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 — documentation:tutorials:nio_ligand_field:fy_rixs_nixs_include [2016/10/10 09:41] (current) 2016/10/09 15:35 Maurits W. Haverkort created 2016/10/09 15:35 Maurits W. Haverkort created Line 1: Line 1: + {{indexmenu_n>​5}} + ====== FY RIXS nIXS include ====== + ### + In order to shorten the examples, make them better readable and focus more on the new part introduced in the calculation we split the input file into several parts which are saved as separate files. The input file attached here defines all operators and calculates the ground-state. The tutorials use these to calculate spectra. + ### + + ​ + -- The example on Fluorescence yield, RIXS and non-resonant IXS all need a very similar + -- starting point. We need to define the Ground-state and some operators on this state. + -- We need to define Hamiltonians with either a 2p or 3s core hole and interactions between + -- these. ​ + + -- Here we create a file that is included in tutorials later + + Verbosity(0) + + NF=28 + NB=0 + IndexDn_2p={ 0, 2, 4} + IndexUp_2p={ 1, 3, 5} + IndexDn_3s={ 6} + IndexUp_3s={ 7} + IndexDn_3d={ 8,​10,​12,​14,​16} + IndexUp_3d={ 9,​11,​13,​15,​17} + IndexDn_Ld={18,​20,​22,​24,​26} + IndexUp_Ld={19,​21,​23,​25,​27} + + -- angular momentum operators on the d-shell + + OppSx_3d ​  ​=NewOperator("​Sx" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppSy_3d ​  ​=NewOperator("​Sy" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppSz_3d ​  ​=NewOperator("​Sz" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppSsqr_3d =NewOperator("​Ssqr"​ ,NF, IndexUp_3d, IndexDn_3d) + OppSplus_3d=NewOperator("​Splus",​NF,​ IndexUp_3d, IndexDn_3d) + OppSmin_3d =NewOperator("​Smin"​ ,NF, IndexUp_3d, IndexDn_3d) + + OppLx_3d ​  ​=NewOperator("​Lx" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppLy_3d ​  ​=NewOperator("​Ly" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppLz_3d ​  ​=NewOperator("​Lz" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppLsqr_3d =NewOperator("​Lsqr"​ ,NF, IndexUp_3d, IndexDn_3d) + OppLplus_3d=NewOperator("​Lplus",​NF,​ IndexUp_3d, IndexDn_3d) + OppLmin_3d =NewOperator("​Lmin"​ ,NF, IndexUp_3d, IndexDn_3d) + + OppJx_3d ​  ​=NewOperator("​Jx" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppJy_3d ​  ​=NewOperator("​Jy" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppJz_3d ​  ​=NewOperator("​Jz" ​  ,NF, IndexUp_3d, IndexDn_3d) + OppJsqr_3d =NewOperator("​Jsqr"​ ,NF, IndexUp_3d, IndexDn_3d) + OppJplus_3d=NewOperator("​Jplus",​NF,​ IndexUp_3d, IndexDn_3d) + OppJmin_3d =NewOperator("​Jmin"​ ,NF, IndexUp_3d, IndexDn_3d) + + Oppldots_3d=NewOperator("​ldots",​NF,​ IndexUp_3d, IndexDn_3d) + + -- Angular momentum operators on the Ligand shell + + OppSx_Ld ​  ​=NewOperator("​Sx" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppSy_Ld ​  ​=NewOperator("​Sy" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppSz_Ld ​  ​=NewOperator("​Sz" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppSsqr_Ld =NewOperator("​Ssqr"​ ,NF, IndexUp_Ld, IndexDn_Ld) + OppSplus_Ld=NewOperator("​Splus",​NF,​ IndexUp_Ld, IndexDn_Ld) + OppSmin_Ld =NewOperator("​Smin"​ ,NF, IndexUp_Ld, IndexDn_Ld) + + OppLx_Ld ​  ​=NewOperator("​Lx" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppLy_Ld ​  ​=NewOperator("​Ly" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppLz_Ld ​  ​=NewOperator("​Lz" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppLsqr_Ld =NewOperator("​Lsqr"​ ,NF, IndexUp_Ld, IndexDn_Ld) + OppLplus_Ld=NewOperator("​Lplus",​NF,​ IndexUp_Ld, IndexDn_Ld) + OppLmin_Ld =NewOperator("​Lmin"​ ,NF, IndexUp_Ld, IndexDn_Ld) + + OppJx_Ld ​  ​=NewOperator("​Jx" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppJy_Ld ​  ​=NewOperator("​Jy" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppJz_Ld ​  ​=NewOperator("​Jz" ​  ,NF, IndexUp_Ld, IndexDn_Ld) + OppJsqr_Ld =NewOperator("​Jsqr"​ ,NF, IndexUp_Ld, IndexDn_Ld) + OppJplus_Ld=NewOperator("​Jplus",​NF,​ IndexUp_Ld, IndexDn_Ld) + OppJmin_Ld =NewOperator("​Jmin"​ ,NF, IndexUp_Ld, IndexDn_Ld) + + -- total angular momentum + OppSx = OppSx_3d + OppSx_Ld + OppSy = OppSy_3d + OppSy_Ld + OppSz = OppSz_3d + OppSz_Ld + OppSsqr = OppSx * OppSx + OppSy * OppSy + OppSz * OppSz + OppLx = OppLx_3d + OppLx_Ld + OppLy = OppLy_3d + OppLy_Ld + OppLz = OppLz_3d + OppLz_Ld + OppLsqr = OppLx * OppLx + OppLy * OppLy + OppLz * OppLz + OppJx = OppJx_3d + OppJx_Ld + OppJy = OppJy_3d + OppJy_Ld + OppJz = OppJz_3d + OppJz_Ld + OppJsqr = OppJx * OppJx + OppJy * OppJy + OppJz * OppJz + + -- define the coulomb operator + -- we here define the part depending on F0 seperately from the part depending on F2 + -- when summing we can put in the numerical values of the slater integrals + + OppF0_3d =NewOperator("​U",​ NF, IndexUp_3d, IndexDn_3d, {1,0,0}) + OppF2_3d =NewOperator("​U",​ NF, IndexUp_3d, IndexDn_3d, {0,1,0}) + OppF4_3d =NewOperator("​U",​ NF, IndexUp_3d, IndexDn_3d, {0,0,1}) + + -- define onsite energies - crystal field + -- Akm = {{k1,​m1,​Akm1},​{k2,​m2,​Akm2},​ ... } + + Akm = PotentialExpandedOnClm("​Oh",​ 2, {0.6,-0.4}) + OpptenDq_3d = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, Akm) + OpptenDq_Ld = NewOperator("​CF",​ NF, IndexUp_Ld, IndexDn_Ld, Akm) + + Akm = PotentialExpandedOnClm("​Oh",​ 2, {1,0}) + OppNeg_3d = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, Akm) + OppNeg_Ld = NewOperator("​CF",​ NF, IndexUp_Ld, IndexDn_Ld, Akm) + Akm = PotentialExpandedOnClm("​Oh",​ 2, {0,1}) + OppNt2g_3d = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, Akm) + OppNt2g_Ld = NewOperator("​CF",​ NF, IndexUp_Ld, IndexDn_Ld, Akm) + + OppNUp_2p = NewOperator("​Number",​ NF, IndexUp_2p, IndexUp_2p, {1,1,1}) + OppNDn_2p = NewOperator("​Number",​ NF, IndexDn_2p, IndexDn_2p, {1,1,1}) + OppN_2p = OppNUp_2p + OppNDn_2p + OppNUp_3s = NewOperator("​Number",​ NF, IndexUp_3s, IndexUp_3s, {1}) + OppNDn_3s = NewOperator("​Number",​ NF, IndexDn_3s, IndexDn_3s, {1}) + OppN_3s = OppNUp_3s + OppNDn_3s + OppNUp_3d = NewOperator("​Number",​ NF, IndexUp_3d, IndexUp_3d, {1,​1,​1,​1,​1}) + OppNDn_3d = NewOperator("​Number",​ NF, IndexDn_3d, IndexDn_3d, {1,​1,​1,​1,​1}) + OppN_3d = OppNUp_3d + OppNDn_3d + OppNUp_Ld = NewOperator("​Number",​ NF, IndexUp_Ld, IndexUp_Ld, {1,​1,​1,​1,​1}) + OppNDn_Ld = NewOperator("​Number",​ NF, IndexDn_Ld, IndexDn_Ld, {1,​1,​1,​1,​1}) + OppN_Ld = OppNUp_Ld + OppNDn_Ld + + -- define L-d interaction + + Akm = PotentialExpandedOnClm("​Oh",​ 2, {1,0}) + OppVeg ​ = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, IndexUp_Ld, IndexDn_Ld,​Akm) +  NewOperator("​CF",​ NF, IndexUp_Ld, IndexDn_Ld, IndexUp_3d, IndexDn_3d, Akm) + Akm = PotentialExpandedOnClm("​Oh",​ 2, {0,1}) + OppVt2g = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, IndexUp_Ld, IndexDn_Ld,​Akm) +  NewOperator("​CF",​ NF, IndexUp_Ld, IndexDn_Ld, IndexUp_3d, IndexDn_3d, Akm) + + -- core valence interaction 2p to 3d + + Oppcldots= NewOperator("​ldots",​ NF, IndexUp_2p, IndexDn_2p) + OppUpdF0 = NewOperator("​U",​ NF, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {1,0}, {0,0}) + OppUpdF2 = NewOperator("​U",​ NF, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {0,1}, {0,0}) + OppUpdG1 = NewOperator("​U",​ NF, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {0,0}, {1,0}) + OppUpdG3 = NewOperator("​U",​ NF, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {0,0}, {0,1}) + + -- core valence interaction 3s to 3d + + OppUsdF0 = NewOperator("​U",​ NF, IndexUp_3s, IndexDn_3s, IndexUp_3d, IndexDn_3d, {1}, {0}) + OppUsdG2 = NewOperator("​U",​ NF, IndexUp_3s, IndexDn_3s, IndexUp_3d, IndexDn_3d, {0}, {1}) + + -- next we define the dipole operator. The dipole operator is given as epsilon.r + -- with epsilon the polarization vector of the light and r the unit position vector + -- We can expand the position vector on (renormalized) spherical harmonics and use + -- the crystal-field operator to create the dipole operator. ​ + + -- we both define the dipole operator between the 2p and 3d shell as well as the dipole ​ + -- operator between the 3s and 2p shell + + -- x polarized light is defined as x = Cos[phi]Sin[theta] = sqrt(1/2) ( C_1^{(-1)} - C_1^{(1)}) + Akm = {{1,​-1,​sqrt(1/​2)},​{1,​ 1,​-sqrt(1/​2)}} + T2p3dx = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, IndexUp_2p, IndexDn_2p, Akm) + T3s2px = NewOperator("​CF",​ NF, IndexUp_2p, IndexDn_2p, IndexUp_3s, IndexDn_3s, Akm) + -- y polarized light is defined as y = Sin[phi]Sin[theta] = sqrt(1/2) I ( C_1^{(-1)} + C_1^{(1)}) + Akm = {{1,​-1,​sqrt(1/​2)*I},​{1,​ 1,​sqrt(1/​2)*I}} + T2p3dy = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, IndexUp_2p, IndexDn_2p, Akm) + T3s2py = NewOperator("​CF",​ NF, IndexUp_2p, IndexDn_2p, IndexUp_3s, IndexDn_3s, Akm) + -- z polarized light is defined as z = Cos[theta] = C_1^{(0)} + Akm = {{1,0,1}} + T2p3dz = NewOperator("​CF",​ NF, IndexUp_3d, IndexDn_3d, IndexUp_2p, IndexDn_2p, Akm) + T3s2pz = NewOperator("​CF",​ NF, IndexUp_2p, IndexDn_2p, IndexUp_3s, IndexDn_3s, Akm) + + -- besides linear polarized light one can define circular polarized light as the sum of + -- x and y polarizations with complex prefactors + T2p3dr = sqrt(1/​2)*(T2p3dx - I * T2p3dy) + T2p3dl =-sqrt(1/​2)*(T2p3dx + I * T2p3dy) + + -- we can remove zero's from the dipole operator by chopping it. + T2p3dr.Chop() + T2p3dl.Chop() + + -- the 3d to 2p dipole transition is the conjugate transpose of the 2p to 3d dipole transition + T3d2px = ConjugateTranspose(T2p3dx) + T3d2py = ConjugateTranspose(T2p3dy) + T3d2pz = ConjugateTranspose(T2p3dz) + T3d2pl = ConjugateTranspose(T2p3dl) + T3d2pr = ConjugateTranspose(T2p3dr) + ​ + + + ===== Table of contents ===== + {{indexmenu>​.#​1|msort}}