Calculation of multipolar exchange interactions remains a challenging issue in many aspects. Although there were many works based on fitting the model Hamiltonians with experiments, predictions of the coupling constants based on first-principle schemes remain lacking. Currently there are two studies implemented first-principles approach to explore multipolar exchange interactions. An early study was developed in 80's. It is based on a mean field approach that can greatly reduce the complexity of coupling constants induced by RKKY mechanism, so the multipolar exchange Hamiltonian can be described by just a few unknown parameters and can be obtained by fitting with experiment data.<ref>R.{{cite journal | last=Siemann and| B.first=Robert R.| last2=Cooper,Phys.| Rev.first2=Bernard LettR. 44,| 1015title=Planar Coupling Mechanism Explaining Anomalous Magnetic Structures in Cerium and Actinide Intermetallics | journal=Physical Review Letters | publisher=American Physical Society (1980APS) | volume=44 | issue=15 | date=14 April 1980 | issn=0031-9007 | doi=10.1103/physrevlett.44.1015 | pages=1015–1019}}</ref> Later on, a first-principles approach to estimate the unknown parameters was further developed and got good agreements with a few selected compounds, e.g. cerium momnpnictides.<ref>J.{{cite M.journal | last=Wills and| B.first=John RM. | last2=Cooper,Phys.| Revfirst2=Bernard R. | title=First-principles calculations for a model Hamiltonian treatment of hybridizing light actinide compounds | journal=Physical Review B 42,| 4682publisher=American Physical Society (1990APS) | volume=42 | issue=7 | date=1 August 1990 | issn=0163-1829 | doi=10.1103/physrevb.42.4682 | pages=4682–4693}}</ref> Another first-principle approach was also proposed recently.<ref name="multipolar exchange"/> It maps all the coupling constants induced by all static exchange mechanisms to a series of DFT+U total energy calculations and got agreement with uranium dioxide.
