Line data Source code
1 : !--------------------------------------------------------------------------------
2 : ! Copyright (c) 2016 Peter Grünberg Institut, Forschungszentrum Jülich, Germany
3 : ! This file is part of FLEUR and available as free software under the conditions
4 : ! of the MIT license as expressed in the LICENSE file in more detail.
5 : !--------------------------------------------------------------------------------
6 :
7 : module m_wann_tlmw
8 : use m_juDFT
9 : contains
10 0 : subroutine wann_tlmw(
11 0 : > nwfs,lwf,mrwf,
12 0 : > l_nocosoc,spi,jspin,
13 0 : < tlmwf)
14 : c*********************************************************************
15 : c Express the angular part of the trial orbital
16 : c in terms of spherical harmonics.
17 : c Y. Mokrousov
18 : c*********************************************************************
19 : c Modifications for soc and noco.
20 : c Tidied-up version.
21 : c Frank Freimuth
22 : c*********************************************************************
23 :
24 : implicit none
25 :
26 : integer, intent (in) :: nwfs
27 : integer, intent (in) :: lwf(nwfs),mrwf(nwfs)
28 : logical, intent (in) :: l_nocosoc
29 : integer, intent (in) :: spi(nwfs),jspin
30 : complex, intent (out) :: tlmwf(0:3,-3:3,nwfs)
31 :
32 : integer :: nwf,l,lr,mr,m,i,ii,j,jj
33 : complex :: tlm(0:3,-3:3,1:7)
34 : complex :: ic
35 : intrinsic :: cmplx,sqrt,cos,sin
36 :
37 0 : ic = cmplx(0.,1.)
38 :
39 : c..in this part the 'primary' matrices for the basic non-hybridized
40 : c..states are constructed, the coefficients are written to the tlm
41 : c..these coefficients arise due to the fact that the tws comprise the
42 : c..real harmonics, while the wave functions operate in terms of normal
43 : c..ones
44 :
45 0 : tlm(:,:,:) = cmplx(0.,0.)
46 :
47 0 : do l = 0,3
48 :
49 0 : if (l.eq.0) then
50 : c..s-state
51 0 : tlm(0,0,1) = cmplx(1.,0.)
52 :
53 0 : elseif (l.eq.1) then
54 : c..pz-state
55 0 : tlm(1,0,1) = cmplx(1.,0.)
56 : c..px-state
57 0 : tlm(1,-1,2) = cmplx(1.,0.)/(sqrt(2.))
58 0 : tlm(1,1,2) = -cmplx(1.,0.)/(sqrt(2.))
59 : c..py-state
60 0 : tlm(1,-1,3) = ic/(sqrt(2.))
61 0 : tlm(1,1,3) = ic/(sqrt(2.))
62 :
63 0 : elseif (l.eq.2) then
64 : c..dz2-state
65 0 : tlm(2,0,1) = cmplx(1.,0.)
66 : c..dxz-state
67 0 : tlm(2,1,2) = -cmplx(1.,0.)/(sqrt(2.))
68 0 : tlm(2,-1,2) = cmplx(1.,0.)/(sqrt(2.))
69 : c..dyz-state
70 0 : tlm(2,1,3) = ic/(sqrt(2.))
71 0 : tlm(2,-1,3) = ic/(sqrt(2.))
72 : c..dx2-y2-state
73 0 : tlm(2,2,4) = cmplx(1.,0.)/(sqrt(2.))
74 0 : tlm(2,-2,4) = cmplx(1.,0.)/(sqrt(2.))
75 : c..dxy-state
76 0 : tlm(2,2,5) = -ic/(sqrt(2.))
77 0 : tlm(2,-2,5) = ic/(sqrt(2.))
78 :
79 : elseif (l.eq.3)then
80 : c..
81 0 : tlm(3,0,1) = cmplx(1.,0.)
82 : c..
83 0 : tlm(3,1,2) = -cmplx(1.,0.)/(sqrt(2.))
84 0 : tlm(3,-1,2) = cmplx(1.,0.)/(sqrt(2.))
85 : c..
86 0 : tlm(3,1,3) = ic/(sqrt(2.))
87 0 : tlm(3,-1,3) = ic/(sqrt(2.))
88 : c..
89 0 : tlm(3,2,4) = cmplx(1.,0.)/(sqrt(2.))
90 0 : tlm(3,-2,4) = cmplx(1.,0.)/(sqrt(2.))
91 : c..
92 0 : tlm(3,2,5) = -ic/(sqrt(2.))
93 0 : tlm(3,-2,5) = ic/(sqrt(2.))
94 : c..
95 0 : tlm(3,3,6) = -cmplx(1.,0.)/(sqrt(2.))
96 0 : tlm(3,-3,6) = cmplx(1.,0.)/(sqrt(2.))
97 : c..
98 0 : tlm(3,3,7) = ic/(sqrt(2.))
99 0 : tlm(3,-3,7) = ic/(sqrt(2.))
100 : else
101 : CALL juDFT_error("no tlm for this l",calledby ="wann_tlmw")
102 : endif
103 :
104 : enddo
105 :
106 : c..now we are ready for more complex hybridized states, which
107 : c..correspond to the negative values of lwf
108 :
109 0 : tlmwf(:,:,:) = cmplx(0.,0.)
110 :
111 0 : do nwf = 1,nwfs
112 :
113 0 : if( ((3-2*jspin).ne.spi(nwf)).and.l_nocosoc ) cycle
114 :
115 0 : lr = lwf(nwf)
116 0 : mr = mrwf(nwf)
117 :
118 0 : if (lr.ge.0) then
119 0 : tlmwf(lr,:,nwf) = tlm(lr,:,mr)
120 0 : elseif (lr.eq.-1) then
121 :
122 0 : if (mr.eq.1) then
123 : c..sp-1
124 0 : tlmwf(0,:,nwf) = (1./(sqrt(2.)))*tlm(0,:,1)
125 0 : tlmwf(1,:,nwf) = (1./(sqrt(2.)))*tlm(1,:,2)
126 0 : elseif (mr.eq.2) then
127 : c..sp-2
128 0 : tlmwf(0,:,nwf) = (1./(sqrt(2.)))*tlm(0,:,1)
129 0 : tlmwf(1,:,nwf) = -(1./(sqrt(2.)))*tlm(1,:,2)
130 : endif
131 :
132 0 : elseif (lr.eq.-2) then
133 :
134 0 : if (mr.eq.1) then
135 : c..sp2-1
136 0 : tlmwf(0,:,nwf) = (1./(sqrt(3.)))*tlm(0,:,1)
137 : tlmwf(1,:,nwf) = -(1./(sqrt(6.)))*tlm(1,:,2) +
138 0 : + (1./(sqrt(2.)))*tlm(1,:,3)
139 0 : elseif (mr.eq.2) then
140 : c..sp2-2
141 0 : tlmwf(0,:,nwf) = (1./(sqrt(3.)))*tlm(0,:,1)
142 : tlmwf(1,:,nwf) = -(1./(sqrt(6.)))*tlm(1,:,2)
143 0 : + -(1./(sqrt(2.)))*tlm(1,:,3)
144 0 : elseif (mr.eq.3) then
145 : c..sp2-3
146 0 : tlmwf(0,:,nwf) = (1./(sqrt(3.)))*tlm(0,:,1)
147 0 : tlmwf(1,:,nwf) = (2./(sqrt(6.)))*tlm(1,:,2)
148 : endif
149 :
150 0 : elseif (lr.eq.-3) then
151 :
152 0 : if (mr.eq.1) then
153 : c..sp3-1
154 0 : tlmwf(0,:,nwf) = 0.5*tlm(0,:,1)
155 0 : tlmwf(1,:,nwf) = 0.5*( tlm(1,:,2)+tlm(1,:,3)+tlm(1,:,1) )
156 0 : elseif (mr.eq.2) then
157 : c..sp3-2
158 0 : tlmwf(0,:,nwf) = 0.5*tlm(0,:,1)
159 0 : tlmwf(1,:,nwf) = 0.5*( tlm(1,:,2)-tlm(1,:,3)-tlm(1,:,1) )
160 0 : elseif (mr.eq.3) then
161 : c..sp3-4
162 0 : tlmwf(0,:,nwf) = 0.5*tlm(0,:,1)
163 0 : tlmwf(1,:,nwf) = 0.5*(-tlm(1,:,2)+tlm(1,:,3)-tlm(1,:,1) )
164 0 : elseif (mr.eq.4) then
165 : c..sp3-4
166 0 : tlmwf(0,:,nwf) = 0.5*tlm(0,:,1)
167 0 : tlmwf(1,:,nwf) = 0.5*(-tlm(1,:,2)-tlm(1,:,3)+tlm(1,:,1) )
168 : endif
169 :
170 0 : elseif (lr.eq.-4) then
171 :
172 0 : if (mr.eq.1) then
173 : c..sp3d-1
174 0 : tlmwf(0,:,nwf) = (1./(sqrt(3.)))*tlm(0,:,1)
175 : tlmwf(1,:,nwf) = -(1./(sqrt(6.)))*tlm(1,:,2)
176 0 : & +(1./(sqrt(2.)))*tlm(1,:,3)
177 0 : elseif (mr.eq.2) then
178 : c..sp3d-2
179 0 : tlmwf(0,:,nwf) = (1./(sqrt(3.)))*tlm(0,:,1)
180 : tlmwf(1,:,nwf) = -(1./(sqrt(6.)))*tlm(1,:,2)
181 0 : & -(1./(sqrt(2.)))*tlm(1,:,3)
182 0 : elseif (mr.eq.3) then
183 : c..sp3d-3
184 0 : tlmwf(0,:,nwf) = (1./(sqrt(3.)))*tlm(0,:,1)
185 0 : tlmwf(1,:,nwf) = (2./(sqrt(6.)))*tlm(1,:,2)
186 0 : elseif (mr.eq.4) then
187 : c..sp3d-4
188 0 : tlmwf(1,:,nwf) = (1./(sqrt(2.)))*tlm(1,:,1)
189 0 : tlmwf(2,:,nwf) = (1./(sqrt(2.)))*tlm(2,:,1)
190 0 : elseif (mr.eq.5) then
191 : c..sp3d-5
192 0 : tlmwf(1,:,nwf) = -(1./(sqrt(2.)))*tlm(1,:,1)
193 0 : tlmwf(2,:,nwf) = (1./(sqrt(2.)))*tlm(2,:,1)
194 : endif
195 :
196 0 : elseif (lr.eq.-5) then
197 :
198 0 : if (mr.eq.1) then
199 : c..sp3d2-1
200 0 : tlmwf(0,:,nwf) = (1./(sqrt(6.)))*tlm(0,:,1)
201 0 : tlmwf(1,:,nwf) = -(1./(sqrt(2.)))*tlm(1,:,2)
202 : tlmwf(2,:,nwf) = -(1./(sqrt(12.)))*tlm(2,:,1)
203 0 : & +0.5*tlm(2,:,4)
204 0 : elseif (mr.eq.2) then
205 : c..sp3d2-2
206 0 : tlmwf(0,:,nwf) = (1./(sqrt(6.)))*tlm(0,:,1)
207 0 : tlmwf(1,:,nwf) = (1./(sqrt(2.)))*tlm(1,:,2)
208 : tlmwf(2,:,nwf) = -(1./(sqrt(12.)))*tlm(2,:,1)
209 0 : & +0.5*tlm(2,:,4)
210 0 : elseif (mr.eq.3) then
211 : c..sp3d2-3
212 0 : tlmwf(0,:,nwf) = (1./(sqrt(6.)))*tlm(0,:,1)
213 0 : tlmwf(1,:,nwf) = -(1./(sqrt(2.)))*tlm(1,:,3)
214 : tlmwf(2,:,nwf) = -(1./(sqrt(12.)))*tlm(2,:,1)
215 0 : & -0.5*tlm(2,:,4)
216 0 : elseif (mr.eq.4) then
217 : c..sp3d2-4
218 0 : tlmwf(0,:,nwf) = (1./(sqrt(6.)))*tlm(0,:,1)
219 0 : tlmwf(1,:,nwf) = (1./(sqrt(2.)))*tlm(1,:,3)
220 : tlmwf(2,:,nwf) = -(1./(sqrt(12.)))*tlm(2,:,1)
221 0 : & -0.5*tlm(2,:,4)
222 0 : elseif (mr.eq.5) then
223 : c..sp3d2-5
224 0 : tlmwf(0,:,nwf) = (1./(sqrt(6.)))*tlm(0,:,1)
225 0 : tlmwf(1,:,nwf) = -(1./(sqrt(2.)))*tlm(1,:,1)
226 0 : tlmwf(2,:,nwf) = (1./(sqrt(3.)))*tlm(2,:,1)
227 0 : elseif (mr.eq.6) then
228 : c..sp3d2-5
229 0 : tlmwf(0,:,nwf) = (1./(sqrt(6.)))*tlm(0,:,1)
230 0 : tlmwf(1,:,nwf) = (1./(sqrt(2.)))*tlm(1,:,1)
231 0 : tlmwf(2,:,nwf) = (1./(sqrt(3.)))*tlm(2,:,1)
232 : endif
233 :
234 : else
235 0 : CALL juDFT_error("no tlmw for this lr",calledby="wann_tlmw")
236 : endif
237 :
238 : enddo
239 :
240 0 : end subroutine wann_tlmw
241 : end module m_wann_tlmw
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