic, 13C NMR, DFT Studies on Chlorofullerene (C60Cl6): A Potential Bioactive Agent

Abstract. The present work comprises the systematic computational chemical findings on Chlorofullerene (C60Cl6). The molecular structure of C60Cl6 was optimized by density function theory (DFT)/B3LYP model of 6-31G(d,p) basis set using Gaussian 09 program. The infrared and Raman spectra were simulated and assigned for C60Cl6 molecule. Carbon – chlorine stretching vibrations are found to be in the range 150-900 cm-1 and the chains are strongly affected with the radial vibrations of the carbon sphere. The optimized geometries at ground-state of the molecules are calculated without any geometrical restriction, except those enforced by symmetry and the molecules are found to be minima on their respective potential energy surfaces. The optimized structures have been subjected to Gauge including atomic orbital (GIAO), the chemical shielding tensors using B3LYP/6-31G(d,p) in solvent phase with the aim of calculating 13C chemical shift values with respect to trimethylsilane (TMS) as computational reference. Molecular acuteness and stability were investigated using the Frontier molecular orbitals (FMO) analysis. The molecular electrostatic potential (MEP) mapping provides a valuable information regarding the net electrostatic effect produced by net charge distribution of the molecule. Chlorofullerenes are considered to be promising compounds for the investigation of biological action which show pronounced anti-HIV action and low toxicity. Hence, these results set goal in scheming the biocompatible molecules which will be useful in the field of carbon nano medicine and drug delivery application.

Relativistic DFT Calculations of Cadmium and Selenium Solid-State NMR Spectra of CdSe Nanocrystal Surfaces.

Solid-state NMR spectra have been used to probe the structure of CdSe nanocrystals and propose detailed models of their surface structures. Density functional theory (DFT)-optimized cluster models that represent probable molecular structures of carboxylate-coordinated surface sites have been proposed. However, to the best of our knowledge, 113Cd and 77Se chemical shifts have not been calculated for these surface models. We performed relativistic DFT calculations of cadmium and selenium magnetic shielding tensors on model compounds with previously measured solid-state NMR spectra with (i) the four-component Dirac-Kohn-Sham (DKS) Hamiltonian and (ii) the scalar and (iii) spin-orbit levels within the ZORA Hamiltonian. Molecular clusters with Cd and Se sites in varying bonding environments were used to model CdSe (100) and CdSe(111) surfaces capped with carboxylic acid ligands. Our calculations identify the observed 113Cd isotropic chemical shifts δ(iso) of -465, -318, and -146 ppm arising from CdSeO3, CdSe2O2, and CdSe3O surface groups, respectively, with very good agreement with experimental measurements. The 113Cd chemical shifts linearly decrease with the number of O-neighbors. The calculated spans (δ11 - δ33) encompass the experimental values for CdSe3O and CdSe2O2 clusters but are slightly larger than the measured value for CdSeO3 clusters. Relativistic DFT calculations predicted a one-bond 113Cd-77Se scalar coupling of 258 Hz, which is in good agreement with the experimental values of 250 Hz. With a dense coverage of carboxylic acid ligands, the CdSe (100) surface shows a distribution of Cd-Se bond lengths and J-couplings. Relativistic DFT simulations thus aid in interpretation of NMR spectra of CdSe nanocrystals and related nanomaterials.

Quantum Effects of Hydrogen Nuclei on the Nuclear Magnetic Shielding Tensor of Ice Ih.

Ice is the most fundamental hydrogen-bonded system in which the hydrogen nuclear quantum effect significantly impacts the structure and relevant thermochemical and spectroscopic properties. While ice was experimentally investigated using proton nuclear magnetic resonance spectroscopy more than 40 years ago, the corresponding theoretical investigations have been rarely reported due to the difficulty in evaluating how the proton nuclear quantum effect influences the spectral characteristics of such a condensed material. In this study, we applied a combination of the ONIOM and multicomponent molecular orbital (MC_MO) methods for calculating the anisotropic and isotropic components of the nuclear magnetic shielding tensor of the hexagonal ice crystal to quantify the effects of nuclear quantum fluctuations on the spectroscopic properties of ice. The nuclear magnetic shielding values computed by incorporating the hydrogen nuclear quantum effect reasonably agree with the experimental values. The nuclear quantum effects were found to increase the anisotropic component of the magnetic shielding tensor while decreasing the isotropic component. Such a difference can be explained by their distinct dependence on the electrostatic field and hydrogen-bonding structural parameters.

Synthesis and Molecular Structures of 1-Carboxyl-4-Amino-2-Aza-3-Oxo-[2.2.2] Bicyclooctane

The novel bicycloamino acid, 1−carboxyl−4−amino−2−aza−3−oxo−[2.2.2] bicyclooctane was synthesized and its physical characteristics have been compared to those predicted using quantum chemical calculations. The crystal structure of novel compound was determined by X-ray diffraction measurements at room temperature. Unit cell is monoclinic, with space group P 21/n (14) and a = 5.8587(6) Ǻ, b = 11.2454(16) Ǻ, c = 13.9723(16) Ǻ, β=97.840(6)°, Z = 2. Refinement was performed using all 1598 reflections with R = 0.4085 and wR = 0.6024. Theoretical calculation of full optimization and atomic net charge, and frontier orbital energies of the title compound was carried out at the B3LYP/6−31G(d,p) level. The NMR chemical shielding tensors and vibrational frequencies were calculated with B3LYP/6-311+G(2d, p)− level in which were close values and similar spectrum structures with experimental results and used to interpret the experimental measurements.

Transition metal (X = Mn, Fe, Co, Ni, Cu, Zn)-doped graphene as gas sensor for CO2 and NO2 detection: a molecular modeling framework by DFT perspective.

In this research, CO2 and NO2 adsorption on doped nanographene (NG) sheets with transition metals (Fe, Ni, Zn) and (Mn, Co, Cu), respectively, have been applied for scavenging of these toxic gases as the environmental pollutants. The values of changes of atomic charge density have illustrated a more significant charge transfer for Ni-doped C-NG through CO2 adsorption and a more remarkable charge transfer for Co-doped C-NG through NO2 adsorption. The data of NMR spectroscopy has depicted several fluctuations around the graph of Zn-doped on the nanographene surface. The thermodynamic results from IR spectroscopy have indicated that [Formula: see text] values are almost similar for doped metal transitions of Mn, Co, and Cu on the C-NG nanosheet, while [Formula: see text] has the largest gap of Gibbs free energy adsorption with dipole moment. The Langmuir adsorption model with a three-layered ONIOM using CAM-B3LYP functional accompanying LANL2DZ, EPR-III and 6-31 + G (d,p) basis sets due to Gaussian 16 revision C.01 program on the complexes of CO2 → (Fe, Ni, Zn) and NO2 → (Mn, Co, Cu) doped on the C-NG has been accomplished. Then, NMR and IR spectroscopy, nuclear quadrupole resonance, and natural bond orbital analysis have been accomplished for evaluating chemical shielding tensors, thermodynamic properties, electric potential, and occupancy fluctuation through bond orbitals, respectively. In addition, frontier orbitals of LUMO, HOMO, and also a series of chemical reactivity parameters have been calculated. Finally, time-dependent-DFT method due to UV-VIS spectrums has been accomplished to discern the low-lying excited states of CO2 and NO2 adsorption on the (Fe, Ni, Zn) and (Mn, Co, Cu), respectively, doped C-NG sheet.

A relativistic relationship between parity-violating nuclear spin-rotation tensors and parity-violating NMR shielding tensors.

The nuclear-spin-dependent parity-violation contributions to the nuclear magnetic resonance shielding and nuclear spin-rotation tensors (σPV and MPV, respectively) are known to be formally related to one another in the non-relativistic regime. In this work, the polarization propagator formalism and the linear response within the elimination of small components model are used to show a new and more general relationship between them, which is valid within the relativistic framework. The full set of the zeroth- and first-order relativistic contributions to σPV and MPV are also given here for the first time, and these results are compared with previous findings. According to four-component relativistic calculations, the electronic spin-orbit effects are the most significant ones for the isotropic values of σPV and MPV in the H2X2 series of molecules (with X = O, S, Se, Te, and Po). When only scalar relativistic effects are taken into account, the non-relativistic relationship between σPV and MPV does hold. However, when the spin-orbit effects are taken into consideration, this old non-relativistic relationship breaks down, and therefore, the new one must be considered.

Crystal structure, spectroscopic analysis, electronic properties and molecular docking study of costunolide for inhibitor capacity against Onchocerca volvulus main protease

Costunolide, a naturally occurring sesquiterpene lactone, was investigated experimentally and theoretically to determine the structural, electronic, spectroscopic, and chemical reactivity properties. As deduced from a single crystal X-ray diffraction (XRD) analysis, the absolute configurations of the two chiral centres were assigned as (6R,7S). Vibrational frequencies (IR, UV and NMR), electronic properties (HOMO and LUMO), and the molecular structure of costunolide were investigated by DFT calculations using Gaussian 09 molecular package at the B3LYP/6-311++G(d,p) level of theory. NMR chemical shifts were calculated from the magnetic shielding tensors obtained through the gauge-independent atomic orbital (GIAO) method, while the UV-vis spectrum was simulated by time dependent-DFT (TD-DFT) calculations. All calculations showed correlations to experimental data. The 6-311+G(2d,p) basis set was additionally used for better correlation in NMR studies. The first order hyperpolarizability value indicated that costunolide has nonlinear optical (NLO) properties. Costunolide stability arising from hyperconjugative interactions and charge delocalisation was analysed using natural bond orbital (NBO). Thermodynamic parameters also correlated in the temperature range 100–700 K. The molecular docking results showed that costunolide binds strongly to the Onchocerca volvulus main protease with a relative binding affinity of –5.94 kcal mol–1 and an inhibition constant of 44.61 µM.

A computational evidence of the intermolecular hydrogen bonding in leflunomide: Chemical shielding tensors

A computational investigation has been performed without any symmetry constraints at the B3LYP/6-31++G** level for the evidencing of hydrogen bonding interactions in the real crystalline structure of Leflunomide (LFM) via chemical shielding (CS) tensors at the site of 14C, 17O, 15N, 1H nucleus. In this study, one molecule (monomer), three molecules (trimer), and five-molecules (cluster) of Leflunomide’s conformer have been modeled by accessible crystal coordinates. The CS tensors have been computed for 3 models of structure to indicate the effects of the hydrogen bonding interactions on the parameters of NMR. The evaluated NMR parameters of 14C, 17O, 15N, 1H nuclei of Leflunomide show specific tendencies from the monomer to the target molecule in the cluster as a result of the involvement in the intermolecular CO…HN type of hydrogen bonding interaction. Chemical shift of 14C, 17O, 15N, 1H nuclei significantly alter from monomer to the target molecule in trimer because of formation of inter-molecular CO…HN kind of the hydrogen bonding interaction whereas this alternation was insignificant via the target molecule in trimer to pentamer as a result of do not change numbers and types of the hydrogen bonding interactions.

Benchmark accuracy of predicted NMR observables for quadrupolar 14 N and 17 O nuclei in molecular crystals.

Nuclear quadrupole resonances for and 17 O nuclei are exquisitely sensitive to interactions with surrounding atoms. As a result, nitrogen and oxygen solid-state nuclear magnetic resonance (ssNMR) provides a powerful tool for investigating structure and dynamics in complex systems. First-principles calculations are increasingly used to facilitate spectral assignment and to evaluate and adjust crystal structures. Recent work combining the strengths of planewave density functional theory (DFT) calculations with a single molecule correction obtained using a higher level of theory has proven successful in improving the accuracy of predicted chemical shielding (CS) tensors and 17 O quadrupolar coupling constants ( ). Here we extend this work by examining the accuracy of predicted 14 N and 17 O electric field gradient (EFG) tensor components obtained using alternative planewave-corrections involving cluster and two-body fragment-based calculations. We benchmark the accuracy of CS and EFG tensor predictions for both nitrogen and oxygen using planewave, two-body fragment, and enhanced planewave-corrected techniques. Combining planewave and two-body fragment calculations reduces the error in predicted 17 O values by 35% relative to traditional planewave calculations. These enhanced planewave-correction methods improve the accuracy of 17 O and 14 N EFG tensor components by 15% relative to planewave DFT but yield minimal improvement relative to a simple molecular correction. However, in structural environments involving either high symmetry or strong intermolecular interactions, enhanced planewave-corrected methods provide a distinct advantage.

Chemical shift tensors as probes of chalcogen bonds: solid-state NMR study of telluradiazole-XCN− (X = O, S, Se) salt cocrystals

We report experimental 125Te magic-angle spinning solid-state nuclear magnetic resonance (MAS NMR) measurements of the tellurium chemical shift (CS) tensors in three [K(18-crown-6)]+ 3,4-dicyano-1,2,5-telluradiazole-XCN− (X = O, S, Se) salt cocrystals featuring chalcogen bonds. These data are compared to those for pure 3,4-dicyano-1,2,5-telluradiazole (1). A reduction in the span of the 125Te CS tensor is consistently noted in the salt cocrystals compared to pure 1. Isotopically 15N-labelled [K(18-crown-6)]+[1-OC15N]−, which features a chalcogen bond between Te and the cyanate nitrogen atom, is synthesized using KOC15N, and the nitrogen CS tensors are measured for both samples via 15N slow MAS NMR spectroscopy. Possible dynamic disorder of the cyanate ions in KOCN is ruled out. Two crystallographically distinct nitrogen sites are resolved for the salt cocrystal. Upon formation of [K(18-crown-6)]+[1-OC15N]−, the 15N isotropic CS and CS tensor span both decrease relative to the values for pure KOC15N, and the axial symmetry of this tensor is lost. These findings are supplemented with a series of density functional theory calculations of magnetic shielding tensors using cluster models or periodic boundary conditions. Inclusion of spin–orbit relativistic effects in the calculation of tellurium shielding tensors is particularly important in achieving agreement with experiment.

Synthesis, crystal structure and 19F NMR parameters modelling of CaTiF6(H2O)2 yielding to a revision of the bond-valence parameters for the Ti4+/F− ion pair

CaTiF6(H2O)2 was synthetized by a solvothermal method and was found to be isostructural to SrTiF6⋅2H2O. The structure, refined from Powder X-Ray Diffraction (PXRD) data, is built from the connectivity of dimers [Ca2F10(H2O)4] of square antiprisms (SAP) [CaF5(H2O)3] and TiF6 octahedra. To assign the six 19F NMR resonances to the six fluorine crystallographic sites of same multiplicity, 19F magnetic shielding tensors have been calculated using the GIPAW method. Unusually, the plot of the experimental 19F isotropic chemical shift (δiso) values, as a function of the calculated 19F isotropic shielding (σiso) values, shows a much better alignment for the experimental structure than for the DFT-optimized one. Whereas, the dynamics of the structural water molecules under experimental conditions are not captured by the optimized structure, the experimental averaged structure provides a good account of the experimental data and a reliable assignment of the 19F resonances to the F sites. Finally, the previously established bond-valence (BV) parameter Rij for the Ti4+/F− ion pair (1.76 ​Å) leads to overestimated BV sum values for Ti. This trend has been observed for almost all other fluorotitanates. We then undertook to refine its value, using the Ti–F bond lengths from 70 carefully selected structures containing 134 Ti sites forming TiF6 octahedra, and leading to Rij ​= ​1.706 ​Å.

Parity-violating contributions to nuclear spin-rotation interactions and to NMR shielding constants in tetrahedral molecules

In natural processes involving weak interactions, a violation of spatial parity conservation should appear. Although the parity-violation effects are expected to be observable in molecular systems, their tiny magnitude has prevented their detection to date. We present a theoretical analysis of four-component relativistic nuclear-spin-dependent parity-violating nuclear spin-rotation and NMR shielding tensors in a set of tetrahedral chiral molecules. This work emphasizes the significant contribution of the ligands and the electronic structure of the chiral center in enhancing these effects, paving the way for the targeted design of promising molecules for measurements.

Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H3PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

Reference interaction site model self-consistent field with constrained spatial electron density approach for nuclear magnetic shielding in solution.

We propose a new hybrid approach combining quantum chemistry and statistical mechanics of liquids for calculating the nuclear magnetic resonance (NMR) chemical shifts of solvated molecules. Based on the reference interaction site model self-consistent field with constrained spatial electron density distribution (RISM-SCF-cSED) method, the electronic structure of molecules in solution is obtained, and the expression for the nuclear magnetic shielding tensor is derived as the second-order derivative of the Helmholtz energy of the solution system. We implemented a method for calculating chemical shifts and applied it to an adenine molecule in water, where hydrogen bonding plays a crucial role in electronic and solvation structures. We also performed the calculations of 17O chemical shifts, which showed remarkable solvent dependence. While converged results could not be sometimes obtained using the conventional method, in the present framework with RISM-SCF-cSED, an adequate representation of electron density is guaranteed, making it possible to obtain an NMR shielding constant stably. This introduction of cSED is key to extending the method's applicability to obtain the chemical shift of various chemical species. The present demonstration illustrates our approach's superiority in terms of numerical robustness and accuracy.