Basis-set dependence of nuclear spin-spin coupling constants

The convergence of NMR indirect spin-spin coupling constants with the extension of the basis set is analyzed, based on calculations carried out at the multiconfigurational self-consistent-field level for the HF and H₂O systems. For the dominant and difficult Fermi-contact contribution, the standard correlation-consistent basis sets of electronic-structure theory are not suitable, lacking flexibility in the core region. Improved but not satisfactory convergence of the couplings is observed when decontracting the s functions of the correlation-consistent cc-pVXZ basis sets for 2≤X≤6. Next, by systematically extending these basis sets with tight s functions, new sets are obtained that are sufficiently flexible for accurate calculations of indirect nuclear spin-spin couplings, without sacrificing the smooth convergence behavior of the correlation-consistent basis sets. Received: 22 September 1997 / Accepted: 30 December 1997     

Benchmarking NMR indirect nuclear spin-spin coupling constants: SOPPA, SOPPA(CC2), and SOPPA(CCSD) versus CCSD

Accurate calculations of NMR indirect nuclear spin-spin coupling constants require especially optimized basis sets and correlated wave function methods such as CCSD or SOPPA(CCSD). Both methods scale as N(6), where N is the number of orbitals, which prevents routine applications to molecules with more than 10-15 nonhydrogen atoms. We have therefore developed a modification of the SOPPA(CCSD) method in which the CCSD singles and doubles amplitudes are replaced by CC2 singles and doubles amplitudes. This new method, called SOPPA(CC2), scales only as N(5), like the original SOPPA-method. The performance of the SOPPA(CC2) method for the calculation of indirect nuclear spin-spin coupling constants is compared to SOPPA and SOPPA(CCSD) employing a set of benchmark molecules. We also investigate the basis set dependence by employing three different basis sets optimized for spin-spin coupling constants, namely the HuzIV-su4, ccJ-pVTZ, and ccJ-pVQZ basis sets. The results of the corresponding CCSD calculations are used as a theoretical reference.     

1-Cyclohepta-2,4,6-trienyl-selanes--a 77Se NMR study: indirect nuclear 77Se--13C spin-spin coupling constants and application of density functional theory (DFT) calculations

1-Cyclohepta-2,4,6-trienyl-selanes Se(C(7)H(7))(2) (2c), R--Se--C(7)H(7) with R = Bu, (t)Bu, Ph, 4-F--C(6)H(4) (12a,b,c,d) were prepared by the reaction of the corresponding silanes, Si(SeMe(3))(2) and R--Se--SiMe(3), respectively, with tropylium bromide C(7)H(7)Br. In spite of the low stability of the selanes even in dilute solutions and at low temperature, they could be characterised by their (1)H, (13)C and (77)Se NMR parameters. Coupling constants (1)J((77)Se,(13)C) were measured and calculated by DFT methods at the B3LYP/6-311+G(d,p) level of theory. The comparison of experimental and calculated coupling constants (1)J((77)Se,(13)C) included numerous selenium carbon compounds with largely different Se--C bonds, revealing a satisfactory agreement. Both the spin-dipole (SD) and the paramagnetic spin-orbital (PSO) terms contributed significantly to the spin-spin coupling interaction, in addition to the Fermi contact (FC) term.     

Stereochemical study of iminodihydrofurans based on experimental measurements and SOPPA calculations of (13)C-(13)C spin-spin coupling constants

Configurational assignment and conformational analysis of a series of iminodihydrofurans obtained from cyanoacetylenic alcohols were performed on the basis of experimental measurements and high-level ab initio calculations of their (13)C-(13)C spin-spin coupling constants. The title compounds were shown to form and exist in solution as the individual Z isomers, adopting the orthogonal orientation of the amino, alkylamino and dialkylamino groups and the s-trans orientation of the CONH(2) group at the C(4) position of the 2,5-dihydro-2-iminofuran moiety.     

Non-empirical calculations of NMR indirect spin-spin coupling constants. Part 13: configurational assignment of aminosulfonylamidines

Carbon-carbon coupling constants have been experimentally measured using the INADEQUATE pulse sequence in the series of N-[1,2-bis(dialkylamino)-2-arylethylidene]arylsulfonamides obtained from N-(1-aryl-2,2,2-trichloroethyl)amides of arylsulfonic acids. Comparison of the experimental J(C,C) in this series with those calculated at the SOPPA (Second-Order Polarization Propagator Approach) level in the model aminosulfonylamidine provided an unambiguous assignment at the C=N bond of the eight-title aminosulfonylamidines to E-configuration, while the unknown J(C,C) couplings in their inaccessible diverse Z isomers have been predicted with high reliability. The established marked difference between J(C,C) of the corresponding carbon-carbon bonds in cis and trans orientations to the nitrogen lone pair in aminosulfonylamidines provides a powerful tool in the configurational assignment at the C=N bond in a wide series of the related systems containing the C=N-SO2R moiety.     

Spin-orbit corrections to the indirect nuclear spin-spin coupling constants in XH4 (X = C, Si, Ge, and Sn)

Summary Using the quadratic response function at theab initio SCF level of approximation we have calculated the relativistic corrections from the spin-orbit Hamiltonian,H ^SO, to the indirect nuclear spin-spin coupling constants of XH₄ (X = C, Si, Ge, and Sn). We find that the spin-orbit contributions toJ _X-H are small, amounting only to about 1% forJ _Sn-H. For the geminal H-H coupling constants the relativistic corrections are numerically smaller than forJ _X-H, but in some cases relatively larger compared to the actual magnitude ofJ _H-H. We also investigate the use of an effective one-electron spin-orbit Hamiltonian rather than the fullH ^SO in the calculation of these corrections.     

Non-empirical calculations of NMR indirect carbon-carbon coupling constants. Part 6: propellanes

A full set of carbon-carbon coupling constants have been calculated at the SOPPA level in the series of six most representative propellanes. Special attention was focused on spin-spin couplings involving both bridgehead carbons, and these data were rationalized in terms of the multipath coupling mechanism and hybridization effects. Many unknown couplings in the propellane frameworks were predicted with high reliability.     

Indirect nuclear spin-spin coupling constants in 1,2-diboretane-3-ylidene, a homoaromatic system with pi and sigma 3c/2e bonds. Comparison of experimental data with calculations using density functional theory (DFT)

The non-classical 1,2-diboretane-3-ylidene 1a was studied by 13C and 29Si NMR spectroscopy in order to obtain coupling constants 1J(13C,11B) and 1J(29Si,13C). The magnitudes of 1J(13C,11B) were deduced from linewidth measurements in low-temperature 13C and 11B NMR spectra. Calculation of the coupling constants for model compounds related to 1a, using DFT methods based on optimized geometries [B3LYP/6-311+G(d,p)], gave data in agreement with the experiments. Furthermore, the calculations predict for the first time a negative sign of 1J(13C,11B) which mirrors the bonding situation in 1 as described by theory.     

Non‐empirical calculations of NMR indirect carbon–carbon coupling constants. Part 4: Bicycloalkanes

A systematic study of the one‐bond and long‐range J(C,C), J(C,H) and J(H,H) in the series of nine bicycloalkanes was performed at the SOPPA level with special emphasis on the coupling transmission mechanisms at bridgeheads. Many unknown couplings were predicted with high reliability. Further refinement of SOPPA computational scheme adjusted for better performance was carried out using bicyclo[1.1.1]pentane as a benchmark to investigate the influence of geometry, basis set and electronic correlation. The calculations performed demonstrated that classical ab initio SOPPA applied with the locally dense Dunning's sets augmented with inner core s‐functions used for coupled carbons and Sauer's sets augmented with tight s‐functions used for coupled hydrogens performs perfectly well in reproducing experimental values of different types of coupling constants (the estimated reliability is ca 1–2 Hz) in relatively large organic molecules of up to 11 carbon atoms. Additive coupling increments were derived for J(C,C), J(C,H) and J(H,H) based on the calculated values of coupling constants within SOPPA in the model bicycloalkanes, in reasonably good agreement with the known values obtained earlier on pure empirical grounds. Most of the bridgehead couplings in all but one bicycloalkane appeared to be essentially additive within ca 2–3 Hz while bicyclo[1.1.1]pentane demonstrated dramatic non‐additivity of ?14.5 Hz for J(C,C), +16.6 Hz for J(H,H) and ?5.5 Hz for J(C,H), in line with previous findings. Non‐additivity effects in the latter compound established at the SOPPA level should be attributed to the through‐space non‐bonded interactions at bridgeheads due to the essential overlapping of the bridgehead rear lobes which provides an additional and effective non‐bonding coupling path for the bridgehead carbons and their protons in the bicyclopentane framework. Copyright © 2003 John Wiley & Sons, Ltd.     

Non‐empirical calculations of NMR indirect carbon‐carbon coupling constants. Part 5: Bridged bicycloalkanes

All possible J(C,C) of the bicarbocyclic frameworks together with J(C,H) and J(H,H) at bridgeheads in the series of six bridged bicycloalkanes, bicyclo[1.1.0]butane, bicyclo[2.1.0]pentane, bicyclo[3.1.0]hexane, bicyclo[2.2.0]hexane, bicyclo[3.2.0]heptane and bicyclo[3.3.0]octane, were calculated at the SOPPA level with correlation consistent Dunning sets cc‐pVTZ‐Cs augmented with inner core s‐functions and locally dense Sauer sets aug‐cc‐pVTZ‐J augmented with tight s‐functions and rationalized in terms of the multipath coupling mechanism and hybridization effects explaining many interesting structural trends. Copyright © 2003 John Wiley & Sons, Ltd.     

Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) in the Kohn–Sham (KS) complete basis set (CBS) limit. Correlation‐consistent cc‐pVxZ and cc‐pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ‐pVxZ, unc‐ccJ‐pVxZ, and aug‐cc‐pVTZ‐J) and polarization‐consistent pc‐n and pcJ‐n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT‐predicted isotropic shieldings, spin–spin values, and the experimental values was good and similar for the modified correlation‐consistent and polarization‐consistent basis sets. The BHandH method predicted the most accurate ¹H, ¹⁷O isotropic shieldings and ¹J(OH) coupling constant (deviations from experiment of about ? 0.2 and ? 1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and ¹J(OH) is similar to the more advanced methods, second‐order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit. Copyright © 2008 John Wiley & Sons, Ltd.     

Spin–orbit corrections to the indirect nuclear spin–spin coupling constants in XH4 (X=C, Si, Ge, and Sn)

Summary.  Using the quadratic response function at the ab initio SCF level of approximation we have calculated the relativistic corrections from the spin–orbit Hamiltonian, H ^SO, to the indirect nuclear spin–spin coupling constants of XH₄ (X=C, Si, Ge, and Sn). We find that the spin–orbit contributions to J _X–H are small, amounting only to about 1% for J _Sn–H. For the geminal H–H coupling constants the relativistic corrections are numerically smaller than for J _X–H, but in some cases relatively larger compared to the actual magnitude of J _H–H. We also investigate the use of an effective one-electron spin–orbit Hamiltonian rather than the full H ^SO in the calculation of these corrections. Received July 12, 1996 / Final revision received September 12, 1996 / Accepted September 17, 1996     

H2O,H2, HF,F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH/XZP Kohn–Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H₂O, H₂, HF, F₂ and F₂O nuclear isotropic shielding constants in the BHandH Kohn–Sham basis set limit was shown. The results of two‐ and three‐parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization‐consistent basis sets pcS‐n and pcJ‐n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ‐n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Understanding the conformational dependence of spin-spin coupling constants: through-bond and through-space J(31P,31P) coupling in tetraphosphane-1,4-diides [M(L)x]2[P4R4

The characteristic dependence of J(31P,31P) spin-spin coupling constants of alkali metal tetraphosphane-1,4-diides on structure and composition has been analyzed by density functional methods. The computations confirm that the structure of the contact ion pairs is conserved in solution. Calculations on model systems M2P4H4, on naked P4H4(2-) anions, and on models including point charges, show that the role of the cations is mainly structural and to a smaller extent electrostatic. Three of the four J(P,P) coupling constants depend characteristically on the conformation of the anion, which in turn is determined by the substituents R and by cation-anion interactions. Several couplings exhibit a large through-space component and are thus strongly dependent on the relative orientation of nonbonding electron pairs on the phosphorus atoms involved. This is shown by visualization of coupling pathways using the recently introduced coupling energy density (CED), in combination with the electron localization function (ELF).     

Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin–spin coupling constants (SSCC) using polarization‐consistent and XZP basis sets and B3LYP and BHandH density functionals

Efficient B3LYP and BHandH density functionals were used to estimate methanol's nuclear magnetic isotropic shieldings and spin–spin coupling constants in the basis set limit. Polarization‐consistent pcS‐n and pcJ‐n (n = 0, 1, 2, 3 and 4), and segmented contracted XZP, where X = D, T, Q and 5, basis sets were used and the results fitted with simple mathematical formulas. The performance of the methods was assessed from comparison with experiment and higher level calculations. ¹J(CH) and ³J(HH) values were determined from very diluted solutions in deuterochloroform and compared with theoretical predictions. The agreement between complete basis set (CBS) density functional theory (DFT) predicted isotropic shieldings and spin–spin values and experiment was good. The BHandH/pcS‐n methanol shieldings obtained using structures optimized at the same level of theory are approaching the accuracy of the advanced coupled‐cluster‐singles‐doubles‐approximate triples (CCSD(T)) calculations. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Eremophilane esters of Robinsonecio gerberifolius and their rearranged products. Study of the coupling constants (2)J(H, H), (3)J(H, H) and (4)J(H, H)

In the course of the basic hydrolysis of four eremophilane esters isolated from Robinsonecio gerberifolius, some rearrangements, eliminations, and additions occurred. Five compounds were obtained, three of them not previously described. Additionally, a new sesquiterpene was produced by autooxidation of compound 1. The (1)H and (13)C NMR spectra of these compounds were completely assigned by utilization of HMQC, HMBC, COSY, DEPT, and NOESY techniques. The long-range coupling constants of the peroxide 10 are reported, and all its coupling constants (2)J(H, H), (3)J(H, H), and (4)J(H, H) are calculated at the B3LYP/6-31G(d,p) level of theory. Their magnitude is explained in terms of electronic delocalization and the additivity of stereoelectronic effects.     

One‐bond 29Si‐1H spin‐spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations,relativistic effects,and vibrational corrections

A number of most representative second order polarization propagator approach (SOPPA) based wavefunction methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), and density functional theory (DFT) based methods, B3LYP, PBE0, KT2, and KT3, have been benchmarked in the calculation of the one‐bond ²⁹Si‐¹H spin‐spin coupling constants in the series of halosilanes SiH_nX_4?n (X = F, Cl, Br, I), both at the non‐relativistic and full four‐parameter Dirac's relativistic levels taking into account vibrational corrections. At the non‐relativistic level, the wavefunction methods showed much better results as compared with those of DFT. At the DFT level, out of four tested functionals, the Perdew, Burke, and Ernzerhof's PBE0 showed best performance. Taking into account, relativistic effects and vibrational corrections noticeably improves wavefunction methods results, but generally worsens DFT results. Copyright © 2013 John Wiley & Sons, Ltd.     

Electronic influences on 3J(C,H) coupling constants via -S-, -S(O)- and -SO2-: their determination, calculation and comparison of detection methods

3J(C,H) coupling constants via a sulfur atom in two series of compounds, both including a sulfide, a sulfoxide and a sulfone, were detected experimentally and calculated by quantum mechanical methods. In the first series (1-3) the coupling between a hydrogen, bonded to an sp3 carbon, and an sp2 carbon is treated; the second series (4-6) deals with the coupling between a hydrogen, bonded to an sp3 carbon, and an sp3 carbon. Different pulse sequences (broadband HMBC, SelJres, 1D HSQMBC, J-HMBC-2, selective J-resolved long-range experiment and IMPEACH-MBC) proved to be useful in determining the long-range 3J(C,H) coupling constants. However, the dynamic behaviour of two of the compounds (4 and 6) led to weighted averages of the two coupling constants expected (concerning equatorial and axial positions of the corresponding hydrogens). DFT calculations proved to be useful to calculate not only the 3J(C,H) coupling constants but also the different contributions of FC, PSO, DSO and SD terms; the calculation of the Fermi contact term (FC) was found to be sufficient for the correct estimation of 3J(C,H) coupling constants.     

Stereochemical behavior of 2 J(Se,H) and 3 J(Se,H) spin‐spin coupling constants across sp3 carbons: a theoretical scrutiny

A theoretical study of geminal and vicinal ⁷⁷Se‐¹ H coupling constants in the benchmark dimethyl and diethyl selenides has been performed at the SOPPA level followed by the NJC analysis within the NBO approach to reveal their stereochemical behavior in respect with the three main structural factors, namely, (i) the dihedral angle dependences, (ii) the bond angle dependences and (iii) the lone pair effects. It has been demonstrated that both geminal and vicinal couplings provide a unique stereospecificity in respect with the orientational lone pair effect together with the geometry of a coupling pathway, which is of prime importance for the stereochemical studies of organoselenium compounds. Copyright © 2012 John Wiley & Sons, Ltd.