Regression Formulas for Density Functional Theory Calculated 1H and 13C NMR Chemical Shifts in Toluene-d8

Benchmark Study on the Calculation of 207Pb NMR Chemical Shifts

A benchmark set for the computation of 207Pb nuclear magnetic resonance (NMR) chemical shifts is presented. The PbS50 set includes conformer ensembles of 50 lead-containing molecular compounds and their experimentally measured 207Pb NMR chemical shifts. Various bonding motifs at the Pb center with up to seven bonding partners are included. Six different solvents were used in the measurements. The respective shifts lie in the range between +10745 and -5030 ppm. Several calculation settings are assessed by evaluating computed 207Pb NMR shifts for the use with different density functional approximations (DFAs), relativistic approaches, treatment of the conformational space, and levels for geometry optimization. Relativistic effects were included explicitly with the zeroth order regular approximation (ZORA), for which only the spin-orbit variant was able to yield reliable results. In total, seven GGAs and three hybrid DFAs were tested. Hybrid DFAs significantly outperform GGAs. The most accurate DFAs are mPW1PW with a mean absolute deviation (MAD) of 429 ppm and PBE0 with an MAD of 446 ppm. Conformational influences are small as most compounds are rigid, but more flexible structures still benefit from Boltzmann averaging. Including explicit relativistic treatments such as SO-ZORA in the geometry optimization does not show any significant improvement over the use of effective core potentials (ECPs).

Theoretical insights into the spectroscopic properties of ferrocenyl hetaryl ketones

Quantum chemical calculations have been carried out to elucidate the electronic structure as well as to draw structure-property relationships for a series of ferrocenyl hetaryl ketones by means of simulated NMR, IR and UV-vis spectra. In this series, the list of hetaryl groups included furan-2-yl, thiophen-2-yl, selenophen-2-yl, 1H-pyrrol-2-yl and N-methylpyrrol-2-yl. Density functional theory was employed to determine the ground-state properties of the five ketones while their excited-state properties were modeled using a broad range of theoretical methods, namely from time-dependent density functional theory to multiconfigurational and multireference ab initio approaches. The patterns in the ¹³C and ¹⁷O chemical shifts of the carbonyl group were explained by the geometrical twist of hetaryl rings and by the electronic parameters corresponding to π-bonds conjugation and group hardness. Furthermore, the corresponding ¹³C and ¹⁷O shielding constants were analyzed in terms of both their dia/paramagnetic and Lewis/non-Lewis contributions within the framework of natural chemical shielding theory. The pattern in the vibrational frequency of the carbonyl bond was connected with changes in its bond length and bond order. It was established that the electronic absorption spectra of the studied ketones are largely characterized by low-intensity d → π* transitions in the visible region and the dominant high-intensity π → π* transition in the UV region. Finally, the theoretical methods best suited for modeling the excited-state properties of such ketones were designated.

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.

Combined NMR Spectroscopy and Quantum-Chemical Calculations in Fluorescent 1,2,3-Triazole-4-carboxylic Acids Fine Structures Analysis

The peculiarities of the optical properties of 2-aryl-1,2,3-triazole acids and their sodium salts were investigated in different solvents (1,4-dioxane, dimethyl sulfoxide DMSO, methanol MeOH) and in mixtures with water. The results were discussed in terms of the molecular structure formed by inter- and intramolecular noncovalent interactions (NCIs) and their ability to ionize in anions. Theoretical calculations using the Time-Dependent Density Functional Theory (TDDFT) were carried out in different solvents to support the results. In polar and nonpolar solvents (DMSO, 1,4-dioxane), fluorescence was provided by strong neutral associates. Protic MeOH can weaken the acid molecules' association, forming other fluorescent species. The fluorescent species in water exhibited similar optical characteristics to those of triazole salts; therefore, their anionic character can be assumed. Experimental ¹H and ¹³C-NMR spectra were compared to their corresponding calculated spectra using the Gauge-Independent Atomic Orbital (GIAO) method and several relationships were established. All these findings showed that the obtained photophysical properties of the 2-aryl-1,2,3-triazole acids noticeably depend on the environment and, therefore, are good candidates as sensors for the identification of analytes with labile protons.

Indicuen, a new hopane from Parmotrema indicum Hale growing in Vietnam

One new hopane-type triterpene, indicuen (1), along with eight known compounds (2-9) were isolated from the n-hexane extract of the lichen Parmotrema indicum Hale. The chemical structures of isolated compounds were identified by interpretation of their spectroscopic data (1D, 2D NMR and HRESIMS) combined with DFT-NMR chemical shift calculations and subsequent assignment of DP4+ probabilities and by comparison with the literature. Indicuen represents for a rare hopane bearing a 1-carboxyethyl substituent at C-21 in lichens. Compounds 1-3 and 5-8 were evaluated for α-glucosidase inhibition and cytotoxicity against K562 and HepG2 cancer cell lines. Compounds 1, 5 and 7 exhibited moderate α-glucosidase inhibition with IC₅₀ values of 201.1, 156.3 and 187.4 µM, respectively. Compound 1 also showed weak cytotoxicity toward K562 cell line while others showed no activity.

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.

Isolation and NMR Scaling Factors for the Structure Determination of Lobatolide H, a Flexible Sesquiterpene from Neurolaena lobata

A new flexible germacranolide (1, lobatolide H) was isolated from the aerial parts of Neurolaena lobata. The structure elucidation was performed by classical NMR experiments and DFT NMR calculations. Altogether, 80 theoretical level combinations with existing ¹³C NMR scaling factors were tested, and the best performing ones were applied on 1. ¹H and ¹³C NMR scaling factors were also developed for two combinations utilizing known exomethylene containing derivatives, and the results were complemented by homonuclear coupling constant (J_HH) and TDDFT-ECD calculations to elucidate the stereochemistry of 1. Lobatolide H possessed remarkable antiproliferative activity against human cervical tumor cell lines with different HPV status (SiHa and C33A), induced cell cycle disturbance and exhibited a substantial antimigratory effect in SiHa cells.

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.

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.

DFT Calculations of 31P NMR Chemical Shifts in Palladium Complexes

In this study, comparative analysis of calculated (GIAO method, DFT level) and experimental ³¹P NMR shifts for a wide range of model palladium complexes showed that, on the whole, the theory reproduces the experimental data well. The exceptions are the complexes with the P=O phosphorus, for which there is a systematic underestimation of shielding, the value of which depends on the flexibility of the basis sets, especially at the geometry optimization stage. The use of triple-ζ quality basis sets and additional polarization functions at this stage reduces the underestimation of shielding for such phosphorus atoms. To summarize, in practice, for the rapid assessment of ³¹P NMR shifts, with the exception of the P=O type, a simple PBE0/{6-311G(2d,2p); Pd(SDD)}//PBE0/{6-31+G(d); Pd(SDD)} approximation is quite acceptable (RMSE = 8.9 ppm). Optimal, from the point of view of “price–quality” ratio, is the PBE0/{6-311G(2d,2p); Pd(SDD)}//PBE0/{6-311+G(2d); Pd(SDD)} (RMSE = 8.0 ppm) and the PBE0/{def2-TZVP; Pd(SDD)}//PBE0/{6-311+G(2d); Pd(SDD)} (RMSE = 6.9 ppm) approaches. In all cases, a linear scaling procedure is necessary to minimize systematic errors.

Benchmark Study on the Calculation of 119Sn NMR Chemical Shifts

A new benchmark set termed SnS51 for assessing quantum chemical methods for the computation of ¹¹⁹Sn NMR chemical shifts is presented. It covers 51 unique ¹¹⁹Sn NMR chemical shifts for a selection of 50 tin compounds with diverse bonding motifs and ligands. The experimental reference data are in the spectral range of ±2500 ppm measured in seven different solvents. Fifteen common density functional approximations, two scalar- and one spin-orbit relativistic approach are assessed based on conformer ensembles generated using the CREST/CENSO scheme and state-of-the-art semiempirical (GFN2-xTB), force field (GFN-FF), and composite DFT methods (r²SCAN-3c). Based on the results of this study, the spin-orbit relativistic method combinations of SO-ZORA with PBE0 or revPBE functionals are generally recommended. Both yield mean absolute deviations from experimental data below 100 ppm and excellent linear regression determination coefficients of ≤0.99. If spin-orbit calculations are not affordable, the use of SR-ZORA with B3LYP or X2C with ωB97X or M06 may be considered to obtain qualitative predictions if no severe spin-orbit effects, for example, due to heavy nuclei containing ligands, are expected. An empirical linear scaling correction is demonstrated to be applicable for further improvement, and respective empirical parameters are given. Conformational effects on chemical shifts are studied in detail but are mostly found to be small. However, in specific cases when the ligand sphere differs substantially between conformers, chemical shifts can change by up to several hundred ppm.

A new 26-norlanostane from Phlogacanthus turgidus growing in Vietnam

Chemical investigation on chloroform extract of Phlogacanthus turgidus led to the isolation of one new compound namely turgidol, together with five known triterpenoids, lupeol, lupenone, betulin, betulinic acid, and taraxerol. Their structures and stereochemistry have been determined by 1 D and 2 D NMR analysis, high resolution mass spectrometry, and compared with those in literatures. The relative configuration of turgidol was defined using DFT-NMR chemical shift calculations and subsequent DP4+ probability method. Turgidol, betulin, and betulinic acid were evaluated for cytotoxic activity toward K562 cancer cell line and the alpha-glucosidase inhibition.

Manilkzapotane, a novel dimeric alkylresorcinol derivative from the stem bark of Manilkara zapota

A novel dimeric alkylresorcinol derivative, manilkzapotane (1), along with seven known compounds, lupeol acetate (2), lupeol (3), arjunolic acid (4), ergosterol peroxide (5), taraxerol (6), hederagonic acid (7), and glochidiol (8) were isolated from the stem bark of Manilkara zapota. Their structures were determined on the basis of spectroscopic data. DFT-NMR chemical shift calculations and a modified probability (DP4+) method were applied to define the relative configuration of 1. To the best of our knowledge, this represents the first isolation of a dimeric alkylresorcinol derivative from the Sapotaceae family.

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.

Rukamtenol, a new spiro compound isolated from Flacourtia rukam Zoll. & Moritzi growing in Vietnam

Chemical investigation of chloroform extract of Flacourtia rukam Zoll. & Moritzi stems led to the isolation of one new compound namely rukamtenol together with four known compounds, viz., chaulmooric acid, flacourtin, 3,4,5-trimethoxyphenyl β-D-glucopyranoside, and daucosterol. Their structures and relative stereochemistry have been determined by 1D and 2D NMR analysis, high resolution mass spectroscopy, and compared with those in literatures. Rukamtenol represented the first 2-oxaspiro[4.4]non-8-en-3-one in nature. The relative configuration of rukamtinol was defined using DFT-NMR chemical shift calculations and subsequent DP4 probability method. Rukamtenol, flacourtin, and 3,4,5-trimethoxyphenyl β-D-glucopyranoside were tested for cytotoxic activity toward three MDA-MB-231, HepG2, and RD cancer cell lines. However, they failed to reveal any activity (IC₅₀ > 100 μM) on these cell lines.

Atypical Lindenane-Type Sesquiterpenes from Lindera myrrha

Two new lindenane sesquiterpenes were obtained from the roots of Lindera myrrha. These compounds were structurally elucidated by HRMS data, extensive NMR analyses, and comparison between experimental and theoretical ¹³C-NMR data. Myrrhalindenane A is the first monomeric seco-d lindenane displaying a non-rearranged, cyclohexanic C-ring. Myrrhalindenane B is the second occurrence of an angular lindenane-sesquiterpene related to a C₆-C₇ lactonization.

Total synthesis reveals atypical atropisomerism in a small-molecule natural product, tryptorubin A

Molecular shape defines function in both biological and material settings, and chemists have developed an ever-increasing vernacular to describe these shapes. Noncanonical atropisomers-shape-defined molecules that are formally topologically trivial but are interconvertible only by complex, nonphysical multibond torsions-form a unique subset of atropisomers that differ from both canonical atropisomers (e.g., binaphthyls) and topoisomers (i.e., molecules that have identical connectivity but nonidentical molecular graphs). Small molecules, in contrast to biomacromolecules, are not expected to exhibit such ambiguous shapes. Using total synthesis, we found that the peptidic alkaloid tryptorubin A can be one of two noncanonical atropisomers. We then devised a synthetic strategy that drives the atropospecific synthesis of a noncanonical atrop-defined small molecule.

Toward the comprehensive calculations on the relationship between 1 H, 13 C, 31 P chemical shifts, 2 JPH , and the bonding structure of different phosphoryl benzamides

A comprehensive investigation was performed on ¹ H, ¹³ C, and ³¹ P nuclear magnetic resonance (NMR) chemical shifts (CSs) of phosphoryl benzamide derivatives (C₆ H₅ C(O)NHP(O)R₁ R₂ ), (R₁ , R₂  = aziridine [L₁ ], azetidine [L₂ ], pyrrolidine [L₃ ], piperidine [L₄ ], azepane [L₅ ], 4-methylpiperidine [L₆ ], propane-2-amine [L₇ ], and 2-methylpropane-2-amine [L₈ ]) by the gauge-independent atomic orbital method (GIAO) to find the most accordant level of theory with the experimental values. To achieve this goal, all the structures were optimized using the B3LYP, BP86, PBE1PBE, M06-2X, MPWB1K, and MP2 methods with 6-31+G* basis set. Computed structural parameters demonstrate that BP86 has the best agreement to the experimental values between the other methods. The def2-TZVP and aug-cc-pVDZ basis sets were also employed to inspect the effect of different types of basis sets with higher polarization and diffuse functions. The correlation between the empirical and computational values attests that 6-31+G* basis set is the optimum case regarding minimization of the costs and results. The comparison between calculated and experimental CSs at all mentioned combinations illustrated that in accordance with structural results, the best level of theory in CSs is also BP86/6-31+G*. Besides, ² J_PH values were computed with an acceptable agreement to experimental data at the optimum level of theory. The dependency between ² J_PH and the bonding structure of studied ligands was also scrutinized by the Natural Bond Orbital (NBO) analysis that interprets the relationship between the electronic properties and ² J_PH values.

Method Calibration or Data Fitting?

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

Intramolecular hydrogen bonding in conformationally semi-rigid α-acylmethane derivatives: a theoretical NMR study

Conformational mobility is a core property of organic compounds, and conformational analysis has become a pervasive tool for synthetic design. In this work, we present experimental and computational (employing Density Functional Theory) evidence for unusual intramolecular hydrogen bonding interactions in a series of α-acylmethane derivatives, as well as a discussion of the consequences thereof for their NMR spectroscopic properties.

Improved Quantum Chemical NMR Chemical Shift Prediction of Metabolites in Aqueous Solution toward the Validation of Unknowns

A quantum-chemistry based protocol, termed MOSS-DFT, is presented for the prediction of ¹³C and ¹H NMR chemical shifts of a wide range of organic molecules in aqueous solution, including metabolites. Molecular motif-specific linear scaling parameters are reported for five different density functional theory (DFT) methods (B97-2/pcS-1, B97-2/pcS-2, B97-2/pcS-3, B3LYP/pcS-2, and BLYP/pcS-2), which were applied to a large set of 176 metabolite molecules. The chemical shift root-mean-square deviations (RMSD) for the best method, B97-2/pcS-3, are 1.93 and 0.154 ppm for ¹³C and ¹H chemical shifts, respectively. Excellent results have been obtained for chemical shifts of methyl and aromatic ¹³C and ¹H that are not directly bonded to a heteroatom (O, N, S, or P) with RMSD values of 1.15/0.079 and 1.31/0.118 ppm, respectively. This study not only demonstrates how NMR chemical shift in aqueous environment can be improved over the commonly used global linear scaling approach, but also allows for motif-specific error estimates, which are useful for an improved chemical shift-based verification of metabolite candidates of metabolomics samples containing unknown components.

Vibrational and electronic profiles, molecular docking and biological prediction of 5-methoxy-1-[(5-methoxy- 1H-indol-2-yl)methyl]-1H-indole: Experimental and theoretical investigations

Indole derivatives represent an important class of privileged structures. Spectroscopic (Fourier transform infrared (FT-IR), FT-Raman, 1H and [Formula: see text]C nuclear magnetic resonance (NMR)) investigations of the indole-bearing title compound, namely 5-methoxy-1-[(5-methoxy-1[Formula: see text]-indol-2-yl)methyl]-1[Formula: see text]-indole (MMIMI) have been carried out. The corresponding data of the MMIMI molecule were analyzed to understand its optimized geometry, and inter/intra-molecular interactions. The equilibrium geometry, harmonic vibrational wavenumbers, Frontier orbital energy, and natural bond orbital (NBO) analyses have been performed with the help of density functional theory (DFT) with B3LYP/6-311[Formula: see text]G([Formula: see text],[Formula: see text]) level of theory. The vibrational modes have been unequivocally assigned using potential energy distribution analysis. The theoretically predicted wavenumbers have good agreement with the experimental values. NBO has confirmed the intra-molecular charge transfer interactions. HOMO–LUMO analysis was carried out to explore charge delocalization on the MMIMI molecule. The immunomodulatory activity of the title molecule was predicted using molecular docking approach.

Comparison of experimental and DFT-calculated NMR chemical shifts of 2-amino and 2-hydroxyl substituted phenyl benzimidazoles, benzoxazoles and benzothiazoles in four solvents using the IEF-PCM solvation model

A comparative study of experimental and calculated NMR chemical shifts of six compounds comprising 2-amino and 2-hydroxy phenyl benzoxazoles/benzothiazoles/benzimidazoles in four solvents is reported. The benzimidazoles showed interesting spectral characteristics, which are discussed. The proton and carbon chemical shifts were similar for all solvents. The largest chemical shift deviations were observed in benzene. The chemical shifts were calculated with density functional theory using a suite of four functionals and basis set combinations. The calculated chemical shifts revealed a good match to the experimentally observed values in most of the solvents. The mean absolute error was used as the primary metric. The use of an additional metric is suggested, which is based on the order of chemical shifts. The DP4 probability measures were also used to compare the experimental and calculated chemical shifts for each compound in the four solvents. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

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

(1)H NMR spectra of alcohols in hydrogen bonding solvents: DFT/GIAO calculations of chemical shifts

Proton nuclear magnetic resonance (NMR) shifts of aliphatic alcohols in hydrogen bonding solvents have been computed on the basis of density functional theory by applying the gauge-including atomic orbital method to geometry-optimized alcohol/solvent complexes. The OH proton shifts and hydrogen bond distances for methanol or ethanol complexed with pyridine depend very much on the functional employed and very little on the basis set, provided it is sufficiently large to give the correct quasi-linear hydrogen bond geometry. The CH proton shifts are insensitive to both the functional and the basis set. NMR shifts for all protons in several alcohol/pyridine complexes are calculated at the Perdew, Burke and Ernzerhof PBE0/cc-pVTZ//PBE0/6-311 + G(d,p) level in the gas phase. The results correlate with the shifts for the pyridine-complexed alcohols, determined by analysing data from the NMR titration of alcohols against pyridine. More pragmatically, computed shifts for a wider range of alcohols correlate with experimental shifts in neat pyridine. Shifts for alcohols in dimethylsulfoxide, based on the corresponding complexes in the gas phase, correlate well with the experimental values, but the overall root mean square difference is high (0.23 ppm), shifts for the OH, CHOH and other CH protons being systematically overestimated, by averages of 0.42, 0.21 and 0.06 ppm, respectively. If the computed shifts are corrected accordingly, a very good correlation is obtained with a gradient of 1.00 ± 0.01, an intercept of 0.00 ± 0.02 ppm and a root mean square difference of 0.09 ppm. This is a modest improvement on the result of applying the CHARGE programme to a slightly different set of alcohols. Some alcohol complexes with acetone and acetonitrile were investigated both in the gas phase and in a continuum of the relevant solvent.

Fragment-based (13)C nuclear magnetic resonance chemical shift predictions in molecular crystals: An alternative to planewave methods

We assess the quality of fragment-based ab initio isotropic (13)C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic (13)C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.

Converging nuclear magnetic shielding calculations with respect to basis and system size in protein systems

Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van der Waals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size.

Quantum chemical calculations of31P NMR chemical shifts: scopes and limitations

High level of theory is not necessarily needed to obtain rather accurate predictions of³¹P chemical shifts by GIAO method. For example, the PBE1PBE/6-311G(2d,2p)//PBE1PBE/6-31+G(d) combination allowed to obtain good results for variety of middle-size organophosphorus compounds (M= 200–700 Da).

1H NMR spectra of alcohols and diols in chloroform: DFT/GIAO calculation of chemical shifts

Proton nuclear magnetic resonance (NMR) shifts of aliphatic alcohols in chloroform have been computed on the basis of density functional theory, the solvent being included by the integral-equation-formalism polarisable continuum model of Gaussian 09. Relative energies of all conformers are calculated at the Perdew, Burke and Ernzerhof (PBE)0/6-311+G(d,p) level, and NMR shifts by the gauge-including atomic orbital method with the PBE0/6-311+G(d,p) geometry and the cc-pVTZ basis set. The 208 computed CH proton NMR shifts for 34 alcohols correlate very well with the experimental values, with a gradient of 1.00 ± 0.01 and intercept close to zero; the overall root mean square difference (RMSD) is 0.08 ppm. Shifts for CH protons of diols in chloroform are well correlated with the theoretical values for (isotropic) benzene, with similar gradient and intercept (1.02 ± 0.01, -0.13 ppm), but the overall RMSD is slightly higher, 0.12 ppm. This approach generally gives slightly better results than the CHARGE model of Abraham et al. The shifts of unsaturated alcohols in benzene have been re-examined with Gaussian 09, but the overall fit for CH protons is not improved, and OH proton shifts are worse. Shifts of vinyl protons in alkenols are systematically overestimated, and the correlation of computed shifts against the experimental data for unsaturated alcohols follows a quadratic equation. Splitting the 20 compounds studied into two sets, and applying empirical scaling based on the quadratic for the first set to the second set, gives an RMSD of 0.10 ppm. A multi-standard approach gives a similar result.

1H and 13C NMR scaling factors for the calculation of chemical shifts in commonly used solvents using density functional theory

Calculation of NMR chemical shifts and coupling constants using quantum mechanical calculations [density functional theory (DFT)], has become a very popular tool for the determination of conformation and the assignment of stereochemistry within a molecule. We present the scaling factors (linear regression parameters) from 10 DFT methods for 10 commonly used NMR solvents using the same set of reference compounds. The results were compared with the corresponding gas-phase calculations to assess the inclusion of the polarizable continuum model for solvent effects.

Spectroscopic probe on N-H⋯N, N-H⋯O and controversial C-H⋯O contact in A-T base pair: a DFT study

DNA base pair A-T has been investigated by IR and NMR spectroscopy using DFT methods. The results have been analyzed in terms of infrared vibrational frequencies and (1)H NMR chemical shifts. Different types of interactions N-H⋯N, N-H⋯O and C-H⋯O types have been investigated in DNA base pairs. Although, previous reports argued about the third C-H⋯O type interaction in A-T base pair, such typical interaction has been analyzed thoroughly by IR and NMR spectroscopy using DFT methods. Our results show that the CH⋯O interaction in the A-T base pair is a weak interaction compared to normal hydrogen bond interactions.