I would like to calculate the anisotropic susceptibility of certain molecules, that is, I would like to know how the magnetic susceptibility of the molecule changes as a function of orientation within a magnetic field.
I have access to Gaussian and Molpro as well as some other software packages but I'm not sure where to begin. Has anyone done this before that could point me in the right direction?
Thanks
Consult Problem 9.5, p. 309, of the book Quantum Theory of Many-Particle Systems (Dover, New York, 2003), by AL Fetter, and JD Walecka. By expressing the spin operators in the definition of the magnetic susceptibility in terms of the fermion field operators (the relevant expression is presented in the same problem), it becomes immediately apparent that the magnetic susceptibility is deduced from the two-particle Green function. Similar diagrammatic expansions apply for the two-particle Green function as for the one-particle Green function.
The magnetic susceptibility can also be deduced from the grand potential Ω calculated for a Hamiltonian that includes an external magnetic field as a source term. For the relevant formalism, you may wish to consult the paper by Kenn Kubo: Prog. Theor. Phys. 64, 758 (1980). For the general case, the second-order derivative with respect to the constant external magnetic field (in Eq. (12)) is to be in general replaced by the second-order functional derivative with respect to a spatially-varying external magnetic field. See also Chapter 2 of the book The Theory of Magnetism II, by DC Mattis (Springer, Berlin, 1985).
Thank you very much, Behnam Farid. That is a lot of information for an experimental chemist like me to chew on but it's at least given me somewhere to start!
You are welcome Jason. I did not realise that you are an experimental chemist. Certainly, the formulation of the problem does not suggest so.
Incidentally, with regard to the two-particle Green function, the book by G Stefanucci and R van Leeuwen -- Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge University Press, 2013) -- contains some relatively extensive discussions of it (in particular, on the subject of conserving approximations).
Orca (https://orcaforum.cec.mpg.de/) is very good for computing magnetic properties.
You'll need to do some multiconfigurational calculations (eg. CASSCF) calculations.
Have a look at Atanasov and Nees's paper and the supplementary info for guidance
http://pubs.rsc.org/en/Content/ArticleLanding/2013/SC/c2sc21394j#!divAbstract
Also, look at the ORCA CASSCF tutorial that comes with version 4 of the program.
For the calculation of magnetic susceptibility you need to calculate the spin-Hamiltonian parameters first. For example, if it is a transition metal or lanthanides then you have to calculate zero-field splitting(g,D & E), exchange parameters(J) It can be done using ORCA, MOLCAS softwares. And also you can fit or simulate your data with experimental point using PHI software.
This requires some CASSCF type calculations as mentioned by Keith Hughes above.
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