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documentation:tutorials:nio_ligand_field:temperature [2016/10/09 15:25] – created Maurits W. Haverkortdocumentation:tutorials:nio_ligand_field:temperature [2016/10/10 09:41] (current) – external edit 127.0.0.1
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 +{{indexmenu_n>4}}
 +====== Temperature ======
  
 +###
 +The effect of temperature can be added by calculating excited states and expectation values of excited states. The temperature dependent expectation value is then created using Boltzmann statistics.
 +###
 +
 +###
 +A small example:
 +<code Quanty Temperature.Quanty>
 +-- Sofar we calculated eigenstates and expectation values (or spectra) of these
 +-- eigenstates. At 0 K one would measure the expectation value of the lowest eigenstate
 +-- at finite temperature one would measure an average over several states weighted by
 +-- Boltzmann statistics. In this example we calculate the temperature dependent 
 +-- x-ray absorption spectra of NiO. (Ni L23 edge 2p to 3d) within the ligand-field
 +-- theory approximation
 +
 +-- The first part is an exact copy of example 41
 +
 +Verbosity(0)
 +
 +-- here we calculate the 2p to 3d x-ray absorption of NiO within the Ligand-field theory
 +-- approximation. The first part of the script is very much the same as calculating
 +-- the ground-state with the addition that we now also need a 2p core shell in the basis
 +
 +-- from the previous example we know that within NiO there are 3 states close to each other
 +-- and then there is an energy gap of about 1 eV. We thus only need to consider the 3
 +-- lowest states (Npsi=3 later on)
 +
 +NF=26
 +NB=0
 +IndexDn_2p={ 0, 2, 4}
 +IndexUp_2p={ 1, 3, 5}
 +IndexDn_3d={ 6, 8,10,12,14}
 +IndexUp_3d={ 7, 9,11,13,15}
 +IndexDn_Ld={16,18,20,22,24}
 +IndexUp_Ld={17,19,21,23,25}
 +
 +-- 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_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
 +
 +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})
 +
 +-- dipole transition
 +
 +t=math.sqrt(1/2)
 +
 +Akm = {{1,-1,t},{1, 1,-t}}
 +TXASx = NewOperator("CF", NF, IndexUp_3d, IndexDn_3d, IndexUp_2p, IndexDn_2p, Akm)
 +Akm = {{1,-1,t*I},{1, 1,t*I}}
 +TXASy = NewOperator("CF", NF, IndexUp_3d, IndexDn_3d, IndexUp_2p, IndexDn_2p, Akm)
 +Akm = {{1,0,1}}
 +TXASz = NewOperator("CF", NF, IndexUp_3d, IndexDn_3d, IndexUp_2p, IndexDn_2p, Akm)
 +
 +TXASr = t*(TXASx - I * TXASy)
 +TXASl =-t*(TXASx + I * TXASy)
 +
 +-- We follow the energy definitions as introduced in the group of G.A. Sawatzky (Groningen)
 +-- J. Zaanen, G.A. Sawatzky, and J.W. Allen PRL 55, 418 (1985)
 +-- for parameters of specific materials see
 +-- A.E. Bockquet et al. PRB 55, 1161 (1996)
 +-- After some initial discussion the energies U and Delta refer to the center of a configuration
 +-- The L^10 d^n   configuration has an energy 0
 +-- The L^9  d^n+1 configuration has an energy Delta
 +-- The L^8  d^n+2 configuration has an energy 2*Delta+Udd
 +--
 +-- If we relate this to the onsite energy of the L and d orbitals we find
 +-- 10 eL +  n    ed + n(n-1)     U/2 == 0
 +--  9 eL + (n+1) ed + (n+1)n     U/2 == Delta
 +--  8 eL + (n+2) ed + (n+1)(n+2) U/2 == 2*Delta+U
 +-- 3 equations with 2 unknowns, but with interdependence yield:
 +-- ed = (10*Delta-nd*(19+nd)*U/2)/(10+nd)
 +-- eL = nd*((1+nd)*Udd/2-Delta)/(10+nd)
 +--
 +-- For the final state we/they defined
 +-- The 2p^5 L^10 d^n+1 configuration has an energy 0
 +-- The 2p^5 L^9  d^n+2 configuration has an energy Delta + Udd - Upd
 +-- The 2p^5 L^8  d^n+3 configuration has an energy 2*Delta + 3*Udd - 2*Upd
 +--
 +-- If we relate this to the onsite energy of the p and d orbitals we find
 +-- 6 ep + 10 eL +  n    ed + n(n-1)     Udd/2 + 6 n     Upd == 0
 +-- 6 ep +  9 eL + (n+1) ed + (n+1)n     Udd/2 + 6 (n+1) Upd == Delta
 +-- 6 ep +  8 eL + (n+2) ed + (n+1)(n+2) Udd/2 + 6 (n+2) Upd == 2*Delta+Udd
 +-- 5 ep + 10 eL + (n+1) ed + (n+1)(n)   Udd/2 + 5 (n+1) Upd == 0
 +-- 5 ep +  9 eL + (n+2) ed + (n+2)(n+1) Udd/2 + 5 (n+2) Upd == Delta+Udd-Upd
 +-- 5 ep +  8 eL + (n+3) ed + (n+3)(n+2) Udd/2 + 5 (n+3) Upd == 2*Delta+3*Udd-2*Upd
 +-- 6 equations with 3 unknowns, but with interdependence yield:
 +-- epfinal = (10*Delta + (1+nd)*(nd*Udd/2-(10+nd)*Upd) / (16+nd)
 +-- edfinal = (10*Delta - nd*(31+nd)*Udd/2-90*Upd) / (16+nd)
 +-- eLfinal = ((1+nd)*(nd*Udd/2+6*Upd)-(6+nd)*Delta) / (16+nd)
 +--
 +-- 
 +-- 
 +-- note that ed-ep = Delta - nd * U and not Delta
 +-- note furthermore that ep and ed here are defined for the onsite energy if the system had
 +-- locally nd electrons in the d-shell. In DFT or Hartree Fock the d occupation is in the end not
 +-- nd and thus the onsite energy of the Kohn-Sham orbitals is not equal to ep and ed in model
 +-- calculations.
 +--
 +-- note furthermore that ep and eL actually should be different for most systems. We happily ignore this fact
 +-- 
 +-- We normally take U and Delta as experimentally determined parameters
 +
 +-- number of electrons (formal valence)
 +nd = 8
 +-- parameters from experiment (core level PES)
 +Udd     =  7.3
 +Upd     =  8.5
 +Delta   =  4.7
 +-- parameters obtained from DFT (PRB 85, 165113 (2012))
 +F2dd    = 11.14 
 +F4dd    =  6.87
 +F2pd    =  6.67
 +G1pd    =  4.92
 +G3pd    =  2.80
 +tenDq   =  0.56
 +tenDqL  =  1.44
 +Veg     =  2.06
 +Vt2g    =  1.21
 +zeta_3d =  0.081
 +zeta_2p = 11.51
 +Bz      =  0.000001
 +Hz      =  0.120
 +
 +ed      = (10*Delta-nd*(19+nd)*Udd/2)/(10+nd)
 +eL      = nd*((1+nd)*Udd/2-Delta)/(10+nd)
 +
 +epfinal = (10*Delta + (1+nd)*(nd*Udd/2-(10+nd)*Upd)) / (16+nd)
 +edfinal = (10*Delta - nd*(31+nd)*Udd/2-90*Upd) / (16+nd)
 +eLfinal = ((1+nd)*(nd*Udd/2+6*Upd) - (6+nd)*Delta) / (16+nd)
 +
 +F0dd    = Udd + (F2dd+F4dd) * 2/63
 +F0pd    = Upd + (1/15)*G1pd + (3/70)*G3pd
 +
 +Hamiltonian =  F0dd*OppF0_3d + F2dd*OppF2_3d + F4dd*OppF4_3d + zeta_3d*Oppldots_3d + Bz*(2*OppSz_3d + OppLz_3d) + Hz * OppSz_3d + tenDq*OpptenDq_3d + tenDqL*OpptenDq_Ld + Veg * OppVeg + Vt2g * OppVt2g + ed * OppN_3d + eL * OppN_Ld
 +            
 +XASHamiltonian =  F0dd*OppF0_3d + F2dd*OppF2_3d + F4dd*OppF4_3d + zeta_3d*Oppldots_3d + Bz*(2*OppSz_3d + OppLz_3d)+ Hz * OppSz_3d + tenDq*OpptenDq_3d + tenDqL*OpptenDq_Ld + Veg * OppVeg + Vt2g * OppVt2g + edfinal * OppN_3d + eLfinal * OppN_Ld + epfinal * OppN_2p + zeta_2p * Oppcldots + F0pd * OppUpdF0 + F2pd * OppUpdF2 + G1pd * OppUpdG1 + G3pd * OppUpdG3  
 +               
 +-- we now can create the lowest Npsi eigenstates:
 +Npsi=3
 +-- in order to make sure we have a filling of 8 electrons we need to define some restrictions
 +StartRestrictions = {NF, NB, {"000000 1111111111 0000000000",8,8}, {"111111 0000000000 1111111111",16,16}}
 +
 +psiList = Eigensystem(Hamiltonian, StartRestrictions, Npsi)
 +oppList={Hamiltonian, OppSsqr, OppLsqr, OppJsqr, OppSz_3d, OppLz_3d, Oppldots_3d, OppF2_3d, OppF4_3d, OppNeg_3d, OppNt2g_3d, OppNeg_Ld, OppNt2g_Ld, OppN_3d}
 +
 +-- print of some expectation values
 +
 +print("  #    <E>      <S^2>    <L^2>    <J^2>    <S_z^3d> <L_z^3d> <l.s>    <F[2]>   <F[4]>   <Neg^3d> <Nt2g^3d><Neg^Ld> <Nt2g^Ld><N^3d>");
 +for i = 1,#psiList do
 +  io.write(string.format("%3i ",i))
 +  for j = 1,#oppList do
 +    expectationvalue = Chop(psiList[i]*oppList[j]*psiList[i])
 +    io.write(string.format("%8.3f ",expectationvalue))
 +  end
 +  io.write("\n")
 +end
 +
 +-- We calculate the x-ray absorption spectra for z, right circular and left circular polarized light for the 3 lowest eigen-states. (9 spectra in total)
 +
 +XASSpectra = CreateSpectra(XASHamiltonian, {TXASz, TXASr, TXASl}, psiList, {{"Emin",-15}, {"Emax",25}, {"NE",2000}, {"Gamma",0.1}})
 +
 +-- and put some additional energy broadening on it (0.4 Gaussian and energy dependent lorenzian)
 +XASSpectra.Broaden(0.4, {{-3.7, 0.45}, {-2.2, 0.65}, { 0.0, 0.65}, { 1.0, 2.00}, { 6  , 2.00}, { 8  , 0.80}, {13.2, 0.80}, {14.0, 0.90}, {16.0, 0.90}, {17.0, 2.00}})
 +
 +-- and now we start to do things different in order to include temperature averaging
 +-- We have calculated three states. The energy of these states is:
 +Enlist = {}
 +for i=1,#psiList do
 +  Enlist[i] = psiList[i] * Hamiltonian * psiList[i]
 +end
 +-- In order to calculate occupation numbers we need to calculate E^(-Energy/(kb T))
 +-- If the ground-state has an energy of -3.5 eV and we calculate this pre-factor at a temperature
 +-- of 10 Kelvin we get E^(3.5/(10*8.6*10^(-5))) = 8.3 * 10^(1763) a number so large it does
 +-- not fit in the computer memory. The solution is simple, we need to make sure the lowest
 +-- energy is zero.
 +for i=2,#psiList do
 +  Enlist[i] = Enlist[i] - Enlist[1]
 +end
 +Enlist[1]=0
 +
 +-- Besides the energy I would like to look at the magnetic moment, both spin and angular part
 +-- so also here we calculate the expectation values in a list
 +Szlist = {}
 +Lzlist = {}
 +for i=1,#psiList do
 +  Szlist[i] = psiList[i] * OppSz_3d * psiList[i]
 +  Lzlist[i] = psiList[i] * OppLz_3d * psiList[i]
 +end
 +
 +-- We can now calcualte the temperature dependent expectation values:
 +p={}
 +print("Temperature, Total Energy,  Magnetic Moment, Sz,            Lz")
 +for T=1,1000,10 do
 +  Z=0
 +  SzT=0
 +  LzT=0
 +  ET=0
 +  for i=1,#psiList do
 +    p[i] = exp(-Enlist[i]/(EnergyUnits.Kelvin.value * T))
 +    Z = Z + p[i]
 +    SzT = SzT + p[i] * Szlist[i]
 +    LzT = LzT + p[i] * Lzlist[i]
 +    ET  = ET  + p[i] * Enlist[i]
 +  end
 +  SzT = SzT / Z
 +  LzT = LzT / Z
 +  MzT = -LzT - 2*SzT
 +  
 +  io.write(string.format("%8i ",T))
 +  io.write(string.format("%14.8f ",ET))
 +  io.write(string.format("%14.8f   ",MzT))
 +  io.write(string.format("%14.8f ",SzT))
 +  io.write(string.format("%14.8f\n",LzT))
 +end
 +
 +-- Note that in order to see the magnetic phase transition you need to make Hz in the Hamiltonian
 +-- temperature dependent. This can be done using self consistent loops. (The mathematica version
 +-- has an example of this, will make it here at some point as well)
 +
 +-- The first column shows you how much energy you need to add to the system in order to heat
 +-- it. (specific heat) Be aware though that most of the specific heat is due to phonons, not
 +-- included in this calculation. It does capture nicely the electronic contribution to the
 +-- specific heat. (Including the change at cross overs for excited states (important in rare-
 +-- earth systems) and Lambda peaks for phase transitions
 +
 +-- Now the temperature dependent XAS:
 +
 +-- The object XASSpectra contains 9 spectra. For 3 different polarizations and 3 different states
 +-- What we need to do is to sum them according to Boltzmann statistics.
 +
 +T = 100
 +Z=0
 +for i=1,#psiList do
 +  p[i] = exp(-Enlist[i]/(EnergyUnits.Kelvin.value * T))
 +  Z = Z + p[i]
 +end
 +-- we now create the Bolzmann summ for z, right and left polarized absorption (at T=100 Kelvin)
 +XASSpectraT100 = Spectra.Sum(XASSpectra,{p[1]/Z,p[2]/Z,p[3]/Z, 0,0,0, 0,0,0},{0,0,0, p[1]/Z,p[2]/Z,p[3]/Z, 0,0,0},{0,0,0, 0,0,0, p[1]/Z,p[2]/Z,p[3]/Z})
 +
 +-- and the same at 1000 Kelvin
 +T = 1000
 +Z=0
 +for i=1,#psiList do
 +  p[i] = exp(-Enlist[i]/(EnergyUnits.Kelvin.value * T))
 +  Z = Z + p[i]
 +end
 +-- we now create the Bolzmann summ for z, right and left polarized absorption (at T=1000 Kelvin) (note again that we still have a large magnetization here as the exchange-field is not temperature dependent)
 +XASSpectraT1000 = Spectra.Sum(XASSpectra,{p[1]/Z,p[2]/Z,p[3]/Z, 0,0,0, 0,0,0},{0,0,0, p[1]/Z,p[2]/Z,p[3]/Z, 0,0,0},{0,0,0, 0,0,0, p[1]/Z,p[2]/Z,p[3]/Z})
 +
 +
 +-- We can print the spectra to file
 +XASSpectraT100.Print({{"file","XASSpectraT100.dat"}})
 +XASSpectraT1000.Print({{"file","XASSpectraT1000.dat"}})
 +
 +
 +gnuplotInput = [[
 +set autoscale 
 +set xtic auto 
 +set ytic auto 
 +set style line  1 lt 1 lw 1 lc rgb "#0000FF"
 +set style line  2 lt 1 lw 1 lc rgb "#FF0000"
 +set style line  3 lt 1 lw 1 lc rgb "#00FF00"
 +
 +set xlabel "E (eV)" font "Times,12"
 +set ylabel "Intensity (arb. units)" font "Times,12"
 +
 +set out 'XASSpecT.ps'
 +set size 1.0, 0.6
 +set terminal postscript portrait enhanced color  "Times" 12
 +
 +energyshift=857.6
 +intensityscale=48
 +set xrange [847:877]
 +
 +plot "XASSpectraT100.dat"  using ($1+energyshift):((-$3-$5-$7) * intensityscale) title 'isotropic theory T=100K' with lines ls 1,\
 +     "XASSpectraT1000.dat" using ($1+energyshift):((-$3-$5-$7) * intensityscale) title 'isotropic theory T=1000K' with lines ls 2,\
 +     "NiO_Experiment/XAS_L23_PRB_57_11623_1998" using 1:2 title 'isotropic experiment' with lines ls 3,\
 +     "XASSpectraT100.dat"  using ($1+energyshift):(($5-$7) * intensityscale) title 'XMCD theory T=100K' with lines ls 1,\
 +     "XASSpectraT1000.dat" using ($1+energyshift):(($5-$7) * intensityscale) title 'XMCD theory T=1000K' with lines ls 2
 +
 +
 +
 +]]
 +
 +-- write the gnuplot script to a file
 +file = io.open("XASSpecT.gnuplot", "w")
 +file:write(gnuplotInput)
 +file:close()
 +
 +-- and finally call gnuplot to execute the script
 +os.execute("gnuplot XASSpecT.gnuplot")
 +-- as I like pdf to view and eps to include in the manuel I transform the format
 +os.execute(" ps2pdf XASSpecT.ps ; ps2eps XASSpecT.ps ;  mv XASSpecT.eps temp.eps ; eps2eps temp.eps XASSpecT.eps ; rm temp.eps")
 +</code>
 +###
 +
 +###
 +The output is:
 +<file Quanty_Output Temperature.out>
 +  #    <E>      <S^2>    <L^2>    <J^2>    <S_z^3d> <L_z^3d> <l.s>    <F[2]>   <F[4]>   <Neg^3d> <Nt2g^3d><Neg^Ld> <Nt2g^Ld><N^3d>
 +  1   -3.503    1.999   12.000   15.095   -0.908   -0.281   -0.305   -1.042   -0.924    2.186    5.990    3.825    6.000    8.175 
 +  2   -3.395    1.999   12.000   15.160   -0.004   -0.002   -0.322   -1.043   -0.925    2.189    5.988    3.823    6.000    8.178 
 +  3   -3.286    1.999   12.000   15.211    0.903    0.278   -0.336   -1.043   -0.925    2.193    5.987    3.820    6.000    8.180 
 +Temperature, Total Energy,  Magnetic Moment, Sz,            Lz
 +       1     0.00000000     2.09639244      -0.90751752    -0.28135740
 +      11     0.00000000     2.09639244      -0.90751752    -0.28135740
 +      21     0.00000000     2.09639244      -0.90751752    -0.28135740
 +      31     0.00000000     2.09639244      -0.90751752    -0.28135740
 +      41     0.00000000     2.09639244      -0.90751752    -0.28135740
 +      51     0.00000000     2.09639244      -0.90751752    -0.28135740
 +      61     0.00000000     2.09639244      -0.90751752    -0.28135740
 +      71     0.00000000     2.09639240      -0.90751750    -0.28135739
 +      81     0.00000002     2.09639208      -0.90751736    -0.28135735
 +      91     0.00000011     2.09639041      -0.90751664    -0.28135713
 +     101     0.00000042     2.09638445      -0.90751406    -0.28135633
 +     111     0.00000128     2.09636784      -0.90750687    -0.28135410
 +     121     0.00000327     2.09632960      -0.90749031    -0.28134898
 +     131     0.00000724     2.09625331      -0.90745727    -0.28133877
 +     141     0.00001431     2.09611725      -0.90739835    -0.28132054
 +     151     0.00002587     2.09589513      -0.90730217    -0.28129080
 +     161     0.00004345     2.09555736      -0.90715590    -0.28124556
 +     171     0.00006869     2.09507255      -0.90694596    -0.28118063
 +     181     0.00010326     2.09440895      -0.90665860    -0.28109175
 +     191     0.00014878     2.09353581      -0.90628050    -0.28097481
 +     201     0.00020678     2.09242436      -0.90579920    -0.28082596
 +     211     0.00027865     2.09104862      -0.90520345    -0.28064171
 +     221     0.00036565     2.08938584      -0.90448341    -0.28041902
 +     231     0.00046884     2.08741683      -0.90363076    -0.28015531
 +     241     0.00058915     2.08512592      -0.90263871    -0.27984850
 +     251     0.00072732     2.08250098      -0.90150202    -0.27949695
 +     261     0.00088395     2.07953318      -0.90021685    -0.27909949
 +     271     0.00105950     2.07621676      -0.89878071    -0.27865534
 +     281     0.00125430     2.07254875      -0.89719232    -0.27816410
 +     291     0.00146857     2.06852868      -0.89545148    -0.27762573
 +     301     0.00170243     2.06415828      -0.89355892    -0.27704043
 +     311     0.00195590     2.05944119      -0.89151624    -0.27640872
 +     321     0.00222896     2.05438273      -0.88932572    -0.27573129
 +     331     0.00252149     2.04898959      -0.88699027    -0.27500905
 +     341     0.00283333     2.04326969      -0.88451332    -0.27424305
 +     351     0.00316429     2.03723192      -0.88189871    -0.27343450
 +     361     0.00351411     2.03088598      -0.87915065    -0.27258468
 +     371     0.00388252     2.02424225      -0.87627363    -0.27169500
 +     381     0.00426920     2.01731161      -0.87327236    -0.27076690
 +     391     0.00467384     2.01010537      -0.87015173    -0.26980191
 +     401     0.00509608     2.00263511      -0.86691677    -0.26880157
 +     411     0.00553555     1.99491262      -0.86357258    -0.26776747
 +     421     0.00599187     1.98694984      -0.86012432    -0.26670120
 +     431     0.00646466     1.97875875      -0.85657719    -0.26560437
 +     441     0.00695351     1.97035131      -0.85293636    -0.26447859
 +     451     0.00745802     1.96173945      -0.84920700    -0.26332544
 +     461     0.00797777     1.95293497      -0.84539423    -0.26214651
 +     471     0.00851235     1.94394955      -0.84150309    -0.26094337
 +     481     0.00906134     1.93479468      -0.83753856    -0.25971755
 +     491     0.00962431     1.92548164      -0.83350554    -0.25847056
 +     501     0.01020084     1.91602149      -0.82940880    -0.25720389
 +     511     0.01079052     1.90642502      -0.82525301    -0.25591899
 +     521     0.01139292     1.89670276      -0.82104276    -0.25461725
 +     531     0.01200762     1.88686496      -0.81678245    -0.25330005
 +     541     0.01263421     1.87692156      -0.81247641    -0.25196873
 +     551     0.01327227     1.86688221      -0.80812881    -0.25062458
 +     561     0.01392140     1.85675621      -0.80374369    -0.24926884
 +     571     0.01458119     1.84655259      -0.79932494    -0.24790272
 +     581     0.01525123     1.83628003      -0.79487633    -0.24652738
 +     591     0.01593114     1.82594688      -0.79040147    -0.24514394
 +     601     0.01662053     1.81556118      -0.78590385    -0.24375348
 +     611     0.01731900     1.80513065      -0.78138681    -0.24235703
 +     621     0.01802619     1.79466269      -0.77685356    -0.24095557
 +     631     0.01874172     1.78416436      -0.77230714    -0.23955007
 +     641     0.01946523     1.77364244      -0.76775051    -0.23814142
 +     651     0.02019636     1.76310338      -0.76318645    -0.23673048
 +     661     0.02093476     1.75255334      -0.75861763    -0.23531809
 +     671     0.02168008     1.74199819      -0.75404658    -0.23390503
 +     681     0.02243199     1.73144349      -0.74947573    -0.23249203
 +     691     0.02319017     1.72089454      -0.74490736    -0.23107982
 +     701     0.02395428     1.71035636      -0.74034365    -0.22966906
 +     711     0.02472402     1.69983370      -0.73578666    -0.22826038
 +     721     0.02549907     1.68933105      -0.73123833    -0.22685440
 +     731     0.02627915     1.67885267      -0.72670050    -0.22545167
 +     741     0.02706395     1.66840255      -0.72217491    -0.22405274
 +     751     0.02785320     1.65798447      -0.71766318    -0.22265810
 +     761     0.02864662     1.64760198      -0.71316687    -0.22126824
 +     771     0.02944393     1.63725840      -0.70868740    -0.21988360
 +     781     0.03024489     1.62695686      -0.70422614    -0.21850459
 +     791     0.03104922     1.61670029      -0.69978434    -0.21713161
 +     801     0.03185669     1.60649141      -0.69536319    -0.21576503
 +     811     0.03266706     1.59633277      -0.69096380    -0.21440517
 +     821     0.03348008     1.58622675      -0.68658719    -0.21305237
 +     831     0.03429555     1.57617555      -0.68223432    -0.21170691
 +     841     0.03511323     1.56618121      -0.67790606    -0.21036908
 +     851     0.03593291     1.55624561      -0.67360325    -0.20903911
 +     861     0.03675440     1.54637050      -0.66932663    -0.20771725
 +     871     0.03757748     1.53655749      -0.66507689    -0.20640371
 +     881     0.03840196     1.52680804      -0.66085468    -0.20509868
 +     891     0.03922767     1.51712348      -0.65666057    -0.20380234
 +     901     0.04005441     1.50750505      -0.65249509    -0.20251486
 +     911     0.04088201     1.49795385      -0.64835873    -0.20123639
 +     921     0.04171030     1.48847088      -0.64425191    -0.19996706
 +     931     0.04253913     1.47905702      -0.64017502    -0.19870698
 +     941     0.04336832     1.46971308      -0.63612841    -0.19745627
 +     951     0.04419774     1.46043977      -0.63211237    -0.19621502
 +     961     0.04502722     1.45123768      -0.62812719    -0.19498331
 +     971     0.04585664     1.44210737      -0.62417308    -0.19376121
 +     981     0.04668585     1.43304928      -0.62025025    -0.19254878
 +     991     0.04751472     1.42406379      -0.61635886    -0.19134607
 +</file>
 +###
 +
 +
 +===== Table of contents =====
 +{{indexmenu>.#1|msort}}

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