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

Application of Density Functional Theory to Molecular Engineering of Pharmaceutical Formulations

This review systematically examines the pivotal applications of the Density Functional Theory (DFT) in drug formulation design, emphasizing its capability to elucidate molecular interaction mechanisms through quantum mechanical calculations. By solving the Kohn-Sham equations with precision up to 0.1 kcal/mol, DFT enables accurate electronic structure reconstruction, providing theoretical guidance for optimizing drug-excipient composite systems. In solid dosage forms, DFT clarifies the electronic driving forces governing active pharmaceutical ingredient (API)-excipient co-crystallization, predicting reactive sites and guiding stability-oriented co-crystal design. For nanodelivery systems, DFT optimizes carrier surface charge distribution through van der Waals interactions and π-π stacking energy calculations, thereby enhancing targeting efficiency. Furthermore, DFT combined with solvation models (e.g., COSMO) quantitatively evaluates polar environmental effects on drug release kinetics, delivering critical thermodynamic parameters (e.g., ΔG) for controlled-release formulation development. Notably, DFT-driven co-crystal thermodynamic analysis and pH-responsive release mechanism modeling substantially reduce experimental validation cycles. While DFT faces challenges in dynamic simulations of complex solvent environments, its integration with molecular mechanics and multiscale frameworks has achieved computational breakthroughs. This work offers interdisciplinary methodology support for accelerating data-driven formulation design.

Inclusion complexes of novel formyl chromone Schiff bases with β-Cyclodextrin: Synthesis, characterization, DNA binding studies and in-vitro release study

The present study involved the synthesis of five novel Schiff bases (SB1-SB5) of formyl chromone and their inclusion complexes with β-cyclodextrin through kneading approach to enhance the solubility and stability of SBs. Characterization was conducted using FTIR, NMR, SEM, TEM, p-XRD, and Mass Spectrometry. UV fluorescence and pH stability studies confirmed the formation of the inclusion complex. Structural validation of complexes was conducted via molecular docking (PDB ID: 1BFN) and 50 ns MD simulation study. DFT studies were performed on SBs using B3LYP/6-31 + G(d,p) basis set. All SBs exhibited favorable ADME properties and high binding interactions were observed in molecular docking with ctDNA (PDB Id: 1BNA). Further, in-vitro UV absorption and fluorescence experiments demonstrated strong ctDNA interactions for all Schiff bases, with binding constants in the order of 105 M-1, indicating groove binding mode. Among the SBs, SB4 exhibited the highest affinity for DNA grooves, with a binding constant (Kb) of 1.7 × 106 M-1. However, the SB4/β-Cyd inclusion complex also interacted with DNA but with low binding constants compared to SB4. An in-vitro release study of SB4/β-Cyd, revealed 78.92 % dissolution of the inclusion complex, highlighting its potential for enhanced solubility and stability in biological systems.

DFT Approach for Predicting 13C NMR Shifts of Atoms Directly Coordinated to Pt: Scopes and Limitations

In this study, comparative analysis of calculated and experimental 13C NMR shifts for a wide range of model platinum complexes showed that, on the whole, the theory reproduces the experimental data well. The chemical shifts of carbon atoms directly bonded to Pt can be calculated well only within the framework of the fully relativistic matrix Dirac-Kohn-Sham (mDKS) level (R2 = 0.9973, RMSE = 3.7 ppm); however, for carbon atoms not bonded to metal, a more simple, non-relativistic approach can be used. Effective locally dense basis set schemes were developed for practical applications. The efficiency of the protocol is demonstrated using the example of the isomeric structure determination in case of several possible coordination modes.

Through-space H-F coupling in a series of 4-substituted-1H-1,2,3-triazoles

In the 1H-NMR spectra of a series of N-1 substituted 4-substituted-1H-1,2,3-triazoles that have been prepared, the lone heterocyclic ring hydrogen (H-5) appears as a singlet in all cases except those compounds that contain a 2-fluorophenyl moiety at Position 4. In those cases, H-5 is a doublet with J ~3.7 Hz. Based on computational chemistry results and geometric considerations, we attribute this splitting to through-space H-F coupling.

Bent naphthodithiophenes: synthesis and characterization of isomeric fluorophores

Thiophene-containing heteroarenes are one of the most well-known classes of π-conjugated building blocks for photoactive molecules. Isomeric naphthodithiophenes (NDTs) are at the forefront of this research area due to their straightforward synthesis and derivatization. Notably, NDT geometries that are bent - such as naphtho[2,1-b:3,4-b']dithiophene (α-NDT) and naphtho[1,2-b:4,3-b']dithiophene (β-NDT) - are seldom employed as photoactive small molecules. This report investigates how remote substituents impact the photophysical properties of isomeric α- and β-NDTs. The orientation of the thiophene units plays a critical role in the emission: in the α(OHex)R2 series conjugation from the end-caps to the NDT core is apparent, while in the β(Oi-Pent)R2 series minimal change is observed unless strong electron acceptors, such as β(Oi-Pent)(PhCF3)2, are employed. This push-pull acceptor-donor-acceptor (A-D-A) fluorophore exhibits positive fluorosolvatochromism that correlates with increasing solvent polarity parameter, E T(30). In total, these results highlight how remote substituents are able to modulate the emission of isomeric bent NDTs.

Accurate Structural Elucidation of Samoquasine A and an Unknown Homologue Using a Computation-Based Machine Learning Protocol

The structure of samoquasine A has long been a subject of controversy, which was resolved only upon its successful total synthesis. We examined the structures of the associated compounds using the state-of-the-art SVM-M protocol. The method accurately discriminated all putative structures historically attributed to samoquasine A from a pool of 48 isomeric structures, confirming that samoquasine A is indeed identical to perlolidine. Furthermore, by applying the SVM-M protocol to an additional pool of 67 isomeric structures, we successfully assigned a yet unknown natural product, initially misidentified as perlolidine, as a novel oxime, (E)-3H-cyclopenta[c]quinolin-3-one oxime, representing the first reported cyclone oxime-quinoline natural product.

Study of heavy atom influence on poly-halogenated compounds using DP4/MM-DP4+/DP4+: insights and trends

Nuclear magnetic resonance (NMR) spectroscopy complemented by density functional theory (DFT) calculations is a crucial tool for structural elucidation. Nevertheless, the precision of NMR predictions is influenced by the 'heavy atom effect', wherein heavy atoms affect the shielding values of neighboring light atoms (HALA effect). Standard practice in the field involves removing the conflicting signals. However, in the case of polyhalogenated molecules, this is challenging due to the significant amount of information that ends up being lost. In this study the HALA is thoroughly investigated in the context of three leading probability methods: DP4, MM-DP4+, and DP4+. The results show that DP4+ is more sensitive to C-Cl or C-Br signals, which is a consequence of the longer bond lengths computed with DFT. Removing conflicting signals is highly effective in DP4+, but has an uncertain outcome in methods based on molecular mechanics geometries, such as DP4 and MM-DP4+. A detailed investigation of the effect of bond distance on the corresponding chemical shifts has also been conducted.

DFT approach towards accurate prediction of 1H/13C NMR chemical shifts for dipterocarpol oxime

A computational NMR approach for accurate predicting the 1H/13C chemical shifts of triterpenoid oximes featuring the screening of 144 DFT methods was demonstrated. Efficiently synthesized dipterocarpol oxime was employed as a model compound. The six highest accurate methods from the screening generated root-mean-square-error (RMSE) values in the range of 0.84 ppm (0.55%) to 1.14 ppm (0.75%) for calculated 13C shifts. For 1H results, simple, economical 6-31G basis set unexpectedly outperformed other more expensive basic sets; and the couple of it with selected functionals provided high accuracy shifts (0.0617 ppm (1.49%) ≤ RMSE ≤ 0.0870 ppm (2.04%)). These computational results strongly supported the proton and carbon assignments of the oxime including the difficult ones of diastereotopic methyl groups, the methyl groups attached to an internal olefin, and diastereotopic α-protons.

Preparative three-dimensional GC and nuclear magnetic resonance for the isolation and identification of two sesquiterpene ethers from Dictyota Dichotoma

Separation science plays a crucial role in the isolation of novel compounds contained in complex matrices. Yet their rationale employment needs preliminary structure elucidation, which usually requires sufficient aliquots of grade substances to characterize the molecule by nuclear magnetic resonance experiments. In this study, two peculiar oxa-tricycloundecane ethers were isolated by means of preparative multidimensional gas chromatography from the brown alga species Dictyota dichotoma (Huds.) Lam., aiming to assign their 3D structures. Density functional theory simulations were carried out to select the correct configurational species matching the experimental NMR data (in terms of enantiomeric couples). In this case, the theoretical approach was crucial as the protonic signal overlap and spectral overcrowding were preventing any other unambiguous structural information. Just after the identification through the density functional theory data matching of the correct relative configuration it was possible to verify an enhanced self-consistency with the experimental data, confirming the stereochemistry. The results obtained further pave the way toward structure elucidation of highly asymmetric molecules, whose configuration cannot be inferred by other means or strategies.

Synthesis, Characterization, and DFT Calculations of a New Sulfamethoxazole Schiff Base and Its Metal Complexes

A new Schiff base, 4-((1E,2E)-3-(furan-2-yl)allylidene)amino)-N-(5-methylisoxazol-3-yl) benzene-sulfonamide (L), was synthesized by thermal condensation of 3-(2-furyl)acrolein and sulfamethoxazole (SMX), and the furan Schiff base (L) was converted to a phenol Schiff base (L') according to the Diels-Alder [4 + 2] cycloaddition reaction and studied experimentally. The structural and spectroscopic properties of the Schiff base were also corroborated by utilizing density functional theory (DFT) calculations. Furthermore, a series of lanthanide and transition metal complexes of the Schiff base were synthesized from the nitrate salts of Gd, Sm, Nd, and Zn (L1, L2, L3, and L4), respectively. Various spectroscopic studies confirmed the chemical structures of the Schiff-base ligand and its complexes. Based on the spectral studies, a nine-coordinated geometry was assigned to the lanthanide complexes and a six-coordinated geometry to the zinc complex. The elemental analysis data confirmed the suggested structure of the metal complexes, and the TGA studies confirmed the presence of one coordinated water molecule in the lanthanide complexes and one crystalline water molecule in the zinc complex; in addition, the conductivity showed the neutral nature of the complexes. Therefore, it is suggested that the ligand acts as a bidentate through coordinates to each metal atom by the isoxazole nitrogen and oxygen atoms of the sulfur dioxide moiety of the SMX based on FTIR studies. The ligand and its complexes were tested for their anti-inflammatory, anti-hemolytic, and antioxidant activities by various colorimetric methods. These complexes were found to exhibit potential effects of the selected biological activities.

Experimental and Computational Investigation of the Oxime Bond Stereochemistry in c-Jun N-terminal Kinase 3 Inhibitors 11H-Indeno[1,2-b]quinoxalin-11-one Oxime and Tryptanthrin-6-oxime

11H-Indeno[1,2-b]quinoxalin-11-one oxime (IQ-1) and tryptanthrin-6-oxime are potent c-Jun N-terminal kinase 3 (JNK-3) inhibitors demonstrating neuroprotective, anti-inflammatory and anti-arthritic activity. However, the stereochemical configuration of the oxime carbon-nitrogen double bond (E- or Z-) in these compounds was so far unknown. In this contribution, we report the results of the determination of the double bond configuration in the solid state by single crystal X-ray diffraction and in solution by 1D and 2D NMR techniques and DFT calculations. It was found that both in the solid state and in solution, IQ-1 adopts the E-configuration stabilized by intermolecular hydrogen bonds, in contrast to previously assumed Z-configuration that could be stabilized only by an intramolecular hydrogen bond.

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

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

Anomalous 1 H NMR chemical shift behavior of substituted benzoic acid esters

Benzoic acid esters represent key building blocks for many drug discovery and development programs and have been advanced as potent PDE4 inhibitors for inhaled administration for treatment of respiratory diseases. This class of compounds has also been employed in myriad industrial processes and as common food preservatives. Recent work directed toward the synthesis of intermediates for a proprietary medicinal chemistry program led us to observe that the ¹ H NMR chemical shifts of substituents ortho to the benzoic acid ester moiety defied conventional iterative chemical shift prediction protocols. To explore these unexpected results, we initiated a detailed computational study employing density functional theory (DFT) calculations to better understand the unexpectedly large variance in expected versus experimental NMR chemical shifts.

DELTA50: A Highly Accurate Database of Experimental 1H and 13C NMR Chemical Shifts Applied to DFT Benchmarking

Density functional theory (DFT) benchmark studies of ¹H and ¹³C NMR chemical shifts often yield differing conclusions, likely due to non-optimal test molecules and non-standardized data acquisition. To address this issue, we carefully selected and measured ¹H and ¹³C NMR chemical shifts for 50 structurally diverse small organic molecules containing atoms from only the first two rows of the periodic table. Our NMR dataset, DELTA50, was used to calculate linear scaling factors and to evaluate the accuracy of 73 density functionals, 40 basis sets, 3 solvent models, and 3 gauge-referencing schemes. The best performing DFT methodologies for ¹H and ¹³C NMR chemical shift predictions were WP04/6-311++G(2d,p) and ωB97X-D/def2-SVP, respectively, when combined with the polarizable continuum solvent model (PCM) and gauge-independent atomic orbital (GIAO) method. Geometries should be optimized at the B3LYP-D3/6-311G(d,p) level including the PCM solvent model for the best accuracy. Predictions of 20 organic compounds and natural products from a separate probe set had root-mean-square deviations (RMSD) of 0.07 to 0.19 for ¹H and 0.5 to 2.9 for ¹³C. Maximum deviations were less than 0.5 and 6.5 ppm for ¹H and ¹³C, respectively.

13C NMR spectroscopic data of aporphine alkaloids

This study involves aporphine alkaloids identified through ¹³C Nuclear Magnetic Resonance (NMR) spectroscopic data. For the present publication, articles were selected from several databases on aporphine alkaloids from 1994 to 2021. In this class, more than 700 compounds have been registered, with 221 were included in this section, among which 122 were characterized for the first time in the investigated period. The study also addresses their biosynthetic pathways, classifying substances according to their structural characteristics based on established literature. Furthermore, pharmacological activities related to the aporphine alkaloids highlighted in this section are also presented, giving an overview of the various applications of these compounds.

Improving the accuracy of 31P NMR chemical shift calculations by use of scaling methods

Calculation of ³¹P NMR chemical shifts for a series of tri- and tetracoordinate phosphorus compounds using several basis sets and density functional theory (DFT) functionals gave a modest fit to experimental chemical shifts, but an excellent linear fit when plotted against the experimental values. The resultant scaling methods were then applied to a variety of "large" compounds previously selected by Latypov et al. and a set of stereoisomeric and unusual compounds selected here. No one method was best for all structural types. For compounds that contain P-P bonds and P-C multiple bonds, the Latypov et al. method using the PBE0 functional was best (mean absolute deviation/root mean square deviation (MAD/RMSD) = 6.9/8.5 ppm and 6.6/8.2 ppm, respectively), but for the full set of compounds gave higher deviations (MAD/RMSD = 8.2/12.3 ppm), and failed by over 60 ppm for a three-membered phosphorus heterocycle. Use of the M06-2X functional for both the structural optimization and NMR chemical shift calculation was best overall for the compounds without P-C multiple bonds (MAD/RMSD = 5.4/7.1 ppm), but failed by 30-49 ppm for compounds having any P-C multiple-bond character. Failures of these magnitudes have not been reported previously for these widely used functionals. These failures were then used to screen a variety of recommended functionals, leading to better overall methods for calculation of these chemical shifts: optimization with the M06-2X functional and NMR calculation with the PBE0 or ωB97x-D functionals gave values for MAD/RMSD = 6.9/8.5 ppm and 6.8/9.1 ppm, respectively, over an experimental chemical shift range of -181 to 356 ppm. Due to the unexplained failures observed, we recommend use of more than one method when looking at novel structures.

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.

Improving IDP theoretical chemical shift accuracy and efficiency through a combined MD/ADMA/DFT and machine learning approach

This work extends the multi-scale computational scheme for the quantum mechanics (QM) calculations of Nuclear Magnetic Resonance (NMR) chemical shifts (CSs) in proteins that lack a well-defined 3D structure. The scheme couples the sampling of an intrinsically disordered protein (IDP) by classical molecular dynamics (MD) with protein fragmentation using the adjustable density matrix assembler (ADMA) and density functional theory (DFT) calculations. In contrast to our early investigation on IDPs (Pavlíková Přecechtělová et al., J. Chem. Theory Comput., 2019, 15, 5642-5658) and the state-of-the art NMR calculations for structured proteins, a partial re-optimization was implemented on the raw MD geometries in vibrational normal mode coordinates to enhance the accuracy of the MD/ADMA/DFT computational scheme. In addition, machine-learning based cluster analysis was performed on the scheme to explore its potential in producing protein structure ensembles (CLUSTER ensembles) that yield accurate CSs at a reduced computational cost. The performance of the cluster-based calculations is validated against results obtained with conventional structural ensembles consisting of MD snapshots extracted from the MD trajectory at regular time intervals (REGULAR ensembles). CS calculations performed with the refined MD/ADMA/DFT framework employed the 6-311++G(d,p) basis set that outperformed IGLO-III calculations with the same density functional approximation (B3LYP) and both explicit and implicit solvation. The partial geometry optimization did not universally improve the agreement of computed CSs with the experiment but substantially decreased errors associated with the ensemble averaging. A CLUSTER ensemble with 50 structures yielded ensemble averages close to those obtained with a REGULAR ensemble consisting of 500 MD frames. The cluster based calculations thus required only a fraction of the computational time.

DFT calculations of 1H- and 13C-NMR chemical shifts of 3-methyl-1-phenyl-4-(phenyldiazenyl)-1H-pyrazol-5-amine in solution

Geometries of the 3-methyl-1-phenyl-4-(phenyldiazenyl)-1H-pyrazol-5-amine azo-dye compound and its tautomer were optimized using B3LYP and M06-2X functionals in coupling with TZVP and 6-311 + G(d,p) basis sets. The ¹H- and ¹³C-NMR chemical shifts of all species were predicted using 13 density functional theory (DFT) approaches in coupling with TZVP and 6-311 + G(d,p) basis sets at the different optimized geometries by applying the using GIAO method using the eight geometries. The selected functionals are characterized by having different amount of Hartree-Fock exchange. The selected DFT methods were B3LYP, M06-2X, BP86, B97XD, TPSSTPSS, PBE1PBE, CAM-B3LYP, wB97XD, LSDA, HSEH1PBE, PW91PW91, LC-WPBE, and B3PW91. The results obtained were compared with the available experimental data using different statistical descriptors such as root mean square error (RMSE) and maximum absolute error (MAE). Results revealed that the prediction of the ¹H-NMR chemical shifts has more significant dependence on the applied geometry than that of the prediction of the ¹³C-NMR chemical shifts. Among all the examined functionals, B97D and TPSSTPSS functionals were found to be the most accurate ones, while the M06-2X functional is the least accurate one. Results also revealed that the prediction of NMR chemical shifts using TZVP basis sets results is more accurate results than 6-311 + G(2d,p) basis set.

Impact of solvent interactions on 1H and 13C chemical shifts investigated using DFT and a reference dataset recorded in CDCl3 and CCl4

1H and 13C chemical shifts of 35 small, rigid molecules were measured under standardized conditions in chloroform-d and in tetrachloromethane. The solvent change mainly affects carbon shifts of polar functional groups. This difference due to specific interactions with CDCl3 cannot be adequately reproduced by DFT calculations in implicit solvent. The new dataset provides an accurate basis for the validation and calibration of shift calculations, especially with respect to improved solvent models.

Solvent Dependent Nuclear Magnetic Resonance Molecular Parameters Based on a Polarization Consistent Screened Range Separated Hybrid Density Functional Theory Framework

Nuclear magnetic resonance (NMR) properties of solvated molecules are significantly affected by the solvent. We, therefore, employ a polarization consistent framework that efficiently addresses the solvent polarizing environment effects. Toward this goal a dielectric screened range separated hybrid (SRSH) functional is invoked with a polarizable continuum model (PCM) to properly represent the orbital gap in the condensed phase. We build on the success of range separated hybrid (RSH) functionals to address the erroneous tendency of traditional density functional theory (DFT) to collapse the orbital gap. Recently, the impact of RSH that properly opens up the orbital gap in gas-phase calculations on NMR properties has been assessed. Here, we report the use of SRSH-PCM that produces properly solute orbital gaps in calculating isotropic nuclear magnetic shielding and chemical shift parameters of molecular systems in the condensed phase. We show that in contrast to simpler DFT-PCM approaches, SRSH-PCM successfully follows expected dielectric constant trends.

Efficiently Computing NMR 1H and 13C Chemical Shifts of Saccharides in Aqueous Environment

Determining the structure of saccharides in their native environment is crucial to understanding their function and more accurately targeting their utilization. Nuclear magnetic resonance observables such as the nuclear Overhauser effect or spin-spin coupling constants are routinely utilized to study saccharides in their native water environment. However, while highly sensitive to the local environment, chemical shifts are mostly overlooked, despite being commonly measured for compounds identification. Although chemical shifts carry considerable structural information, their direct association with structure is notoriously difficult. This is mostly due to the similarity in the chemical nature of most saccharides causing similar physicochemical environments close to sugar C and H atoms, resulting in comparable chemical shifts. The rise of computational power allows one to compute reliable chemical shifts and use them to determine atomistic details of these sugars in solution. However, any prediction is severely limited by the computational protocol used and its accuracy. In this work, we studied a set of 31 saccharides on which we evaluated various computational protocols to calculate the total number of 375 ¹H and 327 ¹³C chemical shifts of sugars in an aqueous environment. Our study proposes two cost-effective protocols for simulating ¹H and ¹³C chemical shifts that we recommend for further use. These protocols can help with the interpretation of experimental spectra, but we also show that they are also capable of structure prediction independently. This is possible because of the low mean absolute deviations of calculated shifts from the experiment (0.06 ppm for ¹H and 1.09 ppm for ¹³C). We explore different solvation methods, basis sets, and optimization schemes to reach such accuracy. A correct sampling of the conformation phase space of flexible sugar molecules is also key to obtaining accurately converged theoretical chemical shifts. The linear regression method was applied to convert the calculated isotropic nuclear magnetic shielding constants to simulated chemical shifts comparable with the experiment. The achieved level of accuracy can help in utilizing chemical shifts for elucidating the 3D atomistic structure of saccharides in aqueous solutions. All linear regression parameters obtained on our extensive set of sugars for all the tested protocols can be reutilized in future works.

Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for ¹³C, ¹⁵N, ¹⁷O, ¹⁹F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for ¹H and ¹³C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental ¹³C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.

Towards Elucidating Structure–Spectra Relationships in Rhamnogalacturonan II: Computational Protocols for Accurate 13C and 1H Shifts for Apiose and Its Borate Esters

Apiose is a naturally occurring, uncommon branched-chain pentose found in plant cell walls as part of the complex polysaccharide Rhamnogalacturonan II (RG-II). The structural elucidation of the three-dimensional structure of RG-II by nuclear magnetic resonance (NMR) spectroscopy is significantly complicated by the ability of apiose to cross-link via borate ester linkages to form RG-II dimers. Here, we developed a computational approach to gain insight into the structure–spectra relationships of apio–borate complexes in an effort to complement experimental assignments of NMR signals in RG-II. Our protocol involved structure optimizations using density functional theory (DFT) followed by isotropic magnetic shielding constant calculations using the gauge-invariant atomic orbital (GIAO) approach to predict chemical shifts. We evaluated the accuracy of 23 different functional–basis set (FBS) combinations with and without implicit solvation for predicting the experimental 1H and 13C shifts of a methyl apioside and its three borate derivatives. The computed NMR predictions were evaluated on the basis of the overall shift accuracy, relative shift ordering, and the ability to distinguish between dimers and monomers. We demonstrate that the consideration of implicit solvation during geometry optimizations in addition to the magnetic shielding constant calculations greatly increases the accuracy of NMR chemical shift predictions and can correctly reproduce the ordering of the 13C shifts and yield predictions that are, on average, within 1.50 ppm for 13C and 0.12 ppm for 1H shifts for apio–borate compounds.

Which DFT factors influence the accuracy of 1H, 13C and 195Pt NMR chemical shift predictions in organopolymetallic square-planar complexes? New scaling parameters for homo- and hetero-multimetallic compounds and their direct applications

Because of their chemical heterogeneity, stereochemical complexity and the presence of heavy atoms involving orbitals with high quantum number L, organopolymetallic complexes require considerable focus during their NMR spectral interpretation.

DFT approach to predict 13C NMR chemical shifts of hydrocarbon species adsorbed on Zn-modified zeolite

13C MAS NMR spectroscopy is a powerful technique to study the mechanisms of hydrocarbon transformations on heterogeneous catalysts. It can reliably identify the surface intermediates and the adsorbed products based...

Do Double-Hybrid Exchange-Correlation Functionals Provide Accurate Chemical Shifts? A Benchmark Assessment for Proton NMR

A benchmark density functional theory (DFT) study of ¹H NMR chemical shifts for data sets comprising 200 chemical shifts, including complex natural products, has been carried out to assess the performance of DFT methods. Two new benchmark data sets, NMRH33 and NMRH148, have been established. The meta-GGA revTPSS performs remarkably well against the NMRH33 benchmark set (mean absolute deviation (MAD), 0.10 ppm; maximum deviation (max), 0.26 ppm) with the smallest MAD of all evaluated functionals. The best-performing double-hybrid density functional (DHDF), revDSD-BLYP (MAD, 0.16 ppm; max, 0.35 ppm), performs similarly to hybrid-GGA methods (e.g., mPW1PW91/6-311G(d) (MAD, 0.15 ppm; max, 0.36 ppm)), but at a considerably higher computational cost. The results indicate that currently available double-hybrid DFT methods offer no benefit over GGA (including hybrid and meta) functionals in the calculation of ¹H NMR chemical shifts.

1H/13C chemical shift calculations for biaryls: DFT approaches to geometry optimization

Twelve common density functional methods and seven basis sets for geometry optimization were evaluated on the accuracy of 1H/13C NMR chemical shift calculations for biaryls. For these functionals, 1H shifts calculations for gas phase optimized geometries were significantly less accurate than those for in-solution optimized structures, while 13C results were not strongly influenced by geometry optimization methods and solvent effects. B3LYP, B3PW91, mPW1PW91 and ωB97XD were the best-performing functionals with lowest errors; among seven basis sets, DGDZVP2 and 6-31G(d,p) outperformed the others. The combination of these functionals and basis sets resulted in high accuracy with CMAEmin = 0.0327 ppm (0.76%) and 0.888 ppm (0.58%) for 1H and 13C, respectively. The selected functionals and basis set were validated when consistently producing optimized structures with high accuracy results for 1H and 13C chemical shift calculations of two other biaryls. This study highly recommends the IEFPCM/B3LYP, B3PW91, mPW1PW91 or ωB97XD/DGDZVP2 or 6-31G(d,p) level of theory for the geometry optimization step, especially the solvent incorporation, which would lead to high accuracy 1H/13C calculation. This work would assist in the fully structural assignments of biaryls and provide insights into in-solution biaryl conformations.

Accurate acid dissociation constant (pKa) calculation for the sulfachloropyridazine and similar molecules

Accurate calculation of the acid dissociation constant (pK_a) has fundamental importance for the description of molecular systems with pharmacological activities. The search for a more appropriate procedure for its determination is always welcome and has aroused increasing interest from the scientific community. In this sense, this work presents a computational study involving the combination of ten DFT functionals (M062X, M06L, B3LYP, BLYP, PBEPBE, BP86, LC-BLYP, SPBE, CAM-B3LYP, LC-PBEPBE) and HF method, eight basis set functions (6-311G, 6-311 + G, 6-311G(d,p), 6-311 + G(d,p), 6-311+ +G(d,p), 6-311(2d,2p), 6-311+ +G(2d,2p), and aug-cc-pVDZ), and three solvation models (SMD, PCM, and CPCM) for an accurate sulfachloropyridazine (SCR) pK_a determination. It was found that the smallest deviation (0.02 unit of pK_a) between the current study and experimental result was achieved with the BLYP/6-311 + G(d,p)/PCM combination. Therefore, this combination was extended to calculate the pK_a of six SCR similar molecules selected through the eletroshape similarity method. For all these molecules, the difference between the obtained results and experimental data ranged between 0.14 and 0.69 units of pK_a. This feature suggests that the obtained combination can determine pK_a with experimental precision for complexes that are formed by sulfonamide functional group (SO₂NHR). Graphical Abstract A computational study involving the combination of different levels of theory, basis sets and solvation models for an accurate sulfanamide pK_a determination.

Structural Refinement of Carbimazole by NMR Crystallography

The characterization of the three-dimensional structure of solids is of major importance, especially in the pharmaceutical field. In the present work, NMR crystallography methods are applied with the aim to refine the crystal structure of carbimazole, an active pharmaceutical ingredient used for the treatment of hyperthyroidism and Grave’s disease. Starting from previously reported X-ray diffraction data, two refined structures were obtained by geometry optimization methods. Experimental ¹H and ¹³C isotropic chemical shift measured by the suitable ¹H and ¹³C high-resolution solid state NMR techniques were compared with DFT-GIPAW calculated values, allowing the quality of the obtained structure to be experimentally checked. The refined structure was further validated through the analysis of ¹H-¹H and ¹H-¹³C 2D NMR correlation experiments. The final structure differs from that previously obtained from X-ray diffraction data mostly for the position of hydrogen atoms.

Computational NMR of Carbohydrates: Theoretical Background, Applications, and Perspectives

This review is written amid a marked progress in the calculation of NMR parameters of carbohydrates substantiated by a vast amount of experimental data coming from several laboratories worldwide. By no means are we trying to cover in the present compilation a huge amount of all available data. The main idea of the present review was only to outline general trends and perspectives in this dynamically developing area on the background of a marked progress in theoretical and computational NMR. Presented material is arranged in three basic sections: (1)-a brief theoretical introduction; (2)-applications and perspectives in computational NMR of monosaccharides; and (3)-calculation of NMR chemical shifts and spin-spin coupling constants of di- and polysaccharides.

Implementation and Validation of Local Hybrid Functionals with Calibrated Exchange-Energy Densities for Nuclear Shielding Constants

A recently reported coupled-perturbed Kohn-Sham implementation to compute nuclear shielding constants with gauge-including atomic orbitals and local hybrid functionals has been extended to cover higher derivatives of the density in the local mixing function (LMF) of the local hybrid as well as the calibration function (CF) needed to deal with the ambiguity of exchange-energy densities. This allowed the first evaluation of state-of-the-art local hybrids with "calibrated" exchange-energy densities for nuclear shieldings. Compared to previously evaluated simpler local hybrids without a CF, appreciable improvements are found for proton shieldings. Furthermore, the recent LH20t functional is still competitive with the outstanding performance of the uncalibrated LH12ct-SsirSVWN and LH12ct-SsifSVWN LHs for heavier nuclei, suggesting that LH20t is possibly the most robust choice of any rung-four functional for computing the nuclear shieldings of main-group nuclei so far. Interestingly, the presence of a CF in the functional significantly reduces the number of artifacts introduced by the widely used Maximoff-Scuseria framework to treat the local kinetic energy τ. The latter occurs in so-called t-LMFs used in many of the present local hybrids. In any case, the use of Dobson's current-density functional framework is also recommended with more advanced calibrated τ-dependent local hybrid functionals.

Structural characterisation of natural products by means of quantum chemical calculations of NMR parameters: new insights

In this review, we focus in all aspects of NMR simulation of natural products, from the fundamentals to the new computational toolboxes available, combining advanced quantum chemical calculations with upstream data processing and machine learning.

Comprehensive Benchmark Study on the Calculation of 29Si NMR Chemical Shifts

A comprehensive and diverse benchmark set for the calculation of ²⁹Si NMR chemical shifts is presented. The SiS146 set includes 100 silicon containing compounds with 146 experimentally determined reference ²⁹Si NMR chemical shifts measured in nine different solvents in a range from -400 to +828 ppm. Silicon atoms bound to main group elements as well as transition metals with coordination numbers of 2-6 in various bonding patterns including multiple bonds and coordinative and aromatic bonding are represented. The performance of various common and specialized density functional approximations including (meta-)GGA, hybrid, and double-hybrid functionals in combination with different AO basis sets and for differently optimized geometries is evaluated. The role of scalar-relativistic effects is further investigated by inclusion of the zeroth order regular approximation (ZORA) method into the calculations. GGA density functional approximations (DFAs) are found to outperform hybrid DFAs with B97-D3 performing best with an MAD of 7.2 ppm for the subset including only light atoms (Z < 18), while TPSSh is the best tested hybrid functional with an MAD of 10.3 ppm. For ²⁹Si cores in the vicinity of heavier atoms, the application of ZORA proved indispensable. Inclusion of spin-orbit effects into the ²⁹Si NMR chemical shift calculation decreases the mean absolute deviations by up to 74% compared to calculations applying effective core potentials.

Halogen Bond of Halonium Ions: Benchmarking DFT Methods for the Description of NMR Chemical Shifts

Because of their anisotropic electron distribution and electron deficiency, halonium ions are unusually strong halogen-bond donors that form strong and directional three-center, four-electron halogen bonds. These halogen bonds have received considerable attention owing to their applicability in supramolecular and synthetic chemistry and have been intensely studied using spectroscopic and crystallographic techniques over the past decade. Their computational treatment faces different challenges to those of conventional weak and neutral halogen bonds. Literature studies have used a variety of wave functions and DFT functionals for prediction of their geometries and NMR chemical shifts, however, without any systematic evaluation of the accuracy of these methods being available. In order to provide guidance for future studies, we present the assessment of the accuracy of 12 common DFT functionals along with the Hartree-Fock (HF) and the second-order Møller-Plesset perturbation theory (MP2) methods, selected from an initial set of 36 prescreened functionals, for the prediction of 1H, 13C, and 15N NMR chemical shifts of [N-X-N]+ halogen-bond complexes, where X = F, Cl, Br, and I. Using a benchmark set of 14 complexes, providing 170 high-quality experimental chemical shifts, we show that the choice of the DFT functional is more important than that of the basis set. The M06 functional in combination with the aug-cc-pVTZ basis set is demonstrated to provide the overall most accurate NMR chemical shifts, whereas LC-ωPBE, ωB97X-D, LC-TPSS, CAM-B3LYP, and B3LYP to show acceptable performance. Our results are expected to provide a guideline to facilitate future developments and applications of the [N-X-N]+ halogen bond.

Dynamic chiral cyclohexanohemicucurbit[12]uril

NMR spectroscopy and DFT modeling studies of chiral cyclohexanohemicucurbit[12]uril indicate that the macrocycle adopts a concave octagonal shape with two distinct conformational flexibilities in solution. Methylene bridge flipping occurs at temperatures above 265 K, while urea monomers rotate at temperatures above 308 K, resulting in the loss of confined space within the macrocycle.

Pharmaceutical Hydrates Analysis-Overview of Methods and Recent Advances

This review discusses a set of instrumental and computational methods that are used to characterize hydrated forms of APIs (active pharmaceutical ingredients). The focus has been put on highlighting advantages as well as on presenting some limitations of the selected analytical approaches. This has been performed in order to facilitate the choice of an appropriate method depending on the type of the structural feature that is to be analyzed, that is, degree of hydration, crystal structure and dynamics, and (de)hydration kinetics. The presented techniques include X-ray diffraction (single crystal X-ray diffraction (SCXRD), powder X-ray diffraction (PXRD)), spectroscopic (solid state nuclear magnetic resonance spectroscopy (ssNMR), Fourier-transformed infrared spectroscopy (FT-IR), Raman spectroscopy), thermal (differential scanning calorimetry (DSC), thermogravimetric analysis (TGA)), gravimetric (dynamic vapour sorption (DVS)), and computational (molecular mechanics (MM), Quantum Mechanics (QM), molecular dynamics (MD)) methods. Further, the successful applications of the presented methods in the studies of hydrated APIs as well as studies on the excipients' influence on these processes have been described in many examples.

Solvent optimization and conformational flexibility effects on 1 H and 13 C NMR scaling factors

The effects of including (a) implicit solvent in geometry optimizations, (b) conformationally flexible molecules in test sets, and (c) empirical dispersion D3(BJ) on scaling factors for predicting ¹ H and ¹³ C NMR chemical shifts were explored. Scaling factors with optimizations performed in the gas phase and with a Polarizable Continuum Model (PCM) solvent model were obtained for 12 organic solvents, including 2,2,2-trifluroethanol and chlorobenzene, for which scaling factors have been developed for the first time. Scaling factors for aromatic solvents were split into primary and secondary scaling factors to account for CH-π effects. Including empirical dispersion D3(BJ) did not lead to significant improvement.