c
c
c     ###################################################
c     ##  COPYRIGHT (C)  1990  by  Jay William Ponder  ##
c     ##              All Rights Reserved              ##
c     ###################################################
c
c     ##############################################################
c     ##                                                          ##
c     ##  subroutine echarge1  --  charge-charge energy & derivs  ##
c     ##                                                          ##
c     ##############################################################
c
c
c     "echarge1" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c
c
      subroutine echarge1
      implicit none
      include 'sizes.i'
      include 'cutoff.i'
      include 'warp.i'
c
c
c     choose the method for summing over pairwise interactions
c
      if (use_smooth) then
         call echarge1g
      else if (use_ewald) then
         if (use_clist) then
            call echarge1f
         else if (use_lights) then
            call echarge1e
         else
            call echarge1d
         end if
      else if (use_clist) then
         call echarge1c
      else if (use_lights) then
         call echarge1b
      else
         call echarge1a
      end if
      return
      end
c
c
c     ###############################################################
c     ##                                                           ##
c     ##  subroutine echarge1a  --  charge derivs via double loop  ##
c     ##                                                           ##
c     ###############################################################
c
c
c     "echarge1a" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c     using a pairwise double loop
c
c
      subroutine echarge1a
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'bound.i'
      include 'cell.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'couple.i'
      include 'deriv.i'
      include 'energi.i'
      include 'group.i'
      include 'inter.i'
      include 'molcul.i'
      include 'shunt.i'
      include 'usage.i'
      include 'virial.i'
      integer i,j,k
      integer ii,kk
      integer in,kn
      integer ic,kc
      real*8 e,fgrp,de,dc
      real*8 f,fi,fik
      real*8 r,r2,rb,rb2
      real*8 xi,yi,zi
      real*8 xr,yr,zr
      real*8 xc,yc,zc
      real*8 xic,yic,zic
      real*8 dedx,dedy,dedz
      real*8 dedxc,dedyc,dedzc
      real*8 shift,taper,trans
      real*8 dtaper,dtrans
      real*8 rc,rc2,rc3,rc4
      real*8 rc5,rc6,rc7
      real*8 vxx,vyy,vzz
      real*8 vyx,vzx,vzy
      real*8, allocatable :: cscale(:)
      logical proceed,usei
      character*6 mode
c
c
c     zero out the charge interaction energy and derivatives
c
      ec = 0.0d0
      do i = 1, n
         dec(1,i) = 0.0d0
         dec(2,i) = 0.0d0
         dec(3,i) = 0.0d0
      end do
      if (nion .eq. 0)  return
c
c     perform dynamic allocation of some local arrays
c
      allocate (cscale(n))
c
c     set array needed to scale connected atom interactions
c
      do i = 1, n
         cscale(i) = 1.0d0
      end do
c
c     set conversion factor, cutoff and switching coefficients
c
      f = electric / dielec
      mode = 'CHARGE'
      call switch (mode)
c
c     compute the charge interaction energy and first derivatives
c
      do ii = 1, nion-1
         i = iion(ii)
         in = jion(ii)
         ic = kion(ii)
         xic = x(ic)
         yic = y(ic)
         zic = z(ic)
         xi = x(i) - xic
         yi = y(i) - yic
         zi = z(i) - zic
         fi = f * pchg(ii)
         usei = (use(i) .or. use(ic))
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     decide whether to compute the current interaction
c
         do kk = ii+1, nion
            k = iion(kk)
            kn = jion(kk)
            kc = kion(kk)
            proceed = .true.
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            if (proceed)  proceed = (usei .or. use(k) .or. use(kc))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               xc = xic - x(kc)
               yc = yic - y(kc)
               zc = zic - z(kc)
               if (use_bounds)  call image (xc,yc,zc)
               rc2 = xc*xc + yc*yc + zc*zc
               if (rc2 .le. off2) then
                  xr = xc + xi - x(k) + x(kc)
                  yr = yc + yi - y(k) + y(kc)
                  zr = zc + zi - z(k) + z(kc)
                  r2 = xr*xr + yr*yr + zr*zr
                  r = sqrt(r2)
                  rb = r + ebuffer
                  rb2 = rb * rb
                  fik = fi * pchg(kk) * cscale(kn)
                  e = fik / rb
                  de = -fik / rb2
                  dc = 0.0d0
c
c     use shifted energy switching if near the cutoff distance
c
                  shift = fik / (0.5d0*(off+cut))
                  e = e - shift
                  if (rc2 .gt. cut2) then
                     rc = sqrt(rc2)
                     rc3 = rc2 * rc
                     rc4 = rc2 * rc2
                     rc5 = rc2 * rc3
                     rc6 = rc3 * rc3
                     rc7 = rc3 * rc4
                     taper = c5*rc5 + c4*rc4 + c3*rc3
     &                          + c2*rc2 + c1*rc + c0
                     dtaper = 5.0d0*c5*rc4 + 4.0d0*c4*rc3
     &                           + 3.0d0*c3*rc2 + 2.0d0*c2*rc + c1
                     trans = fik * (f7*rc7 + f6*rc6 + f5*rc5 + f4*rc4
     &                               + f3*rc3 + f2*rc2 + f1*rc + f0)
                     dtrans = fik * (7.0d0*f7*rc6 + 6.0d0*f6*rc5
     &                               + 5.0d0*f5*rc4 + 4.0d0*f4*rc3
     &                             + 3.0d0*f3*rc2 + 2.0d0*f2*rc + f1)
                     dc = (e*dtaper + dtrans) / rc
                     de = de * taper
                     e = e*taper + trans
                  end if
c
c     scale the interaction based on its group membership
c
                  if (use_group) then
                     e = e * fgrp
                     de = de * fgrp
                     dc = dc * fgrp
                  end if
c
c     form the chain rule terms for derivative expressions
c
                  de = de / r
                  dedx = de * xr
                  dedy = de * yr
                  dedz = de * zr
                  dedxc = dc * xc
                  dedyc = dc * yc
                  dedzc = dc * zc
c
c     increment the overall energy and derivative expressions
c
                  ec = ec + e
                  dec(1,i) = dec(1,i) + dedx
                  dec(2,i) = dec(2,i) + dedy
                  dec(3,i) = dec(3,i) + dedz
                  dec(1,ic) = dec(1,ic) + dedxc
                  dec(2,ic) = dec(2,ic) + dedyc
                  dec(3,ic) = dec(3,ic) + dedzc
                  dec(1,k) = dec(1,k) - dedx
                  dec(2,k) = dec(2,k) - dedy
                  dec(3,k) = dec(3,k) - dedz
                  dec(1,kc) = dec(1,kc) - dedxc
                  dec(2,kc) = dec(2,kc) - dedyc
                  dec(3,kc) = dec(3,kc) - dedzc
c
c     increment the internal virial tensor components
c
                  vxx = xr*dedx + xc*dedxc
                  vyx = yr*dedx + yc*dedxc
                  vzx = zr*dedx + zc*dedxc
                  vyy = yr*dedy + yc*dedyc
                  vzy = zr*dedy + zc*dedyc
                  vzz = zr*dedz + zc*dedzc
                  vir(1,1) = vir(1,1) + vxx
                  vir(2,1) = vir(2,1) + vyx
                  vir(3,1) = vir(3,1) + vzx
                  vir(1,2) = vir(1,2) + vyx
                  vir(2,2) = vir(2,2) + vyy
                  vir(3,2) = vir(3,2) + vzy
                  vir(1,3) = vir(1,3) + vzx
                  vir(2,3) = vir(2,3) + vzy
                  vir(3,3) = vir(3,3) + vzz
c
c     increment the total intermolecular energy
c
                  if (molcule(i) .ne. molcule(k)) then
                     einter = einter + e
                  end if
               end if
            end if
         end do
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     for periodic boundary conditions with large cutoffs
c     neighbors must be found by the replicates method
c
      if (.not. use_replica)  return
c
c     calculate interaction energy with other unit cells
c
      do ii = 1, nion
         i = iion(ii)
         in = jion(ii)
         ic = kion(ii)
         usei = (use(i) .or. use(ic))
         xic = x(ic)
         yic = y(ic)
         zic = z(ic)
         xi = x(i) - xic
         yi = y(i) - yic
         zi = z(i) - zic
         fi = f * pchg(ii)
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     decide whether to compute the current interaction
c
         do kk = ii, nion
            k = iion(kk)
            kn = jion(kk)
            kc = kion(kk)
            proceed = .true.
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            if (proceed)  proceed = (usei .or. use(k) .or. use(kc))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               do j = 1, ncell
                  xc = xic - x(kc)
                  yc = yic - y(kc)
                  zc = zic - z(kc)
                  call imager (xc,yc,zc,j)
                  rc2 = xc*xc + yc*yc + zc*zc
                  if (rc2 .le. off2) then
                     xr = xc + xi - x(k) + x(kc)
                     yr = yc + yi - y(k) + y(kc)
                     zr = zc + zi - z(k) + z(kc)
                     r2 = xr*xr + yr*yr + zr*zr
                     r = sqrt(r2)
                     rb = r + ebuffer
                     rb2 = rb * rb
                     fik = fi * pchg(kk)
                     if (use_polymer) then
                        if (r2 .le. polycut2)  fik = fik * cscale(kn)
                     end if
                     e = fik / rb
                     de = -fik / rb2
                     dc = 0.0d0
c
c     use shifted energy switching if near the cutoff distance
c
                     shift = fik / (0.5d0*(off+cut))
                     e = e - shift
                     if (rc2 .gt. cut2) then
                        rc = sqrt(rc2)
                        rc3 = rc2 * rc
                        rc4 = rc2 * rc2
                        rc5 = rc2 * rc3
                        rc6 = rc3 * rc3
                        rc7 = rc3 * rc4
                        taper = c5*rc5 + c4*rc4 + c3*rc3
     &                             + c2*rc2 + c1*rc + c0
                        dtaper = 5.0d0*c5*rc4 + 4.0d0*c4*rc3
     &                              + 3.0d0*c3*rc2 + 2.0d0*c2*rc + c1
                        trans = fik * (f7*rc7 + f6*rc6 + f5*rc5 + f4*rc4
     &                                  + f3*rc3 + f2*rc2 + f1*rc + f0)
                        dtrans = fik * (7.0d0*f7*rc6 + 6.0d0*f6*rc5
     &                                  + 5.0d0*f5*rc4 + 4.0d0*f4*rc3
     &                                + 3.0d0*f3*rc2 + 2.0d0*f2*rc + f1)
                        dc = (e*dtaper + dtrans) / rc
                        de = de * taper
                        e = e*taper + trans
                     end if
c
c     scale the interaction based on its group membership
c
                     if (use_group) then
                        e = e * fgrp
                        de = de * fgrp
                        dc = dc * fgrp
                     end if
c
c     form the chain rule terms for derivative expressions
c
                     de = de / r
                     dedx = de * xr
                     dedy = de * yr
                     dedz = de * zr
                     dedxc = dc * xc
                     dedyc = dc * yc
                     dedzc = dc * zc
c
c     increment the energy and gradient values
c
                     if (i .eq. k)  e = 0.5d0 * e
                     ec = ec + e
                     dec(1,i) = dec(1,i) + dedx
                     dec(2,i) = dec(2,i) + dedy
                     dec(3,i) = dec(3,i) + dedz
                     dec(1,ic) = dec(1,ic) + dedxc
                     dec(2,ic) = dec(2,ic) + dedyc
                     dec(3,ic) = dec(3,ic) + dedzc
                     if (i .ne. k) then
                        dec(1,k) = dec(1,k) - dedx
                        dec(2,k) = dec(2,k) - dedy
                        dec(3,k) = dec(3,k) - dedz
                        dec(1,kc) = dec(1,kc) - dedxc
                        dec(2,kc) = dec(2,kc) - dedyc
                        dec(3,kc) = dec(3,kc) - dedzc
                     end if
c
c     increment the internal virial tensor components
c
                     vxx = xr*dedx + xc*dedxc
                     vyx = yr*dedx + yc*dedxc
                     vzx = zr*dedx + zc*dedxc
                     vyy = yr*dedy + yc*dedyc
                     vzy = zr*dedy + zc*dedyc
                     vzz = zr*dedz + zc*dedzc
                     vir(1,1) = vir(1,1) + vxx
                     vir(2,1) = vir(2,1) + vyx
                     vir(3,1) = vir(3,1) + vzx
                     vir(1,2) = vir(1,2) + vyx
                     vir(2,2) = vir(2,2) + vyy
                     vir(3,2) = vir(3,2) + vzy
                     vir(1,3) = vir(1,3) + vzx
                     vir(2,3) = vir(2,3) + vzy
                     vir(3,3) = vir(3,3) + vzz
c
c     increment the total intermolecular energy
c
                     einter = einter + e
                  end if
               end do
            end if
         end do
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     perform deallocation of some local arrays
c
      deallocate (cscale)
      return
      end
c
c
c     ################################################################
c     ##                                                            ##
c     ##  subroutine echarge1b  --  method of lights charge derivs  ##
c     ##                                                            ##
c     ################################################################
c
c
c     "echarge1b" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c     using the method of lights
c
c
      subroutine echarge1b
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'bound.i'
      include 'boxes.i'
      include 'cell.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'couple.i'
      include 'deriv.i'
      include 'energi.i'
      include 'group.i'
      include 'inter.i'
      include 'light.i'
      include 'molcul.i'
      include 'shunt.i'
      include 'usage.i'
      include 'virial.i'
      integer i,j,k,ii,kk
      integer in,ic,kn,kc
      integer kgy,kgz,kmap
      integer start,stop
      real*8 e,fgrp,de,dc
      real*8 f,fi,fik
      real*8 r,r2,rb,rb2
      real*8 xi,yi,zi
      real*8 xr,yr,zr
      real*8 xc,yc,zc
      real*8 xic,yic,zic
      real*8 dedx,dedy,dedz
      real*8 dedxc,dedyc,dedzc
      real*8 shift,taper,trans
      real*8 dtaper,dtrans
      real*8 rc,rc2,rc3,rc4
      real*8 rc5,rc6,rc7
      real*8 vxx,vyy,vzz
      real*8 vyx,vzx,vzy
      real*8, allocatable :: cscale(:)
      real*8, allocatable :: xsort(:)
      real*8, allocatable :: ysort(:)
      real*8, allocatable :: zsort(:)
      logical proceed,usei
      logical prime,repeat
      character*6 mode
c
c
c     zero out the charge interaction energy and derivatives
c
      ec = 0.0d0
      do i = 1, n
         dec(1,i) = 0.0d0
         dec(2,i) = 0.0d0
         dec(3,i) = 0.0d0
      end do
      if (nion .eq. 0)  return
c
c     perform dynamic allocation of some local arrays
c
      allocate (cscale(n))
      allocate (xsort(8*n))
      allocate (ysort(8*n))
      allocate (zsort(8*n))
c
c     set array needed to scale connected atom interactions
c
      do i = 1, n
         cscale(i) = 1.0d0
      end do
c
c     set conversion factor, cutoff and switching coefficients
c
      f = electric / dielec
      mode = 'CHARGE'
      call switch (mode)
c
c     transfer the interaction site coordinates to sorting arrays
c
      do i = 1, nion
         k = kion(i)
         xsort(i) = x(k)
         ysort(i) = y(k)
         zsort(i) = z(k)
      end do
c
c     use the method of lights to generate neighbors
c
      call lights (off,nion,xsort,ysort,zsort)
c
c     loop over all atoms computing the interactions
c
      do ii = 1, nion
         i = iion(ii)
         in = jion(ii)
         ic = kion(ii)
         xic = xsort(rgx(ii))
         yic = ysort(rgy(ii))
         zic = zsort(rgz(ii))
         xi = x(i) - x(ic)
         yi = y(i) - y(ic)
         zi = z(i) - z(ic)
         fi = f * pchg(ii)
         usei = (use(i) .or. use(ic))
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     loop over method of lights neighbors of current atom
c
         if (kbx(ii) .le. kex(ii)) then
            repeat = .false.
            start = kbx(ii) + 1
            stop = kex(ii)
         else
            repeat = .true.
            start = 1
            stop = kex(ii)
         end if
   10    continue
         do j = start, stop
            kk = locx(j)
            kgy = rgy(kk)
            if (kby(ii) .le. key(ii)) then
               if (kgy.lt.kby(ii) .or. kgy.gt.key(ii))  goto 20
            else
               if (kgy.lt.kby(ii) .and. kgy.gt.key(ii))  goto 20
            end if
            kgz = rgz(kk)
            if (kbz(ii) .le. kez(ii)) then
               if (kgz.lt.kbz(ii) .or. kgz.gt.kez(ii))  goto 20
            else
               if (kgz.lt.kbz(ii) .and. kgz.gt.kez(ii))  goto 20
            end if
            kmap = kk - ((kk-1)/nion)*nion
            k = iion(kmap)
            kn = jion(kmap)
            kc = kion(kmap)
            prime = (kk .le. nion)
c
c     decide whether to compute the current interaction
c
            proceed = .true.
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            if (proceed)  proceed = (usei .or. use(k) .or. use(kc))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               xc = xic - xsort(j)
               yc = yic - ysort(kgy)
               zc = zic - zsort(kgz)
               if (use_bounds) then
                  if (abs(xc) .gt. xcell2)  xc = xc - sign(xcell,xc)
                  if (abs(yc) .gt. ycell2)  yc = yc - sign(ycell,yc)
                  if (abs(zc) .gt. zcell2)  zc = zc - sign(zcell,zc)
                  if (monoclinic) then
                     xc = xc + zc*beta_cos
                     zc = zc * beta_sin
                  else if (triclinic) then
                     xc = xc + yc*gamma_cos + zc*beta_cos
                     yc = yc*gamma_sin + zc*beta_term
                     zc = zc * gamma_term
                  end if
               end if
               rc2 = xc*xc + yc*yc + zc*zc
               if (rc2 .le. off2) then
                  xr = xc + xi - x(k) + x(kc)
                  yr = yc + yi - y(k) + y(kc)
                  zr = zc + zi - z(k) + z(kc)
                  r2 = xr*xr + yr*yr + zr*zr
                  r = sqrt(r2)
                  rb = r + ebuffer
                  rb2 = rb * rb
                  fik = fi * pchg(kmap)
                  if (prime)  fik = fik * cscale(kn)
                  if (use_polymer) then
                     if (r2 .gt. polycut2)  fik = fi * pchg(kmap)
                  end if
                  e = fik / rb
                  de = -fik / rb2
                  dc = 0.0d0
c
c     use shifted energy switching if near the cutoff distance
c
                  shift = fik / (0.5d0*(off+cut))
                  e = e - shift
                  if (rc2 .gt. cut2) then
                     rc = sqrt(rc2)
                     rc3 = rc2 * rc
                     rc4 = rc2 * rc2
                     rc5 = rc2 * rc3
                     rc6 = rc3 * rc3
                     rc7 = rc3 * rc4
                     taper = c5*rc5 + c4*rc4 + c3*rc3
     &                          + c2*rc2 + c1*rc + c0
                     dtaper = 5.0d0*c5*rc4 + 4.0d0*c4*rc3
     &                           + 3.0d0*c3*rc2 + 2.0d0*c2*rc + c1
                     trans = fik * (f7*rc7 + f6*rc6 + f5*rc5 + f4*rc4
     &                               + f3*rc3 + f2*rc2 + f1*rc + f0)
                     dtrans = fik * (7.0d0*f7*rc6 + 6.0d0*f6*rc5
     &                               + 5.0d0*f5*rc4 + 4.0d0*f4*rc3
     &                             + 3.0d0*f3*rc2 + 2.0d0*f2*rc + f1)
                     dc = (e*dtaper + dtrans) / rc
                     de = de * taper
                     e = e*taper + trans
                  end if
c
c     scale the interaction based on its group membership
c
                  if (use_group) then
                     e = e * fgrp
                     de = de * fgrp
                     dc = dc * fgrp
                  end if
c
c     form the chain rule terms for derivative expressions
c
                  de = de / r
                  dedx = de * xr
                  dedy = de * yr
                  dedz = de * zr
                  dedxc = dc * xc
                  dedyc = dc * yc
                  dedzc = dc * zc
c
c     increment the overall energy and derivative expressions
c
                  ec = ec + e
                  dec(1,i) = dec(1,i) + dedx
                  dec(2,i) = dec(2,i) + dedy
                  dec(3,i) = dec(3,i) + dedz
                  dec(1,ic) = dec(1,ic) + dedxc
                  dec(2,ic) = dec(2,ic) + dedyc
                  dec(3,ic) = dec(3,ic) + dedzc
                  dec(1,k) = dec(1,k) - dedx
                  dec(2,k) = dec(2,k) - dedy
                  dec(3,k) = dec(3,k) - dedz
                  dec(1,kc) = dec(1,kc) - dedxc
                  dec(2,kc) = dec(2,kc) - dedyc
                  dec(3,kc) = dec(3,kc) - dedzc
c
c     increment the internal virial tensor components
c
                  vxx = xr*dedx + xc*dedxc
                  vyx = yr*dedx + yc*dedxc
                  vzx = zr*dedx + zc*dedxc
                  vyy = yr*dedy + yc*dedyc
                  vzy = zr*dedy + zc*dedyc
                  vzz = zr*dedz + zc*dedzc
                  vir(1,1) = vir(1,1) + vxx
                  vir(2,1) = vir(2,1) + vyx
                  vir(3,1) = vir(3,1) + vzx
                  vir(1,2) = vir(1,2) + vyx
                  vir(2,2) = vir(2,2) + vyy
                  vir(3,2) = vir(3,2) + vzy
                  vir(1,3) = vir(1,3) + vzx
                  vir(2,3) = vir(2,3) + vzy
                  vir(3,3) = vir(3,3) + vzz
c
c     increment the total intermolecular energy
c
                  if (.not.prime .or. molcule(i).ne.molcule(k)) then
                     einter = einter + e
                  end if
               end if
            end if
   20       continue
         end do
         if (repeat) then
            repeat = .false.
            start = kbx(ii) + 1
            stop = nlight
            goto 10
         end if
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     perform deallocation of some local arrays
c
      deallocate (cscale)
      deallocate (xsort)
      deallocate (ysort)
      deallocate (zsort)
      return
      end
c
c
c     #################################################################
c     ##                                                             ##
c     ##  subroutine echarge1c  --  charge derivs via neighbor list  ##
c     ##                                                             ##
c     #################################################################
c
c
c     "echarge1c" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c     using a pairwise neighbor list
c
c
      subroutine echarge1c
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'bound.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'couple.i'
      include 'deriv.i'
      include 'energi.i'
      include 'group.i'
      include 'inter.i'
      include 'molcul.i'
      include 'neigh.i'
      include 'shunt.i'
      include 'usage.i'
      include 'virial.i'
      integer i,j,k
      integer ii,kk,kkk
      integer in,kn,ic,kc
      real*8 e,fgrp,de,dc
      real*8 f,fi,fik
      real*8 r,r2,rb,rb2
      real*8 xi,yi,zi
      real*8 xr,yr,zr
      real*8 xc,yc,zc
      real*8 xic,yic,zic
      real*8 dedx,dedy,dedz
      real*8 dedxc,dedyc,dedzc
      real*8 shift,taper,trans
      real*8 dtaper,dtrans
      real*8 rc,rc2,rc3,rc4
      real*8 rc5,rc6,rc7
      real*8 vxx,vyy,vzz
      real*8 vyx,vzx,vzy
      real*8, allocatable :: cscale(:)
      logical proceed,usei
      character*6 mode
c
c
c     zero out the charge interaction energy and derivatives
c
      ec = 0.0d0
      do i = 1, n
         dec(1,i) = 0.0d0
         dec(2,i) = 0.0d0
         dec(3,i) = 0.0d0
      end do
      if (nion .eq. 0)  return
c
c     perform dynamic allocation of some local arrays
c
      allocate (cscale(n))
c
c     set array needed to scale connected atom interactions
c
      do i = 1, n
         cscale(i) = 1.0d0
      end do
c
c     set conversion factor, cutoff and switching coefficients
c
      f = electric / dielec
      mode = 'CHARGE'
      call switch (mode)
c
c     compute the charge interaction energy and first derivatives
c
      do ii = 1, nion
         i = iion(ii)
         in = jion(ii)
         ic = kion(ii)
         xic = x(ic)
         yic = y(ic)
         zic = z(ic)
         xi = x(i) - xic
         yi = y(i) - yic
         zi = z(i) - zic
         fi = f * pchg(ii)
         usei = (use(i) .or. use(ic))
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     decide whether to compute the current interaction
c
         do kkk = 1, nelst(ii)
            kk = elst(kkk,ii)
            k = iion(kk)
            kn = jion(kk)
            kc = kion(kk)
            proceed = .true.
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            if (proceed)  proceed = (usei .or. use(k) .or. use(kc))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               xc = xic - x(kc)
               yc = yic - y(kc)
               zc = zic - z(kc)
               if (use_bounds)  call image (xc,yc,zc)
               rc2 = xc*xc + yc*yc + zc*zc
               if (rc2 .le. off2) then
                  xr = xc + xi - x(k) + x(kc)
                  yr = yc + yi - y(k) + y(kc)
                  zr = zc + zi - z(k) + z(kc)
                  r2 = xr*xr + yr*yr + zr*zr
                  r = sqrt(r2)
                  rb = r + ebuffer
                  rb2 = rb * rb
                  fik = fi * pchg(kk) * cscale(kn)
                  e = fik / rb
                  de = -fik / rb2
                  dc = 0.0d0
c
c     use shifted energy switching if near the cutoff distance
c
                  shift = fik / (0.5d0*(off+cut))
                  e = e - shift
                  if (rc2 .gt. cut2) then
                     rc = sqrt(rc2)
                     rc3 = rc2 * rc
                     rc4 = rc2 * rc2
                     rc5 = rc2 * rc3
                     rc6 = rc3 * rc3
                     rc7 = rc3 * rc4
                     taper = c5*rc5 + c4*rc4 + c3*rc3
     &                          + c2*rc2 + c1*rc + c0
                     dtaper = 5.0d0*c5*rc4 + 4.0d0*c4*rc3
     &                           + 3.0d0*c3*rc2 + 2.0d0*c2*rc + c1
                     trans = fik * (f7*rc7 + f6*rc6 + f5*rc5 + f4*rc4
     &                               + f3*rc3 + f2*rc2 + f1*rc + f0)
                     dtrans = fik * (7.0d0*f7*rc6 + 6.0d0*f6*rc5
     &                               + 5.0d0*f5*rc4 + 4.0d0*f4*rc3
     &                             + 3.0d0*f3*rc2 + 2.0d0*f2*rc + f1)
                     dc = (e*dtaper + dtrans) / rc
                     de = de * taper
                     e = e*taper + trans
                  end if
c
c     scale the interaction based on its group membership
c
                  if (use_group) then
                     e = e * fgrp
                     de = de * fgrp
                     dc = dc * fgrp
                  end if
c
c     form the chain rule terms for derivative expressions
c
                  de = de / r
                  dedx = de * xr
                  dedy = de * yr
                  dedz = de * zr
                  dedxc = dc * xc
                  dedyc = dc * yc
                  dedzc = dc * zc
c
c     increment the overall energy and derivative expressions
c
                  ec = ec + e
                  dec(1,i) = dec(1,i) + dedx
                  dec(2,i) = dec(2,i) + dedy
                  dec(3,i) = dec(3,i) + dedz
                  dec(1,ic) = dec(1,ic) + dedxc
                  dec(2,ic) = dec(2,ic) + dedyc
                  dec(3,ic) = dec(3,ic) + dedzc
                  dec(1,k) = dec(1,k) - dedx
                  dec(2,k) = dec(2,k) - dedy
                  dec(3,k) = dec(3,k) - dedz
                  dec(1,kc) = dec(1,kc) - dedxc
                  dec(2,kc) = dec(2,kc) - dedyc
                  dec(3,kc) = dec(3,kc) - dedzc
c
c     increment the internal virial tensor components
c
                  vxx = xr*dedx + xc*dedxc
                  vyx = yr*dedx + yc*dedxc
                  vzx = zr*dedx + zc*dedxc
                  vyy = yr*dedy + yc*dedyc
                  vzy = zr*dedy + zc*dedyc
                  vzz = zr*dedz + zc*dedzc
                  vir(1,1) = vir(1,1) + vxx
                  vir(2,1) = vir(2,1) + vyx
                  vir(3,1) = vir(3,1) + vzx
                  vir(1,2) = vir(1,2) + vyx
                  vir(2,2) = vir(2,2) + vyy
                  vir(3,2) = vir(3,2) + vzy
                  vir(1,3) = vir(1,3) + vzx
                  vir(2,3) = vir(2,3) + vzy
                  vir(3,3) = vir(3,3) + vzz
c
c     increment the total intermolecular energy
c
                  if (molcule(i) .ne. molcule(k)) then
                     einter = einter + e
                  end if
               end if
            end if
         end do
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     perform deallocation of some local arrays
c
      deallocate (cscale)
      return
      end
c
c
c     #################################################################
c     ##                                                             ##
c     ##  subroutine echarge1d  --  double loop Ewald charge derivs  ##
c     ##                                                             ##
c     #################################################################
c
c
c     "echarge1d" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c     using a particle mesh Ewald summation
c
c
      subroutine echarge1d
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'bound.i'
      include 'boxes.i'
      include 'cell.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'couple.i'
      include 'deriv.i'
      include 'energi.i'
      include 'ewald.i'
      include 'group.i'
      include 'inter.i'
      include 'math.i'
      include 'molcul.i'
      include 'shunt.i'
      include 'usage.i'
      include 'virial.i'
      integer i,j,k
      integer ii,kk
      integer in,kn
      real*8 e,de,efix
      real*8 eintra
      real*8 f,fi,fik,fs
      real*8 r,r2,rew
      real*8 rb,rb2
      real*8 fgrp,term
      real*8 xi,yi,zi
      real*8 xr,yr,zr
      real*8 xd,yd,zd
      real*8 erfc,erfterm
      real*8 scale,scaleterm
      real*8 dedx,dedy,dedz
      real*8 vxx,vyy,vzz
      real*8 vyx,vzx,vzy
      real*8, allocatable :: cscale(:)
      logical proceed,usei
      character*6 mode
      external erfc
c
c
c     zero out the Ewald summation energy and derivatives
c
      ec = 0.0d0
      do i = 1, n
         dec(1,i) = 0.0d0
         dec(2,i) = 0.0d0
         dec(3,i) = 0.0d0
      end do
      if (nion .eq. 0)  return
c
c     perform dynamic allocation of some local arrays
c
      allocate (cscale(n))
c
c     set array needed to scale connected atom interactions
c
      do i = 1, n
         cscale(i) = 1.0d0
      end do
c
c     zero out the intramolecular portion of the Ewald energy
c
      eintra = 0.0d0
c
c     set conversion factor, cutoff and switching coefficients
c
      f = electric / dielec
      mode = 'EWALD'
      call switch (mode)
c
c     compute the Ewald self-energy term over all the atoms
c
      fs = -f * aewald / sqrtpi
      do ii = 1, nion
         e = fs * pchg(ii)**2
         ec = ec + e
      end do
c
c     compute the cell dipole boundary correction term
c
      if (boundary .eq. 'VACUUM') then
         xd = 0.0d0
         yd = 0.0d0
         zd = 0.0d0
         do ii = 1, nion
            i = iion(ii)
            xd = xd + pchg(ii)*x(i)
            yd = yd + pchg(ii)*y(i)
            zd = zd + pchg(ii)*z(i)
         end do
         term = (2.0d0/3.0d0) * f * (pi/volbox)
         e = term * (xd*xd+yd*yd+zd*zd)
         ec = ec + e
         do ii = 1, nion
            i = iion(ii)
            de = 2.0d0 * term * pchg(ii)
            dedx = de * xd
            dedy = de * yd
            dedz = de * zd
            dec(1,i) = dec(1,i) + dedx
            dec(2,i) = dec(2,i) + dedy
            dec(3,i) = dec(3,i) + dedz
         end do
      end if
c
c     compute reciprocal space Ewald energy and first derivatives
c
      call ecrecip1
c
c     compute the real space Ewald energy and first derivatives
c
      do ii = 1, nion-1
         i = iion(ii)
         in = jion(ii)
         usei = use(i)
         xi = x(i)
         yi = y(i)
         zi = z(i)
         fi = f * pchg(ii)
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     decide whether to compute the current interaction
c
         do kk = ii+1, nion
            k = iion(kk)
            kn = jion(kk)
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            proceed = .true.
            if (proceed)  proceed = (usei .or. use(k))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               xr = xi - x(k)
               yr = yi - y(k)
               zr = zi - z(k)
c
c     find energy for interactions within real space cutoff
c
               call image (xr,yr,zr)
               r2 = xr*xr + yr*yr + zr*zr
               if (r2 .le. off2) then
                  r = sqrt(r2)
                  rb = r + ebuffer
                  rb2 = rb * rb
                  fik = fi * pchg(kk)
                  rew = aewald * r
                  erfterm = erfc (rew)
                  scale = cscale(kn)
                  if (use_group)  scale = scale * fgrp
                  scaleterm = scale - 1.0d0
                  e = (fik/rb) * (erfterm+scaleterm)
                  de = -fik * ((erfterm+scaleterm)/rb2
     &                    + (2.0d0*aewald/sqrtpi)*exp(-rew**2)/r)
c
c     form the chain rule terms for derivative expressions
c
                  de = de / r
                  dedx = de * xr
                  dedy = de * yr
                  dedz = de * zr
c
c     increment the overall energy and derivative expressions
c
                  ec = ec + e
                  dec(1,i) = dec(1,i) + dedx
                  dec(2,i) = dec(2,i) + dedy
                  dec(3,i) = dec(3,i) + dedz
                  dec(1,k) = dec(1,k) - dedx
                  dec(2,k) = dec(2,k) - dedy
                  dec(3,k) = dec(3,k) - dedz
c
c     increment the internal virial tensor components
c
                  vxx = xr * dedx
                  vyx = yr * dedx
                  vzx = zr * dedx
                  vyy = yr * dedy
                  vzy = zr * dedy
                  vzz = zr * dedz
                  vir(1,1) = vir(1,1) + vxx
                  vir(2,1) = vir(2,1) + vyx
                  vir(3,1) = vir(3,1) + vzx
                  vir(1,2) = vir(1,2) + vyx
                  vir(2,2) = vir(2,2) + vyy
                  vir(3,2) = vir(3,2) + vzy
                  vir(1,3) = vir(1,3) + vzx
                  vir(2,3) = vir(2,3) + vzy
                  vir(3,3) = vir(3,3) + vzz
c
c     increment the total intramolecular energy
c
                  if (molcule(i) .eq. molcule(k)) then
                     efix = (fik/rb) * scale
                     eintra = eintra + efix
                  end if
               end if
            end if
         end do
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     for periodic boundary conditions with large cutoffs
c     neighbors must be found by the replicates method
c
      if (.not. use_replica)  return
c
c     calculate real space portion involving other unit cells
c
      do ii = 1, nion
         i = iion(ii)
         in = jion(ii)
         usei = use(i)
         xi = x(i)
         yi = y(i)
         zi = z(i)
         fi = f * pchg(ii)
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     decide whether to compute the current interaction
c
         do kk = ii, nion
            k = iion(kk)
            kn = jion(kk)
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            proceed = .true.
            if (proceed)  proceed = (usei .or. use(k))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               do j = 1, ncell
                  xr = xi - x(k)
                  yr = yi - y(k)
                  zr = zi - z(k)
c
c     find appropriate image and check the real space cutoff
c
                  call imager (xr,yr,zr,j)
                  r2 = xr*xr + yr*yr + zr*zr
                  if (r2 .le. off2) then
                     r = sqrt(r2)
                     rb = r + ebuffer
                     rb2 = rb * rb
                     fik = fi * pchg(kk)
                     rew = aewald * r
                     erfterm = erfc (rew)
                     scale = 1.0d0
                     if (use_group)  scale = scale * fgrp
                     if (use_polymer) then
                        if (r2 .le. polycut2) then
                           scale = scale * cscale(kn)
                        end if
                     end if
                     scaleterm = scale - 1.0d0
                     e = (fik/rb) * (erfterm+scaleterm)
                     de = -fik * ((erfterm+scaleterm)/rb2
     &                       + (2.0d0*aewald/sqrtpi)*exp(-rew**2)/r)
c
c     form the chain rule terms for derivative expressions
c
                     de = de / r
                     dedx = de * xr
                     dedy = de * yr
                     dedz = de * zr
c
c     increment the energy and gradient values
c
                     if (i .eq. k)  e = 0.5d0 * e
                     ec = ec + e
                     dec(1,i) = dec(1,i) + dedx
                     dec(2,i) = dec(2,i) + dedy
                     dec(3,i) = dec(3,i) + dedz
                     if (i .ne. k) then
                        dec(1,k) = dec(1,k) - dedx
                        dec(2,k) = dec(2,k) - dedy
                        dec(3,k) = dec(3,k) - dedz
                     end if
c
c     increment the internal virial tensor components
c
                     vxx = xr * dedx
                     vyx = yr * dedx
                     vzx = zr * dedx
                     vyy = yr * dedy
                     vzy = zr * dedy
                     vzz = zr * dedz
                     vir(1,1) = vir(1,1) + vxx
                     vir(2,1) = vir(2,1) + vyx
                     vir(3,1) = vir(3,1) + vzx
                     vir(1,2) = vir(1,2) + vyx
                     vir(2,2) = vir(2,2) + vyy
                     vir(3,2) = vir(3,2) + vzy
                     vir(1,3) = vir(1,3) + vzx
                     vir(2,3) = vir(2,3) + vzy
                     vir(3,3) = vir(3,3) + vzz
                  end if
               end do
            end if
         end do
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     intermolecular energy is total minus intramolecular part
c
      einter = einter + ec - eintra
c
c     perform deallocation of some local arrays
c
      deallocate (cscale)
      return
      end
c
c
c     ################################################################
c     ##                                                            ##
c     ##  subroutine echarge1e  --  Ewald charge derivs via lights  ##
c     ##                                                            ##
c     ################################################################
c
c
c     "echarge1e" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c     using a particle mesh Ewald summation and the method of lights
c
c
      subroutine echarge1e
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'bound.i'
      include 'boxes.i'
      include 'cell.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'couple.i'
      include 'deriv.i'
      include 'energi.i'
      include 'ewald.i'
      include 'group.i'
      include 'inter.i'
      include 'light.i'
      include 'math.i'
      include 'molcul.i'
      include 'shunt.i'
      include 'usage.i'
      include 'virial.i'
      integer i,j,k
      integer ii,kk,in,kn
      integer kgy,kgz,kmap
      integer start,stop
      real*8 e,de,efix
      real*8 eintra
      real*8 f,fi,fik,fs
      real*8 r,r2,rew
      real*8 rb,rb2
      real*8 fgrp,term
      real*8 xi,yi,zi
      real*8 xr,yr,zr
      real*8 xd,yd,zd
      real*8 erfc,erfterm
      real*8 scale,scaleterm
      real*8 dedx,dedy,dedz
      real*8 vxx,vyy,vzz
      real*8 vyx,vzx,vzy
      real*8, allocatable :: cscale(:)
      real*8, allocatable :: xsort(:)
      real*8, allocatable :: ysort(:)
      real*8, allocatable :: zsort(:)
      logical proceed,usei
      logical prime,repeat
      character*6 mode
      external erfc
c
c
c     zero out the Ewald summation energy and derivatives
c
      ec = 0.0d0
      do i = 1, n
         dec(1,i) = 0.0d0
         dec(2,i) = 0.0d0
         dec(3,i) = 0.0d0
      end do
      if (nion .eq. 0)  return
c
c     perform dynamic allocation of some local arrays
c
      allocate (cscale(n))
      allocate (xsort(8*n))
      allocate (ysort(8*n))
      allocate (zsort(8*n))
c
c     set array needed to scale connected atom interactions
c
      do i = 1, n
         cscale(i) = 1.0d0
      end do
c
c     zero out the intramolecular portion of the Ewald energy
c
      eintra = 0.0d0
c
c     set conversion factor, cutoff and switching coefficients
c
      f = electric / dielec
      mode = 'EWALD'
      call switch (mode)
c
c     compute the Ewald self-energy term over all the atoms
c
      fs = -f * aewald / sqrtpi
      do ii = 1, nion
         e = fs * pchg(ii)**2
         ec = ec + e
      end do
c
c     compute the cell dipole boundary correction term
c
      if (boundary .eq. 'VACUUM') then
         xd = 0.0d0
         yd = 0.0d0
         zd = 0.0d0
         do ii = 1, nion
            i = iion(ii)
            xd = xd + pchg(ii)*x(i)
            yd = yd + pchg(ii)*y(i)
            zd = zd + pchg(ii)*z(i)
         end do
         term = (2.0d0/3.0d0) * f * (pi/volbox)
         e = term * (xd*xd+yd*yd+zd*zd)
         ec = ec + e
         do ii = 1, nion
            i = iion(ii)
            de = 2.0d0 * term * pchg(ii)
            dedx = de * xd
            dedy = de * yd
            dedz = de * zd
            dec(1,i) = dec(1,i) + dedx
            dec(2,i) = dec(2,i) + dedy
            dec(3,i) = dec(3,i) + dedz
         end do
      end if
c
c     compute reciprocal space Ewald energy and first derivatives
c
      call ecrecip1
c
c     compute the real space portion of the Ewald summation;
c     transfer the interaction site coordinates to sorting arrays
c
      do i = 1, nion
         k = iion(i)
         xsort(i) = x(k)
         ysort(i) = y(k)
         zsort(i) = z(k)
      end do
c
c     use the method of lights to generate neighbors
c
      call lights (off,nion,xsort,ysort,zsort)
c
c     loop over all atoms computing the interactions
c
      do ii = 1, nion
         i = iion(ii)
         in = jion(ii)
         xi = xsort(rgx(ii))
         yi = ysort(rgy(ii))
         zi = zsort(rgz(ii))
         fi = f * pchg(ii)
         usei = (use(i))
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     loop over method of lights neighbors of current atom
c
         if (kbx(ii) .le. kex(ii)) then
            repeat = .false.
            start = kbx(ii) + 1
            stop = kex(ii)
         else
            repeat = .true.
            start = 1
            stop = kex(ii)
         end if
   10    continue
         do j = start, stop
            kk = locx(j)
            kgy = rgy(kk)
            if (kby(ii) .le. key(ii)) then
               if (kgy.lt.kby(ii) .or. kgy.gt.key(ii))  goto 20
            else
               if (kgy.lt.kby(ii) .and. kgy.gt.key(ii))  goto 20
            end if
            kgz = rgz(kk)
            if (kbz(ii) .le. kez(ii)) then
               if (kgz.lt.kbz(ii) .or. kgz.gt.kez(ii))  goto 20
            else
               if (kgz.lt.kbz(ii) .and. kgz.gt.kez(ii))  goto 20
            end if
            kmap = kk - ((kk-1)/nion)*nion
            k = iion(kmap)
            kn = jion(kmap)
            prime = (kk .le. nion)
c
c     decide whether to compute the current interaction
c
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            proceed = .true.
            if (proceed)  proceed = (usei .or. use(k))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               xr = xi - xsort(j)
               yr = yi - ysort(kgy)
               zr = zi - zsort(kgz)
c
c     find energy for interactions within real space cutoff
c
               if (use_bounds) then
                  if (abs(xr) .gt. xcell2)  xr = xr - sign(xcell,xr)
                  if (abs(yr) .gt. ycell2)  yr = yr - sign(ycell,yr)
                  if (abs(zr) .gt. zcell2)  zr = zr - sign(zcell,zr)
                  if (monoclinic) then
                     xr = xr + zr*beta_cos
                     zr = zr * beta_sin
                  else if (triclinic) then
                     xr = xr + yr*gamma_cos + zr*beta_cos
                     yr = yr*gamma_sin + zr*beta_term
                     zr = zr * gamma_term
                  end if
               end if
               r2 = xr*xr + yr*yr + zr*zr
               if (r2 .le. off2) then
                  r = sqrt(r2)
                  rb = r + ebuffer
                  rb2 = rb * rb
                  rew = aewald * r
                  erfterm = erfc (rew)
                  scale = 1.0d0
                  if (prime)  scale = cscale(kn)
                  if (use_group)  scale = scale * fgrp
                  fik = fi * pchg(kmap)
                  if (use_polymer) then
                     if (r2 .gt. polycut2)  fik = fi * pchg(kmap)
                  end if
                  scaleterm = scale - 1.0d0
                  e = (fik/rb) * (erfterm+scaleterm)
                  de = -fik * ((erfterm+scaleterm)/rb2
     &                    + (2.0d0*aewald/sqrtpi)*exp(-rew**2)/r)
c
c     form the chain rule terms for derivative expressions
c
                  de = de / r
                  dedx = de * xr
                  dedy = de * yr
                  dedz = de * zr
c
c     increment the overall energy and derivative expressions
c
                  ec = ec + e
                  dec(1,i) = dec(1,i) + dedx
                  dec(2,i) = dec(2,i) + dedy
                  dec(3,i) = dec(3,i) + dedz
                  dec(1,k) = dec(1,k) - dedx
                  dec(2,k) = dec(2,k) - dedy
                  dec(3,k) = dec(3,k) - dedz
c
c     increment the internal virial tensor components
c
                  vxx = xr * dedx
                  vyx = yr * dedx
                  vzx = zr * dedx
                  vyy = yr * dedy
                  vzy = zr * dedy
                  vzz = zr * dedz
                  vir(1,1) = vir(1,1) + vxx
                  vir(2,1) = vir(2,1) + vyx
                  vir(3,1) = vir(3,1) + vzx
                  vir(1,2) = vir(1,2) + vyx
                  vir(2,2) = vir(2,2) + vyy
                  vir(3,2) = vir(3,2) + vzy
                  vir(1,3) = vir(1,3) + vzx
                  vir(2,3) = vir(2,3) + vzy
                  vir(3,3) = vir(3,3) + vzz
c
c     increment the total intramolecular energy
c
                  if (prime .and. molcule(i).eq.molcule(k)) then
                     efix = (fik/rb) * scale
                     eintra = eintra + efix
                  end if
               end if
            end if
   20       continue
         end do
         if (repeat) then
            repeat = .false.
            start = kbx(ii) + 1
            stop = nlight
            goto 10
         end if
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     intermolecular energy is total minus intramolecular part
c
      einter = einter + ec - eintra
c
c     perform deallocation of some local arrays
c
      deallocate (cscale)
      deallocate (xsort)
      deallocate (ysort)
      deallocate (zsort)
      return
      end
c
c
c     ##############################################################
c     ##                                                          ##
c     ##  subroutine echarge1f  --  Ewald charge derivs via list  ##
c     ##                                                          ##
c     ##############################################################
c
c
c     "echarge1f" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c     using a particle mesh Ewald summation and a neighbor list
c
c
      subroutine echarge1f
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'bound.i'
      include 'boxes.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'couple.i'
      include 'deriv.i'
      include 'energi.i'
      include 'ewald.i'
      include 'group.i'
      include 'inter.i'
      include 'math.i'
      include 'molcul.i'
      include 'neigh.i'
      include 'shunt.i'
      include 'usage.i'
      include 'virial.i'
      integer i,j,k
      integer ii,kk,kkk
      integer in,kn
      real*8 e,de,efix
      real*8 eintra
      real*8 f,fi,fik,fs
      real*8 r,r2,rew
      real*8 rb,rb2
      real*8 fgrp,term
      real*8 xi,yi,zi
      real*8 xr,yr,zr
      real*8 xd,yd,zd
      real*8 erfc,erfterm
      real*8 scale,scaleterm
      real*8 dedx,dedy,dedz
      real*8 vxx,vyy,vzz
      real*8 vyx,vzx,vzy
      real*8 ect,eintrat
      real*8 virt(3,3)
      real*8, allocatable :: cscale(:)
      real*8, allocatable :: dect1(:,:)
      real*8, allocatable :: dect2(:,:)
      logical proceed,usei
      character*6 mode
      external erfc
c
c
c     zero out the Ewald summation energy and derivatives
c
      ec = 0.0d0
      do i = 1, n
         dec(1,i) = 0.0d0
         dec(2,i) = 0.0d0
         dec(3,i) = 0.0d0
      end do
      if (nion .eq. 0)  return
c
c     perform dynamic allocation of some local arrays
c
      allocate (cscale(n))
      allocate (dect1(3,n))
      allocate (dect2(3,n))
c
c     set array needed to scale connected atom interactions
c
      do i = 1, n
         cscale(i) = 1.0d0
      end do
c
c     zero out the intramolecular portion of the Ewald energy
c
      eintra = 0.0d0
c
c     set conversion factor, cutoff and switching coefficients
c
      f = electric / dielec
      mode = 'EWALD'
      call switch (mode)
c
c     compute the Ewald self-energy term over all the atoms
c
      fs = -f * aewald / sqrtpi
      do ii = 1, nion
         e = fs * pchg(ii)**2
         ec = ec + e
      end do
c
c     compute the cell dipole boundary correction term
c
      if (boundary .eq. 'VACUUM') then
         xd = 0.0d0
         yd = 0.0d0
         zd = 0.0d0
         do ii = 1, nion
            i = iion(ii)
            xd = xd + pchg(ii)*x(i)
            yd = yd + pchg(ii)*y(i)
            zd = zd + pchg(ii)*z(i)
         end do
         term = (2.0d0/3.0d0) * f * (pi/volbox)
         e = term * (xd*xd+yd*yd+zd*zd)
         ec = ec + e
         do ii = 1, nion
            i = iion(ii)
            de = 2.0d0 * term * pchg(ii)
            dedx = de * xd
            dedy = de * yd
            dedz = de * zd
            dec(1,i) = dec(1,i) + dedx
            dec(2,i) = dec(2,i) + dedy
            dec(3,i) = dec(3,i) + dedz
         end do
      end if
c
c     compute reciprocal space Ewald energy and first derivatives
c
      call ecrecip1
c
c     initialize local variables for OpenMP calculation
c
      ect = ec
      eintrat = eintra
      do i = 1, n
         dect1(1,i) = 0.0d0
         dect1(2,i) = 0.0d0
         dect1(3,i) = 0.0d0
         dect2(1,i) = 0.0d0
         dect2(2,i) = 0.0d0
         dect2(3,i) = 0.0d0
      end do
      do i = 1, 3
         virt(1,i) = vir(1,i)
         virt(2,i) = vir(2,i)
         virt(3,i) = vir(3,i)
      end do
c
c     set OpenMP directives for the major loop structure
c
!$OMP PARALLEL default(private) shared(nion,iion,jion,use,
!$OMP& x,y,z,f,pchg,nelst,elst,n12,n13,n14,n15,i12,i13,i14,
!$OMP& i15,c2scale,c3scale,c4scale,c5scale,use_group,off2,
!$OMP& aewald,molcule,ebuffer) firstprivate(cscale)
!$OMP& shared(ect,eintrat,dect1,dect2,virt)
!$OMP DO reduction(+:ect,eintrat,dect1,dect2,virt)
!$OMP& schedule(dynamic)
c
c     compute the real space Ewald energy and first derivatives
c	  
      do ii = 1, nion
         i = iion(ii)
         in = jion(ii)
         usei = use(i)
         xi = x(i)
         yi = y(i)
         zi = z(i)
         fi = f * pchg(ii)
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     decide whether to compute the current interaction
c
         do kkk = 1, nelst(ii)
            kk = elst(kkk,ii)
            k = iion(kk)
            kn = jion(kk)
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            proceed = .true.
            if (proceed)  proceed = (usei .or. use(k))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               xr = xi - x(k)
               yr = yi - y(k)
               zr = zi - z(k)
c
c     find energy for interactions within real space cutoff
c
               call image (xr,yr,zr)
               r2 = xr*xr + yr*yr + zr*zr
               if (r2 .le. off2) then
                  r = sqrt(r2)
                  rb = r + ebuffer
                  rb2 = rb * rb
                  fik = fi * pchg(kk)
                  rew = aewald * r
                  erfterm = erfc (rew)
                  scale = cscale(kn)
                  if (use_group)  scale = scale * fgrp
                  scaleterm = scale - 1.0d0
                  e = (fik/rb) * (erfterm+scaleterm)
                  de = -fik * ((erfterm+scaleterm)/rb2
     &                    + (2.0d0*aewald/sqrtpi)*exp(-rew**2)/r)
c
c     form the chain rule terms for derivative expressions
c
                  de = de / r
                  dedx = de * xr
                  dedy = de * yr
                  dedz = de * zr
c
c     increment the overall energy and derivative expressions
c
                 ect = ect + e
                 dect1(1,i) = dect1(1,i) + dedx
                 dect1(2,i) = dect1(2,i) + dedy
                 dect1(3,i) = dect1(3,i) + dedz
                 dect2(1,k) = dect2(1,k) - dedx
                 dect2(2,k) = dect2(2,k) - dedy
                 dect2(3,k) = dect2(3,k) - dedz
c
c     increment the internal virial tensor components
c
                  vxx = xr * dedx
                  vyx = yr * dedx
                  vzx = zr * dedx
                  vyy = yr * dedy
                  vzy = zr * dedy
                  vzz = zr * dedz
                  virt(1,1) = virt(1,1) + vxx
                  virt(2,1) = virt(2,1) + vyx
                  virt(3,1) = virt(3,1) + vzx
                  virt(1,2) = virt(1,2) + vyx
                  virt(2,2) = virt(2,2) + vyy
                  virt(3,2) = virt(3,2) + vzy
                  virt(1,3) = virt(1,3) + vzx
                  virt(2,3) = virt(2,3) + vzy
                  virt(3,3) = virt(3,3) + vzz
c
c     increment the total intramolecular energy
c
                  if (molcule(i) .eq. molcule(k)) then
                     efix = (fik/rb) * scale
                     eintrat = eintrat + efix
                  end if
               end if
            end if
         end do
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     end OpenMP directives for the major loop structure
c
!$OMP END DO
!$OMP END PARALLEL
c
c     add local copies to global variables for OpenMP calculation
c
      ec = ect
      eintra = eintrat
      do i = 1, n
         dec(1,i) = dec(1,i) + dect1(1,i) + dect2(1,i)
         dec(2,i) = dec(2,i) + dect1(2,i) + dect2(2,i)
         dec(3,i) = dec(3,i) + dect1(3,i) + dect2(3,i)
      end do
      do i = 1, 3
         vir(1,i) = virt(1,i)
         vir(2,i) = virt(2,i)
         vir(3,i) = virt(3,i)
      end do	  
c
c     intermolecular energy is total minus intramolecular part
c
      einter = einter + ec - eintra
c
c     perform deallocation of some local arrays
c
      deallocate (cscale)
      deallocate (dect1)
      deallocate (dect2)
      return
      end
c
c
c     ##################################################################
c     ##                                                              ##
c     ##  subroutine echarge1g  --  charge derivatives for smoothing  ##
c     ##                                                              ##
c     ##################################################################
c
c
c     "echarge1g" calculates the charge-charge interaction energy
c     and first derivatives with respect to Cartesian coordinates
c     for use with potential smoothing methods
c
c
      subroutine echarge1g
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'couple.i'
      include 'deriv.i'
      include 'energi.i'
      include 'group.i'
      include 'inter.i'
      include 'math.i'
      include 'molcul.i'
      include 'usage.i'
      include 'warp.i'
      integer i,j,k
      integer ii,kk
      integer in,kn
      real*8 e,de,fgrp
      real*8 r,r2,rb,rb2
      real*8 f,fi,fik
      real*8 xi,yi,zi
      real*8 xr,yr,zr
      real*8 dedx,dedy,dedz
      real*8 erf,erfterm
      real*8 expcut,expterm
      real*8 wterm,width
      real*8 width2,width3
      real*8, allocatable :: cscale(:)
      logical proceed,usei
      external erf
c
c
c     zero out the charge interaction energy and derivatives
c
      ec = 0.0d0
      do i = 1, n
         dec(1,i) = 0.0d0
         dec(2,i) = 0.0d0
         dec(3,i) = 0.0d0
      end do
      if (nion .eq. 0)  return
c
c     perform dynamic allocation of some local arrays
c
      allocate (cscale(n))
c
c     set array needed to scale connected atom interactions
c
      do i = 1, n
         cscale(i) = 1.0d0
      end do
c
c     set the energy units conversion factor
c
      f = electric / dielec
      expcut = -50.0d0
c
c     set the extent of smoothing to be performed
c
      width = deform * diffc
      if (use_dem) then
         if (width .gt. 0.0d0)  width = 0.5d0 / sqrt(width)
      else if (use_gda) then
         wterm = sqrt(3.0d0/(2.0d0*diffc))
      end if
      width2 = width * width
      width3 = width * width2
c
c     compute the charge interaction energy and first derivatives
c
      do ii = 1, nion-1
         i = iion(ii)
         in = jion(ii)
         usei = (use(i))
         xi = x(i)
         yi = y(i)
         zi = z(i)
         fi = f * pchg(ii)
c
c     set interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = c2scale
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = c3scale
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = c4scale
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = c5scale
         end do
c
c     decide whether to compute the current interaction
c
         do kk = ii+1, nion
            k = iion(kk)
            kn = jion(kk)
            proceed = .true.
            if (use_group)  call groups (proceed,fgrp,i,k,0,0,0,0)
            if (proceed)  proceed = (usei .or. use(k))
c
c     compute the energy contribution for this interaction
c
            if (proceed) then
               xr = xi - x(k)
               yr = yi - y(k)
               zr = zi - z(k)
               r2 = xr*xr + yr*yr + zr*zr
               r = sqrt(r2)
               rb = r + ebuffer
               rb2 = rb * rb
               fik = fi * pchg(kk) * cscale(kn)
               e = fik / rb
               de = -fik / rb2
c
c     transform the potential function via smoothing
c
               if (use_dem) then
                  if (width .gt. 0.0d0) then
                     erfterm = erf(width*rb)
                     expterm = -rb2 * width2
                     if (expterm .gt. expcut) then
                        expterm = 2.0d0*fik*width*exp(expterm)
     &                               / (sqrtpi*rb)
                     else
                        expterm = 0.0d0
                     end if
                     e = e * erfterm
                     de = de*erfterm + expterm
                  end if
               else if (use_gda) then
                  width = m2(i) + m2(k)
                  if (width .gt. 0.0d0) then
                     width = wterm / sqrt(width)
                     erfterm = erf(width*rb)
                     expterm = -rb2 * width * width
                     if (expterm .gt. expcut) then
                        expterm = 2.0d0*fik*width*exp(expterm)
     &                               / (sqrtpi*rb)
                     else
                        expterm = 0.0d0
                     end if
                     e = e * erfterm
                     de = de*erfterm + expterm
                  end if
               else if (use_tophat) then
                  if (width .gt. rb) then
                     e = fik * (3.0d0*width2-rb2) / (2.0d0*width3)
                     de = -fik * rb / width3
                  end if
               else if (use_stophat) then
                  wterm = rb + width
                  e = fik / wterm
                  de = -fik / (wterm*wterm)
               end if
c
c     scale the interaction based on its group membership
c
               if (use_group) then
                  e = e * fgrp
                  de = de * fgrp
               end if
c
c     form the chain rule terms for derivative expressions
c
               de = de / r
               dedx = de * xr
               dedy = de * yr
               dedz = de * zr
c
c     increment the overall energy and derivative expressions
c
               ec = ec + e
               dec(1,i) = dec(1,i) + dedx
               dec(2,i) = dec(2,i) + dedy
               dec(3,i) = dec(3,i) + dedz
               dec(1,k) = dec(1,k) - dedx
               dec(2,k) = dec(2,k) - dedy
               dec(3,k) = dec(3,k) - dedz
c
c     increment the total intermolecular energy
c
               if (molcule(i) .ne. molcule(k)) then
                  einter = einter + e
               end if
            end if
         end do
c
c     reset interaction scaling coefficients for connected atoms
c
         do j = 1, n12(in)
            cscale(i12(j,in)) = 1.0d0
         end do
         do j = 1, n13(in)
            cscale(i13(j,in)) = 1.0d0
         end do
         do j = 1, n14(in)
            cscale(i14(j,in)) = 1.0d0
         end do
         do j = 1, n15(in)
            cscale(i15(j,in)) = 1.0d0
         end do
      end do
c
c     perform deallocation of some local arrays
c
      deallocate (cscale)
      return
      end
c
c
c     #################################################################
c     ##                                                             ##
c     ##  subroutine ecrecip1  --  PME recip energy and derivatives  ##
c     ##                                                             ##
c     #################################################################
c
c
c     "ecrecip1" evaluates the reciprocal space portion of the particle
c     mesh Ewald summation energy and gradient due to partial charges
c
c     literature reference:
c
c     U. Essmann, L. Perera, M. L Berkowitz, T. Darden, H. Lee and
c     L. G. Pedersen, "A Smooth Particle Mesh Ewald Method", Journal
c     of Chemical Physics, 103, 8577-8593 (1995)
c
c     modifications for nonperiodic systems suggested by Tom Darden
c     during May 2007
c
c
      subroutine ecrecip1
      implicit none
      include 'sizes.i'
      include 'atoms.i'
      include 'bound.i'
      include 'boxes.i'
      include 'charge.i'
      include 'chgpot.i'
      include 'deriv.i'
      include 'energi.i'
      include 'ewald.i'
      include 'math.i'
      include 'pme.i'
      include 'virial.i'
      integer i,j,k
      integer isite,iatm
      integer i0,j0,k0
      integer it1,it2,it3
      integer k1,k2,k3
      integer m1,m2,m3
      integer nf1,nf2,nf3
      integer nff,npoint
      integer igrd0,jgrd0,kgrd0
      real*8 e,term,expterm
      real*8 vterm,pterm
      real*8 volterm
      real*8 f,fi,denom
      real*8 hsq,struc2
      real*8 de1,de2,de3
      real*8 dn1,dn2,dn3
      real*8 t1,t2,t3
      real*8 dt1,dt2,dt3
      real*8 h1,h2,h3
      real*8 r1,r2,r3
c
c
c     zero out the particle mesh Ewald charge grid
c
      do k = 1, nfft3
         do j = 1, nfft2
            do i = 1, nfft1
               qgrid(1,i,j,k) = 0.0d0
               qgrid(2,i,j,k) = 0.0d0
            end do
         end do
      end do
c
c     get B-spline coefficients and put charges onto grid
c
      call bspline_fill
      call table_fill
      call grid_pchg
c
c     perform the 3-D FFT forward transformation
c
      call fftfront
c
c     use scalar sum to get reciprocal space energy and virial
c
      f = 0.5d0 * electric / dielec
      npoint = nfft1 * nfft2 * nfft3
      pterm = (pi/aewald)**2
      volterm = pi * volbox
      nff = nfft1 * nfft2
      nf1 = (nfft1+1) / 2
      nf2 = (nfft2+1) / 2
      nf3 = (nfft3+1) / 2
      do i = 1, npoint-1
         k3 = i/nff + 1
         j = i - (k3-1)*nff
         k2 = j/nfft1 + 1
         k1 = j - (k2-1)*nfft1 + 1
         m1 = k1 - 1
         m2 = k2 - 1
         m3 = k3 - 1
         if (k1 .gt. nf1)  m1 = m1 - nfft1
         if (k2 .gt. nf2)  m2 = m2 - nfft2
         if (k3 .gt. nf3)  m3 = m3 - nfft3
         r1 = dble(m1)
         r2 = dble(m2)
         r3 = dble(m3)
         h1 = recip(1,1)*r1 + recip(1,2)*r2 + recip(1,3)*r3
         h2 = recip(2,1)*r1 + recip(2,2)*r2 + recip(2,3)*r3
         h3 = recip(3,1)*r1 + recip(3,2)*r2 + recip(3,3)*r3
         hsq = h1*h1 + h2*h2 + h3*h3
         term = -pterm * hsq
         expterm = 0.0d0
         if (term .gt. -50.0d0) then
            denom = volterm*hsq*bsmod1(k1)*bsmod2(k2)*bsmod3(k3)
            expterm = exp(term) / denom
            if (.not. use_bounds) then
               expterm = expterm * (1.0d0-cos(pi*xbox*sqrt(hsq)))
            else if (octahedron) then
               if (mod(m1+m2+m3,2) .ne. 0)  expterm = 0.0d0
            end if
            struc2 = qgrid(1,k1,k2,k3)**2 + qgrid(2,k1,k2,k3)**2
            e = f * expterm * struc2
            ec = ec + e
            vterm = (2.0d0/hsq) * (1.0d0-term) * e
            vir(1,1) = vir(1,1) + h1*h1*vterm - e
            vir(2,1) = vir(2,1) + h1*h2*vterm
            vir(3,1) = vir(3,1) + h1*h3*vterm
            vir(1,2) = vir(1,2) + h2*h1*vterm
            vir(2,2) = vir(2,2) + h2*h2*vterm - e
            vir(3,2) = vir(3,2) + h2*h3*vterm
            vir(1,3) = vir(1,3) + h3*h1*vterm
            vir(2,3) = vir(2,3) + h3*h2*vterm
            vir(3,3) = vir(3,3) + h3*h3*vterm - e
         end if
         qgrid(1,k1,k2,k3) = expterm * qgrid(1,k1,k2,k3)
         qgrid(2,k1,k2,k3) = expterm * qgrid(2,k1,k2,k3)
      end do
c
c     account for the zeroth grid point for a finite system
c
      if (.not. use_bounds) then
         expterm = 0.5d0 * pi / xbox
         struc2 = qgrid(1,1,1,1)**2 + qgrid(2,1,1,1)**2
         e = f * expterm * struc2
         ec = ec + e
         qgrid(1,1,1,1) = expterm * qgrid(1,1,1,1)
         qgrid(2,1,1,1) = expterm * qgrid(2,1,1,1)
      end if
c
c     perform the 3-D FFT backward transformation
c
      call fftback
c
c     get first derivatives of the reciprocal space energy
c
      f = electric / dielec
      dn1 = dble(nfft1)
      dn2 = dble(nfft2)
      dn3 = dble(nfft3)
      do isite = 1, nion
         iatm = iion(isite)
         igrd0 = igrid(1,iatm)
         jgrd0 = igrid(2,iatm)
         kgrd0 = igrid(3,iatm)
         fi = f * pchg(isite)
         de1 = 0.0d0
         de2 = 0.0d0
         de3 = 0.0d0
         k0 = kgrd0
         do it3 = 1, bsorder
            k0 = k0 + 1
            k = k0 + 1 + (nfft3-sign(nfft3,k0))/2
            t3 = thetai3(1,it3,iatm)
            dt3 = dn3 * thetai3(2,it3,iatm)
            j0 = jgrd0
            do it2 = 1, bsorder
               j0 = j0 + 1
               j = j0 + 1 + (nfft2-sign(nfft2,j0))/2
               t2 = thetai2(1,it2,iatm)
               dt2 = dn2 * thetai2(2,it2,iatm)
               i0 = igrd0
               do it1 = 1, bsorder
                  i0 = i0 + 1
                  i = i0 + 1 + (nfft1-sign(nfft1,i0))/2
                  t1 = thetai1(1,it1,iatm)
                  dt1 = dn1 * thetai1(2,it1,iatm)
                  term = qgrid(1,i,j,k)
                  de1 = de1 + term*dt1*t2*t3
                  de2 = de2 + term*dt2*t1*t3
                  de3 = de3 + term*dt3*t1*t2
               end do
            end do
         end do
         dec(1,iatm) = dec(1,iatm) + fi*(recip(1,1)*de1+recip(1,2)*de2
     &                                      +recip(1,3)*de3)
         dec(2,iatm) = dec(2,iatm) + fi*(recip(2,1)*de1+recip(2,2)*de2
     &                                      +recip(2,3)*de3)
         dec(3,iatm) = dec(3,iatm) + fi*(recip(3,1)*de1+recip(3,2)*de2
     &                                      +recip(3,3)*de3)
      end do
      return
      end
