Analyzing the stable isotopic ratio of Ca offers valuable insights into a wide range of applications, from climate reconstruction to bone cancer diagnosis and agricultural nutrient improvement. While the first hydration shell of Ca in solution is expected to play a major role in its fractionation properties, the coordination of Ca in water remains a subject of debate. In this work, Ca 2+ in water has been modeled by means of ab initio molecular dynamics simulations using various exchange and correlation functionals and at different temperatures. Results show a significant effect of the functional on the average Ca 2+ coordination, depending on its tendency to over-or under-structure liquid water. The BLYP functional with Grimme-D2 correction was judged as the most accurate among those tested, based on its accuracy to reproduce water structural and diffusion properties. Using this functional, the effect of temperature has been systematically investigated, focusing on means to limit the uncertainty in our assessments of the average coordination of Ca 2+ ions by (1) estimating the number of water exchanges in the simulations, and (2) implementing a statistical approach based on Markov chains.

The findings indicate, especially, that our simulations at 300K, 350K, and 400K do not yield converged results, due to potential equilibration problems. These observations impose substantial constraints on the trustworthiness of numerous estimates in the existing literature that depend on trajectories with insufficient exchanges. We estimate Ca 2+ coordination values of 6.8 ± 0.1, 6.8 ± 0.1, 6.7 ± 0.2 and 6.7 ± 0.2 at 600, 550, 500 and 450K respectively. At lower temperatures (300, 350, and 400K), while obtaining definitive values for Ca 2+ coordination remains challenging, our research does indicate a potential temperature-related influence on coordination with an average Ca 2+ coordination at 300K as low as 6.2.