Origin of ¹³C NMR chemical shifts elucidated based on molecular orbital theory: paramagnetic contributions from orbital-to-orbital transitions for the pre-α, α, β, α-X, β-X and ipso-X effects, along with effects from characteristic bonds and groups

¹³C NMR chemical shifts (δ(C)) were analysed via MO theory, together with the origin, using σ ^d(C), σ ^p(C) and σ ^t(C), where C^4- was selected as the standard for the analysis since σ ^p(C: C^4-) = 0 ppm. An excellent relationship was observed between σ ^d(C) and the charges on C for (C⁴⁺, C²⁺, C⁰, C^2- and C^4-) and (C^4-, CH₂ ^2-, CH₃ ^- and CH₄). However, such a relationship was not observed for the carbon species other than those above. The occupied-to-unoccupied orbital (ψ _i →ψ _a ) transitions were mainly employed for the analysis. The origin was explained by the pre-α, α, β, α-X, β-X and ipso-X effects. The pre-α effect of an approximately 20 ppm downfield shift is theoretically predicted, and the observed α and β effects of approximately 10-15 ppm downfield shifts are well reproduced by the calculations, as are the variations in the α-X, β-X and ipso-X effects. Large downfield shifts caused by the formation of ethene (∼120 ppm), ethyne (∼60 ppm) and benzene (∼126 ppm) from ethane and carbonyl (∼146 ppm) and carboxyl (∼110 ppm) groups from CH₃OH are also reproduced well by the calculations. The analysis and illustration of σ ^p(C) through the ψ _i →ψ _a transitions enables us to visualize the effects and to understand the δ(C) values for the C atoms in the specific positions of the species. The occupied-to-occupied orbital (ψ _i →ψ _j ) transitions are also examined. The theoretical investigations reproduce the observed results of δ(C). The origin for δ(C) and the mechanism are visualized, which allows us to image the process in principle. The role of C in the specific position of a compound in question can be more easily understood, which will aid in the development of highly functional compounds based on NMR.