关注：

1)  自旋-轨道耦合一般发生在重金属原子上

2)  电子之间的强关联作用也可以发生在氢原子上

Parameter-free calculation of single-particle electronic excitations in YH3. Physical Review B, 2002, 66(7): 075104.

The second explanation for the large gap in YH3 and LaH3 involves strong local electron-electron interactions. The discrepancy between the calculated band overlap and the observed optical gap of YH3 is almost 4 eV. This is comparable to what is found in transition metal oxides such as NiO.
In the latter material strong on-site correlations between localized
d electrons play an important role and are poorly
described by the LDA. B

Based on this analogy, it was suggested
that YH3 is a strongly correlated system with strong
on-site interactions between two electrons on a hydrogen
site.

   A number of groups have pursued this idea and have
studied model Hamiltonians of a nearest neighbor tightbinding
type, modified by on-site and/or nearest neighbor
two-electron terms. The parameters in these models are then
                   fitted to results obtained from ~constrained! LDA calculavan      

tions, and/or from molecular calculations that incorporate
correlation explicitly, or have been simply estimated.

Most of
the focus has been on LaH3 because its cubic structure
makes it much easier to treat.
Wang and Chen considered a lattice of hydrogen atoms
including on-site ~Hubbard! and nearest-neighbor twoelectron
Coulomb interactions, which supress the accumulation
of electrons on hydrogen sites.3 

Exact diagonalization
of this Hamiltonian for a cluster of hydrogen atoms does not
produce a gap, so they concluded that LaH3 cannot be
viewed as a Hubbard-type correlation-driven insulator 

In all of these model approaches a crucial role is assigned
to rather different forms of electron correlation. Because
only a very limited number of the two-electron terms can be
included in any calculation, the final results of the calculations
rely heavily on the choice of parameters in the model.
Since the main goal of these calculations is to improve upon
the LDA calculations, it is surprising that not more attention
is paid to the more obvious shortcomings of an LDA calculation.
In the first place there is a well-known problem with
the LDA lowest Kohn-Sham level in the single electron hydrogen
atom.36 Although the total energy of H0 is near the
expected value of 21 Ry, the one-electron energy level lies
at ;20.5 Ry instead of at 21 Ry. In an LDA calculation
one therefore expects the bands derived from the atomic hydrogen
1s state to be positioned too high in energy. Correcting

size of the correction would depend of course on the effective
valence of hydrogen in YH3 and the shift of 0.7 eV
proposed by Ng et al.34 seems to be only a lower bound. In
the second place there is the ‘‘band gap’’ problem of LDA
calculations discussed above. Finally, we note that the quoted
experimental gap is deduced from optical experiments so
that, depending on the optical matrix elements the optical
gap may be very different from the fundamental band gap
deduced from a band structure. As an example, the fundamental
gap in silicon is 1.2 eV, whereas the direct optical gap
is 3.4 eV.
Quasiparticle calculations within the so-called GW approximation
are a practical means to obtain accurate band
structures without using arbitrary fit parameters,37,38 and accurate
band gaps have been obtained for a wide range of
semiconductors and insulators using this scheme.37,38 Remarkably,
GW calculations even produce not unreasonable
gaps for materials with strong on-site interactions such as
NiO ~Ref. 39! and MnO.40
for this artifact might by itself produce a gap in YH3. The