Multiwfn forum

rikaaardoss

Member

Registered: 2020-07-29

Posts: 22

Question about spin contamination in Gaussian16

I have a small question regarding the assignment of spin contamination in a biradical (singlet) system. My output shows the following:

<Sx>= 0.0000 <Sy>= 0.0000 <Sz>= 0.0000 <S**2>= 0.9770 S= 0.6077
<L.S>= 0.00000000000
Annihilation of the first spin contaminant:
S**2 before annihilation 0.9770, after 0.2087

As far as I understand, in this case, the spin contaminant taken is 0.2087 and the value 0.9770 represents the multiplicity of my compound, my question is S=0.6077 exactly what does it mean?

Thank you in advance

R.

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

Website

Re: Question about spin contamination in Gaussian16

Ideal spin multiplicity of singlet is 0, therefore spin contamination currently is 0.9770. For an ideal singlet biradical, it is 1.0.

S is solved according to: S(S+1)=<S**2>

rikaaardoss

Member

Registered: 2020-07-29

Posts: 22

Re: Question about spin contamination in Gaussian16

Thanks for the answer, but it is not very clear to me. Why does a biradical singlet have a value of S = 1? Regarding the example I mentioned previously, the results show a high spin contamination?

R.

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

Website

Re: Question about spin contamination in Gaussian16

For ideal biradical singlet system, an alpha and a beta electron occupy an alpha spin orbital and a beta spin orbital, respectively, and the overlap between the two orbitals is negligible. While other occupied MOs are basically paired. In this case, according to the equation of evaluating expectation of S^2 operator in Section 3.100.5 of Multiwfn manual, <S^2> will be 1.0.

rikaaardoss

Member

Registered: 2020-07-29

Posts: 22

Re: Question about spin contamination in Gaussian16

Thanks for the clarification, I just have one last question: The values "0.6077" and "0.2087" what exactly do they refer to? What I thought was that 0.2087 was the spin contamination obtained after the annihilation process ( being the ideal value 0 for a singlet system, i.e. it is 20.87% contaminated).

R.

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

Website

Re: Question about spin contamination in Gaussian16

The larger the deviation of printed <S**2> to ideal <S**2>, the larger the spin contamination. However, there is no widely accepted definition of percentage spin contamination.