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quadrupole.f90
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module quadrupole
use accuracy, only : hik, ik, rk, ark, cl, out,&
vellgt, planck, avogno, boltz, pi, small_
use diatom_module, only : job, Intensity, quantaT, eigen, basis,&
nQuadrupoles, quadrupoletm, duo_j0, fieldT, poten,&
three_j, jmin_global
use timer, only : IOstart, Arraystart, Arraystop, ArrayMinus,&
Timerstart, Timerstop, MemoryReport, &
TimerReport, memory_limit, memory_now
use symmetry, only : sym, correlate_to_Cs
private
public qm_tranint
type ElevelT
integer(ik) :: jind ! J index
integer(ik) :: igamma
integer(ik) :: ilevel
end type ElevelT
type(ElevelT), allocatable :: Elevel(:)
integer(ik) :: nEigenLevels
! Wilfrid Somogyi: Routine for evaluating the quadrupole moment matrix elements
! and linestrength equations. Adapted from dipole.f90 for the
! case of a symmetric tensor of rank two.
contains
subroutine qm_tranint
! computes the partition function and calls qm_intensity to calculate
! the electric quadrupole transition moments, linestrengths and
! intensities if required.
implicit none
! counter, indexes, etc.
real(rk) :: jMin, jMax, jValMin, jVal_
integer(ik) :: nJ, jInd
integer(ik) :: indLevel, indGamma, indState, guParity, &
indSym
! calculation variables
real(rk) :: energy, beta, expEn, part
integer(ik) :: irrep
real(rk), allocatable :: jVal(:), qPart(:,:)
! assorted
integer(ik) :: info, iVerbose = 4
! find the min and max J values to compute transitions for
jMax = maxval(Intensity%J(1:2))
jMin = minval(Intensity%J(1:2))
jMin = max(jmin_global, jMin)
! now find lowest possible J value of system to make sure all
! energies J > 0 are included in line list file regardless of the
! value Intensity%J, otherwise energy list numbering will not be
! consistent with the actual J values.
jValMin = 0
if ( mod(nint(2.0_rk * job%j_list(1)), 2) /= 0 ) jValMin = 0.5_rk
jValMin = max(jmin_global, jValMin)
! now count number of J states
jVal_ = jValMin
nJ = 1
do while ( jVal_ < jMax )
jVal_ = jVal_ + 1.0_rk
nJ = nJ + 1
enddo
! prepare arrays to store J values and partition functions
allocate(jVal(nJ), stat=info)
if ( info /= 0 ) then
stop 'qm_tranint allocation error: jVal - out of memory'
endif
allocate(qPart(20, nJ), stat=info)
if ( info /= 0 ) then
stop 'qm_tranint allocation error: qPart - out of memory'
endif
! add J values to array
jVal_ = jValMin
jInd = 1
Jval(jind) = Jval_
do while (Jval_<Jmax)
jind = jind + 1
Jval_ = Jval_ + 1.0_rk
Jval(jind) = Jval_
end do
call duo_j0(iverbose, jVal)
if ( job%shift_to_zpe ) then
do jInd = 1, nJ
jVal_ = jVal(jInd)
do indGamma = 1, sym%NrepresCs
!
irrep = correlate_to_Cs(indGamma, guParity)
!
do indLevel = 1, eigen(jInd, indGamma)%Nlevels
!
! for homonuclear Nrepres = 4 and the irrep can be
! reconstructed from parity and g/u
!
indState = eigen(jInd, indGamma)%quanta(indLevel)%istate
guParity = poten(indState)%parity%gu
indSym = correlate_to_Cs(indGamma, guParity)
!
if (Intensity%gns(indSym)<small_) cycle
! if energy of state < ZPE then adjust ZPE
energy = eigen(jInd, indGamma)%val(indLevel)
Intensity%ZPE = min(Intensity%ZPE, energy)
enddo
enddo
enddo
! write out result
if ( iverbose >= 2 ) then
write(out, '(/"Zero point energy (ZPE) = ",f18.6,"&
& (global zero, used for intensities)")') Intensity%ZPE
endif
if ( iverbose >= 4 ) then
write(out, "(/'Partition function = ',f18.4,'&
& T = ',f12.2)") Intensity%part_func, Intensity%temperature
endif
endif
select case ( trim(Intensity%action) )
case('ABSORPTION', 'EMISSION', 'TM')
call Sort_levels(iVerbose, nJ, jVal(1:nJ))
beta = planck * vellgt / (boltz * Intensity%temperature)
if ( Intensity%part_func < small_ ) then
Intensity%part_func = 0
do jInd = 1, nJ
jVal_ = jVal(jInd)
do indGamma = 1, sym%NrepresCs
do indLevel = 1, eigen(jInd, indGamma)%Nlevels
energy = eigen(jInd, indGamma)%val(indLevel)
irrep = eigen(jInd, indGamma)%quanta(indLevel)%igamma
! for homonuclear Nrepres = 4 and the irrep can be
! reconstructed from parity and g/u
indState = eigen(jInd, indGamma)%quanta(indLevel)%istate
guParity = poten(indState)%parity%gu
indSym = correlate_to_Cs(indGamma, guParity)
! calculate the Boltzmann exponent of the energy
expEn = exp( -(energy - Intensity%ZPE) * beta)
! add to partition function
Intensity%part_func = Intensity%part_func &
& + Intensity%gns(indSym) &
& * (2.0_rk*jVal_ + 1.0_rk) * expEn
enddo
enddo
enddo
! write out result
if ( iVerbose >= 4 ) then
write(out, &
"(/'Partition function = ',f18.4,' T = ',f12.2)" &
) intensity%part_func, intensity%temperature
endif
endif
! if absorption, emission of tm then calculate linestrengths
call qm_intensity(jVal, iVerbose)
write(out, '(/a)') 'done'
case('PARTFUNC')
write(out, '(/a)') 'compute partition function'
qPart = 0
do jInd = 1, nJ
jVal_ = jVal(jInd)
do indGamma = 1, sym%NrepresCs
do indLevel = 1, eigen(jInd, indGamma)%Nlevels
energy = eigen(jInd, indGamma)%val(indLevel)
irrep = eigen(jInd, indGamma)%quanta(indLevel)%igamma
! for homonuclear Nrepres = 4 and the irrep can be
! reconstructed from parity and g/u
indState = eigen(jInd, indGamma)%quanta(indLevel)%istate
guParity = poten(indState)%parity%gu
indSym = correlate_to_Cs(indGamma, guParity)
! calculate the Boltzmann exponent of the energy
expEn = exp( -(energy - Intensity%ZPE) * beta)
! add to partition function
qPart(irrep, jInd) = qPart(irrep, jInd) &
& + Intensity%gns(indSym) &
& * (2.0_rk*jVal_ + 1.0_rk) * expEn
enddo
enddo
enddo
! sum of partition function
part = sum(qPart(:,:))
do jInd = 1, nJ
do irrep = 1, sym%NrepresCs
write(out, '(i4,1x,f18.1,1x,es16.8)') &
irrep, jVal(jInd), qPart(irrep, jInd)
enddo
enddo
! write out result
write(out, '(es16.8)') part
end select
call MemoryReport
call TimerReport
end subroutine qm_tranint
subroutine qm_intensity(Jval, iVerbose)
! performs the actual transition moment, linestrength and intensity
! calculations when called by qm_tranint
implicit none
! I/O variables
real(rk), intent(in) :: jVal(:)
integer(ik), intent(in) :: iVerbose
! filenames, identifiers, etc.
character(len=cl) :: filename, ioname
integer(ik) :: enunit, transUnit, info
integer(ik), allocatable :: richUnit(:, :)
character(len=130) :: myFmt
character(len=12) :: char_Jf, char_Ji, char_LF
character(len=1) :: letLFa, letLFb
character(len=2) :: letLF, dir
integer(ik) :: nDecimals, alloc_p
! indexes and counters
integer(ik) :: nJ, Jmax_, indJ, indI, indF, IDj
integer(ik) :: iLFa, iLFb, iLF, iflag_rich
integer(ik) :: nTrans, indTrans, nLower
integer(ik) :: indGamma, guParity, indTau, &
indGammaI, indGammaF, indSymI, indSymF
integer(ik) :: nLevels, nLevelsI, nLevelsF,&
indLevelI, indLevelF
integer(ik) :: nLevelsG(sym%Nrepresen)
integer(ik) :: indRoot, k, k_
! (pseudo) quantum numbers
real(rk), allocatable :: vecI(:), vecF(:)
type(quantaT), pointer :: quantaI, quantaF
real(rk) :: j_, jI, jF
integer(ik) :: ivibI, ivibF, vI, vF, ilambdaI, ilambdaF,parityI
integer(ik) :: vF_, ilambdaF_
real(rk) :: spinI, spinF, sigmaI, sigmaF, &
omegaI, omegaF
real(rk) :: spinF_, sigmaF_, iomegaF_
character(len=10) :: statename
character(len=1) :: ef, pm, branch
! calculation variables
real(rk) :: energyI, energyF
integer(ik) :: istateI, istateF
integer(ik) :: nRepresen, dimenMax, dimenI, dimenF, &
iGammaPair(sym%nRepresen)
real(hik) :: matSize
real(rk) :: beta, inten_cm_mol, emcoef, A_coef_s_1, &
A_einst, boltz_fc, absorption_int, unitConv, vacPerm
real(rk) :: lande, nu_if, lineStr, linestr2, tm, ddot
real(rk), allocatable :: halfLineStr(:)
! cash transitons
real(rk),allocatable :: acoef_RAM(:),nu_ram(:)
integer(ik),allocatable :: indexi_RAM(:),indexf_RAM(:)
! logicals
logical :: intSpin = .true.
logical :: passed, passed_
call TimerStart('Intensity calculations')
! define values of some constants
beta = planck * vellgt / (boltz * Intensity%temperature)
inten_cm_mol = 8.0d-36*pi**3 / (3.0_rk * planck * vellgt)
emcoef = planck*vellgt/(4.0_rk*pi)
!
! vacuum permittivity (NIST 2018) - needs to be
! properly programmed later
vacPerm = 8.8541878128d-12
! conversion factor for Q[a.u] -> Q[S.I],
! h[erg.s] -> h[J.s] and nu_if[/cm] -> nu_if[/m]
unitConv = 2.012914458d-62
! calculate the common factor for the Einstein coefficient
A_coef_s_1 = unitConv*(8.0_rk * pi**5)/(5.0_rk * vacPerm * planck)
!
if ( sym%maxdegen > 2) then
write(out, "('qm_intensity: this procedure has not been tested&
& for the symmetries with degeneracies higher than 2...&
& In fact, this procedure has not been tested at all!')" &
)
endif
nRepresen = sym%NrepresCs
! define number of J states from input
nJ = size(Jval)
if ( trim(Intensity%linelist_file) /= 'NONE' ) then
! prepare and open the .states file
filename = trim(Intensity%linelist_file)//'.states'
write(ioname, '(a, i4)') 'Energy file'
call IOStart(trim(ioname), enunit)
open(unit = enunit, action='write', &
status='replace', file=filename)
! prepare and open the .trans file
filename = trim(Intensity%linelist_file)//'.trans'
write(ioname, '(a, i4)') 'Transition file'
call IOStart(trim(ioname), transUnit)
open(unit = transUnit, action='write', &
status='replace', file=filename)
! calculate matrix elements
if ( Intensity%matelem ) then
! define maximum J value
Jmax_ = nint( maxval(Jval(:)) )
allocate( richUnit(nJ, nJ) )
! loop over initial J states
do indI = 1, nJ
! assign value of initial J and write as string to char_Ji
jI = Jval(indI)
write(char_Ji, '(i12)') nint(jI)
do indF = 1, nJ
! assign value of final J
! only loop over jF > jI, permute to calculate others
jF = Jval(indF)
if ( jF < jI) cycle
! J selection rules
if ( nint(abs(jI - jF)) > 2 &
.or. nint(jI + jF) < 2 &
) cycle
! write to file final J value as string to char_Jf
write(char_Jf, '(i12)') nint(jF)
! New RichMol format - one file for all components
filename = 'matelem_Q'//&
'_j'//trim(adjustl(char_Ji))//&
'_j'//trim(adjustl(char_Jf))//&
'_'//trim(Intensity%linelist_file)//'.rchm'
! open RichMol file for matrix elements between jI, jF
call IOstart(trim(filename), richUnit(indI, indF))
open(unit = richUnit(indI, indF), action='write', &
status = 'replace', file=filename)
! add headers to RichMol file
write(richUnit(indI, indF), "('Start richmol format')")
write(richUnit(indI, indF), "('Q ',' 2',' 9')")
write(richUnit(indI, indF), "('M-tensor')")
! nine cartesian LF-components
do iLFa = 1, 3
letLFa = 'x'
if ( iLFa > 3) letLFa = 'y'
if ( iLFa > 6) letLFa = 'z'
do iLFb = 1, 3
letLFb = 'x'
if ( iLFb == 2) letLFb = 'y'
if ( iLFb == 3) letLFb = 'z'
! concatenate first and second index and convert iLFa
! and iLFb to a single running index over all 9 comps.
! 1=xx, 2=xy, 3=xz, 4=yx, 5=yy, 6=yz, 7=zx, 8=zy, 9=zz
letLF = letLFa//letLFb
iLF = 3*(iLFa - 1) + iLFb
! flag for imaginary components
iflag_rich = -1
if ( iLFa == 2 .and. iLFb /= 2 &
.or. iLFa /= 2 .and. iLFb == 2 &
) iflag_rich = 0
write(char_LF, '(i12)') iLF
write(richUnit(indI, indF), "('alpha',i5,i3,1x,a2)") &
iLF, iflag_rich, letLF
! calculate the part of the matrix element equation
! that corresponds to the molecule -> lab transformation
call do_LF_matrix_elements(iLFa, iLFb, &
richUnit(indI, indF), &
jI, jF)
enddo
! heading for next section
write(richUnit(indI, indF), "('K-tensor')")
enddo
enddo
enddo
endif
endif
! estimate the maximum size of the basis set
dimenMax = 0
do indJ = 1, nJ
do indGamma = 1, nRepresen
dimenMax = max(dimenmax, eigen(indJ, indGamma)%Ndimen)
enddo
enddo
! count the number of transitions that need to be calculated first
! this will help keep track of the calculation progress, also count
! the number of lower levels from which transitions occur
nTrans = 0
nLower = 0
indRoot = 0
! number of initial states
nLevels = nEigenLevels
! for a given symmetry, iGamma, with some g_ns(iGamma) we find
! it's counterpart jGamma /= iGamma with the same g_ns(iGamma). It
! is assumed that there is only one such pair in the case of
! absorption and emission calculations
call find_igamma_pair(iGammaPair)
call TimerStart('Intens_Filter-1')
do indI = 1, nJ
jI = JVal(indI)
!
do indGammaI = 1, nRepresen
nLevelsI = eigen(indI, indGammaI)%Nlevels
do indLevelI = 1, nLevelsI
! obtain the energy and quanta of the initial state
energyI = eigen(indI, indGammaI)%val(indLevelI)
! obtain the symmetry of the initial state
istateI = eigen(indI, indGammaI)%quanta(indLevelI)%iState
guParity = poten(istateI)%parity%gu
indSymI = correlate_to_Cs(indGammaI, guParity)
! check energy of lower state is in range and > ZPE
call energy_filter_ul(jI, energyI, passed, 'lower')
if ( .not. passed ) cycle
nLower = nLower + 1
do indF = 1, nJ
jF = jVal(indF)
do indGammaF = 1, nRepresen
nLevelsF = eigen(indF, indGammaF)%Nlevels
do indLevelF = 1, nLevelsF
! obtain the energy and quanta of the final state
energyF = eigen(indF, indGammaF)%val(indLevelF)
! obtain the symmetry of the final state
istateF = eigen(indF, indGammaF)&
%quanta(indLevelF)%iState
guParity = poten(istateF)%parity%gu
indSymF = correlate_to_Cs(indGammaF, guParity)
! check the Intensity of the transition passes filter
call intens_filter(jI, jF, energyI, energyF, &
indSymI, indSymF, iGammaPair, &
passed)
if ( Intensity%matelem ) then
call matelem_filter(jI, jF, energyI, energyF, &
indSymI, indSymF, iGammaPair, &
passed)
endif
if ( passed ) then
nTrans = nTrans + 1
endif
enddo
enddo
enddo
enddo
enddo
enddo
call TimerStop('Intens_Filter-1')
! we now count the number of states with a given symmetry
nLevelsG = 0
if ( mod(eigen(1,1)%quanta(1)%imulti, 2) == 0) intSpin = .false.
allocate(vecI(dimenMax), stat = info)
call ArrayStart('intensity-vecI', info, size(vecI), kind(vecI))
do indI = 1, nJ
jI = jVal(indI)
j_ = -1 ! for output in RichMol format (w/ mat. elems.)
do indGammaI = 1, nRepresen
! number of initial levels
nLevelsI = eigen(indI, indGammaI)%Nlevels
dimenI = eigen(indI, indGammaI)%Ndimen
do indLevelI = 1, nLevelsI
! obtain the energy of the initial state
energyI = eigen(indI, indGammaI)%val(indLevelI)
! obtain the symmetry of the state
istateI = eigen(indI, indGammaI)%quanta(indLevelI)%istate
guParity = poten(istateI)%parity%gu
indSymI = correlate_to_Cs(indGammaI, guParity)
! ignore states with zero nuclear spin statistical weighting
if ( Intensity%gns(indSymI) < small_ ) cycle
! indRoot is a running number over states
indRoot = indRoot + 1
eigen(indI, indGammaI)%quanta(indLevelI)%iroot = indRoot
if ( trim(Intensity%linelist_file) /= 'NONE') then
! assign quantum numbers for initial state
quantaI => eigen(indI, indGammaI)%quanta(indLevelI)
ivibI = quantaI%ivib
vI = quantaI%v
spinI = quantaI%spin
sigmaI = quantaI%sigma
ilambdaI = quantaI%ilambda
omegaI = quantaI%omega
parityI = quantaI%iparity
statename = trim(quantaI%name)
! reconstruct +/- and e/f parities
if ( parityI == 1) then
pm = '-'
else
pm = '+'
endif
if ( mod( nint(2.0_rk*jI), 2 ) == 1 ) then
indTau = mod( nint(jI - 0.5), 2 )
else
indTau = mod( nint(jI), 2 )
endif
if ( indTau == parityI ) then
ef = 'e'
else
ef = 'f'
endif
! the variable nDecimals determines the number of decimal
! places to which we print the energy levels. By default we
! use 6 decimals for energies up to 100,000 /cm, sacrificing
! more for higher energies in order that the value fits
! within the 12 allocated character spaces. The present
! format works for energies -10,000 /cm < E < 1e11 /cm.
nDecimals = 6 - max(0, &
int(log10(abs(energyI - Intensity%ZPE) + 1.d-6) - 4))
! if requested, calculate and print the Lande g-factor for
! the selected eigenstate
if ( Intensity%lande_calc ) then
lande = 0
vecI(1:dimenI) = eigen(indI, indGammaI)%&
vect(1:dimenI, indLevelI)
if ( jI > 0 ) then
do k = 1, dimenI
spinF = basis(indI)%icontr(k)%spin
sigmaF = basis(indI)%icontr(k)%sigma
ilambdaF = basis(indI)%icontr(k)%ilambda
omegaF = basis(indI)%icontr(k)%omega
vF = basis(indI)%icontr(k)%ivib
do k_ = 1, dimenI
spinF_ = basis(indI)%icontr(k)%spin
sigmaF_ = basis(indI)%icontr(k)%sigma
ilambdaF_ = basis(indI)%icontr(k)%ilambda
iomegaF_ = basis(indI)%icontr(k)%omega
vF_ = basis(indI)%icontr(k)%ivib
!!!!!
if ( ilambdaF /= ilambdaF_ &
.or. nint(spinF - spinF_) /= 0 &
.or. vF /= vF_ ) cycle
if ( k == k_ ) then
lande = lande + vecI(k)*vecI(k)*omegaF &
*(real(ilambdaF, rk) + 2.0023_rk*sigmaF)
elseif ( nint(abs(sigmaF_ - sigmaF)) == 1 ) then
lande = lande + vecI(k)*vecI(k_) &
*sqrt( &
spinF*(spinF + 1.0_rk) &
- sigmaF*(sigmaF + sigmaF_ - sigmaF) &
) &
*sqrt( &
jI*(jI + 1.0_rk) &
- omegaF*(omegaF + iomegaF_ - omegaF) &
) &
* (2.002319_rk/2.0_rk)
endif
enddo
enddo
lande = lande / ( jI*(jI + 1.0_rk) )
endif
! if integer spin, then integerise quantum numbers
if ( intSpin ) then
write(myFmt, '(A,i0,a)') &
"(i12,1x,f12.",ndecimals,",1x,i6,1x,i7,1x,f13.6,1x,&
&a1,1x,a1,1x,a10,1x,i3,1x,i2,2i8)"
write(enunit, myFmt) &
indRoot, energyI - Intensity%ZPE, &
nint( Intensity%gns(indSymI)*(2.0_rk*jI + 1.0_rk) ), &
nint(jI), lande, pm, ef, statename, &
vI, ilambdaI, nint(sigmaI), nint(omegaI)
! if not then write quantum numbers as reals
else
write(myFmt, '(A,i0,a)') &
"(i12,1x,f12.",ndecimals,",1x,i6,1x,f7.1,1x,f13.6,1x,&
&a1,1x,a1,1x,a10,1x,i3,1x,i2,2f8.1)"
write(enunit, myFmt) &
indRoot, (energyI - Intensity%ZPE), &
nint( Intensity%gns(indSymI)*(2.0_rk*jI + 1.0_rk) ), &
jI, lande, pm, ef, statename, &
vI, ilambdaI, sigmaI, omegaI
endif
! alternative format for RichMol matrix elements
elseif ( Intensity%matelem ) then
nDecimals = 6 - max(0, &
int(log10(abs(energyI - Intensity%ZPE) + 1.d-6) - 4))
if ( nint(2*jI) /= nint(2*j_) ) then
j_ = jI
IDj = 0
endif
IDj = IDj + 1
quantaI%iJ_ID = IDj
! if integer spin, then integerise quantum numbers
if ( intSpin ) then
write(myFmt, '(a)') &
"(i6,1x,i8,1x,i2,1x,i2,3x,e21.14,5x,a4,i3,1x,a2,i4,&
&1x,a2,f8.4,1x,i6,1x,i6,1x,i4,1x,i6,1x,a1,1x,a10)"
write(enunit, myFmt) &
nint(j_), IDj, parityI+1, 1, energyI-Intensity%ZPE, &
'tau:', parityI, 'j:', nint(j_), 'c', 1.000_rk, &
nint(omegaI), vI, ilambdaI, nint(sigmaI), pm, statename
! if not then write quantum numbers as reals
else
write(myFmt, '(A,i0,a)') &
"(i7,1x,i12,1x,i1,1x,i2,1x,f12.",ndecimals,&
",1x,f7.1,1x,i6,1x,i4,1x,f7.1,1x,a1,1x,a10)"
write(enunit, myFmt) &
nint(j_), IDj, parityI+1, 1, energyI-Intensity%ZPE, &
omegaI, vI, ilambdaI, sigmaI, pm, statename
endif
! standard output format if matelem or lande not required
else
nDecimals = 6 - max(0, &
int(log10(abs(energyI - Intensity%ZPE) + 1.d-6) - 4))
! if integer spin, then integerise quantum numbers
if ( intSpin ) then
write(myFmt, '(A,i0,a)') &
"(i12,1x,f12.", ndecimals, &
",1x,i6,1x,i7,1x,a1,1x,a1,1x,a10,1x,i3,1x,i2,2i8)"
write(enunit, myFmt) &
indRoot, energyI-Intensity%ZPE, &
nint( Intensity%gns(indSymI)*(2.0_rk*jI + 1.0_rk) ), &
nint(jI), pm, ef, statename, vI, ilambdaI, &
nint(sigmaI), nint(omegaI)
! if not then write quantum numbers as reals
else
write(myFmt, '(A,i0,a)') &
"(i12,1x,f12.", ndecimals, &
",1x,i6,1x,f7.1,1x,a1,1x,a1,1x,a10,1x,i3,1x,i2,2f8.1)"
write(enunit, myFmt) &
indRoot, energyI-Intensity%ZPE, &
nint( Intensity%gns(indSymI)*(2.0_rk*jI + 1.0_rk) ), &
jI, pm, ef, statename, vI, ilambdaI, sigmaI, omegaI
endif
endif
endif
call energy_filter_ul(jI, energyI, passed, 'upper')
call energy_filter_ul(jI, energyI, passed_, 'lower')
if ( .not. passed &
.and. .not. passed_) cycle
istateI = eigen(indI, indGammaI)%quanta(indLevelI)%istate
guParity = poten(istateI)%parity%gu
indSymI = correlate_to_Cs(indGammaI, guParity)
nLevelsG(indSymI) = nLevelsG(indSymI) + 1
enddo
enddo
enddo
deallocate(vecI)
call ArrayStop('intensity-vecI')
if ( trim(Intensity%linelist_file) /= "NONE") then
close(enunit, status='keep')
endif
write(myFmt, '(a,i0,a)') &
"('number of states for each sym = ',", sym%Nrepresen, "i8)"
write(out, myFmt) nLevelsG(:)
matSize = int( sum(nLevelsG(:)), hik )
if ( iVerbose >= 4 ) then
write(out, "(/'Quadrupole moment integration (i)...')")
endif
if ( nTrans == 0 ) then
write(out, "('qm_intensity: the transition filters are too tight:&
& no entry')")
stop 'qm_intensity: the filters are too tight'
endif
write(out, "(/'...done!')")
allocate(vecI(dimenMax), vecF(dimenMax), stat=info)
call ArrayStart('intensity-vectors', info, size(vecI), kind(vecI))
call ArrayStart('intensity-vectors', info, size(vecF), kind(vecF))
!!! why is this duplicated from above?
write(myFmt, '(a,i0,a)') &
"('number of states for each sym = ',", sym%Nrepresen, "i8)"
write(out, myFmt) nLevelsG(:)
if ( iVerbose >= 0 ) then
write(out, "('Total number of lower states = ',i8)") nLower
write(out, "('Total number of transitions = ',i8)") nTrans
endif
if ( iVerbose >= 0 ) then
write(out, "(/'Statistical weight g_ns =',4f12.1)") &
Intensity%gns(1:)
endif
! To speed up line strength evaluation, we perform the calculation:
! S_{if} = | <i|a|f> |^2 = | \sum_{nm} C_in C_fm <n|a|m> |^2
! in three steps:
! 1. Evaluate the expansion of the initial state:
! s_{im} = sum_{n} C_in <n|a|m>
! 2. Evaluate the product with the expansion of the final state:
! s_{if} = sum_{m} C_fm s_{im}
! 3. Square the result to obtain S_{if}
! S_{if} = s_{if}^2
!
! The transitory object s_{im} we refer to as 'half linestrength',
! with corresponding variable "half_linestr".
! initialise array to store eigenvectors
allocate(halfLineStr(dimenMax), stat=info)
call ArrayStart('halfLineStr', info, &
size(halfLineStr), kind(halfLineStr))
if ( iVerbose >= 5) call MemoryReport
!
if (trim(intensity%linelist_file)/="NONE") then
write(out,"(/'This is a line list production only, intensity print-out is swtitched off')")
write(out,"('To see intensities in the standard output remove the keyword LINELIST from INTENSITY'/)")
else
! prepare the table header
write(out, "(/a,a,a,a)") &
'Linestrength S(f<-i) [Debye**2],', &
'Transition moments [Debye],', &
'Einstein coefficient A(if) [1/s],', &
'and Intensities [cm/mol]'
! depending on the case we have different file formats
select case ( trim(intensity%action) )
! absorption lines
case('ABSORPTION')
write(out, &
! Fixed width output
"(/t5,'J',t7,'Gamma <-',t18,'J',t21,'Gamma',t27,'Typ',t37,&
&'Ei',t44,'<-',t52,'Ef',t64,'nu_if',8x,'S(f<-i)',10x,'A(if)',&
&12x,'I(f<-i)',7x,'State v lambda sigma omega <- State v &
&lambda sigma omega ')" &
!
! CSV output
! "('dir, J_i, Gamma_i, J_f, Gamma_f, Branch,&
! & E_i, Ef, nu_if,&
! & S_fi, A_if, I_fi,&
! & state_f, v_f, lambda_f, sigma_f, omega_f,&
! & state_i, v_i, lambda_i, sigma_i, omega_i')"&
)
dir = '<-'
! emission lines
case('EMISSION')
write(out, &
"(/t5,'J',t7,'Gamma ->',t18,'J',t21,'Gamma',t27,'Typ',t37,&
&'Ei',t44,'->',t52,'Ef',t64,'nu_if',8x,'S(i->f)',10x,'A(if)',&
&12x,'I(i->f)',7x,'State v lambda sigma omega -> State v &
&lambda sigma omega ')" &
)
dir = '->'
! Transition moments
case('TM')
write(out, &
"(/t4,'J',t6,'Gamma <-',t17,'J',t19,'Gamma',t25,'Typ',t35,&
&'Ei',t42,'<-',t52,'Ef',t65,'nu_if',10x,'TM(f->i)')" &
)
end select
endif
deallocate(vecF)
! ------------------------------------------------
! now begin the actual line intensity calculations
! ------------------------------------------------
! counter for the no. transitions
indTrans = 0
! loop over initial J states and assign corresponding J value
do indI = 1, nJ
jI = jVal(indI)
!
if (trim(intensity%linelist_file)/="NONE".and.iverbose>=4) write(out,"('J = ',f9.1)") jI
!
! loop over symmetries
do indGammaI = 1, nRepresen
! no. of levels in, and dimension of, basis for initial state
nLevelsI = eigen(indI, indGammaI)%nLevels
dimenI = eigen(indI, indGammaI)%nDimen
! loop over final J states and assign corresponding J value
do indF = 1, nJ
jF = jVal(indF)
! J selection rules for quadrupole operator
if ( abs(nint(jI - jF)) > 2 &
.or. abs(nint(jI + jF)) < 2) cycle
! loop over symmetries
do indGammaF = 1, nRepresen
! no. of levels in, and dimension of, basis for final state
nLevelsF = eigen(indF, indGammaF)%nLevels
dimenF = eigen(indF, indGammaF)%nDimen
! loop over levels in the initial state
loopLevelsI : do indLevelI = 1, nLevelsI
! energy and quantum numbers of initial state
energyI = eigen(indI, indGammaI)%val(indLevelI)
quantaI => eigen(indI, indGammaI)%quanta(indLevelI)
istateI = quantaI%istate ! electronic state
ivibI = quantaI%ivib ! vibrational (contracted)
vI = quantaI%v ! vibrational
spinI = quantaI%spin ! electron spin
sigmaI = quantaI%sigma ! spin projection
ilambdaI = quantaI%ilambda ! e- orb. ang. mom. projection
omegaI = quantaI%omega ! tot. ang. mom. proj. mol. ax.
! reconstruct symmetry for C2v case
guParity = poten(istateI)%parity%gu
indSymI = correlate_to_Cs(indGammaI, guParity)
! apply energy filter to initial (lower) state
call energy_filter_ul(jI, energyI, passed, 'lower')
if ( .not. passed ) cycle loopLevelsI
! vector of basis state coefficients for inital state
vecI(1:dimenI) = eigen(indI, indGammaI)&
%vect(1:dimenI, indLevelI)
!
halfLineStr = 0
!
! -----
! Before the actual calculations we check if there are any
! allowed transitions from current level of jI to any
! levels of jF, if not skip initial J state level.
! loop over levels in the final state to check for trans.
do indLevelF = 1, nLevelsF
energyF = eigen(indF, indGammaF)%val(indLevelF)
quantaF => eigen(indF, indGammaF)%quanta(indLevelF)
istateF = quantaF%istate ! electronic state
ivibF = quantaF%ivib ! vibrational (contracted)
vF = quantaF%v ! vibrational
spinF = quantaF%spin ! electron spin
sigmaF = quantaF%sigma ! spin projection
ilambdaF = quantaF%ilambda ! e- orb. ang. mom. projection
omegaF = quantaF%omega ! tot. ang. mom. proj. mol. ax
! reconstruct symmetry for C2v case
guParity = poten(istateF)%parity%gu
indSymF = correlate_to_Cs(indGammaF, guParity)
! apply transition intensity filter, result of which is
! overidden by mat. elem. filter if we want mat. elems.
call intens_filter(jI, jF, energyI, energyF, &
indSymI, indSymF, iGammaPair, passed)
if ( Intensity%matelem ) then
call matelem_filter(jI, jF, energyI, energyF, &
indSymI, indSymF, iGammaPair, passed)
endif
if ( passed ) exit