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c Extern "C" declaration has the form:
c
c void meam_dens_init_(int *, int *, int *, double *, int *, int *, int *, double *,
c int *, int *, int *, int *,
c double *, double *, double *, double *, double *, double *,
c double *, double *, double *, double *, double *, int *);
c
c
c Call from pair_meam.cpp has the form:
c
c meam_dens_init_(&i,&nmax,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 rho0,&arho1[0][0],&arho2[0][0],arho2b,
c &arho3[0][0],&arho3b[0][0],&t_ave[0][0],&tsq_ave[0][0],&errorflag);
c
subroutine meam_dens_init(i, nmax,
$ ntype, type, fmap, x,
$ numneigh, firstneigh,
$ numneigh_full, firstneigh_full,
$ scrfcn, dscrfcn, fcpair, rho0, arho1, arho2, arho2b,
$ arho3, arho3b, t_ave, tsq_ave, errorflag)
use meam_data
implicit none
integer i, nmax, ntype, type, fmap
real*8 x
integer numneigh, firstneigh, numneigh_full, firstneigh_full
real*8 scrfcn, dscrfcn, fcpair
real*8 rho0, arho1, arho2
real*8 arho2b, arho3, arho3b, t_ave, tsq_ave
integer errorflag
integer j,jn
dimension x(3,nmax)
dimension type(nmax), fmap(ntype)
dimension firstneigh(numneigh), firstneigh_full(numneigh_full)
dimension scrfcn(numneigh), dscrfcn(numneigh), fcpair(numneigh)
dimension rho0(nmax), arho1(3,nmax), arho2(6,nmax)
dimension arho2b(nmax), arho3(10,nmax), arho3b(3,nmax)
dimension t_ave(3,nmax), tsq_ave(3,nmax)
errorflag = 0
c Compute screening function and derivatives
call getscreen(i, nmax, scrfcn, dscrfcn, fcpair, x,
$ numneigh, firstneigh,
$ numneigh_full, firstneigh_full,
$ ntype, type, fmap)
c Calculate intermediate density terms to be communicated
call calc_rho1(i, nmax, ntype, type, fmap, x,
$ numneigh, firstneigh,
$ scrfcn, fcpair, rho0, arho1, arho2, arho2b,
$ arho3, arho3b, t_ave, tsq_ave)
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine getscreen(i, nmax, scrfcn, dscrfcn, fcpair, x,
$ numneigh, firstneigh,
$ numneigh_full, firstneigh_full,
$ ntype, type, fmap)
use meam_data
implicit none
integer i, nmax
real*8 scrfcn, dscrfcn, fcpair, x
integer numneigh, firstneigh, numneigh_full, firstneigh_full
integer ntype, type, fmap
dimension scrfcn(numneigh), dscrfcn(numneigh)
dimension fcpair(numneigh), x(3,nmax)
dimension firstneigh(numneigh), firstneigh_full(numneigh_full)
dimension type(nmax), fmap(ntype)
integer jn,j,kn,k
integer elti,eltj,eltk
real*8 xitmp,yitmp,zitmp,delxij,delyij,delzij,rij2,rij
real*8 xjtmp,yjtmp,zjtmp,delxik,delyik,delzik,rik2,rik
real*8 xktmp,yktmp,zktmp,delxjk,delyjk,delzjk,rjk2,rjk
real*8 xik,xjk,sij,fcij,sfcij,dfcij,sikj,dfikj,cikj
real*8 Cmin,Cmax,delc,ebound,rbound,a,coef1,coef2
real*8 coef1a,coef1b,coef2a,coef2b
real*8 dcikj
real*8 dC1a,dC1b,dC2a,dC2b
real*8 rnorm,fc,dfc,drinv
drinv = 1.d0/delr_meam
elti = fmap(type(i))
if (elti.gt.0) then
xitmp = x(1,i)
yitmp = x(2,i)
zitmp = x(3,i)
do jn = 1,numneigh
j = firstneigh(jn)
eltj = fmap(type(j))
if (eltj.gt.0) then
c First compute screening function itself, sij
xjtmp = x(1,j)
yjtmp = x(2,j)
zjtmp = x(3,j)
delxij = xjtmp - xitmp
delyij = yjtmp - yitmp
delzij = zjtmp - zitmp
rij2 = delxij*delxij + delyij*delyij + delzij*delzij
rij = sqrt(rij2)
if (rij.gt.rc_meam) then
fcij = 0.0
dfcij = 0.d0
sij = 0.d0
else
rnorm = (rc_meam-rij)*drinv
call screen(i, j, nmax, x, rij2, sij,
$ numneigh_full, firstneigh_full, ntype, type, fmap)
call dfcut(rnorm,fc,dfc)
fcij = fc
dfcij = dfc*drinv
endif
c Now compute derivatives
dscrfcn(jn) = 0.d0
sfcij = sij*fcij
if (sfcij.eq.0.d0.or.sfcij.eq.1.d0) goto 100
rbound = ebound_meam(elti,eltj) * rij2
do kn = 1,numneigh_full
k = firstneigh_full(kn)
if (k.eq.j) goto 10
eltk = fmap(type(k))
if (eltk.eq.0) goto 10
xktmp = x(1,k)
yktmp = x(2,k)
zktmp = x(3,k)
delxjk = xktmp - xjtmp
delyjk = yktmp - yjtmp
delzjk = zktmp - zjtmp
rjk2 = delxjk*delxjk + delyjk*delyjk + delzjk*delzjk
if (rjk2.gt.rbound) goto 10
delxik = xktmp - xitmp
delyik = yktmp - yitmp
delzik = zktmp - zitmp
rik2 = delxik*delxik + delyik*delyik + delzik*delzik
if (rik2.gt.rbound) goto 10
xik = rik2/rij2
xjk = rjk2/rij2
a = 1 - (xik-xjk)*(xik-xjk)
c if a < 0, then ellipse equation doesn't describe this case and
c atom k can't possibly screen i-j
if (a.le.0.d0) goto 10
cikj = (2.d0*(xik+xjk) + a - 2.d0)/a
Cmax = Cmax_meam(elti,eltj,eltk)
Cmin = Cmin_meam(elti,eltj,eltk)
if (cikj.ge.Cmax) then
goto 10
c Note that cikj may be slightly negative (within numerical
c tolerance) if atoms are colinear, so don't reject that case here
c (other negative cikj cases were handled by the test on "a" above)
c Note that we never have 0<cikj<Cmin here, else sij=0 (rejected above)
else
delc = Cmax - Cmin
cikj = (cikj-Cmin)/delc
call dfcut(cikj,sikj,dfikj)
coef1 = dfikj/(delc*sikj)
call dCfunc(rij2,rik2,rjk2,dCikj)
dscrfcn(jn) = dscrfcn(jn) + coef1*dCikj
endif
10 continue
enddo
coef1 = sfcij
coef2 = sij*dfcij/rij
dscrfcn(jn) = dscrfcn(jn)*coef1 - coef2
100 continue
scrfcn(jn) = sij
fcpair(jn) = fcij
endif
enddo
endif
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine calc_rho1(i, nmax, ntype, type, fmap, x,
$ numneigh, firstneigh,
$ scrfcn, fcpair, rho0, arho1, arho2, arho2b,
$ arho3, arho3b, t_ave, tsq_ave)
use meam_data
implicit none
integer i, nmax, ntype, type, fmap
real*8 x
integer numneigh, firstneigh
real*8 scrfcn, fcpair, rho0, arho1, arho2
real*8 arho2b, arho3, arho3b, t_ave, tsq_ave
dimension type(nmax), fmap(ntype), x(3,nmax)
dimension firstneigh(numneigh)
dimension scrfcn(numneigh), fcpair(numneigh)
dimension rho0(nmax), arho1(3,nmax), arho2(6,nmax)
dimension arho2b(nmax), arho3(10,nmax), arho3b(3,nmax)
dimension t_ave(3,nmax), tsq_ave(3,nmax)
integer jn,j,m,n,p,elti,eltj
integer nv2,nv3
real*8 xtmp,ytmp,ztmp,delij(3),rij2,rij,sij
real*8 ai,aj,rhoa0j,rhoa1j,rhoa2j,rhoa3j,A1j,A2j,A3j
real*8 G,Gbar,gam,shp(3)
real*8 ro0i,ro0j
real*8 rhoa0i,rhoa1i,rhoa2i,rhoa3i,A1i,A2i,A3i
elti = fmap(type(i))
xtmp = x(1,i)
ytmp = x(2,i)
ztmp = x(3,i)
do jn = 1,numneigh
if (scrfcn(jn).ne.0.d0) then
j = firstneigh(jn)
sij = scrfcn(jn)*fcpair(jn)
delij(1) = x(1,j) - xtmp
delij(2) = x(2,j) - ytmp
delij(3) = x(3,j) - ztmp
rij2 = delij(1)*delij(1) + delij(2)*delij(2)
$ + delij(3)*delij(3)
if (rij2.lt.cutforcesq) then
eltj = fmap(type(j))
rij = sqrt(rij2)
ai = rij/re_meam(elti,elti) - 1.d0
aj = rij/re_meam(eltj,eltj) - 1.d0
ro0i = rho0_meam(elti)
ro0j = rho0_meam(eltj)
rhoa0j = ro0j*fm_exp(-beta0_meam(eltj)*aj)*sij
rhoa1j = ro0j*fm_exp(-beta1_meam(eltj)*aj)*sij
rhoa2j = ro0j*fm_exp(-beta2_meam(eltj)*aj)*sij
rhoa3j = ro0j*fm_exp(-beta3_meam(eltj)*aj)*sij
rhoa0i = ro0i*fm_exp(-beta0_meam(elti)*ai)*sij
rhoa1i = ro0i*fm_exp(-beta1_meam(elti)*ai)*sij
rhoa2i = ro0i*fm_exp(-beta2_meam(elti)*ai)*sij
rhoa3i = ro0i*fm_exp(-beta3_meam(elti)*ai)*sij
if (ialloy.eq.1) then
rhoa1j = rhoa1j * t1_meam(eltj)
rhoa2j = rhoa2j * t2_meam(eltj)
rhoa3j = rhoa3j * t3_meam(eltj)
rhoa1i = rhoa1i * t1_meam(elti)
rhoa2i = rhoa2i * t2_meam(elti)
rhoa3i = rhoa3i * t3_meam(elti)
endif
rho0(i) = rho0(i) + rhoa0j
rho0(j) = rho0(j) + rhoa0i
c For ialloy = 2, use single-element value (not average)
if (ialloy.ne.2) then
t_ave(1,i) = t_ave(1,i) + t1_meam(eltj)*rhoa0j
t_ave(2,i) = t_ave(2,i) + t2_meam(eltj)*rhoa0j
t_ave(3,i) = t_ave(3,i) + t3_meam(eltj)*rhoa0j
t_ave(1,j) = t_ave(1,j) + t1_meam(elti)*rhoa0i
t_ave(2,j) = t_ave(2,j) + t2_meam(elti)*rhoa0i
t_ave(3,j) = t_ave(3,j) + t3_meam(elti)*rhoa0i
endif
if (ialloy.eq.1) then
tsq_ave(1,i) = tsq_ave(1,i) +
$ t1_meam(eltj)*t1_meam(eltj)*rhoa0j
tsq_ave(2,i) = tsq_ave(2,i) +
$ t2_meam(eltj)*t2_meam(eltj)*rhoa0j
tsq_ave(3,i) = tsq_ave(3,i) +
$ t3_meam(eltj)*t3_meam(eltj)*rhoa0j
tsq_ave(1,j) = tsq_ave(1,j) +
$ t1_meam(elti)*t1_meam(elti)*rhoa0i
tsq_ave(2,j) = tsq_ave(2,j) +
$ t2_meam(elti)*t2_meam(elti)*rhoa0i
tsq_ave(3,j) = tsq_ave(3,j) +
$ t3_meam(elti)*t3_meam(elti)*rhoa0i
endif
Arho2b(i) = Arho2b(i) + rhoa2j
Arho2b(j) = Arho2b(j) + rhoa2i
A1j = rhoa1j/rij
A2j = rhoa2j/rij2
A3j = rhoa3j/(rij2*rij)
A1i = rhoa1i/rij
A2i = rhoa2i/rij2
A3i = rhoa3i/(rij2*rij)
nv2 = 1
nv3 = 1
do m = 1,3
Arho1(m,i) = Arho1(m,i) + A1j*delij(m)
Arho1(m,j) = Arho1(m,j) - A1i*delij(m)
Arho3b(m,i) = Arho3b(m,i) + rhoa3j*delij(m)/rij
Arho3b(m,j) = Arho3b(m,j) - rhoa3i*delij(m)/rij
do n = m,3
Arho2(nv2,i) = Arho2(nv2,i) + A2j*delij(m)*delij(n)
Arho2(nv2,j) = Arho2(nv2,j) + A2i*delij(m)*delij(n)
nv2 = nv2+1
do p = n,3
Arho3(nv3,i) = Arho3(nv3,i)
$ + A3j*delij(m)*delij(n)*delij(p)
Arho3(nv3,j) = Arho3(nv3,j)
$ - A3i*delij(m)*delij(n)*delij(p)
nv3 = nv3+1
enddo
enddo
enddo
endif
endif
enddo
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine screen(i, j, nmax, x, rijsq, sij,
$ numneigh_full, firstneigh_full, ntype, type, fmap)
c Screening function
c Inputs: i = atom 1 id (integer)
c j = atom 2 id (integer)
c rijsq = squared distance between i and j
c Outputs: sij = screening function
use meam_data
implicit none
integer i,j,nmax,k,nk,m
real*8 x,rijsq,sij
integer numneigh_full, firstneigh_full
integer ntype, type, fmap
dimension x(3,nmax), firstneigh_full(numneigh_full)
dimension type(nmax), fmap(ntype)
integer elti,eltj,eltk
real*8 delxik,delyik,delzik
real*8 delxjk,delyjk,delzjk
real*8 riksq,rjksq,xik,xjk,cikj,a,delc,sikj,fcij,rij
real*8 Cmax,Cmin,rbound
sij = 1.d0
elti = fmap(type(i))
eltj = fmap(type(j))
c if rjksq > ebound*rijsq, atom k is definitely outside the ellipse
rbound = ebound_meam(elti,eltj)*rijsq
do nk = 1,numneigh_full
k = firstneigh_full(nk)
eltk = fmap(type(k))
if (k.eq.j) goto 10
delxjk = x(1,k) - x(1,j)
delyjk = x(2,k) - x(2,j)
delzjk = x(3,k) - x(3,j)
rjksq = delxjk*delxjk + delyjk*delyjk + delzjk*delzjk
if (rjksq.gt.rbound) goto 10
delxik = x(1,k) - x(1,i)
delyik = x(2,k) - x(2,i)
delzik = x(3,k) - x(3,i)
riksq = delxik*delxik + delyik*delyik + delzik*delzik
if (riksq.gt.rbound) goto 10
xik = riksq/rijsq
xjk = rjksq/rijsq
a = 1 - (xik-xjk)*(xik-xjk)
c if a < 0, then ellipse equation doesn't describe this case and
c atom k can't possibly screen i-j
if (a.le.0.d0) goto 10
cikj = (2.d0*(xik+xjk) + a - 2.d0)/a
Cmax = Cmax_meam(elti,eltj,eltk)
Cmin = Cmin_meam(elti,eltj,eltk)
if (cikj.ge.Cmax) then
goto 10
c note that cikj may be slightly negative (within numerical
c tolerance) if atoms are colinear, so don't reject that case here
c (other negative cikj cases were handled by the test on "a" above)
else if (cikj.le.Cmin) then
sij = 0.d0
goto 20
else
delc = Cmax - Cmin
cikj = (cikj-Cmin)/delc
call fcut(cikj,sikj)
endif
sij = sij * sikj
10 continue
enddo
20 continue
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine dsij(i,j,k,jn,nmax,numneigh,rij2,dsij1,dsij2,
$ ntype,type,fmap,x,scrfcn,fcpair)
c Inputs: i,j,k = id's of 3 atom triplet
c jn = id of i-j pair
c rij2 = squared distance between i and j
c Outputs: dsij1 = deriv. of sij w.r.t. rik
c dsij2 = deriv. of sij w.r.t. rjk
use meam_data
implicit none
integer i,j,k,jn,nmax,numneigh
integer elti,eltj,eltk
real*8 rij2,rik2,rjk2,dsij1,dsij2
integer ntype, type, fmap
real*8 x, scrfcn, fcpair
dimension type(nmax), fmap(ntype)
dimension x(3,nmax), scrfcn(numneigh), fcpair(numneigh)
real*8 dxik,dyik,dzik
real*8 dxjk,dyjk,dzjk
real*8 rbound,delc,sij,xik,xjk,cikj,sikj,dfc,a
real*8 Cmax,Cmin,dCikj1,dCikj2
sij = scrfcn(jn)*fcpair(jn)
elti = fmap(type(i))
eltj = fmap(type(j))
eltk = fmap(type(k))
Cmax = Cmax_meam(elti,eltj,eltk)
Cmin = Cmin_meam(elti,eltj,eltk)
dsij1 = 0.d0
dsij2 = 0.d0
if ((sij.ne.0.d0).and.(sij.ne.1.d0)) then
rbound = rij2*ebound_meam(elti,eltj)
delc = Cmax-Cmin
dxjk = x(1,k) - x(1,j)
dyjk = x(2,k) - x(2,j)
dzjk = x(3,k) - x(3,j)
rjk2 = dxjk*dxjk + dyjk*dyjk + dzjk*dzjk
if (rjk2.le.rbound) then
dxik = x(1,k) - x(1,i)
dyik = x(2,k) - x(2,i)
dzik = x(3,k) - x(3,i)
rik2 = dxik*dxik + dyik*dyik + dzik*dzik
if (rik2.le.rbound) then
xik = rik2/rij2
xjk = rjk2/rij2
a = 1 - (xik-xjk)*(xik-xjk)
if (a.ne.0.d0) then
cikj = (2.d0*(xik+xjk) + a - 2.d0)/a
if (cikj.ge.Cmin.and.cikj.le.Cmax) then
cikj = (cikj-Cmin)/delc
call dfcut(cikj,sikj,dfc)
call dCfunc2(rij2,rik2,rjk2,dCikj1,dCikj2)
a = sij/delc*dfc/sikj
dsij1 = a*dCikj1
dsij2 = a*dCikj2
endif
endif
endif
endif
endif
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine fcut(xi,fc)
c cutoff function
implicit none
real*8 xi,fc
real*8 a
if (xi.ge.1.d0) then
fc = 1.d0
else if (xi.le.0.d0) then
fc = 0.d0
else
a = 1.d0-xi
a = a*a
a = a*a
a = 1.d0-a
fc = a*a
c fc = xi
endif
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine dfcut(xi,fc,dfc)
c cutoff function and its derivative
implicit none
real*8 xi,fc,dfc,a,a3,a4
if (xi.ge.1.d0) then
fc = 1.d0
dfc = 0.d0
else if (xi.le.0.d0) then
fc = 0.d0
dfc = 0.d0
else
a = 1.d0-xi
a3 = a*a*a
a4 = a*a3
fc = (1.d0-a4)**2
dfc = 8*(1.d0-a4)*a3
c fc = xi
c dfc = 1.d0
endif
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine dCfunc(rij2,rik2,rjk2,dCikj)
c Inputs: rij,rij2,rik2,rjk2
c Outputs: dCikj = derivative of Cikj w.r.t. rij
implicit none
real*8 rij2,rik2,rjk2,dCikj
real*8 rij4,a,b,denom
rij4 = rij2*rij2
a = rik2-rjk2
b = rik2+rjk2
denom = rij4 - a*a
denom = denom*denom
dCikj = -4*(-2*rij2*a*a + rij4*b + a*a*b)/denom
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine dCfunc2(rij2,rik2,rjk2,dCikj1,dCikj2)
c Inputs: rij,rij2,rik2,rjk2
c Outputs: dCikj1 = derivative of Cikj w.r.t. rik
c dCikj2 = derivative of Cikj w.r.t. rjk
implicit none
real*8 rij2,rik2,rjk2,dCikj1,dCikj2
real*8 rij4,rik4,rjk4,a,b,denom
rij4 = rij2*rij2
rik4 = rik2*rik2
rjk4 = rjk2*rjk2
a = rik2-rjk2
b = rik2+rjk2
denom = rij4 - a*a
denom = denom*denom
dCikj1 = 4*rij2*(rij4 + rik4 + 2*rik2*rjk2 - 3*rjk4 - 2*rij2*a)/
$ denom
dCikj2 = 4*rij2*(rij4 - 3*rik4 + 2*rik2*rjk2 + rjk4 + 2*rij2*a)/
$ denom
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
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