Origin of the additive relationship for 13C NMR chemical shifts of alkanes as studied by ab initio GIAO calculations

Abstract

¹³ C NMR chemical shifts for conformers of alkanes from methane to heptane were calculated by the ab initio GIAO method. Conformationally averaged calculated chemical shifts were satisfactorily correlated with the corresponding experimental chemical shifts measured in solutions, yielding an additive relationship by using the additive shift parameters as defined for the experimental additive relationship. For the individual calculated ¹³C chemical shifts of the alkane conformers, a new additive relationship was successfully constructed by employing four substituent and eight conformation additive shift parameters. It is elucidated that the mere presence of the γ(C_{k± 3})-carbon brings about an upfield shift for the C_k carbon despite the conformation of the 2(C_{k± 1}–C_{k± 2})-bond, and that the presence of the 1(C_k–C_{k± 1})-, 2-, and/or successive 2,3(C_{k± 1}–C_{k± 2}–C_{k± 3})-gauche bonds results in notable upfield shifts for the C_k carbon: the former two effects are related with the so-called vicinal- and γ-gauche effects, respectively. Additive relationships for the anisotropy and the symmetry parameter of the ¹³C chemical shift tensors were also examined.