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hehe

Member

Registered: 2025-10-30

Posts: 2

Yamaguchi Approximate spin projection method

Hi Tian Lu,
                I would like some advice on optimising transition metal complex (or treatment of the electronic energies of transition metal complex). I have a metal center with a radical nearby that is antiferromagnetically coupled.

With hybrid DFT (10-25% HF exchange), spin-contamination will obviously pop up due to the use of single KS determinant. Due to this issue, your broken-symmetry energy can get "infiltrated" by higher spin states (spin contamination). Yamaguchi suggests using an alpha parameter to approximate the pure-spin state using your BS energy and HS energy (correcting the energy due to spin contamination). This alpha term is calculated using the spin of your system at HS and BS.

Introduced in orca (https://orca-manual.mpi-muelheim.mpg.de … ion-eq-eap),
They have presented a way to not only correct this spin contaminated energy but additionally, get an analytical gradient (from this spin-correction energy surface) to carry out geometry optimsation in orca.

I have couple of questions regarding this

1) If Hybrid DFT (or DFT for that matter)'s exchange correlation function is designed to work well for its parameters. How is using a single alpha parameter consistently for all functionals (I suspect the alpha parameter will not change significantly across the same spin system unless significantly large HF % for the hybrid DFT) suppose to be robust for all hybrid DFT functionals?

2) However, at the same time, the exchange correlation functional is parameterised for well-defined spin eigen-states (non spin contaminated states). So, using Yamaguchi's method to correct the errors associated with BS energies sounds fair as well. Although i have seen arguments that it needs more attention if core is more polarised/not closed shell (Phys. Chem. Chem. Phys., 2015,17, 14375-14382)

I have seen several papers that do geometry optimisation without Yamaguchi method applied and then do a single point energy with the Yamaguchi AP correction term. This has usually resulted in match with experimental (which definitely can be concidental...)

Coming to my 3rd question
3) Is it fair to apply to both geometry optimisation and single point energies or is it ok to apply to only single point energies ?
i guess it is difficult to say considering that it may or maynot change geometries significantly and when it does, it becomes a considerable task?

Appreciate your thoughts on this matter as im unsure on how to treat my system in the best manner.

Kind regards,
hehe

sobereva

Tian Lu (Multiwfn developer)

From: Athens, Greece

Registered: 2017-09-11

Posts: 2,134

Website

Re: Yamaguchi Approximate spin projection method

Dear hehe,

1 The idea of Yamaguchi's approximate spin-projection (AP) method is independent to specific DFT functionals, it should work for most hybrid functionals. Chemical Physics Letters 483 (2009) 168–171 applied AP to B3LYP calculations and the result is satisfactory. So, at least, AP should also work well for PBE0, which is very suitable for studying transition metal complexes and have similar HF composition to B3LYP.

2 Using standard (i.e. without AP) symmetry-broken UKS formalism to optimize antiferromagnetic transition metal complexes is very common in literatures and the result is generally reasonable. AP may bring slight benefits in specific circumstances, see Chemical Physics Letters 442 (2007) 445–450 for example. When symmetry-broken UKS fails heavily in geometry optimization, simply including AP is unlikely helpful, and CASSCF or multi-reference methods should be used instead.

3 In most cases, using AP only for single point calculation and ignoring it in geometry optimization is safe.

Best,

Tian Lu

hehe

Member

Registered: 2025-10-30

Posts: 2

Re: Yamaguchi Approximate spin projection method

Thanks Tian Lu for your thoughts.

I will likely try standard approaches first and may test BS-DFT with AP for geometry optimisation of specific TS or intermediates.