SCS-MP2 on molecular crystals

Background

Cohesive energies of molecular crystals are a stringent test for electronic-structure methods, because the binding is dominated by weak interactions that cheap methods miss. The cohesive energy per molecule is written as

$$E_\mathrm{coh} = \frac{E_\mathrm{bulk}}{Z} - E_\mathrm{mol},$$

where $E_\mathrm{bulk}$ is the energy of the crystal unit cell, $Z$ is the number of molecules in that cell, and $E_\mathrm{mol}$ is the energy of an isolated molecule. Experimental sublimation enthalpies pin this quantity down tightly, and a method’s errors thus show up directly. The paper behind this repository asks whether periodic spin-component-scaled MP2 can deliver kJ/mol accuracy on the X23 benchmark set of 23 molecular crystals.

Spin-component scaling

MP2 correlation energy separates into contributions from opposite-spin and same-spin electron pairs, and the SCS family of methods rescales the two pieces independently. The scaled correlation energy reads

$$E_\mathrm{corr} = c_\mathrm{os}\, E_\mathrm{os} + c_\mathrm{ss}\, E_\mathrm{ss},$$

where $E_\mathrm{os}$ and $E_\mathrm{ss}$ are the opposite-spin and same-spin pair energies and $c_\mathrm{os}$, $c_\mathrm{ss}$ are empirical coefficients. Plain MP2 corresponds to setting both coefficients to one. The appeal for molecular crystals is that a cheap reweighting of quantities MP2 already computes might repair its known biases for noncovalent binding.

Convergence

Getting a defensible answer required converging every number to both the thermodynamic limit and the complete-basis-set limit, which the study does to about 2 kJ/mol precision. At that level of control, the residual disagreement with experiment belongs to the method rather than to the calculation. The converged results give a mean absolute error of 12.9 kJ/mol against experimental cohesive energies, comparable to dispersion-corrected DFT of the PBE+TS type.

Repository

This repository keeps the pieces a reader would need to redo or reuse that work. The crystal and molecule geometries are provided in both xyz and VASP cell formats, alongside the custom augmented cc-pVXZ basis sets built for the basis-convergence study. Two worksheets carry the numbers behind the paper’s tables, one with the cohesive energies, basis-set extrapolation fits, and BSSE estimation, and one documenting basis-set convergence across basis sizes.

With Hong-Zhou Ye and Tim Berkelbach at Columbia. Everything is Apache-licensed so the results can be reproduced or repurposed.