Predictive coupled-cluster isomer orderings for some Si${}_n$C${}_m$ ($m, n\le 12$) clusters; A pragmatic comparison between DFT and complete basis limit coupled-cluster benchmarks

Abstract

The accurate determination of the preferred ${\rm Si}_{12}{\rm C}_{12}$ isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC$_3$ to ${\rm Si}_{12}{\rm C}_{12}$. It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and CCSD extrapolation with triple-$\zeta$ (T) correlation, the {\it closo} ${\rm Si}_{12}{\rm C}_{12}$ isomer is identified to be the preferred isomer in support of previous calculations [J. Chem. Phys. 2015, 142, 034303]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post MBPT(2) correlation energy is found to be an excellent balance between efficiency and accuracy.