c
c
c     ##########################################################
c     ##  COPYRIGHT (C) 2014 by Chao Lu & Jay William Ponder  ##
c     ##                  All Rights Reserved                 ##
c     ##########################################################
c
c     ###############################################################
c     ##                                                           ##
c     ##  subroutine eangtor  --  angle-torsion cross term energy  ##
c     ##                                                           ##
c     ###############################################################
c
c
c     "eangtor" calculates the angle-torsion potential energy
c
c
      subroutine eangtor
      use angtor
      use atoms
      use angbnd
      use bound
      use energi
      use group
      use math
      use torpot
      use tors
      use usage
      implicit none
      integer i,k,iangtor
      integer ia,ib,ic,id
      real*8 e,e1,e2
      real*8 eps,fgrp
      real*8 rba,rcb,rdc
      real*8 rt2,ru2,rtru
      real*8 dot,dt
      real*8 xt,yt,zt
      real*8 xu,yu,zu
      real*8 xtu,ytu,ztu
      real*8 v1,v2,v3
      real*8 c1,c2,c3
      real*8 s1,s2,s3
      real*8 sine,cosine
      real*8 sine2,cosine2
      real*8 sine3,cosine3
      real*8 phi1,phi2,phi3
      real*8 angle,cosang
      real*8 xia,yia,zia
      real*8 xib,yib,zib
      real*8 xic,yic,zic
      real*8 xid,yid,zid
      real*8 xba,yba,zba
      real*8 xcb,ycb,zcb
      real*8 xdc,ydc,zdc
      logical proceed
c
c
c     zero out the energy due to extra potential terms
c
      eat = 0.0d0
      if (nangtor .eq. 0)  return
c
c     set tolerance for minimum distance and angle values
c
      eps = 0.0001d0
c
c     OpenMP directives for the major loop structure
c
!$OMP PARALLEL default(private) shared(nangtor,iat,itors,kant,anat,
!$OMP& tors1,tors2,tors3,use,x,y,z,atorunit,eps,use_group,use_polymer)
!$OMP& shared(eat)
!$OMP DO reduction(+:eat)
c
c     calculate the angle-torsion interaction energy term
c
      do iangtor = 1, nangtor
         i = iat(1,iangtor)
         ia = itors(1,i)
         ib = itors(2,i)
         ic = itors(3,i)
         id = itors(4,i)
c
c     decide whether to compute the current interaction
c
         proceed = .true.
         if (use_group)  call groups (proceed,fgrp,ia,ib,ic,id,0,0)
         if (proceed)  proceed = (use(ia) .or. use(ib) .or.
     &                              use(ic) .or. use(id))
c
c     compute the value of the torsional angle
c
         if (proceed) then
            xia = x(ia)
            yia = y(ia)
            zia = z(ia)
            xib = x(ib)
            yib = y(ib)
            zib = z(ib)
            xic = x(ic)
            yic = y(ic)
            zic = z(ic)
            xid = x(id)
            yid = y(id)
            zid = z(id)
            xba = xib - xia
            yba = yib - yia
            zba = zib - zia
            xcb = xic - xib
            ycb = yic - yib
            zcb = zic - zib
            xdc = xid - xic
            ydc = yid - yic
            zdc = zid - zic
            if (use_polymer) then
               call image (xba,yba,zba)
               call image (xcb,ycb,zcb)
               call image (xdc,ydc,zdc)
            end if
            rba = sqrt(max(xba*xba+yba*yba+zba*zba,eps))
            rcb = sqrt(max(xcb*xcb+ycb*ycb+zcb*zcb,eps))
            rdc = sqrt(max(xdc*xdc+ydc*ydc+zdc*zdc,eps))
            xt = yba*zcb - ycb*zba
            yt = zba*xcb - zcb*xba
            zt = xba*ycb - xcb*yba
            xu = ycb*zdc - ydc*zcb
            yu = zcb*xdc - zdc*xcb
            zu = xcb*ydc - xdc*ycb
            xtu = yt*zu - yu*zt
            ytu = zt*xu - zu*xt
            ztu = xt*yu - xu*yt
            rt2 = max(xt*xt+yt*yt+zt*zt,eps)
            ru2 = max(xu*xu+yu*yu+zu*zu,eps)
            rtru = sqrt(rt2*ru2)
            cosine = (xt*xu + yt*yu + zt*zu) / rtru
            sine = (xcb*xtu + ycb*ytu + zcb*ztu) / (rcb*rtru)
c
c     compute multiple angle trigonometry and phase terms
c
            c1 = tors1(3,i)
            s1 = tors1(4,i)
            c2 = tors2(3,i)
            s2 = tors2(4,i)
            c3 = tors3(3,i)
            s3 = tors3(4,i)
            cosine2 = cosine*cosine - sine*sine
            sine2 = 2.0d0 * cosine * sine
            cosine3 = cosine*cosine2 - sine*sine2
            sine3 = cosine*sine2 + sine*cosine2
            phi1 = 1.0d0 + (cosine*c1 + sine*s1)
            phi2 = 1.0d0 + (cosine2*c2 + sine2*s2)
            phi3 = 1.0d0 + (cosine3*c3 + sine3*s3)
c
c     get the angle-torsion values for the first angle
c
            v1 = kant(1,iangtor)
            v2 = kant(2,iangtor)
            v3 = kant(3,iangtor)
            k = iat(2,iangtor)
            dot = xba*xcb + yba*ycb + zba*zcb
            cosang = -dot / (rba*rcb)
            angle = radian * acos(cosang)
            dt = angle - anat(k)
            e1 = atorunit * dt * (v1*phi1 + v2*phi2 + v3*phi3)
c
c     get the angle-torsion values for the second angle
c
            v1 = kant(4,iangtor)
            v2 = kant(5,iangtor)
            v3 = kant(6,iangtor)
            k = iat(3,iangtor)
            dot = xcb*xdc + ycb*ydc + zcb*zdc
            cosang = -dot / (rcb*rdc)
            angle = radian * acos(cosang)
            dt = angle - anat(k)
            e2 = atorunit * dt * (v1*phi1 + v2*phi2 + v3*phi3)
c
c     scale the interaction based on its group membership
c
            if (use_group) then
               e1 = e1 * fgrp
               e2 = e2 * fgrp
            end if
c
c     increment the total angle-torsion energy
c
            e = e1 + e2
            eat = eat + e
         end if
      end do
c
c     OpenMP directives for the major loop structure
c
!$OMP END DO
!$OMP END PARALLEL
      return
      end