A Continuous Transferable Core-Valence Geometry Correction

Core-valence (CV) correlation causes systematic milliangstrom-scale bond contractions in main-group molecules. We develop an analytic radial model for the structural all-electron-frozen-core (AE-FC) correction otherwise obtained from explicit second-order Møller-Plesset perturbation theory (MP2) calculations. Calibrated once at the MP2/cc-pwCVTZ level, the model can be applied to geometries generated with different FC parent methods. The data set comprises 11 atomic references, 91 molecular systems, 145 radial scans, 116 angular scans, and 9966 molecular geometries with paired AE and FC energies. After atomic-reference subtraction, radial profiles are accurately described by A + B exp(Cr), whereas angular profiles are much smaller near equilibrium and serve as validation data. The model therefore targets the geometry-driving CV response rather than the full CV energy itself. The fitted field reproduces AE-FC bond shifts obtained from independent AE and FC optimizations with r = 0.973 and a root-mean-square residual of 0.512 mÅ. Analysis of the optimized geometries supports the reduction of bond-class parameters to additive atomic increments and reveals period- and group-dependent trends. The compressed correction transfers without refitting to larger held-out H/C/O molecules and enables direct transformation of FC into AE geometries without additional all-electron optimizations.