Theory and computation of nuclear shielding Free

Both theoretical and combined theoretical and experimental NMR works reported in 2021, totaling 130 papers, are reviewed in this chapter. Many of them deal with proton/carbon NMR spectroscopy while phosphorus, nitrogen, silicon, and several others, more exotic nuclei including metals, are also investigated in qualitative and quantitative studies. As a continuation of previous efforts to gather and critically discuss NMR techniques and studies, several new review articles have been published in 2021. Besides, numerous efforts on novel methodology dealing with nuclear shielding calculation and its analysis have been reported.

In many cases theoretical predictions of nuclear shieldings have been compared with experimental data and the inclusion of solvent via PCM approach, as well as ZPVC and TC corrections improved their predictive power. The use of discrete solvent molecules in the first solvation sphere, additionally combined with PCM approach, was still uncommon.

The chapter is arbitrary divided into 6 sections, which describe closely related reports on basic and applied studies dealing with theoretical calculation of nuclear shielding. Since the majority of the work is devoted to the theoretical support of experimental data, the current chapter should be a convenient source of information for experimental chemists who use molecular modeling as support for NMR spectral assignment and prediction of properties of new compounds. The use of DFT has been now well-established in computational prediction of nuclear magnetic shieldings. In particular, many reports deal with DFT supported analysis of experimental NMR spectra or prediction of nuclear shieldings in newly designed chemical compounds. Such works are mainly published in Journal of Molecular Structure and Spectrochimica Acta. Part A. On the contrary, theoretical extensions and new methodologies are often reported in the Journal of Chemical Physics, the Journal of Physical Chemistry or the Journal of Chemical Theory and Computation.

The hybrid density functional B3LYP has typically been used for both geometry optimization and prediction of nuclear shieldings within the gauge-including atomic orbital (GIAO^1,2 ) approach. The use of other functionals and the analysis of their performance will be subsequently described in the chapter. However, we will not discuss modeling of the second most important NMR parameter – indirect spin-spin coupling constant (SSCC). For the reader's convenience, the recent reviews on this important topic – complementary to nuclear shielding parameters, are available in separate chapters published by Jaźwiński.^3,4 

In a previous Specialist Periodical Reports on Nuclear Magnetic Resonance several review papers on calculation of nuclear shielding of numerous magnetically active nuclei were discussed.⁵ 

As a continuation of his previous publishing activity, Krivdin reported on the performance of theoretical protocols leading to accurate prediction of ⁷⁷Se NMR shieldings in solution.⁶  Obviously, selenium is a fairly heavy nuclei and treatment of relativistic effect is important for reliable calculation of its nuclear magnetic shielding and chemical shift. In the subsequent review,⁷  Krivdin demonstrates that inclusion of relativistic correction is far more important for heavier metal nuclei, including ¹⁰⁹Ag, ¹¹³Cd, ¹¹⁹Sn, ¹²⁵Te, ¹⁹⁵Pt, ¹⁹⁹Hg, ²⁰⁵Tl, and ²⁰⁷Pb in their complexes.

Due to the importance of carbohydrates, many experimental and theoretical reports on sugars relay on NMR techniques. Thus, computational modeling of NMR parameters of carbohydrates, covering theoretical background, applications and future perspective, was recently published in Molecules.⁸ 

Recently, Hansen reported on NMR of natural products as potential drugs.⁹  Special attention was given to different forms of medium size organic compounds and their structural changes due to formation of intramolecular hydrogen bonding, tautomerism and ionic structures. DFT calculated proton and carbon nuclear shielding and chemical shift were used as an additional but indispensable tool to support experimental results.

Mazurek, Szeleszczuk and Pisklak¹⁰  reported on ab initio molecular dynamics (aiMD) and quantum chemical NMR parameters calculations for closer reproduction of experimental results. It is worth mentioning that aiMD has been available as a result of tremendous progress in computer hardware. Obviously, aiMD is far more accurate than any force field (FF) based dynamics and leads to more reliable NMR parameters. The modeled NMR parameters are also easily controlled by temperature or pressure changes.

Theoretical calculation of nuclear shielding is closely related to the correct determination of chemical structure and reactivity. Thus, any progress in accuracy and speed of GIAO NMR calculation is reflected in faster and better support of experimental spectra analysis. Obviously, a parallel progress in computer hardware is also essential for running larger jobs. In case of DFT, improvements in the density functional “recipe” and subsequent benchmark studies, often with respect to high-level coupled cluster combined with large and dedicated basis sets or experiment, are often reported in a form of benchmark calculations. Schattenberg and Kaupp evaluated modern density functionals by benchmarking nuclear shielding constants of main-group nuclei.¹¹  Numerous density functionals were benchmarked for ³¹P and ¹⁹F nuclear shielding prediction with additional improvement caused by linear regression. They observed that B3LYP/6-311 + G(2d,p) geometry with subsequent GIAO NMR calculation at mPW1PW91/6-311 + G(2d,p) level of theory works best for ³¹P chemical shifts predictions. For ¹⁹F nuclei, GIAO PBE0/6-311 + G(2d,p) calculations on B3LYP/6-311 + G(2d,p) geometry produced the best results.^12  195Pt NMR is often used in studies on platinum anticancer drugs and for studying catalytic centers. In order to reliably predict nuclear shielding of such heavy nuclei, the relativistic correction should be performed with a special method, such as two-component ZORA, or dedicated basis sets. Silva et al.¹³  proposed NMR-DKH basis sets for more accurate calculation of ¹⁹⁵Pt NMR in a set of selected platinum complexes. Kleinpeter and Koch¹⁴  investigated the σ-acceptor and π-donor stabilization in O, S and halogen analogues of N-heterocyclic carbenes (NHCs) using spectroscopic and magnetic criteria (NICS). GIAO MP2 calculations of nuclear shielding with Cholesky-decomposed (CD) two-electron integrals were suggested.¹⁵  The proposed implementation enabled nuclear shielding calculation for about 100 atoms containing over 1000 basis functions. Another efficient low-scaling MP2 computation of NMR shieldings with Cholesky-decomposed densities and an attenuated Coulomb metric was proposed by Ochsenfeld et al.¹⁶  Shenderovich and Denisov provided a theoretic study of the impact of an external electric field on the geometry and NMR properties of hydrogen bond.¹⁷  They also studied NMR properties of CN- as two-faced hydrogen bonding acceptor.¹⁸  Sarotti et al.¹⁹  reported on further development of DP4 + method in order to design an universal and customized method used in combination with GIAO NMR results. Nazarski²⁰  reported on the identification of diastereomeric structures from NMR spectra using statistical and/or artificial neural network (ANN) methods. An improved statistical approach for conformational analysis from carbon-13 chemical shifts was proposed by Cotos-Yáñez et al.²¹  Colherinhas^22,23  updated atomic charge parameters of aliphatic as well as hydroxylic, sulfur-containing and amidic²⁴  amino acids in order to improve the performance of molecular modeling via MD + DFT-GIAO-NMR calculations. Abraham et al.²⁵  used MM/QM calculations of ¹³C chemical shifts in the conformational analysis of some monosaccharides and sucrose. Semenov and Krivdin²⁶  benchmarked DFT calculations of ¹³C NMR chemical shifts of some natural antimalarial compounds with a new basis set, named 3z-S, and also proposed lower cost NMR computations of large strychnobaillonine molecule.²⁷  Sauer et al.²⁸  reported on TPSSh as the best density functional combined with 6-311 + +G(2d,p) basis set for predicting ¹H and ¹³C chemical shifts of protonated alkylpyrroles. The impact of relativistic effect on ¹³C NMR shielding in carbide-bridged complexes was studied theoretically.²⁹  Steinmann and Sauer³⁰  designed the aug-cc-pVTZ-J basis set for the p-block fourth-row elements, i.e. Ga, Ge, As, Se, and Br. Olejniczak, Antušek and Jaszuński³¹  performed relativistic frozen density embedding calculations of solvent effects on the NMR shielding constants of transition metal nuclei. Stoychev et al.³²  reported on domain-based local pair natural orbital DLPNO-MP2 second derivatives for the efficient computation of polarizabilities and NMR shieldings of large molecules. Adamowicz et al.³³  introduced a quantum-mechanical non-Born–Oppenheimer model of a molecule in a strong magnetic field. Schattenberg and Kaupp³⁴  implemented and validated local hybrid functionals with calibrated exchange-energy densities for NMR calculations. They also tested the impact of current tau-dependent exchange-correlation functionals on calculated NMR shieldings.³⁵  QED effect on the nuclear magnetic shielding of ³He was reported.³⁶  Efficient implementation of paramagnetic NMR shielding tensors and ring currents calculation was reported and tested on selected heavy element compounds.³⁷  Microsolvation of Sr²⁺ and Ba²⁺ cations was modeled and nuclear magnetic shieldings, corrected for relativistic effects, were also predicted.³⁸  Within a machine learning (ML) strategy, Ramakrishnan et al.³⁹  gathered predicted ¹³C nuclear shieldings in a form of benchmarks for atoms-in-molecules core with new data for 134 000 molecules. Bond covalency in s- and f-block metal(ii)-silanide was tested using experimental ²⁹Si NMR spectroscopy supported by GIAO calculations of nuclear shieldings.⁴⁰  Electronic structure of a ruthenium phosphinidene complex was studied via an analysis of ³¹P NMR chemical shift tensors.⁴¹  Absolute NMR shielding scales in methyl halides were derived from experimental and calculated nuclear spin-rotation constants.⁴²  Latypov et al.⁴³  reported on accurate prediction of ¹³C nuclear shieldings for atoms directly coordinated to diamagnetic nickel ion. Rusakova and Rusakov⁴⁴  analyzed ⁷⁷Se and ¹²⁵Te NMR structure parameters as well as their structural applications by quantum mechanical calculations. As revealed by DFT calculations in another study, visualization of NMR shielding effect in fullerene-ZnPc aggregates provides characteristic patterns of ZnP-based hosts and its encapsulation nature.⁴⁵ 

DFT studies of nuclear shielding constitute the most abundant set of published works. Most of them are very similar and only the object of the studies (molecules, interacting molecules or the impact of varied environment) are different from one another. Some DFT works will be discussed together with theory developments or in separate reviews. Several authors reported on synthesis, structure and spectroscopic properties of molecular systems. Analysis of their structure was supported by molecular modeling and GIAO calculations of nuclear shielding. Finally, the predicted theoretical shieldings were converted to chemical shift and compared with experimental data. Sometimes molecular docking to potential host molecule was also checked. Javed et al.,⁴⁶  reported on such complex studies for diethyl-5-amino-3-methylthiophene-2,4-dicarboxylate. These authors⁴⁷  also studied the anti-microbial drug sulfathiazole and the experimental NMR data were supported by GIAO calculations. Similar reports on novel 4-[3-(3-methoxy-phenyl)-3-oxo-propenyl]-benzonitrile compound,⁴⁸  1-(2-hydroxy-4-propoxy-3-propylphenyl) ethanones bearing thiotetrazole,⁴⁹  1-(3-methoxy-phenyl)-3-naphthalen-1-ylpropenone,⁵⁰  10-methoxy-10H-furo[3,2-g]chromeno[2,3-b][1,3]thiazolo[5,4-e]pyridine-2,10(3H)-dione⁵¹  and (E)-1-(2,5-dichlorothiophen-3-yl)-3-(thiophen-2-yl)-2-propen-1-one⁵²  were also published. Sezgin et al.⁵³  reported on the synthesis, experimental and theoretical characterization of a novel azo molecule, 2,2-dimethyl-5-(m-tolyldiazenyl)-1,3-dioxane-4,6-dione, and tested its antibacterial properties. Dede et al.⁵⁴  published a similar report on novel naphthoquinone based diimine molecule. Halogen [Cl, Br] substituted N-phenylbenzo[g]indazole derivatives as antimicrobial agents were synthesized and characterized experimentally⁵⁵  and the GIAO predicted ¹H and ¹³C NMR parameters supported the assignment of their experimental spectra. A novel compound, 4,5-dihydro-9-methoxy-4-(5-methylisoxazol-3-yl)benzo[f][1,4] oxazepin-3(2H)-one, with potential antimicrobial activity, was synthesized and its structural and spectroscopic properties, including DFT calculations of GIAO parameters, were tested.⁵⁶  Complexation of Schiff base derived curcumin and l-tyrosine with Al(iii), Ag(i), and Pb(ii) diamagnetic metal ions was studied experimentally and GIAO calculations supported the analysis of the observed NMR spectra.⁵⁷  Synthesis and experimental characteristics, supported by GIAO NMR calculations, on several novel pyrrole-3-ones⁵⁸  and 2-(piperidin-1-ylmethyl)-isoindoline-1,3-dione⁵⁹  were reported. An interesting study on mechanochemical synthesis of the catechol-theophylline cocrystal was reported.⁶⁰  The authors determined its molecular structure and studied the spectroscopic properties with the support of molecular modeling including GIAO calculations. Experimental investigation on ring stability and ring-opening polymerization behavior of cyclic thionylphosphazenes in the presence of Lewis acid catalysts was supported by DFT calculations and NMR parameters were derived from the corresponding GIAO calculations.⁶¹  4-Phenylamino-3-penten-2-one and several derivatives⁶²  were synthesized and characterized experimentally. Subsequent DFT calculations enabled prediction of nuclear shieldings using the GIAO approach. Sadlej and Jaźwiński⁶³  investigated complexation of 1-methylpiperidine, 1,2-dimethylpyrrolidin, and 1,2-dimethylpiperidine with rhodium(ii) tetracarboxylates and examined conformations of free and complexed ligands using GIAO NMR calculations. Elguero et al.⁶⁴  investigated the reaction of hydrazines with α,β-unsaturated carbonyl compounds and used GIAO NMR calculations to support their experimental data. Hiremath studied spectroscopic properties and reactivity of (5-chloro-benzofuran-3-yl)-acetic acid hydrazide with experiment and DFT calculations with multinuclear shieldings predicted by GIAO.⁶⁵  Kleinpeter and Koch used a magnetic criterion in studies of intramolecular carbene stabilization.⁶⁶  Kanimozhi and Arjunan studied the structure and vibrations of 4-nitroindole and 7-nitroindole by spectroscopic and DFT methods.⁶⁷  Recently, spectroscopic, quantum chemical calculations – including GIAO prediction of nuclear shieldings, and molecular docking studies on 1-amino-5-chloroanthraquinone (a potential drug therapy for thyroid cancer), have been reported.⁶⁸  As revealed by Gerothanassis,⁶⁹  revision of structure of geometric isomers of conjugated linolenic acids, hexadecatrienyl pheromones, and model triene-containing compounds was achieved as a result of close symbiosis between experimental and theoretical NMR approaches. Claramunt et al.⁷⁰  reported on multinuclear NMR and DFT calculations supporting the conformational analysis of 2,5-diaryl-4-methyl-2,4-dihydro-3H-1,2,4-triazol-3-ones. The loliolide molecule and its isomers were studied theoretically and their nuclear shieldings were predicted.⁷¹  Czernek and Brus⁷²  analyzed the variation of ¹H NMR parameters for host-guest complexes.

Alkorta and Elguero⁷³  reported on theoretical study of inversion barriers and NMR chemical shifts of 3-pyrazolines (2,3-dihydro-1H-pyrazoles). Schindler⁷⁴  predicted GIAO-MP2 spectra of E- and Z-clothianidin which were experimentally confirmed by low temperature NMR studies. This led to the identification for the first time of the unknown Z-isomer of clothianidin. Colherinhas et al.⁷⁵  performed MD, GIAO-NMR and TDDFT studies on hydrated isoleucine zwitterion. ¹H NMR spectra, structure, and conformational exchange of S-n-alkyl-tetrahydrothiophenium cations of some ionic liquids, supported by nuclear shielding calculations, were reported.⁷⁶  Okovytyy et al.⁷⁷  reported on the tautomerism and spectral parameters of azo dyes based on a number of isomeric N-tolylnaphthylamines. They also calculated nuclear shieldings and in some cases used the recently developed STO^##-3G_el basis set.^78,79 

Miyamoto and Hada⁸⁰  analyzed ¹³C NMR chemical shifts in substituted benzenes using natural perturbation orbitals and substitution effects. Hansen et al.⁸¹  reported on the synthesis and NMR conformational characterization of azo-hydrazone molecular switches supported by GIAO NMR calculations. Erdoğan and Serdaroğlu⁸²  synthesized and characterized a novel pyrene-sulfathiazole-based potential drug candidate, (E)-4-((pyren-1-ylmethylene)amino)-N-(thiazol-2-yl)benzenesulfonamide. They employed both spectroscopic and molecular modeling methods with inclusion of GIAO NMR parameters prediction to perform its characterization.

Structure, spectroscopic properties and reactivity of natural products are of great importance in pharmacy and drug development. Thus, experimental NMR studies on natural products are essential and in many cases theoretical modeling efficiently supports assignment of spectral peaks originating from natural sources.

Degradation products of steviol glycosides were characterized by experimental NMR supported by GIAO calculations.⁸³  Five new dimeric phloroglucinol derivatives were isolated from Agrimonia pilosa and their structures established using various spectroscopic techniques.⁸⁴  Analysis of their experimental NMR spectra was supported by GIAO NMR calculations. Polyprenylated acylphloroglucinols were isolated from the fruits of Garcinia multiflora and their structure, together with absolute configuration determined by NMR, were supported using molecular modeling and GIAO calculations combined with the DP4 + methodology.⁸⁵  New debromoaplysiatoxin analogues⁸⁶  were isolated from marine Cyanobacterium Lyngbya sp. and their absolute configuration confirmed by X-ray studies and GIAO NMR calculations. Complex structures of Forrestiacids A and B were determined using experimental and computational NMR methodology, additionally supported by the DP4 + approach.⁸⁷  Theoretical modeling of structure, spectroscopic, electronic properties, as well as molecular docking of methyl 4-methoxybenzoate from star anise using DFT calculations and GIAO NMR parameters were reported.⁸⁸  Experimental spectroscopic and GIAO NMR calculations enabled structure revision of previously proposed analogues of penitol A and penicitols E-I.⁸⁹  GIAO NMR shift calculations were also used for assigning relative configurations of antibacterial bislactones⁹⁰  and structure of garcipaucinones A and B, derived from Garcinia paucinervis.⁹¹  New alkaloids, spirocollequins A and B were isolated from Colletotrichum boninense and their structures were proposed from the experimental multidimensional NMR studies supported by GIAO calculations and advanced statistical treatment.⁹²  Potential neuroinflammatory inhibitors were isolated from Stephania epigaea H.S. Lo and their structure proposed on the basis of experimental NMR studies and subsequent GIAO NMR calculations.⁹³  Metabolites from Solanum nigrum with neuroprotective properties,⁹⁴  as well as alkaloids from the stems of Picrasma quassioides⁹⁵  were studied experimentally and their structure determined using both experimental and theoretical NMR approaches. Experimental studies on cytotoxic triterpenoid glycosides, isolated from Cyclocarya paliurus, were reported and GIAO NMR calculations were used for their structure determination.⁹⁶  Experimental studies supported by GIAO calculations were conducted on several new compounds, leading in each case to their respective structure proposals: (a) a new phenolic compound, isolated from Eupenicillium sp. HJ002 fungus,⁹⁷  (b) the production of a new polyketide in Penicillium sp. HS-11,⁹⁸  and (c) structures of two new phenylpropanoids and a new dihydrostilbenoid isolated from Magnolia biondii.⁹⁹  Semenov and Krivdin proposed a simple approach for the stereochemical identification of natural products, as well as diverse organic compounds with multiple asymmetric centers using experimental NMR data supported by ¹H and ¹³C NMR calculations combined with DP4 + statistical approach.¹⁰⁰  Semenov and Krivdin¹⁰¹  also demonstrated a feasibility of structure determination using experimental NMR and theoretical prediction of nuclear shieldings in case of a fairly large molecule (trimeric monoterpenoid indole alkaloid strychnohexamine, C₅₉H₆₀N₆O). Structure and NMR properties of spirostanol sapogenins and saponins from Convallaria majalis l. were studied experimentally and theoretically.¹⁰² 

Modeling nuclear shielding tensor in solids is very useful in studies of novel materials and in pharmacy. Obviously, intermolecular interactions are not considered in case of single molecule in the gas phase, serving as a very approximate model of solids (without inclusion of periodicity in crystals). Thus, gauge-including projector-augmented-wave (GIPAW^103,104 ) calculations are necessary to reliably model nuclear shielding tensor in crystals. Unlike for gas phase and liquids, this allows reproduction of nuclear magnetic shielding tensor, including its anisotropic parameter and individual components.

Experimental solid state NMR studies have been reported more and more often in the last years. Most of such works have used ¹³C NMR magic angle spinning (MAS) technique. Potrzebowski et al.¹⁰⁵  reported on close symbiosis between experimental solid-state NMR spectroscopy and single-crystal X-ray diffraction and molecular modeling of crystal structure and its spectroscopic properties in case of teriflunomide. As expected, both experimental techniques are efficiently supported by theoretical modeling of the nuclear magnetic shielding tensor. This was nicely demonstrated¹⁰⁶  on studies of the AND-1184 crystal and its hydrochloride form. Combined solid-state NMR and ab initio modeling¹⁰⁷  were also used to get an insight into benzoic and p-fluorobenzene acids embedded in pores of MCM-41. Vijs et al.¹⁰⁸  reported on favorable benchmarking GIPAW method with respect to molecular nuclear magnetic shielding estimated in the complete basis set limit (CBS). Only in case of proton shielding, a small correction of two-center contributions to the induced current was necessary. Eleven 2,5-diaryl-2,4-dihydro-3H-1,2,4-triazol-3-ones in DMSO were characterized by ¹H, ¹³C, ¹⁵N, and ¹⁹F NMR measurements.¹⁰⁹  Solid ¹³C, ¹⁵N, and ¹⁹F MAS NMR spectra were also recorded. Besides, X-ray structures of selected compounds were determined and the results of GIAO and GIPAW NMR calculations well reproduced experimental data.¹⁰⁹  Marek et al.¹¹⁰  studied crystal and substituent effects on paramagnetic NMR shifts in transition-metal complexes. The NMR parameters were calculated both in vacuo and in model clusters composed of paramagnetic metal ions with acetylacetonate (acac) ligands and compared with experimental data.

Both X-ray and solid state NMR are often used as complementary techniques for structure elucidation and this was nicely demonstrated in case of 1,4-disubstituted 2,5-diketopiperazines.¹¹¹  The term “NMR crystallography” is getting popular and recently, a toolbox for improving the workflow in such studies has been made available.¹¹²  NMR crystallography was also used in structural refinement of carbimazole.¹¹³  Besides, polymorph identification in solid state NMR has been supported by calculation of nuclear shielding tensor.¹¹⁴ 

Solid state NMR studies represent a very efficient tool, providing insight into structures, mechanisms and dynamics of crystalline catalysts. For this purpose, as a support of the experimental work, ⁵¹V nuclear shielding was theoretically predicted in molecular crystals.¹¹⁵  Another study on catalysts involved combined experimental NMR and theoretical modeling of vanadia-alumina catalysts.¹¹⁶  DFT calculations as support of NMR experimental data were also used for structural characterization of phosphate species adsorbed on γ-alumina.¹¹⁷  Among rarely used NMR nuclei is ⁴³Ca. On the other hand, calcium ion is widely distributed in construction materials, as well as in biomaterials. A detailed study on octacalcium phosphate and its hybrid derivatives, investigated using calcium-43 NMR, additionally supported by theoretical calculations, have recently appeared.¹¹⁸  Theoretical calculations on ¹¹B NMR parameters in boron crystalline materials were also reported.¹¹⁹  Dynamic of solid drug ibuprofen and terephthalic acid using ¹⁷O and ²H NMR was studied experimentally and supported by DFT calculations of nuclear shieldings.¹²⁰ 

Graphene has been a hot topic in both basic and applied science. Fluorinated graphene (and graphite) is a good material for NMR studies of its local structure using ¹⁹F NMR, a very sensitive, spin-half NMR nucleus. Polymorphs and local defects of selected model materials have been studied theoretically within GIAO and GIPAW theories.¹²¹  Besides, novel organic-inorganic hybrid perovskite-type hexabromotellurate material has been investigated experimentally and using advanced DFT modeling.¹²² 

In the following, some other examples of nuclear shielding calculation are presented and analyzed. Boron-nitride (BN) nanotubes are popular among the studied nanomaterials and their decoration with metal atoms could significantly modify their properties. Finite models of BN nanotubes were selected for GIAO NMR studies in order to predict their spectral properties.¹²³  Modification of electric field gradient calculation in molecular solids were recently reported.¹²⁴  Alkorta et al.¹²⁵  studied five silver(i) trinuclear pyrazolate complexes. Nuclear shielding of ¹⁰⁹Ag nuclei was accurately predicted using ZORA for inclusion of two-component relativistic correction and the lack of aromaticity of the (PyrAg)3 complex was confirmed by GIAO NMR calculations of NICS magnetic indexes of aromaticity. Aromaticity of uracil and its 5-chalogen derivatives were tested using GIAO NMR calculations of NICS magnetic indexes.¹²⁶  Kleinpeter and Koch employed NICS calculation for testing the nature of carbon-boron bond in boron trapped N-heterocyclic carbenes.¹²⁷  In addition, Kleinpeter et al.¹²⁸  reported on a ²⁹Si and ¹³C NMR conformational equilibrium study of 1-phenyl-1-tert-butylsilacyclohexane. Jakubowska and Pecul¹²⁹  characterized nuclear magnetic shieldings of Zn₂, Cd₂ and Hg₂ dimers with relativistic four-component Dirac–Coulomb hamiltonian. GIAO NMR calculations were used in studies of bonding and aromaticity in electron-rich boron and aluminum clusters.¹³⁰  Host − guest binding of β-cyclodextrin complexes was revealed by experimental NMR spectroscopy and supported by GIAO NMR calculations using the DFT approach.¹³¹ 

CASE

Computer-assisted structure elucidation algorithms

CBS

Complete basis set limit

CCSD

Coupled cluster approach with singles and doubles

CCSD(T)

Coupled cluster approach with singles and doubles and perturbatively included triples

CFOUR

Coupled cluster technique for computational chemistry computer program

CP MAS

Cross polarization magic angle spinning

DFT

Density functional theory

DIRAC

Direct iterative relativistic all-electron calculations computer program

EFG

Electric field gradient

Gaussian

Computer program for atoms and molecules

GIAO

Gauge-including atomic orbital method

GIPAW

Gauge-including projector augmented waves for periodic calculations

HALA

Heavy atom on light atom relativistic effect

HF SCF

Hartree–Fock self-consistent field

LDBS

Locally dense basis set approach

LRESC

Linear response within the elimination of the small component model

ML

Machine learning

MP2

Second order Møller–Plesset perturbation theory

NICS

Nucleous independent chemical shift

NMR

Nuclear magnetic resonance

NN

Neural network approach

NR

Non-relativistic

PCM

Polarizable continuum solvent model

PD4 +

Statistical method for analyzing results of GIAO calculations

RESPECT

Relativistic spectroscopy computer program

RHF

Restricted Hartree–Fock

RMS

Root mean square deviation

QED

Quantum electrodynamic

SSCC

Indirect spin–spin coupling constant

TC

Temperature correction

TMS

Tetramethylsilane

ZORA

Zeroth order regular approximation

ZPVC

Zero-point vibrational correction

This work was partly supported by the University of Opole, Faculty of Chemistry.