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Inertia.f90
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Inertia.f90
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Include 'CompilerVersion.f90'
Subroutine Inertia(N,C,AtomMass,CM,PMOI,PAxes,kRotTyp)
!USE Numerical_Libraries
!USE UNITS
Implicit Real(8) (A-H,O-Z)
Real(8) C(3,N), & ! Atom coordinates (in Angstroems)
AtomMass(N), & ! Atomic masses (in amu)
CM(3), & ! Center of masses (in the initial coordinate system)
PMOI(3), & ! Principal moments of inertia (in a.u.)
PAxes(3,3), & ! Principal axes (in the initial coordinate system)
T(3,3) ! Tensor of inertia (in a.u.)
Real(8) CIPA(3,N) ! Temporary array (coordinates reduced to the princpal axes)
! Subroutine INERTIA calulates center of masses (CM, in Angstroems),
! principal moments of inertia (PMOI, in a.u.),
! principal axes (PAxes), and the type of rotor (kRotTyp).
! Input parameters: number of atoms N, atomic coordinates C(in Angstroems),
! and atomic masses AtomMass (in AMU).
! At outup, C is replaced by the coordinates centered to CM and reduced to principal axes.
! kRotTyp = 1 - Spheric Top
! = 2 - Prolate Symmetric Top
! = 3 - Oblate Symmetric Top
! = 4 - Asymmetric Top
! = 5 - Linear Top
! = 6 - Single atom molecule
au=1.d0/0.529177249d0
PMOI=0.d0
PAxes=0.d0
! Check for single atom molecule
If (N==1) Then
CM(1:3)=C(1:3,1)
C(1:3,1)=0.d0
TotMass=AtomMass(1)
kRotTyp=6
Return
Endif
!
! Center of masses
!
TotMass=0.d0
CM=0.d0
Do i=1,N
TotMass=TotMass+AtomMass(i)
Do k=1,3
CM(k)=CM(k)+AtomMass(i)*C(k,i)
Enddo
Enddo
CM=CM/TotMass
Do i=1,N
Do k=1,3
C(k,i)=C(k,i)-CM(k)
Enddo
Enddo
!
! Tensor of Inertia
!
T=0.d0
Do i=1,N
T(1,1)=T(1,1)+AtomMass(i)*(C(2,i)*C(2,i)+C(3,i)*C(3,i))
T(2,2)=T(2,2)+AtomMass(i)*(C(1,i)*C(1,i)+C(3,i)*C(3,i))
T(3,3)=T(3,3)+AtomMass(i)*(C(1,i)*C(1,i)+C(2,i)*C(2,i))
T(1,2)=T(1,2)-AtomMass(i)*C(1,i)*C(2,i)
T(1,3)=T(1,3)-AtomMass(i)*C(1,i)*C(3,i)
T(2,3)=T(2,3)-AtomMass(i)*C(2,i)*C(3,i)
Enddo
T(2,1)=T(1,2)
T(3,1)=T(1,3)
T(3,2)=T(2,3)
T=T*au*au
!
! Calculate PMOI and PAxes
!
CALL Jacobi(T,3,3,PMOI,PAxes,NRotation)
!Call DEVCSF(3,T,3,PMOI,PAxes,3)
!
! Reduce to principal axes
!
do i=1,N
do j=1,3
CIPA(j,i)=(C(1,i)*PAxes(1,j)+ &
C(2,i)*PAxes(2,j)+ &
C(3,i)*PAxes(3,j))
enddo
enddo
C=CIPA
!
! Rotor type determination
!
kRotTyp=0
ep=1.d-3
epAbs=1.d-3
dm12=DABS(DMIN1(PMOI(1),PMOI(2)))
dm23=DABS(DMIN1(PMOI(2),PMOI(3)))
IF (DABS(PMOI(1)-PMOI(2))/dm12<ep .and. DABS(PMOI(2)-PMOI(3))/dm23<ep) Then
kRotTyp=1 ! Spherical top
! If (IPrint==1) Write(6,'('' Spherical top'')')
ELSE IF (DABS(PMOI(1)-PMOI(2))/dm12<ep .and. DABS(PMOI(3))<epAbs) Then
kRotTyp=5 ! Linear top
! If (IPrint==1) Write(6,'('' Linear top'')')
ELSE IF (DABS(PMOI(1)-PMOI(2))/dm12<ep .and. PMOI(3)<PMOI(2)) Then
kRotTyp=2 ! Prolate symmetric top
! If (IPrint==1) Write(6,'('' Prolate symmetric top'')')
ELSE IF (DABS(PMOI(2)-PMOI(3))/dm23<ep .and. PMOI(1)>PMOI(2)) Then
kRotTyp=3 ! Oblate symmetric top
! If (IPrint==1) Write(6,'('' Oblate symmetric top'')')
ELSE IF (DABS(PMOI(1)-PMOI(2))/dm12>ep .and. DABS(PMOI(2)-PMOI(3))/dm23>ep) Then
kRotTyp=4 ! Asymmetric top
! If (IPrint==1) Write(6,'('' Asymmetric top'')')
ENDIF
End
!******************************************************************************************
Subroutine InertiaNew(mode,iSort,iRHS,N,C,AtomMass,CM,PMOI,PAxes,kRotTyp)
!DEC$ IF (_COMPILER_==1)
USE Numerical_Libraries
!DEC$ ENDIF
Implicit Real(8) (A-H,O-Z)
Real(8) C(3,N), & ! Atom coordinates (in Angstroems)
AtomMass(N), & ! Atomic masses (in amu)
CM(3), & ! Center of masses (in the initial coordinate system)
PMOI(3), & ! Principal moments of inertia (in a.u.)
PAxes(3,3), & ! Principal axes (in the initial coordinate system)
T(3,3),T0(3,3) ! Tensor of inertia (in a.u.)
Real(8) CIPA(3,N) ! Temporary array (coordinates reduced to the princpal axes)
Real(8) X(3),Y(3),Z(3),P(3) ! Temporary arrays
! Subroutine INERTIA calulates center of masses (CM), principal moments of inertia (PMOI),
! principal axes (PAxes), type of rotor (kRotTyp) and reduces molecule to CM and PA if needed.
!
! At INPUT: number of atoms N, atomic coordinates C(in Angstroems or Bohrs),
! and atomic masses AtomMass (in AMU).
!
! At OUTPUT:
! CM - center of masses (in the same units as C)
! PMOI - principal moments of inertia in AMU*(units of C)**2
! PAxes - principal axes (normalized to 1)
! kRotTyp = 1 - Spheric Top
! = 2 - Prolate Symmetric Top
! = 3 - Oblate Symmetric Top
! = 4 - Asymmetric Top
! = 5 - Linear Top
! = 6 - Single atom molecule
!
! Additional control:
! Mode = 0 - C is not changed
! 1 - C is reduced to CM
! 2 - C is reduced to CM and PAxes
! 3 - C is reduced to PAxes without shift of CM (rotated at the initial position)
!
! iSort= 0 - PMOI and PAxes are not sorted
! 1 - PMOI and PAxes are sorted in increasing order of PMOI
! -1 - PMOI and PAxes are sorted in decreasing order of PMOI
!
! iRHS = 1 - PAxes should form right-hand system
! -1 - PAxes should form left-hand system
! 0 - remain PAxes as is
!au=1.d0/0.529177249d0
PMOI=0.d0
PAxes=0.d0
ForAll(k=1:3) PAxes(k,k)=1.d0
! Check for single atom molecule
If (N==1) Then
CM(1:3)=C(1:3,1)
If (Mode==1.or.Mode==2) C(1:3,1)=0.d0
TotMass=AtomMass(1)
kRotTyp=6
Return
Endif
!
! Center of masses
!
TotMass=0.d0
CM=0.d0
Do i=1,N
TotMass=TotMass+AtomMass(i)
Do k=1,3
CM(k)=CM(k)+AtomMass(i)*C(k,i)
Enddo
Enddo
CM=CM/TotMass
Do i=1,N
Do k=1,3
C(k,i)=C(k,i)-CM(k)
Enddo
Enddo
!
! Tensor of Inertia
!
T=0.d0
Do i=1,N
T(1,1)=T(1,1)+AtomMass(i)*(C(2,i)*C(2,i)+C(3,i)*C(3,i))
T(2,2)=T(2,2)+AtomMass(i)*(C(1,i)*C(1,i)+C(3,i)*C(3,i))
T(3,3)=T(3,3)+AtomMass(i)*(C(1,i)*C(1,i)+C(2,i)*C(2,i))
T(1,2)=T(1,2)-AtomMass(i)*C(1,i)*C(2,i)
T(1,3)=T(1,3)-AtomMass(i)*C(1,i)*C(3,i)
T(2,3)=T(2,3)-AtomMass(i)*C(2,i)*C(3,i)
Enddo
T(2,1)=T(1,2)
T(3,1)=T(1,3)
T(3,2)=T(2,3)
!T=T*au*au
!
! Calculate PMOI and PAxes
!
T0=T
!DEC$ IF (_COMPILER_==1)
Call DEVCSF(3,T,3,PMOI,PAxes,3) ! Sorted PMOI (decreasing order)
!DEC$ ELSE
Call JacobiSorted(T,3,3,PMOI,Paxes,itmp,-1)
!DEC$ ENDIF
!
! Rotor type determination
!
kRotTyp=0
ep=1.d-3
epAbs=1.d-3
dm12=DABS(DMIN1(PMOI(1),PMOI(2)))
dm23=DABS(DMIN1(PMOI(2),PMOI(3)))
IF (DABS(PMOI(1)-PMOI(2))/dm12<ep .and. DABS(PMOI(2)-PMOI(3))/dm23<ep) Then
kRotTyp=1 ! Spherical top
! If (IPrint==1) Write(6,'('' Spherical top'')')
ELSE IF (DABS(PMOI(1)-PMOI(2))/dm12<ep .and. DABS(PMOI(3))<epAbs) Then
kRotTyp=5 ! Linear top
! If (IPrint==1) Write(6,'('' Linear top'')')
ELSE IF (DABS(PMOI(1)-PMOI(2))/dm12<ep .and. PMOI(3)<PMOI(2)) Then
kRotTyp=2 ! Prolate symmetric top
! If (IPrint==1) Write(6,'('' Prolate symmetric top'')')
ELSE IF (DABS(PMOI(2)-PMOI(3))/dm23<ep .and. PMOI(1)>PMOI(2)) Then
kRotTyp=3 ! Oblate symmetric top
! If (IPrint==1) Write(6,'('' Oblate symmetric top'')')
ELSE IF (DABS(PMOI(1)-PMOI(2))/dm12>ep .and. DABS(PMOI(2)-PMOI(3))/dm23>ep) Then
kRotTyp=4 ! Asymmetric top
! If (IPrint==1) Write(6,'('' Asymmetric top'')')
ENDIF
!
! Unsorted or increasing PMOI
!
If (iSort>0) Then
tmp=PMOI(1)
PMOI(1)=PMOI(3)
PMOI(3)=tmp
Do k=1,3
tmp=PAxes(k,1)
PAxes(k,1)=PAxes(k,3)
PAxes(k,3)=tmp
Enddo
ElseIf (iSort==0) Then
CALL Jacobi(T0,3,3,PMOI,PAxes,NRotation)
Do j=1,3
tmp=1.d0/DSQRT(Paxes(1,j)**2+PAxes(2,j)**2+PAxes(3,j)**2)
PAxes(1:3,j)=PAxes(1:3,j)*tmp
Enddo
Endif
!
! Check PAxes to be right-hand system
!
If (irhs/=0) Then
X(1:3)=PAxes(1:3,1)
Y(1:3)=PAxes(1:3,2)
Z(1:3)=PAxes(1:3,3)
Call CrossProduct(X,Y,P,PZ)
PZ=P(1)*Z(1)+P(2)*Z(2)+P(3)*Z(3)
If ((PZ<0.d0.and.irhs>0).or.(PZ>0.d0.and.irhs<0)) PAxes(1:3,3)=-Z(1:3)
Endif
!
! Reduce to principal axes
!
If (mode==2.or.mode==3) Then
do i=1,N
do j=1,3
CIPA(j,i)=(C(1,i)*PAxes(1,j)+ &
C(2,i)*PAxes(2,j)+ &
C(3,i)*PAxes(3,j))
enddo
enddo
C=CIPA
Endif
!
! Shift back from CM
!
If (mode==0.or.mode==3) ForAll(k=1:3,i=1:N) C(k,i)=C(k,i)+CM(k)
End