Close Relationships between NMR J-Coupling Alternation (JCA) and Molecular Properties of Carbon Chains

We propose a J-coupling alternation (JCA) value that is demonstrated to be a suitable parameter to evaluate the nuclear magnetic resonance (NMR) indirect spin-spin coupling constants (SSCCs) as a function of molecular properties of chains by increasing their length. As an application, we report a theoretical study of the SSCCs for the interactions between neighbor nuclei in increasingly patterned carbon chains within density functional theory. First, we examine the J-coupling constants between ¹H and ¹³C nuclei ( ⁿ J_HC) considering the separation distance, as well as between two adjacent ¹³C nuclei (¹ J_CC) considering their relative positions in polyynes and cumulenes. Further, we define and determine JCA in terms of the differences of ¹ J_CC, which is investigated as a function of several molecular properties, e.g., cohesive energy, characteristic vibrational frequency, average polarizability, and energy gap of the systems. We also determine JCA for other types of carbon chains, such as diphenyl-capped polyynes, polyacetylene and polythiophene. The behavior of JCA as a function of the energy gap may be related to highly π-conjugated low-band-gap carbon chains. Overall, JCA correlates very well with the electronic properties of these chains, especially with their energy gap, exhibiting positive values for pristine polyyne and polythiophene and negative values for pristine cumulene and plyacetylene. These findings indicate an alternative way to establish an appropriate SSCC descriptor that characterizes the electronic nature of the system, such as the proposed JCA value averaging the whole system, instead of using only the individual J-coupling values to give insights into the properties of large and extended systems.