<div dir="ltr">Dear Prof. Blaha and Wien2k users,<div><br></div><div>I would like to decompose f-orbitals into real basis like fz3, fxz2, fyz2, fxyz, fz(x2-y2), fx(x2-3y2), and fy(3x2-y2) by using "qtl" problem.</div>
<div><br></div><div>First, I set qsplit is 2 (real basis) in case.inq file and then run "x qtl" without the spin-orbit coupling in order to see the crystal field splitting.</div><div><br></div><div>When I saw "case.qtl" file, I found that the decomposed f-orbitals were named as A2, x(T1), y(T1), z(T1), ksi(T2), eta(T2), and zeta(T2).</div>
<div><br></div><div>My first question is these labeling are correct?</div><div><br></div><div>In my knowledge,</div><div>A2 = fxyz</div><div>x(T1) = fx3</div><div>y(T1) = fy3</div><div>z(T1) = fz3</div><div>
ksi(T2) = fx(z2-y2)</div><div>eta(T2) = fy(z2-x2)</div><div>zeta(T2) = fz(x2-y2)</div><div><br></div><div>but real basis are represented as sums of spherical harmonics (l, m) like</div><div>fz3 = (3, 0)</div><div>
fxz2 = (3, 1) - (3, -1)</div><div>fyz2 = (3, 1) + (3, -1)</div><div>fxyz = (3, 2) - (3, -2) <---- This one is exact same as A2 in the cubic harmonic set.</div><div>fz(x2-y2) = (3, 2) + (3, 2)</div>
<div>fx(x2-3y2) = (3, 3) - (3, -3)</div><div>fy(3x2-y2) = (3, 3) + (3, 3)</div><div><br></div><div>The real basis set is different from the cubic basis set, so that these labeling like A2, x(T1), y(T1), ... is not correct in my thought.</div>
<div><br></div><div>Second question is related to the print order of decomposed f-orbitals in "case.qtl" file.</div><div><br></div><div>When I draw the decomposed f-orbital labeled as z(T1) in "case.qtl" file, I realized that this was not z3, but exactly same as A2, that is xyz f-orbital.</div>
<div><br></div><div>I think print order is not correct in case of "qsplit = 2".</div><div><br></div><div>In my feeling, the print order is z(T1), x(T1), y(T1), A2, zeta(T2), ksi(T2), and eta(T2) in "case.qtl" file if these labeling were correct.</div>
<div><br></div><div>Any comments would be appreciated.</div><div><br></div><div><br></div><div>Best wishes,</div><div><br></div><div>Chang-Jong Kang</div></div>