Molecular Origin of ³¹P NMR Chemical Shifts of Phosphate Groups with Bivalent Counterions

The electrostatic interactions of phosphate groups and counterions critically affect the structure, function, and reactivity of DNA or RNA. We present a joint experimental-theoretical investigation of dimethyl phosphate (DMP^-) in aqueous solution, an established model system of the sugar-phosphate backbone. ³¹P NMR spectroscopy, as a probe of phosphate-ion association, reveals a systematic shielding of the ³¹P chemical shift (δ_iso(³¹P)) with variations of Mg²⁺ and Ca²⁺ content and moderate temperature dependence. Enhanced sampling molecular dynamics (MD) and ab initio (GIAO-DF-LMP2) level of theory are used to reveal the microscopic mechanism. Simulations are performed for a configurational ensemble of DMP^--ion geometries and their first solvation shells, demonstrating (i) the spatial convergence of changes of the nuclear shielding constant σ_iso(³¹P), (ii) the intramolecular geometric origin of short-time scale σ_iso(³¹P) fluctuations, and (iii) an average shift of σ_iso(³¹P) of about 3-8 ppm upon contact ion pair formation with Mg²⁺ or Ca²⁺ ions. A quantitative analysis of δ_iso(³¹P) for varying ion content and temperature allows us to extract the temperature-dependent fraction of the contact ion pair species, indicating that solvent-separated or free ion pairs are the energetically preferred species. The results impose boundary conditions for improvements of phosphate ion force fields and establish the interactions underlying the changes of δ_iso(³¹P).