MP2 calculation of 77Se NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the Second‐order Möller‐Plesset perturbation theory (MP2) calculation of ⁷⁷Se NMR chemical shifts (methods and basis sets, relativistic corrections, and solvent effects) are addressed with a special emphasis on relativistic effects. For the latter, paramagnetic contribution (390–466 ppm) dominates over diamagnetic term (192–198 ppm) resulting in a total shielding relativistic correction of about 230–260 ppm (some 15% of the total values of selenium absolute shielding constants). Diamagnetic term is practically constant, while paramagnetic contribution spans over 70–80 ppm. In the ⁷⁷Se NMR chemical shifts scale, relativistic corrections are about 20–30 ppm (some 5% of the total values of selenium chemical shifts). Solvent effects evaluated within the polarizable continuum solvation model are of the same order of magnitude as relativistic corrections (about 5%). For the practical calculations of ⁷⁷Se NMR chemical shifts of the medium‐sized organoselenium compounds, the most efficient computational protocols employing relativistic Dyall's basis sets and taking into account relativistic and solvent corrections are suggested. The best result is characterized by a mean absolute error of 17 ppm for the span of ⁷⁷Se NMR chemical shifts reaching 2500 ppm resulting in a mean absolute percentage error of 0.7%. Copyright © 2015 John Wiley & Sons, Ltd.     

On the accuracy of the GIAO‐DFT calculation of 15N NMR chemical shifts of the nitrogen‐containing heterocycles – a gateway to better agreement with experiment at lower computational cost

The main factors affecting the accuracy and computational cost of the gauge‐independent atomic orbital density functional theory (GIAO‐DFT) calculation of ¹⁵N NMR chemical shifts in the representative series of key nitrogen‐containing heterocycles – azoles and azines – have been systematically analyzed. In the calculation of ¹⁵N NMR chemical shifts, the best result has been achieved with the KT3 functional used in combination with Jensen's pcS‐3 basis set (GIAO‐DFT‐KT3/pcS‐3) resulting in the value of mean absolute error as small as 5 ppm for a range exceeding 270 ppm in a benchmark series of 23 compounds with an overall number of 41 different ¹⁵N NMR chemical shifts. Another essential finding is that basically, the application of the locally dense basis set approach is justified in the calculation of ¹⁵N NMR chemical shifts within the 3–4 ppm error that results in a dramatic decrease in computational cost. Based on the present data, we recommend GIAO‐DFT‐KT3/pcS‐3//pc‐2 as one of the most effective locally dense basis set schemes for the calculation of ¹⁵N NMR chemical shifts. Copyright © 2014 John Wiley & Sons, Ltd.     

On the accuracy factors and computational cost of the GIAO–DFT calculation of 15N NMR chemical shifts of amides

The main factors affecting the accuracy and computational cost of Gauge‐independent Atomic Orbital–density functional theory (GIAO–DFT) calculation of ¹⁵N NMR chemical shifts in the benchmark series of 16 amides are considered. Among those are the choice of the DFT functional and basis set, solvent effects, internal reference conversion factor and applicability of the locally dense basis set (LDBS) scheme. Solvent effects are treated within the polarizable continuum model (PCM) scheme as well as at supermolecular level with solvent molecules considered in explicit way. The best result is found for Keal and Tozer's KT3 functional used in combination with Jensen's pcS‐3 basis set with taking into account solvent effects within the polarizable continuum model. The proposed LDBS scheme implies pcS‐3 on nitrogen and pc‐2 elsewhere in the molecule. The resulting mean average error for the calculated ¹⁵N NMR chemical shifts is about 6 ppm. The application of the LDBS approach tested in a series of 16 amides results in a dramatic decrease in computational cost (more than an order of magnitude in time scale) with insignificant loss of accuracy.     

DFT computational schemes for 15N NMR chemical shifts of the condensed nitrogen-containing heterocycles

A systematic density functional theory (DFT) study of the accuracy factors (functionals, basis sets, and solvent effects) for the computation of ¹⁵N NMR chemical shifts has been performed in the series of condensed nitrogen-containing heterocycles. The behavior of the most representative functionals was examined based on the benchmark calculations of ¹⁵N NMR chemical shifts in the reference set of compounds. It was found that the best agreement with experiment was achieved with OLYP functional in combination with aug-pcS-3(N)//pc-2 locally dense basis set scheme providing mean absolute error of 5.2 ppm in the range of about 300 ppm. Taking into account solvent effects was performed within a general Tomasi's polarizable continuum model scheme. It was also found that computationally demanding supermolecular solvation model computations essentially improved some “difficult” cases, as was illustrated with phenanthroline dissolved in methanol. Based on the performed calculations, some 200 unknown ¹⁵N NMR chemical shifts were predicted with a high level of confidence for about 50 real-life condensed nitrogen-containing heterocycles, which could serve as a practical guide in structural elucidation of this class of compounds.     

On the long‐range relativistic effects in the 15N NMR chemical shifts of halogenated azines

Long‐range β‐ and γ‐relativistic effects of halogens in ¹⁵N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) are shown to be unessential for fluoro‐, chloro‐, and bromo‐derivatives (1–2 ppm in average). However, for iodocontaining compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the ¹⁵N calculation. Taking into account long‐range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full 4‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4‐component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long‐range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵N NMR chemical shifts of halogenated nitrogen‐containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.     

Substitution effects in the 15N NMR chemical shifts of heterocyclic azines evaluated at the GIAO‐DFT level

A systematic study of the accuracy factors for the computation of ¹⁵N NMR chemical shifts in comparison with available experiment in the series of 72 diverse heterocyclic azines substituted with a classical series of substituents (CH₃, F, Cl, Br, NH₂, OCH₃, SCH₃, COCH₃, CONH₂, COOH, and CN) providing marked electronic σ‐ and π‐electronic effects and strongly affecting ¹⁵N NMR chemical shifts is performed. The best computational scheme for heterocyclic azines at the DFT level was found to be KT3/pcS‐3//pc‐2 (IEF‐PCM). A vast amount of unknown ¹⁵N NMR chemical shifts was predicted using the best computational protocol for substituted heterocyclic azines, especially for trizine, tetrazine, and pentazine where experimental ¹⁵N NMR chemical shifts are almost totally unknown throughout the series. It was found that substitution effects in the classical series of substituents providing typical σ‐ and π‐electronic effects followed the expected trends, as derived from the correlations of experimental and calculated ¹⁵N NMR chemical shifts with Swain–Lupton's F and R constants.     

Solvent effects in the GIAO‐DFT calculations of the 15N NMR chemical shifts of azoles and azines

The calculation of ¹⁵N NMR chemical shifts of 27 azoles and azines in 10 different solvents each has been carried out at the gauge including atomic orbitals density functional theory level in gas phase and applying the integral equation formalism polarizable continuum model (IEF‐PCM) and supermolecule solvation models to account for solvent effects. In the calculation of ¹⁵N NMR, chemical shifts of the nitrogen‐containing heterocycles dissolved in nonpolar and polar aprotic solvents, taking into account solvent effect is sufficient within the IEF‐PCM scheme, whereas for polar protic solvents with large dielectric constants, the use of supermolecule solvation model is recommended. A good agreement between calculated 460 values of ¹⁵N NMR chemical shifts and experiment is found with the IEF‐PCM scheme characterized by MAE of 7.1 ppm in the range of more than 300 ppm (about 2%). The best result is achieved with the supermolecule solvation model performing slightly better (MAE 6.5 ppm). Copyright © 2014 John Wiley & Sons, Ltd.     

GIAO‐DFT calculation of 15N NMR chemical shifts of Schiff bases: Accuracy factors and protonation effects

¹⁵N NMR chemical shifts in the representative series of Schiff bases together with their protonated forms have been calculated at the density functional theory level in comparison with available experiment. A number of functionals and basis sets have been tested in terms of a better agreement with experiment. Complimentary to gas phase results, 2 solvation models, namely, a classical Tomasi's polarizable continuum model (PCM) and that in combination with an explicit inclusion of one molecule of solvent into calculation space to form supermolecule 1:1 (SM + PCM), were examined. Best results are achieved with PCM and SM + PCM models resulting in mean absolute errors of calculated ¹⁵N NMR chemical shifts in the whole series of neutral and protonated Schiff bases of accordingly 5.2 and 5.8 ppm as compared with 15.2 ppm in gas phase for the range of about 200 ppm. Noticeable protonation effects (exceeding 100 ppm) in protonated Schiff bases are rationalized in terms of a general natural bond orbital approach.     

DFT computational schemes for 1H and 13C NMR chemical shifts of natural products,exemplified by strychnine

A number of computational schemes based on different Density Functional Theory (DFT) functionals in combination with a number of basis sets were tested in the calculation of ¹H and ¹³C NMR chemical shifts of strychnine, as a typical representative of the vitally important natural products, and used as a challenging benchmark and a rigorous test for such calculations. It was found that the most accurate computational scheme, as compared with experiment, was PBE0/pcSseg-4//pcseg-3 characterized by a mean absolute error of 0.07 ppm for the range of about 7 ppm for ¹H NMR chemical shifts and that of only 1.13 ppm for ¹³C NMR chemical shifts spread over the range of about 150 ppm. For more practical purposes, including investigation of larger molecules from this series, a much more economical computational scheme, PBE0/pcSseg-2//pcseg-2, characterized by almost the same accuracy and much less computational demand, was recommended.     

Four‐component relativistic DFT calculations of 77Se NMR chemical shifts: A gateway to a reliable computational scheme for the medium‐sized organoselenium molecules

A versatile high‐accuracy computational scheme for the ⁷⁷Se nuclear magnetic resonance (NMR) chemical shifts of the medium‐sized organoselenium compounds is suggested within a framework of a full four‐component relativistic density functional theory (DFT). The main accuracy factors (DFT functionals, relativistic geometry, vibrational corrections, and solvent effects) are addressed. The best result is achieved with NMR‐oriented KT2 functional of Keal–Tozer characterized by a fairly small error of only 30 ppm for the span of about 1700 ppm (<2%). © 2015 Wiley Periodicals, Inc.     

Theoretical and experimental study of 15N NMR protonation shifts

A combined theoretical and experimental study revealed that the nature of the upfield (shielding) protonation effect in ¹⁵N NMR originates in the change of the contribution of the sp²‐hybridized nitrogen lone pair on protonation resulting in a marked shielding of nitrogen of about 100 ppm. On the contrary, for amine‐type nitrogen, protonation of the nitrogen lone pair results in the deshielding protonation effect of about 25 ppm, so that the total deshielding protonation effect of about 10 ppm is due to the interplay of the contributions of adjacent natural bond orbitals. A versatile computational scheme for the calculation of ¹⁵N NMR chemical shifts of protonated nitrogen species and their neutral precursors is proposed at the density functional theory level taking into account solvent effects within the supermolecule solvation model. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantum Chemistry Studies on the Fe-Cu Interactions and 31p NMR in Fe（CO）3（Ph2Ppy）2（CuXn） （Xn = Cl2^2-, Cl-, Br-）

In order to study the Fe-Cu interactions and their effects on 31p NMR, the structures of mononuclear complex Fe（CO）3fPhzPpy）a 1 and binuclear complexes Fe（CO）3（PhEPpy）z（CuXn） （2： Xn = Cl2^2-, 3： Xn = Cl-, 4： Xn = Br-） are calculated by density functional theory （DFT） PBE0 method. For complexes 1, 3 and 4, the 31p NMR chemical shifts calculated by PBE0-GIAO method are in good agreement with experimental results. The 31p chemical shift is 82.10 ppm in the designed complex 2. The Fe-Cu interactions （including Fe→Cu and Fe←Cu charge transfer） mainly exhibit the indirect interactions. Moreover, the Fe-Cu（I） interactions （mostly acting as σFe-p→4Scu and aFe-C→4Scu charge transfer） in complexes 3 and 4 are stronger than Fe-Cu（Ⅱ） interactions （mostly acting as σFe-p→4Scu and σFe-p←4Sc,） in complex 2. In complex 2, the stronger Fe←Cu interac- tions, acting as σFe-p←44SCu charge transfer, increase the electron density on P nucleus, which causes the upfield 31p chemical shift compared with mononuclear complex 1. For 3 and 4, although a little deshielding for P nucleus is derived from the delocalization of σFe-p→4Scu due to the Fe→Cu interactions, the stronger σFe-c→np charge-transfer finally increases the electron density on P nucleus. As a result, an upfield 31p chemical shift is observed compared with 1. The stability follows the order of 2〉3=4, indicating that Fe（CO）3（PhzPpy）2（CuCl2） is stable and could be synthesized experimentally. The N-Cu（Ⅱ） interaction plays an important role in the stability of 2. Because the delocalization of σFe-p→4SCu and σFe-c→πc-o weakens the a bonds of Fe-C and ~r bonds of CO, it is favorable for increasing the catalytic activity of binuclear complexes. Complexes 3 and 4 are expected to show higher catalytic activity compared to 2.     

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

A comprehensive investigation was performed on ¹H, ¹³C, and ³¹P nuclear magnetic resonance (NMR) chemical shifts (CSs) of phosphoryl benzamide derivatives (C₆H₅C(O)NHP(O)R₁R₂), (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, ²J_PH values were computed with an acceptable agreement to experimental data at the optimum level of theory. The dependency between ²J_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 ²J_PH values.     

Nonempirical calculations of the one‐bond 29Si–13C spin–spin coupling constants taking into account relativistic and solvent corrections

The computational study of the one‐bond ²⁹Si–¹³C spin–spin coupling constants has been performed at the second‐order polarization propagator approximation (SOPPA) level in the series of 60 diverse silanes with a special focus on the main factors affecting the accuracy of the calculation including the level of theory, the quality of the basis set, and the contribution of solvent and relativistic effects. Among three SOPPA‐based methods, SOPPA(MP2), SOPPA(CC2), and SOPPA(CCSD), the best result was achieved with SOPPA(CCSD) when used in combination with Sauer's basis set aug‐cc‐pVTZ‐J characterized by the mean absolute error of calculated coupling constants against the experiment of ca 2 Hz in the range of ca 200 Hz. The SOPPA(CCSD)/aug‐cc‐pVTZ‐J method is recommended as the most accurate and effective computational scheme for the calculation of ¹J(Si,C). The slightly less accurate but essentially more economical SOPPA(MP2)/aug‐cc‐pVTZ‐J and/or SOPPA(CC2)/aug‐cc‐pVTZ‐J methods are recommended for larger molecular systems. It was shown that solvent and relativistic corrections do not play a major role in the computation of the total values of ¹J(Si,C); however, taking them into account noticeably improves agreement with the experiment. The rovibrational corrections are estimated to be of about 1 Hz or 1–1.5% of the total value of ¹J(Si,C). Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison of calculated DFT/B3LYP and experimental C and O NMR chemical shifts, ab initio HF/6-31G* optimised structures, and single crystal X-ray structures of some substituted methyl 5β-cholan-24-oates

Single crystal X-ray structures (monoclinic space group P2₁) for methyl 3-oxo-5β-cholan-24-oate and methyl 3,12-dioxo-5β-cholan-24-oate have been solved and compared with HF/6-31G* optimised structures. In the crystalline packings the side chains are connected with weak OC(sp³)HO-type of interactions between C25–H and C24–O–C25 and the keto ends with weak C(sp³)HO=C-type of interactions between C4–H and O=C3. The orientations of the side chains, which steric configurations are of great importance to the biological activity of the molecules, are compared with the experimental structure of methyl 3-hydroxy-5β-cholan-24-oate. Probable reasons for the observed differences are discussed. In addition, ¹³C and ¹⁷O NMR chemical shifts of methyl 3-oxo-5β-cholan-24-oate and methyl 3,12-dioxo-5β-cholan-24-oate as well as the epimeric methyl 3-hydroxy-5β-cholan-24-oate and methyl 3β-hydroxy-5β-cholan-24-oate have been calculated (DFT/B3LYP/6-311G*) and compared with the experimental values by linear regression analyses. In general, the correspondence between the theoretical and experimental parameters is good or excellent.     

H, C NMR spectral and single crystal structural studies of toxaphene congeners. Quantum chemical calculations for preferred conformers of 2,5-endo,6-exo,8,9,9,10,10-octachloro-2-bornene and their DFT/GIAO C chemical shifts

The ¹H and ¹³C NMR chemical shifts for six toxaphene congeners: 2-exo,3-endo,6-exo,8,9,10-hexachloro- (1), 2-exo,3-endo,5-exo,9,9,10,10-heptachloro- (2), 2-exo,3-endo,6-exo,8,9,10,10-heptachloro- (3), 2-exo,3-endo,5-exo,6-endo,8,9,10-heptachloro- (4), 2-exo,3-endo,5-exo,6-endo,8,9,9,10-octachlorobornane (5) and 2,5-endo,6-exo,8,9,9,10,10-octachloro-2-bornene (6) are reported. Their chemical shift assignments have been obtained by means of Pulsed Field Gradient (PFG) Double Quantum Filtered (DQF) ¹H,¹H correlation spectroscopy (COSY), PFG ¹H,¹³C Heteronuclear Multiple Quantum Coherence (HMQC) and PFG ¹H,¹³C Heteronuclear Multiple Bond Correlation (HMBC) experiments. A single crystal X-ray structural analysis was made for compounds 1, 3, 4 and 6. The prevalences of two octachlorobornene rotamers (6a,6b) were elucidated by ab initio MO method and single point DFT/GIAO calculations for ¹³C chemical shifts. Theoretical calculations proved that the single crystal structure of 6 corresponds its most stable conformer in solution.     

Stereochemical behavior of geminal and vicinal 77Se–13C spin–spin coupling constants studied at the SOPPA(CC2) level taking into account relativistic corrections

A systematic theoretical study of geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants in the series of the open‐chain selenides and selenium‐containing heterocycles revealed that relativistic effects play an essential role in the selenium–carbon coupling mechanism, especially when the coupling pathway includes a triple bond, contributing to about 10–15% of their total values and noticeably improving the agreement of the calculated couplings with experiment. Both geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants show marked stereochemical behavior as documented by their calculated dihedral angle dependence that could be used as a practical guide in stereochemical studies of organoselenium compounds. Copyright © 2014 John Wiley & Sons, Ltd.     

Combined application of 2D NMR correlation methods and ab initio chemical shift calculations to the structure determination of new heterocyclic compounds

The combined use of 2D NMR correlation methods and ab initio chemical shift calculations is efficient and, in some cases, virtually the only way to determine the structures of new organic compounds. This approach enabled us to establish the structure of the major unusual product of the three-component reaction of imidazo[1,5-a]quinoxalin-4-one, bis(2-chloroethyl)amine hydrochloride, and potassium carbonate in DMF. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2172–2179, December, 2006. Dedicated to Professor A. V. Il’yasov on the occasion of his 70th birthday.     

Exploring Electronic Properties of Si20-n H20-n P n Heterofullerenes (N = 1, 2, 5, and 10) Based on NMR and NBO Analysis: A DFT Study

Abstract

Density functional theory (DFT) calculations are performed to characterize Si_20-nH_20-nP_nheterofullerenes (n = 1, 2, 5, and 10), and to examine the stability of encapsulated X@Si_20-nH_20-nP_nwhere X = Li, Na, and K. To this aim, ²⁹Si, ³¹P, and ¹H chemical shielding (CS) tensors as well as natural charges are calculated for the optimized structures. The local structures around silicon as well as phosphorus nuclei are found to show a good correlation with CSs. However, the similar values of ¹H calculated CSs (26–28 ppm) obtained for all the heterofullerenes mean hydrogen atoms do not detect the local structure around the adjacent silicon and also do not distinguish between isomers of heterofullerenes and the number of P dopants. According to calculated endo-hedral inclusion energies (E_inc), formation of the Li@Si_20-nH_20-nP_ncomplexes, unlike the K@Si_20-nH_20-nP_nones, are exothermic while E_incof the Na@Si_20-nH_20-nP_ncomplexes strongly depends on the position and number of P dopants. Moreover, binding energies for the considered models are found to be in the order of Si_20-nH_20-nP_n> Li@Si_20-nH_20-nP_n> Na@Si_20-nH_20-nP_n> K@Si_20-nH_20-nP_nwhile strongly depending on the pattern of P dopants on the surface of the cage.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the following free supplemental files: Additional figures and tables]