Approaching the Complete Basis Set Limit for Transition Metal Spin–State Energetics

24 January 2024, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


Convergence to the complete basis set (CBS) limit is analyzed for the problem of transition metal (TM) spin-state energetics by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term, (T#). This computational protocol recovers relative spin–state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation 0.4, mean signed deviation 0.2, and maximum deviation 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin–state energetics calculated using CCSD(T) and other wave-function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, MRCI+Q), which justifies efficient focal-point approximations and simplifies construction of multi-method benchmark studies.


spin states
transition metal complexes
basis set incompleteness error
complete basis set limit
explicitly correlated methods
heme models

Supplementary materials

Supporting Information
Additional tables and figures, complete references.


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.