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We present ^{2}H)ethane in gauche and antiperiplanar conformation are carried out at the HF, MP2 and CCSD(T) level of theory using basis sets ranging from double- to quadruple-zeta quality. The methodology is applied to the secondary isotope shifts for 2-fluoronorbornane in order to resolve an ambiguity in the literature on the assignment of

Quantum chemical calculations provide a powerful tool to investigate molecular properties and therefore support the interpretation of experimental findings. This applies especially to NMR chemical shieldings, as these contain a wealth of structural information that is, however, only indirectly related to the molecular structure itself. Nevertheless, in the interplay of theory and experiment, detailed structural information can be obtained by computing and comparing the molecular structure and the associated NMR parameters. In recent years, several studies have demonstrated that NMR chemical shifts can be calculated quantitatively using highly accurate methods [^{19}F chemical shieldings, for example, which range from about −200 to +500 ppm, Harding ^{13}C, ^{17}O and ^{15}N chemical shieldings [

The possibility to calculate zero-point vibrational effects and temperature corrections on NMR chemical shieldings also allows to predict secondary isotope shifts on chemical shieldings Δ_{l}_{h}

In order to calculate isotope shifts, several theoretical approaches have been propsed in the past [

On the right hand side appears the isotropic shielding _{e}_{e}_{r}_{r}Q_{s}

Here _{r}_{rss}_{αα}_{αα}

While calculations of secondary isotope shifts are far from routine applications of quantum chemical methods, previous work has shown that for small molecular systems these calculations can yield quantitative results, provided the correct treatment of vibrational effects on nuclear shieldings is used [

As an example, for which quantum chemical calculations can actually resolve ambiguities in the literature, we would like to revisit in the second part of this work one of the first studies in which various effects on secondary isotope shifts on NMR chemical shieldings were systematically investigated. Lambert

All calculations were carried out using the CFOUR program package [

Given the molecular geometry as obtained from a well converged geometry optimization, the nuclear shieldings and the harmonic force field are calculated. In order to compute the first and second derivative of the nuclear shieldings with respect to the normal coordinates as well as the cubic force field numerically, the nuclei of the molecule have to be displaced along the normal coordinates and at each geometry the nuclear shieldings and the quadratic force field are determined. Subsequently, the vibrational averaged isotropic shieldings are obtained using

For systems with many degrees of freedom, this procedure leads to a large number of calculations owing to the number of vibrational modes, especially in case of unsymmetrical molecules like 2-fluoronorbornanes, where 204 single calculations per compound are required.

As the calculation of the cubic force field and the nuclear shielding are done in two separate calculations, they can be carried out at two different levels of theory. This is advisable as for reliable results for the force field, a different level of theory is required than for NMR chemical shieldings [

It should be noted that the choice of the stepsize of displacement of the nuclei along the normal coordinates in the numerical third derivative procedure introduces an error of about 10^{−3} ppm for the ^{13}C isotope shifts, while for the ^{19}F isotope shifts this error is one order of magnitude larger. In the case of small frequencies (^{−1}) the contributions to the vibrational correction are overestimated, and contributions with (^{−1}) are excluded [^{13}C_{5} in ^{2}H)norbornane, the value of the ^{13}C secondary isotope shift on C_{5} is the same as if the nuclear mass of ^{12}C is used. Therefore, all calculations were done using the mass of ^{12}C for all carbon nuclei, which has been shown to have very little effect on the calculated values as in contrast to the substitution of ^{1}H by ^{2}H (100% mass increase), the mass difference between ^{12}C and ^{13}C is only 8%.

If species are to be identified by their secondary isotope shifts, the relative differences between the values of different compounds are important as well as the absolute values for each species. At the appropriate level of theory, to allow a reasonable assignment, the corresponding error due to method and basis set needs to be lower than the relative isotope shifts.

To estimate the errors of different computational methods, benchmark calculations were carried out for fluoroethane, which constitutes a small model system for which high-level calculations are feasible. The calculated ^{13}C secondary isotope shifts on chemical shieldings of carbon nuclei on the 1 and 2 position and the secondary isotope shifts on chemical shieldings of the ^{19}F nucleus are given in

All isotope shifts are given for T = 0 K and T = 300 K to assess the influence of the temperature correction on the isotope shifts. Temperature effects on secondary isotope shifts can be sizeable, as the inclusion of temperature corrections lowers isotope shifts on fluorine by about 20% at all levels of theory. For carbon atoms, on the other hand, the inclusion of temperature corrections leads to larger isotope effects, especially in the case of C_{1} with deuterium in the antiperiplanar conformation.

Comparison of the isotope shifts obtained at HF/tz2p with those obtained at HF/qz2p level of theory shows that deviations of about 10% arise for the fluorine atom while they amount to about 7% for C_{1} and amount to less than 1% for C_{2}.

While at CCSD(T)/qz2p + MP2/cc-pVTZ level of theory correlation effects are incorporated, at HF/tz2p level of theory this is not the case. This leads to an underestimation of the ^{19}F secondary isotope shifts of at most 0.057 ppm and 0.050 ppm on average at the HF/tz2p level of theory. The isotope effects at C_{1} are underestimated by at most 0.007 ppm and 0.006 ppm on average and at C_{2} they are at most 0.013 ppm larger and on average they are about 0.010 ppm larger than at the CCSD(T)/qz2p + MP2/cc-pVTZ level of theory. The values at the CCSD(T)/qz2p + MP2/cc-pVTZ level show only little deviations from the values given at the MP2/qz2p + MP2/cc-pVTZ level of theory, which leads to the conclusion that, already at the MP2/qz2p level, correlation effects are sufficiently taken into account.

In order to assess the main sources of error at the most cost-effcient level of theory, namely HF/tz2p,

Next, we turn to the errors in the difference between isotope effects on the shieldings of the gauche and antiperiplanar conformations, which is the decisive quantity if the different conformers are to be distinguished by the computed values. As the errors due to basis set effects and level of theory are very systematic, a favourable error compensation can be observed, such that the errors for the relative values are of the same order or less than for the secondary isotope shifts themselves. While the error in the chemical shifts is in the order of 10 ppm [

An early example for exploring dependencies of various parameters on secondary isotope effects on ^{19}F chemical shieldings was conducted by Lambert ^{1}H in the _{N}_{N}_{N}

It is well known that inverting S_{N}_{N}

The secondary isotope shifts of the molecules which were claimed by Lambert _{N}

In

As the synthesis pathway proposed by Lambert _{N}^{19}F shieldings of −0.339 ppm for ^{2}H)norbornane and of 0.005 ppm for ^{2}H)norbornane are computed. In the case of the ^{2}H)norbornane, a secondary isotope shift on ^{19}F of −0.131 ppm is obtained and in the case of ^{2}H)norbornane, this shift amounts to −0.007 ppm. These computed secondary isotope shifts on ^{19}F shieldings are in much better agreement with those observed by Lambert _{N}_{2}NCF_{2}CHFCl (

We carried out the synthesis of ^{19}F and ^{13}C secondary isotope shifts of the corresponding products are given in _{N}_{N}^{2}H)norbornane and ^{2}H)norbornane, ^{19}F and ^{13}C secondary isotope shifts were measured and show good agreement with the calculated ones (^{19}F chemical shielding of ^{2}H)norbornane observed by Lambert

Since a mixture of compounds with ^{2}H in 7- and 3-positions exists after the synthesis, an assignment of the secondary isotope shifts to the corresponding compounds is difficult. As mentioned in Section 2, the uncertainties in the ^{13}C secondary isotope shifts are smaller than those for ^{19}F, and this allows a better assignment of experimental values to the resonating nuclei. Using the calculated isotope shifts leads to assignments given in ^{2}H)norbornane and ^{2}H)norbornane for carbons 4 and 5.

In the present study, we demonstrate how calculations of secondary isotope shifts can be used in order to distinguish different stereoisomers. Benchmark calculations for fluoroethane show, that compared to CCSD(T) calculations, secondary isotope shifts obtained at the MP2 level of theory exhibit an error in the order of 5%. While at the HF level of theory using triple-zeta basis sets, errors can amount 25%, this accuracy is usually still sufficient to even identify different conformers, as the relative secondary isotope effects often differ by more than 50% and sometimes even by an order of magnitude. Therefore, quantum chemical calculations of the differences in secondary isotope shifts can be applied in order to reliably distinguish between various compounds.

An example, where such calculations can be used to resolve ambiguous results in the literature are measurements by Lambert

The authors declare no conflict of interest.

Stanton, J.; Gauss, J.; Harding, M.; Szalay, P. CFOUR, Coupled-Cluster techiques for Computational Chemistry, a quantum-chemical program package; with contributions of Auer, A.A.

Isotropic shielding at CCSD(T)/qz2p level without vibrational corrections for ^{19}F is 426 ppm for ^{13}C_{1}is 115 ppm and for ^{13}C_{2}is 177 ppm.

_{N}

Banert, K. private communication. The NMR spectra of all deuterated 2-fluoronorbornanes were measured with the solvent CDCl3 at 22 °C. The solvent signal [δ(^{13}C) = 77.000] or the value of δ(^{19}F) = 0.000 for CFCl_{3}were utilized as reference standard. All isotope effects were determined after portion-wise adding of the non- deuterated 2-fluoronorbornane to the solution of the corresponding deuterium-labeled compound.

Sample Availability: Not available.

Fluoroethane without deuterium label (

Computed ^{19}F secondary isotope shifts of proposed products occurring from S_{N}_{N}^{19}F secondary isotope shifts obtained by Lambert

Secondary isotope shifts of fluoroethane in ppm with deuterium in gauche and antiperiplanar conformation at different levels of theory for the anharmonic force field _{rss}

_{rss} |
||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| ||||||||||||||

anti | ||||||||||||||

^{19}F ^{a} |
−0.417 | −0.354 | −0.446 | −0.382 | −0.437 | −0.368 | −0.461 | −0.384 | −0.483 | −0.400 | −0.513 | −0.430 | −0.493 | −0.411 |

^{13}C_{1} |
−0.004 | −0.011 | −0.003 | −0.010 | −0.008 | −0.015 | −0.005 | −0.012 | −0.010 | −0.016 | −0.009 | −0.016 | −0.008 | −0.015 |

^{13}C_{2} |
−0.266 | −0.267 | −0.265 | −0.266 | −0.240 | −0.240 | −0.267 | −0.269 | −0.242 | −0.242 | −0.240 | −0.242 | −0.253 | −0.254 |

gauche | ||||||||||||||

^{19}F ^{a} |
−0.142 | −0.115 | −0.156 | −0.130 | −0.142 | −0.114 | −0.157 | −0.126 | −0.156 | −0.124 | −0.180 | −0.148 | −0.191 | −0.158 |

^{13}C_{1} |
−0.033 | −0.038 | −0.030 | −0.036 | −0.039 | −0.044 | −0.036 | −0.041 | −0.043 | −0.047 | −0.041 | −0.045 | −0.041 | −0.045 |

^{13}C_{2} |
−0.269 | −0.270 | −0.267 | −0.268 | −0.248 | −0.248 | −0.270 | −0.271 | −0.249 | −0.250 | −0.246 | −0.248 | −0.262 | −0.263 |

| ||||||||||||||

Δ anti-gauche | ||||||||||||||

^{19}F |
−0.275 | −0.239 | −0.290 | −0.252 | −0.295 | −0.254 | −0.304 | −0.258 | −0.327 | −0.276 | −0.333 | −0.282 | −0.302 | −0.253 |

^{13}C_{1} |
0.029 | 0.027 | 0.027 | 0.026 | 0.031 | 0.029 | 0.031 | 0.029 | 0.033 | 0.031 | 0.032 | 0.029 | 0.033 | 0.030 |

^{13}C_{2} |
0.003 | 0.003 | 0.002 | 0.002 | 0.008 | 0.008 | 0.003 | 0.002 | 0.007 | 0.008 | 0.006 | 0.006 | 0.009 | 0.009 |

The experimental ^{19}F isotope shift is −0.244 ppm [

Secondary isotope shifts of

| |||||
---|---|---|---|---|---|

^{13}C_{1} |
−0.013 | −0.021 | −0.095 | 0.000 | −0.080 |

^{13}C_{2} |
−0.006 | −0.060 | 0.028 | −0.026 | 0.022 |

^{13}C_{3} |
−0.362 | −0.367 | −0.009 | −0.387 | 0.000 |

^{13}C_{4} |
−0.104 | −0.094 | −0.102 | −0.102 | −0.102 |

^{13}C_{5} |
−0.037 | −0.041 | −0.022 | −0.044 | −0.027 |

^{13}C_{6} |
0.004 | 0.004 | −0.024 | −0.005 | −0.032 |

^{13}C_{7} |
−0.022 | −0.011 | −0.344 | −0.030 | −0.341 |

^{19}F |
−0.291 | −0.108 | −0.049 | −0.359 | −0.064 |

Secondary isotope shifts of

| ||||||||
---|---|---|---|---|---|---|---|---|

^{13}C_{1} |
−0.113 | −0.006 | 0.008 | −0.087 | −0.082 | −0.112 | 0.007 | −0.088 |

^{13}C_{2} |
−0.385 | −0.032 | −0.038 | 0.016 | 0.001 | −0.408 | −0.038 | 0.021 |

^{13}C_{3} |
−0.112 | −0.328 | −0.359 | 0.003 | −0.027 | −0.115 | −0.350 | 0.000 |

^{13}C_{4} |
0.010 | −0.086 | −0.101 | −0.089 | −0.086 | 0.010 | −0.101 | −0.090 |

^{13}C_{5} |
0.001 | −0.038 | −0.040 | −0.022 | 0.008 | 0.000 | −0.050 | −0.028 |

^{13}C_{6} |
−0.020 | 0.003 | 0.001 | −0.023 | −0.014 | −0.024 | 0.000 | −0.028 |

^{13}C_{7} |
0.013 | −0.013 | 0.005 | −0.355 | −0.315 | 0.010 | 0.008 | −0.349 |

^{19}F |
−0.794 | −0.339 | −0.131 | −0.007 | 0.005 | −0.799 | −0.156 | −0.008 |