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lammps/lib/meam/meam_force.F
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c Extern "C" declaration has the form:
c
c void meam_force_(int *, int *, int *, double *, int *, int *, int *, double *,
c int *, int *, int *, int *, double *, double *,
c double *, double *, double *, double *, double *, double *,
c double *, double *, double *, double *, double *, double *,
c double *, double *, double *, double *, double *, int *);
c
c Call from pair_meam.cpp has the form:
c
c meam_force_(&i,&nmax,&eflag_either,&eflag_global,&eflag_atom,&vflag_atom,
c &eng_vdwl,eatom,&ntype,type,fmap,&x[0][0],
c &numneigh[i],firstneigh[i],&numneigh_full[i],firstneigh_full[i],
c &scrfcn[offset],&dscrfcn[offset],&fcpair[offset],
c dgamma1,dgamma2,dgamma3,rho0,rho1,rho2,rho3,frhop,
c &arho1[0][0],&arho2[0][0],arho2b,&arho3[0][0],&arho3b[0][0],
c &t_ave[0][0],&f[0][0],&vatom[0][0],&errorflag);
c
subroutine meam_force(i, nmax,
$ eflag_either, eflag_global, eflag_atom, vflag_atom,
$ eng_vdwl, eatom, ntype, type, fmap, x,
$ numneigh, firstneigh, numneigh_full, firstneigh_full,
$ scrfcn, dscrfcn, fcpair,
$ dGamma1, dGamma2, dGamma3, rho0, rho1, rho2, rho3, fp,
$ Arho1, Arho2, Arho2b, Arho3, Arho3b, t_ave, f, vatom,
$ errorflag)
use meam_data
implicit none
integer eflag_either, eflag_global, eflag_atom, vflag_atom
integer nmax, ntype, type, fmap
real*8 eng_vdwl, eatom, x
integer numneigh, firstneigh, numneigh_full, firstneigh_full
real*8 scrfcn, dscrfcn, fcpair
real*8 dGamma1, dGamma2, dGamma3
real*8 rho0, rho1, rho2, rho3, fp
real*8 Arho1, Arho2, Arho2b
real*8 Arho3, Arho3b
real*8 t_ave, f, vatom
integer errorflag
dimension eatom(nmax)
dimension type(nmax), fmap(ntype)
dimension x(3,nmax)
dimension firstneigh(numneigh), firstneigh_full(numneigh_full)
dimension scrfcn(numneigh), dscrfcn(numneigh), fcpair(numneigh)
dimension dGamma1(nmax), dGamma2(nmax), dGamma3(nmax)
dimension rho0(nmax), rho1(nmax), rho2(nmax), rho3(nmax), fp(nmax)
dimension Arho1(3,nmax), Arho2(6,nmax), Arho2b(nmax)
dimension Arho3(10,nmax), Arho3b(3,nmax)
dimension t_ave(3,nmax), f(3,nmax), vatom(6,nmax)
integer i,j,jn,k,kn,kk,m,n,p,q
integer nv2,nv3,elti,eltj,ind
real*8 xitmp,yitmp,zitmp,delij(3),delref(3),rij2,rij,rij3
real*8 delik(3),deljk(3),v(6),fi(3),fj(3)
real*8 Eu,astar,astarp,third,sixth
real*8 pp,phiforce,dUdrij,dUdsij,dUdrijm(3),force,forcem
real*8 B,r,recip,phi,phip,rhop,a
real*8 sij,fcij,dfcij,ds(3)
real*8 a0,a1,a1i,a1j,a2,a2i,a2j
real*8 a3i,a3j,a3i1,a3i2,a3j1,a3j2
real*8 G,dG,Gbar,dGbar,gam,shpi(3),shpj(3),Z,denom
real*8 ai,aj,ro0i,ro0j,invrei,invrej
real*8 b0,rhoa0j,drhoa0j,rhoa0i,drhoa0i
real*8 b1,rhoa1j,drhoa1j,rhoa1i,drhoa1i
real*8 b2,rhoa2j,drhoa2j,rhoa2i,drhoa2i
real*8 a3,a3a,b3,rhoa3j,drhoa3j,rhoa3i,drhoa3i
real*8 drho0dr1,drho0dr2,drho0ds1,drho0ds2
real*8 drho1dr1,drho1dr2,drho1ds1,drho1ds2
real*8 drho1drm1(3),drho1drm2(3)
real*8 drho2dr1,drho2dr2,drho2ds1,drho2ds2
real*8 drho2drm1(3),drho2drm2(3)
real*8 drho3dr1,drho3dr2,drho3ds1,drho3ds2
real*8 drho3drm1(3),drho3drm2(3)
real*8 dt1dr1,dt1dr2,dt1ds1,dt1ds2
real*8 dt2dr1,dt2dr2,dt2ds1,dt2ds2
real*8 dt3dr1,dt3dr2,dt3ds1,dt3ds2
real*8 drhodr1,drhodr2,drhods1,drhods2,drhodrm1(3),drhodrm2(3)
real*8 arg,arg1,arg2
real*8 arg1i1,arg1j1,arg1i2,arg1j2,arg2i2,arg2j2
real*8 arg1i3,arg1j3,arg2i3,arg2j3,arg3i3,arg3j3
real*8 dsij1,dsij2,force1,force2
real*8 t1i,t2i,t3i,t1j,t2j,t3j
errorflag = 0
third = 1.0/3.0
sixth = 1.0/6.0
c Compute forces atom i
elti = fmap(type(i))
xitmp = x(1,i)
yitmp = x(2,i)
zitmp = x(3,i)
c Treat each pair
do jn = 1,numneigh
if (scrfcn(jn).ne.0.d0) then
j = firstneigh(jn)
sij = scrfcn(jn)*fcpair(jn)
delij(1) = x(1,j) - xitmp
delij(2) = x(2,j) - yitmp
delij(3) = x(3,j) - zitmp
rij2 = delij(1)*delij(1) + delij(2)*delij(2)
$ + delij(3)*delij(3)
if (rij2.lt.cutforcesq) then
rij = sqrt(rij2)
r = rij
eltj = fmap(type(j))
c Compute phi and phip
ind = eltind(elti,eltj)
pp = rij*rdrar + 1.0D0
kk = pp
kk = min(kk,nrar-1)
pp = pp - kk
pp = min(pp,1.0D0)
phi = ((phirar3(kk,ind)*pp + phirar2(kk,ind))*pp
$ + phirar1(kk,ind))*pp + phirar(kk,ind)
phip = (phirar6(kk,ind)*pp + phirar5(kk,ind))*pp
$ + phirar4(kk,ind)
recip = 1.0d0/r
if (eflag_either.ne.0) then
if (eflag_global.ne.0) eng_vdwl = eng_vdwl + phi*sij
if (eflag_atom.ne.0) then
eatom(i) = eatom(i) + 0.5*phi*sij
eatom(j) = eatom(j) + 0.5*phi*sij
endif
endif
c write(1,*) "force_meamf: phi: ",phi
c write(1,*) "force_meamf: phip: ",phip
c Compute pair densities and derivatives
invrei = 1.d0/re_meam(elti,elti)
ai = rij*invrei - 1.d0
ro0i = rho0_meam(elti)
rhoa0i = ro0i*exp(-beta0_meam(elti)*ai)
drhoa0i = -beta0_meam(elti)*invrei*rhoa0i
rhoa1i = ro0i*exp(-beta1_meam(elti)*ai)
drhoa1i = -beta1_meam(elti)*invrei*rhoa1i
rhoa2i = ro0i*exp(-beta2_meam(elti)*ai)
drhoa2i = -beta2_meam(elti)*invrei*rhoa2i
rhoa3i = ro0i*exp(-beta3_meam(elti)*ai)
drhoa3i = -beta3_meam(elti)*invrei*rhoa3i
if (elti.ne.eltj) then
invrej = 1.d0/re_meam(eltj,eltj)
aj = rij*invrej - 1.d0
ro0j = rho0_meam(eltj)
rhoa0j = ro0j*exp(-beta0_meam(eltj)*aj)
drhoa0j = -beta0_meam(eltj)*invrej*rhoa0j
rhoa1j = ro0j*exp(-beta1_meam(eltj)*aj)
drhoa1j = -beta1_meam(eltj)*invrej*rhoa1j
rhoa2j = ro0j*exp(-beta2_meam(eltj)*aj)
drhoa2j = -beta2_meam(eltj)*invrej*rhoa2j
rhoa3j = ro0j*exp(-beta3_meam(eltj)*aj)
drhoa3j = -beta3_meam(eltj)*invrej*rhoa3j
else
rhoa0j = rhoa0i
drhoa0j = drhoa0i
rhoa1j = rhoa1i
drhoa1j = drhoa1i
rhoa2j = rhoa2i
drhoa2j = drhoa2i
rhoa3j = rhoa3i
drhoa3j = drhoa3i
endif
nv2 = 1
nv3 = 1
arg1i1 = 0.d0
arg1j1 = 0.d0
arg1i2 = 0.d0
arg1j2 = 0.d0
arg1i3 = 0.d0
arg1j3 = 0.d0
arg3i3 = 0.d0
arg3j3 = 0.d0
do n = 1,3
do p = n,3
do q = p,3
arg = delij(n)*delij(p)*delij(q)*v3D(nv3)
arg1i3 = arg1i3 + Arho3(nv3,i)*arg
arg1j3 = arg1j3 - Arho3(nv3,j)*arg
nv3 = nv3+1
enddo
arg = delij(n)*delij(p)*v2D(nv2)
arg1i2 = arg1i2 + Arho2(nv2,i)*arg
arg1j2 = arg1j2 + Arho2(nv2,j)*arg
nv2 = nv2+1
enddo
arg1i1 = arg1i1 + Arho1(n,i)*delij(n)
arg1j1 = arg1j1 - Arho1(n,j)*delij(n)
arg3i3 = arg3i3 + Arho3b(n,i)*delij(n)
arg3j3 = arg3j3 - Arho3b(n,j)*delij(n)
enddo
c rho0 terms
drho0dr1 = drhoa0j * sij
drho0dr2 = drhoa0i * sij
c rho1 terms
a1 = 2*sij/rij
drho1dr1 = a1*(drhoa1j-rhoa1j/rij)*arg1i1
drho1dr2 = a1*(drhoa1i-rhoa1i/rij)*arg1j1
a1 = 2.d0*sij/rij
do m = 1,3
drho1drm1(m) = a1*rhoa1j*Arho1(m,i)
drho1drm2(m) = -a1*rhoa1i*Arho1(m,j)
enddo
c rho2 terms
a2 = 2*sij/rij2
drho2dr1 = a2*(drhoa2j - 2*rhoa2j/rij)*arg1i2
$ - 2.d0/3.d0*Arho2b(i)*drhoa2j*sij
drho2dr2 = a2*(drhoa2i - 2*rhoa2i/rij)*arg1j2
$ - 2.d0/3.d0*Arho2b(j)*drhoa2i*sij
a2 = 4*sij/rij2
do m = 1,3
drho2drm1(m) = 0.d0
drho2drm2(m) = 0.d0
do n = 1,3
drho2drm1(m) = drho2drm1(m)
$ + Arho2(vind2D(m,n),i)*delij(n)
drho2drm2(m) = drho2drm2(m)
$ - Arho2(vind2D(m,n),j)*delij(n)
enddo
drho2drm1(m) = a2*rhoa2j*drho2drm1(m)
drho2drm2(m) = -a2*rhoa2i*drho2drm2(m)
enddo
c rho3 terms
rij3 = rij*rij2
a3 = 2*sij/rij3
a3a = 6.d0/5.d0*sij/rij
drho3dr1 = a3*(drhoa3j - 3*rhoa3j/rij)*arg1i3
$ - a3a*(drhoa3j - rhoa3j/rij)*arg3i3
drho3dr2 = a3*(drhoa3i - 3*rhoa3i/rij)*arg1j3
$ - a3a*(drhoa3i - rhoa3i/rij)*arg3j3
a3 = 6*sij/rij3
a3a = 6*sij/(5*rij)
do m = 1,3
drho3drm1(m) = 0.d0
drho3drm2(m) = 0.d0
nv2 = 1
do n = 1,3
do p = n,3
arg = delij(n)*delij(p)*v2D(nv2)
drho3drm1(m) = drho3drm1(m)
$ + Arho3(vind3D(m,n,p),i)*arg
drho3drm2(m) = drho3drm2(m)
$ + Arho3(vind3D(m,n,p),j)*arg
nv2 = nv2 + 1
enddo
enddo
drho3drm1(m) = (a3*drho3drm1(m) - a3a*Arho3b(m,i))
$ *rhoa3j
drho3drm2(m) = (-a3*drho3drm2(m) + a3a*Arho3b(m,j))
$ *rhoa3i
enddo
c Compute derivatives of weighting functions t wrt rij
t1i = t_ave(1,i)
t2i = t_ave(2,i)
t3i = t_ave(3,i)
t1j = t_ave(1,j)
t2j = t_ave(2,j)
t3j = t_ave(3,j)
ai = 0.d0
if( rho0(i) .ne. 0.d0 ) then
ai = drhoa0j*sij/rho0(i)
end if
aj = 0.d0
if( rho0(j) .ne. 0.d0 ) then
aj = drhoa0i*sij/rho0(j)
end if
dt1dr1 = ai*(t1_meam(eltj)-t1i)
dt1dr2 = aj*(t1_meam(elti)-t1j)
dt2dr1 = ai*(t2_meam(eltj)-t2i)
dt2dr2 = aj*(t2_meam(elti)-t2j)
dt3dr1 = ai*(t3_meam(eltj)-t3i)
dt3dr2 = aj*(t3_meam(elti)-t3j)
c Compute derivatives of total density wrt rij, sij and rij(3)
call get_shpfcn(shpi,lattce_meam(elti,elti))
call get_shpfcn(shpj,lattce_meam(eltj,eltj))
drhodr1 = dGamma1(i)*drho0dr1
$ + dGamma2(i)*
$ (dt1dr1*rho1(i)+t1i*drho1dr1
$ + dt2dr1*rho2(i)+t2i*drho2dr1
$ + dt3dr1*rho3(i)+t3i*drho3dr1)
$ - dGamma3(i)*
$ (shpi(1)*dt1dr1+shpi(2)*dt2dr1+shpi(3)*dt3dr1)
drhodr2 = dGamma1(j)*drho0dr2
$ + dGamma2(j)*
$ (dt1dr2*rho1(j)+t1j*drho1dr2
$ + dt2dr2*rho2(j)+t2j*drho2dr2
$ + dt3dr2*rho3(j)+t3j*drho3dr2)
$ - dGamma3(j)*
$ (shpj(1)*dt1dr2+shpj(2)*dt2dr2+shpj(3)*dt3dr2)
do m = 1,3
drhodrm1(m) = 0.d0
drhodrm2(m) = 0.d0
drhodrm1(m) = dGamma2(i)*
$ (t1i*drho1drm1(m)
$ + t2i*drho2drm1(m)
$ + t3i*drho3drm1(m))
drhodrm2(m) = dGamma2(j)*
$ (t1j*drho1drm2(m)
$ + t2j*drho2drm2(m)
$ + t3j*drho3drm2(m))
enddo
c Compute derivatives wrt sij, but only if necessary
if (dscrfcn(jn).ne.0.d0) then
drho0ds1 = rhoa0j
drho0ds2 = rhoa0i
a1 = 2.d0/rij
drho1ds1 = a1*rhoa1j*arg1i1
drho1ds2 = a1*rhoa1i*arg1j1
a2 = 2.d0/rij2
drho2ds1 = a2*rhoa2j*arg1i2
$ - 2.d0/3.d0*Arho2b(i)*rhoa2j
drho2ds2 = a2*rhoa2i*arg1j2
$ - 2.d0/3.d0*Arho2b(j)*rhoa2i
a3 = 2.d0/rij3
a3a = 6.d0/(5.d0*rij)
drho3ds1 = a3*rhoa3j*arg1i3 - a3a*rhoa3j*arg3i3
drho3ds2 = a3*rhoa3i*arg1j3 - a3a*rhoa3i*arg3j3
ai = 0.d0
if( rho0(i) .ne. 0.d0 ) then
ai = rhoa0j/rho0(i)
end if
aj = 0.d0
if( rho0(j) .ne. 0.d0 ) then
aj = rhoa0i/rho0(j)
end if
dt1ds1 = ai*(t1_meam(eltj)-t1i)
dt1ds2 = aj*(t1_meam(elti)-t1j)
dt2ds1 = ai*(t2_meam(eltj)-t2i)
dt2ds2 = aj*(t2_meam(elti)-t2j)
dt3ds1 = ai*(t3_meam(eltj)-t3i)
dt3ds2 = aj*(t3_meam(elti)-t3j)
drhods1 = dGamma1(i)*drho0ds1
$ + dGamma2(i)*
$ (dt1ds1*rho1(i)+t1i*drho1ds1
$ + dt2ds1*rho2(i)+t2i*drho2ds1
$ + dt3ds1*rho3(i)+t3i*drho3ds1)
$ - dGamma3(i)*
$ (shpi(1)*dt1ds1+shpi(2)*dt2ds1+shpi(3)*dt3ds1)
drhods2 = dGamma1(j)*drho0ds2
$ + dGamma2(j)*
$ (dt1ds2*rho1(j)+t1j*drho1ds2
$ + dt2ds2*rho2(j)+t2j*drho2ds2
$ + dt3ds2*rho3(j)+t3j*drho3ds2)
$ - dGamma3(j)*
$ (shpj(1)*dt1ds2+shpj(2)*dt2ds2+shpj(3)*dt3ds2)
endif
c Compute derivatives of energy wrt rij, sij and rij(3)
dUdrij = phip*sij
$ + fp(i)*drhodr1 + fp(j)*drhodr2
dUdsij = 0.d0
if (dscrfcn(jn).ne.0.d0) then
dUdsij = phi
$ + fp(i)*drhods1 + fp(j)*drhods2
endif
do m = 1,3
dUdrijm(m) = fp(i)*drhodrm1(m) + fp(j)*drhodrm2(m)
enddo
c Add the part of the force due to dUdrij and dUdsij
force = dUdrij*recip + dUdsij*dscrfcn(jn)
do m = 1,3
forcem = delij(m)*force + dUdrijm(m)
f(m,i) = f(m,i) + forcem
f(m,j) = f(m,j) - forcem
enddo
c Tabulate per-atom virial as symmetrized stress tensor
if (vflag_atom.ne.0) then
fi(1) = delij(1)*force + dUdrijm(1)
fi(2) = delij(2)*force + dUdrijm(2)
fi(3) = delij(3)*force + dUdrijm(3)
v(1) = -0.5 * (delij(1) * fi(1))
v(2) = -0.5 * (delij(2) * fi(2))
v(3) = -0.5 * (delij(3) * fi(3))
v(4) = -0.25 * (delij(1)*fi(2) + delij(2)*fi(1))
v(5) = -0.25 * (delij(1)*fi(3) + delij(3)*fi(1))
v(6) = -0.25 * (delij(2)*fi(3) + delij(3)*fi(2))
vatom(1,i) = vatom(1,i) + v(1)
vatom(2,i) = vatom(2,i) + v(2)
vatom(3,i) = vatom(3,i) + v(3)
vatom(4,i) = vatom(4,i) + v(4)
vatom(5,i) = vatom(5,i) + v(5)
vatom(6,i) = vatom(6,i) + v(6)
vatom(1,j) = vatom(1,j) + v(1)
vatom(2,j) = vatom(2,j) + v(2)
vatom(3,j) = vatom(3,j) + v(3)
vatom(4,j) = vatom(4,j) + v(4)
vatom(5,j) = vatom(5,j) + v(5)
vatom(6,j) = vatom(6,j) + v(6)
endif
c Now compute forces on other atoms k due to change in sij
if (sij.eq.0.d0.or.sij.eq.1.d0) goto 100
do kn = 1,numneigh_full
k = firstneigh_full(kn)
if (k.ne.j) then
call dsij(i,j,k,jn,nmax,numneigh,rij2,dsij1,dsij2,
$ ntype,type,fmap,x,scrfcn,fcpair)
if (dsij1.ne.0.d0.or.dsij2.ne.0.d0) then
force1 = dUdsij*dsij1
force2 = dUdsij*dsij2
do m = 1,3
delik(m) = x(m,k) - x(m,i)
deljk(m) = x(m,k) - x(m,j)
enddo
do m = 1,3
f(m,i) = f(m,i) + force1*delik(m)
f(m,j) = f(m,j) + force2*deljk(m)
f(m,k) = f(m,k) - force1*delik(m)
$ - force2*deljk(m)
enddo
c Tabulate per-atom virial as symmetrized stress tensor
if (vflag_atom.ne.0) then
fi(1) = force1*delik(1)
fi(2) = force1*delik(2)
fi(3) = force1*delik(3)
fj(1) = force2*deljk(1)
fj(2) = force2*deljk(2)
fj(3) = force2*deljk(3)
v(1) = -third * (delik(1)*fi(1) + deljk(1)*fj(1))
v(2) = -third * (delik(2)*fi(2) + deljk(2)*fj(2))
v(3) = -third * (delik(3)*fi(3) + deljk(3)*fj(3))
v(4) = -sixth * (delik(1)*fi(2) + deljk(1)*fj(2) +
$ delik(2)*fi(1) + deljk(2)*fj(1))
v(5) = -sixth * (delik(1)*fi(3) + deljk(1)*fj(3) +
$ delik(3)*fi(1) + deljk(3)*fj(1))
v(6) = -sixth * (delik(2)*fi(3) + deljk(2)*fj(3) +
$ delik(3)*fi(2) + deljk(3)*fj(2))
vatom(1,i) = vatom(1,i) + v(1)
vatom(2,i) = vatom(2,i) + v(2)
vatom(3,i) = vatom(3,i) + v(3)
vatom(4,i) = vatom(4,i) + v(4)
vatom(5,i) = vatom(5,i) + v(5)
vatom(6,i) = vatom(6,i) + v(6)
vatom(1,j) = vatom(1,j) + v(1)
vatom(2,j) = vatom(2,j) + v(2)
vatom(3,j) = vatom(3,j) + v(3)
vatom(4,j) = vatom(4,j) + v(4)
vatom(5,j) = vatom(5,j) + v(5)
vatom(6,j) = vatom(6,j) + v(6)
vatom(1,k) = vatom(1,k) + v(1)
vatom(2,k) = vatom(2,k) + v(2)
vatom(3,k) = vatom(3,k) + v(3)
vatom(4,k) = vatom(4,k) + v(4)
vatom(5,k) = vatom(5,k) + v(5)
vatom(6,k) = vatom(6,k) + v(6)
endif
endif
endif
c end of k loop
enddo
endif
100 continue
endif
c end of j loop
enddo
return
end
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