The relative magnitude of these two quantities determines the crossover temperature from the LS to HS state.

From experiment typical values of the energy difference Delta H are of the order of 1-5 kcal/mol (4-20 kJ/mol). Entropy differences are typically about 30-60 kJ/mol/K. (See table 1 in the Kepp paper below).

This relatively small difference in energy presents a challenge for computational quantum chemistry,

such as calculations based on density functional theory, because of the strong electron correlations associated with the transition metal ions,

Over the past few years some authors have done nice systematic studies of a wide range of compounds with a wide range of DFT exchange-correlation (XC) functionals. Here I will focus on two papers.

Benchmarking Density Functional Methods for Calculation of State Energies of First Row Spin-Crossover Molecules

Jordi Cirera, Mireia Via-Nadal, and Eliseo Ruiz

Theoretical Study of Spin Crossover in 30 Iron Complexes

Kasper P. Kepp

First, these studies are refreshing and important. Too many computational chemistry calculations are dubious because they do not do systematics.

Here I will just discuss the first paper.

Cirera et al. use 8 different XC functionals to study 20 different compounds. They find that only one (!) functional (TPSSh) correctly gives a low spin ground state for all the compounds, i.e. Delta H is positive.

The figure below nicely summarises the results.

Before one gets too excited that one has now found the "right" functional, one should note that when one uses TPSSh to calculate the crossover temperature there is little correlation with the experimental values.

To put all this in a broader context consider the hierarchal figure below which is in the spirit of the metaphor of Jacob's ladder proposed by John Perdew. [The figure is from here]. However, I do not think Jacob's ladder is the best Biblical metaphor.

This highlights the

*ad hoc*nature of DFT based calculations and that one is a long way from anything that should seriously be considered to be a true

*ab initio*calculation.

It should also be noted that all these calculations are for a single molecule in vacuum. However, the experiments are in the solid state (or solution) and so the energetics can be shifted by electrostatic screening and/or solvation. The crossover temperature (which can become a first-order phase transition) may also be shifted by intermolecular elastic interactions.

It is always nice to see ones work highlighted (and properly commented) in such an interesting blog! Way to go, and thanks a lot!

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