2024-10-21 14:01:28 +02:00
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subroutine cart2int(cart,qint)
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implicit none
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! This version merges both coordinate transformation routines into
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! one. JTmod's sscales(2:3) are ignored.
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! This is the first version to be compatible with one of my proper 6D fits
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! Time-stamp: <2024-10-22 13:52:59 dwilliams>
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2024-11-06 13:59:30 +01:00
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! Input (cartesian, in Angström)
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2024-10-21 14:01:28 +02:00
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! cart(:,1): N
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! cart(:,1+i): Hi
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! Output
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2024-11-06 13:37:37 +01:00
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! qint(i): order defined in JTmod.
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2024-10-21 14:01:28 +02:00
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! Internal Variables
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! no(1:3): NO distances 1-3
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! pat_in: temporary coordinates
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! axis: main axis of NO3
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include 'nnparams.incl'
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include 'JTmod.incl'
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real*8 cart(3,4),qint(maxnin)
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real*8 no(3), r1, r2, r3
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real*8 v1(3), v2(3), v3(3)
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real*8 n1(3), n2(3), n3(3), tr(3)
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real*8 ortho(3)
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real*8 pat_in(maxnin)
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logical ignore_umbrella,dbg_umbrella
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logical dbg_distances
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!.. Debugging parameters
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!.. set umbrella to 0
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parameter (ignore_umbrella=.false.)
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! parameter (ignore_umbrella=.true.)
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!.. break if umbrella is not 0
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parameter (dbg_umbrella=.false.)
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! parameter (dbg_umbrella=.true.)
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!.. break for tiny distances
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parameter (dbg_distances=.false.)
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! parameter (dbg_distances=.true.)
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integer k
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!.. get N-O vectors and distances:
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do k=1,3
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v1(k)=cart(k,2)-cart(k,1)
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v2(k)=cart(k,3)-cart(k,1)
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v3(k)=cart(k,4)-cart(k,1)
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enddo
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no(1)=norm(v1,3)
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no(2)=norm(v2,3)
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no(3)=norm(v3,3)
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!.. temporarily store displacements
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do k=1,3
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pat_in(k)=no(k)-offsets(1)
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enddo
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do k=1,3
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v1(k)=v1(k)/no(1)
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v2(k)=v2(k)/no(2)
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v3(k)=v3(k)/no(3)
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enddo
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!.. compute three normal vectors for the ONO planes:
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call xprod(n1,v1,v2)
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call xprod(n2,v2,v3)
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call xprod(n3,v3,v1)
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do k=1,3
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tr(k)=(n1(k)+n2(k)+n3(k))/3.d0
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enddo
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r1=norm(tr,3)
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do k=1,3
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tr(k)=tr(k)/r1
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enddo
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! rotate trisector
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call rot_trisec(tr,v1,v2,v3)
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!.. determine trisector angle:
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if (ignore_umbrella) then
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pat_in(7)=0.0d0
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else
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pat_in(7)=pi/2.0d0 - acos(scalar(v1,tr,3))
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pat_in(7)=sign(pat_in(7),cart(1,2))
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endif
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!.. molecule now lies in yz plane, compute projected ONO angles:
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v1(1)=0.d0
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v2(1)=0.d0
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v3(1)=0.d0
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r1=norm(v1,3)
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r2=norm(v2,3)
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r3=norm(v3,3)
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do k=2,3
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v1(k)=v1(k)/r1
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v2(k)=v2(k)/r2
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v3(k)=v3(k)/r3
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enddo
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! make orthogonal vector to v3
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ortho(1)=0.0d0
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ortho(2)=v3(3)
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ortho(3)=-v3(2)
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!.. projected ONO angles in radians
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pat_in(4)=get_ang(v2,v3,ortho)
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pat_in(5)=get_ang(v1,v3,ortho)
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pat_in(6)=dabs(pat_in(5)-pat_in(4))
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!.. account for rotational order of atoms
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if (pat_in(4).le.pat_in(5)) then
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pat_in(5)=2*pi-pat_in(4)-pat_in(6)
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else
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pat_in(4)=2*pi-pat_in(5)-pat_in(6)
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endif
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pat_in(4)=rad2deg*pat_in(4)-offsets(2)
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pat_in(5)=rad2deg*pat_in(5)-offsets(2)
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pat_in(6)=rad2deg*pat_in(6)-offsets(2)
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pat_in(7)=rad2deg*pat_in(7)
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call genANN_ctrans(pat_in)
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qint(:)=pat_in(:)
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contains
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!-------------------------------------------------------------------
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! compute vector product n1 of vectors v1 x v2
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subroutine xprod(n1,v1,v2)
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implicit none
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real*8 n1(3), v1(3), v2(3)
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n1(1) = v1(2)*v2(3) - v1(3)*v2(2)
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n1(2) = v1(3)*v2(1) - v1(1)*v2(3)
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n1(3) = v1(1)*v2(2) - v1(2)*v2(1)
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end subroutine
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!-------------------------------------------------------------------
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! compute scalar product of vectors v1 and v2:
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real*8 function scalar(v1,v2,n)
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implicit none
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integer i, n
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real*8 v1(*), v2(*)
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scalar=0.d0
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do i=1,n
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scalar=scalar+v1(i)*v2(i)
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enddo
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end function
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!-------------------------------------------------------------------
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! compute norm of vector:
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real*8 function norm(x,n)
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implicit none
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integer i, n
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real*8 x(*)
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norm=0.d0
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do i=1,n
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norm=norm+x(i)**2
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enddo
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norm=sqrt(norm)
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end function
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!-------------------------------------------------------------------
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subroutine rot_trisec(tr,v1,v2,v3)
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implicit none
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real*8 tr(3),v1(3),v2(3),v3(3)
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real*8 vrot(3)
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real*8 rot_ax(3)
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real*8 cos_phi,sin_phi
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! evaluate cos(-phi) and sin(-phi), where phi is the angle between
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! tr and (1,0,0)
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cos_phi=tr(1)
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sin_phi=dsqrt(tr(2)**2+tr(3)**2)
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if (sin_phi.lt.1.0d-12) then
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return
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endif
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! determine rotational axis
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rot_ax(1) = 0.0d0
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rot_ax(2) = tr(3)
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rot_ax(3) = -tr(2)
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! normalize
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rot_ax=rot_ax/sin_phi
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! now the rotation can be done using Rodrigues' rotation formula
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! v'=v*cos(p) + (k x v)sin(p) + k (k*v) (1-cos(p))
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! for v=tr k*v vanishes by construction:
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! check that the rotation does what it should
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call rodrigues(vrot,tr,rot_ax,cos_phi,sin_phi)
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if (dsqrt(vrot(2)**2+vrot(3)**2).gt.1.0d-12) then
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write(6,*) "ERROR: BROKEN TRISECTOR"
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stop
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endif
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tr=vrot
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call rodrigues(vrot,v1,rot_ax,cos_phi,sin_phi)
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v1=vrot
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call rodrigues(vrot,v2,rot_ax,cos_phi,sin_phi)
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v2=vrot
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call rodrigues(vrot,v3,rot_ax,cos_phi,sin_phi)
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v3=vrot
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end subroutine
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!-------------------------------------------------------------------
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subroutine rodrigues(vrot,v,axis,cos_phi,sin_phi)
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implicit none
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real*8 vrot(3),v(3),axis(3)
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real*8 cos_phi,sin_phi
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real*8 ortho(3)
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call xprod(ortho,axis,v)
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vrot = v*cos_phi + ortho*sin_phi
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> + axis*scalar(axis,v,3)*(1-cos_phi)
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end subroutine
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!-------------------------------------------------------------------
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real*8 function get_ang(v,xaxis,yaxis)
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implicit none
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! get normalized [0:2pi) angle from vectors in the yz plane
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real*8 v(3),xaxis(3),yaxis(3)
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real*8 phi
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real*8 pi
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parameter (pi=3.141592653589793d0)
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phi=atan2(scalar(yaxis,v,3),scalar(xaxis,v,3))
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if (phi.lt.0.0d0) then
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phi=2*pi+phi
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endif
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get_ang=phi
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end function
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end subroutine cart2int
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