def coulomb_repulsion(xyza,norma,lmna,alphaa,
xyzb,normb,lmnb,alphab,
xyzc,normc,lmnc,alphac,
xyzd,normd,lmnd,alphad):
"""
Return the coulomb repulsion between four primitive gaussians a,b,c,d with the given origin
, x,y,z, normalization constants norm, angular momena l,m,n, and exponent alpha.
>>> p1 = array((0.,0.,0.),'d')
>>> p2 = array((0.,0.,1.),'d')
>>> lmn = (0,0,0)
>>> isclose(coulomb_repulsion(p1,1.,lmn,1.,p1,1.,lmn,1.,p1,1.,lmn,1.,p1,1.,lmn,1.),4.373355)
True
>>> isclose(coulomb_repulsion(p1,1.,lmn,1.,p1,1.,lmn,1.,p2,1.,lmn,1.,p2,1.,lmn,1.),3.266127)
True
>>> isclose(coulomb_repulsion(p1,1.,lmn,1.,p2,1.,lmn,1.,p1,1.,lmn,1.,p2,1.,lmn,1.),1.6088672)
True
"""
la,ma,na = lmna
lb,mb,nb = lmnb
lc,mc,nc = lmnc
ld,md,nd = lmnd
xa,ya,za = xyza
xb,yb,zb = xyzb
xc,yc,zc = xyzc
xd,yd,zd = xyzd
rab2 = norm2(xyza-xyzb)
rcd2 = norm2(xyzc-xyzd)
xyzp = gaussian_product_center(alphaa,xyza,alphab,xyzb)
xp,yp,zp = xyzp
xyzq = gaussian_product_center(alphac,xyzc,alphad,xyzd)
xq,yq,zq = xyzq
rpq2 = norm2(xyzp-xyzq)
gamma1 = alphaa+alphab
gamma2 = alphac+alphad
delta = 0.25*(1/gamma1+1/gamma2)
Bx = B_array(la,lb,lc,ld,xp,xa,xb,xq,xc,xd,gamma1,gamma2,delta)
By = B_array(ma,mb,mc,md,yp,ya,yb,yq,yc,yd,gamma1,gamma2,delta)
Bz = B_array(na,nb,nc,nd,zp,za,zb,zq,zc,zd,gamma1,gamma2,delta)
sum = 0.
for I in range(la+lb+lc+ld+1):
for J in range(ma+mb+mc+md+1):
for K in range(na+nb+nc+nd+1):
sum = sum + Bx[I]*By[J]*Bz[K]*Fgamma(I+J+K,0.25*rpq2/delta)
return 2*pow(pi,2.5)/(gamma1*gamma2*sqrt(gamma1+gamma2)) \
*exp(-alphaa*alphab*rab2/gamma1) \
*exp(-alphac*alphad*rcd2/gamma2)*sum*norma*normb*normc*normd
def coulomb_repulsion(xyza, norma, lmna, alphaa, xyzb, normb, lmnb, alphab,
xyzc, normc, lmnc, alphac, xyzd, normd, lmnd, alphad):
"""
Return the coulomb repulsion between four primitive gaussians a,b,c,d with the given origin
, x,y,z, normalization constants norm, angular momena l,m,n, and exponent alpha.
>>> p1 = array((0.,0.,0.),'d')
>>> p2 = array((0.,0.,1.),'d')
>>> lmn = (0,0,0)
>>> isclose(coulomb_repulsion(p1,1.,lmn,1.,p1,1.,lmn,1.,p1,1.,lmn,1.,p1,1.,lmn,1.),4.373355)
True
>>> isclose(coulomb_repulsion(p1,1.,lmn,1.,p1,1.,lmn,1.,p2,1.,lmn,1.,p2,1.,lmn,1.),3.266127)
True
>>> isclose(coulomb_repulsion(p1,1.,lmn,1.,p2,1.,lmn,1.,p1,1.,lmn,1.,p2,1.,lmn,1.),1.6088672)
True
"""
la, ma, na = lmna
lb, mb, nb = lmnb
lc, mc, nc = lmnc
ld, md, nd = lmnd
xa, ya, za = xyza
xb, yb, zb = xyzb
xc, yc, zc = xyzc
xd, yd, zd = xyzd
rab2 = norm2(xyza - xyzb)
rcd2 = norm2(xyzc - xyzd)
xyzp = gaussian_product_center(alphaa, xyza, alphab, xyzb)
xp, yp, zp = xyzp
xyzq = gaussian_product_center(alphac, xyzc, alphad, xyzd)
xq, yq, zq = xyzq
rpq2 = norm2(xyzp - xyzq)
gamma1 = alphaa + alphab
gamma2 = alphac + alphad
delta = 0.25 * (1 / gamma1 + 1 / gamma2)
Bx = B_array(la, lb, lc, ld, xp, xa, xb, xq, xc, xd, gamma1, gamma2, delta)
By = B_array(ma, mb, mc, md, yp, ya, yb, yq, yc, yd, gamma1, gamma2, delta)
Bz = B_array(na, nb, nc, nd, zp, za, zb, zq, zc, zd, gamma1, gamma2, delta)
sum = 0.
for I in range(la + lb + lc + ld + 1):
for J in range(ma + mb + mc + md + 1):
for K in range(na + nb + nc + nd + 1):
sum = sum + Bx[I] * By[J] * Bz[K] * Fgamma(
I + J + K, 0.25 * rpq2 / delta)
return 2*pow(pi,2.5)/(gamma1*gamma2*sqrt(gamma1+gamma2)) \
*exp(-alphaa*alphab*rab2/gamma1) \
*exp(-alphac*alphad*rcd2/gamma2)*sum*norma*normb*normc*normd
def term0(aexpn,xyza,bexpn,xyzb,cexpn,xyzc,dexpn,xyzd,mtot):
zeta,eta = float(aexpn+bexpn),float(cexpn+dexpn)
zpe = zeta+eta
xyzp = gaussian_product_center(aexpn,xyza,bexpn,xyzb)
xyzq = gaussian_product_center(cexpn,xyzc,dexpn,xyzd)
rab2 = norm2(xyza-xyzb)
Kab = sqrt(2)*pow(pi,1.25)/(aexpn+bexpn)\
*exp(-aexpn*bexpn/(aexpn+bexpn)*rab2)
rcd2 = norm2(xyzc-xyzd)
Kcd = sqrt(2)*pow(pi,1.25)/(cexpn+dexpn)\
*exp(-cexpn*dexpn/(cexpn+dexpn)*rcd2)
rpq2 = norm2(xyzp-xyzq)
T = zeta*eta/zpe*rpq2
return [Fgamma(m,T)*Kab*Kcd/sqrt(zpe) for m in xrange(mtot+1)]
def term0(aexpn, xyza, bexpn, xyzb, cexpn, xyzc, dexpn, xyzd, mtot):
zeta, eta = float(aexpn + bexpn), float(cexpn + dexpn)
zpe = zeta + eta
xyzp = gaussian_product_center(aexpn, xyza, bexpn, xyzb)
xyzq = gaussian_product_center(cexpn, xyzc, dexpn, xyzd)
rab2 = norm2(xyza - xyzb)
Kab = sqrt(2)*pow(pi,1.25)/(aexpn+bexpn)\
*exp(-aexpn*bexpn/(aexpn+bexpn)*rab2)
rcd2 = norm2(xyzc - xyzd)
Kcd = sqrt(2)*pow(pi,1.25)/(cexpn+dexpn)\
*exp(-cexpn*dexpn/(cexpn+dexpn)*rcd2)
rpq2 = norm2(xyzp - xyzq)
T = zeta * eta / zpe * rpq2
return [Fgamma(m, T) * Kab * Kcd / sqrt(zpe) for m in xrange(mtot + 1)]
def vrr(xyza,norma,lmna,alphaa,
xyzb,normb,alphab,
xyzc,normc,lmnc,alphac,
xyzd,normd,alphad,M):
la,ma,na = lmna
lc,mc,nc = lmnc
xa,ya,za = xyza
xb,yb,zb = xyzb
xc,yc,zc = xyzc
xd,yd,zd = xyzd
px,py,pz = xyzp = gaussian_product_center(alphaa,xyza,alphab,xyzb)
qx,qy,qz = xyzq = gaussian_product_center(alphac,xyzc,alphad,xyzd)
zeta,eta = float(alphaa+alphab),float(alphac+alphad)
wx,wy,wz = xyzw = gaussian_product_center(zeta,xyzp,eta,xyzq)
rab2 = pow(xa-xb,2) + pow(ya-yb,2) + pow(za-zb,2)
Kab = sqrt(2)*pow(pi,1.25)/(alphaa+alphab)\
*exp(-alphaa*alphab/(alphaa+alphab)*rab2)
rcd2 = pow(xc-xd,2) + pow(yc-yd,2) + pow(zc-zd,2)
Kcd = sqrt(2)*pow(pi,1.25)/(alphac+alphad)\
*exp(-alphac*alphad/(alphac+alphad)*rcd2)
rpq2 = pow(px-qx,2) + pow(py-qy,2) + pow(pz-qz,2)
T = zeta*eta/(zeta+eta)*rpq2
mtot = la+ma+na+lc+mc+nc+M
Fgterms = [0]*(mtot+1)
Fgterms[mtot] = Fgamma(mtot,T)
for im in range(mtot-1,-1,-1):
Fgterms[im]=(2.*T*Fgterms[im+1]+exp(-T))/(2.*im+1)
# Todo: setup this as a regular array
# Store the vrr values as a 7 dimensional array
# vrr_terms[la,ma,na,lc,mc,nc,m]
vrr_terms = {}
for im in range(mtot+1):
vrr_terms[0,0,0,0,0,0,im] = (
norma*normb*normc*normd*Kab*Kcd/sqrt(zeta+eta)*Fgterms[im]
)
# Todo: use itertools.product() for the nested for loops
for i in range(la):
for im in range(mtot-i):
vrr_terms[i+1,0,0, 0,0,0, im] = (
(px-xa)*vrr_terms[i,0,0, 0,0,0, im]
+ (wx-px)*vrr_terms[i,0,0, 0,0,0, im+1]
)
if i:
vrr_terms[i+1,0,0, 0,0,0, im] += (
i/2./zeta*( vrr_terms[i-1,0,0, 0,0,0, im]
- eta/(zeta+eta)*vrr_terms[i-1,0,0, 0,0,0, im+1]
))
for j in range(ma):
for i in range(la+1):
for im in range(mtot-i-j):
vrr_terms[i,j+1,0, 0,0,0, im] = (
(py-ya)*vrr_terms[i,j,0, 0,0,0, im]
+ (wy-py)*vrr_terms[i,j,0, 0,0,0, im+1]
)
if j:
vrr_terms[i,j+1,0, 0,0,0, im] += (
j/2./zeta*(vrr_terms[i,j-1,0, 0,0,0, im]
- eta/(zeta+eta)
*vrr_terms[i,j-1,0, 0,0,0, im+1]
))
for k in range(na):
for j in range(ma+1):
for i in range(la+1):
for im in range(mtot-i-j-k):
vrr_terms[i,j,k+1, 0,0,0, im] = (
(pz-za)*vrr_terms[i,j,k, 0,0,0, im]
+ (wz-pz)*vrr_terms[i,j,k, 0,0,0, im+1]
)
if k:
vrr_terms[i,j,k+1, 0,0,0, im] += (
k/2./zeta*(vrr_terms[i,j,k-1, 0,0,0, im]
- eta/(zeta+eta)
*vrr_terms[i,j,k-1, 0,0,0, im+1]
))
for q in range(lc):
for k in range(na+1):
for j in range(ma+1):
for i in range(la+1):
for im in range(mtot-i-j-k-q):
vrr_terms[i,j,k, q+1,0,0, im] = (
(qx-xc)*vrr_terms[i,j,k, q,0,0, im]
+ (wx-qx)*vrr_terms[i,j,k, q,0,0, im+1]
)
if q:
vrr_terms[i,j,k, q+1,0,0, im] += (
q/2./eta*(vrr_terms[i,j,k, q-1,0,0, im]
- zeta/(zeta+eta)
*vrr_terms[i,j,k, q-1,0,0, im+1]
))
if i:
vrr_terms[i,j,k, q+1,0,0, im] += (
i/2./(zeta+eta)*vrr_terms[i-1,j,k, q,0,0, im+1]
)
for r in range(mc):
for q in range(lc+1):
for k in range(na+1):
for j in range(ma+1):
for i in range(la+1):
for im in range(mtot-i-j-k-q-r):
vrr_terms[i,j,k, q,r+1,0, im] = (
(qy-yc)*vrr_terms[i,j,k, q,r,0, im]
+ (wy-qy)*vrr_terms[i,j,k, q,r,0, im+1]
)
if r:
vrr_terms[i,j,k, q,r+1,0, im] += (
r/2./eta*(vrr_terms[i,j,k, q,r-1,0, im]
- zeta/(zeta+eta)
*vrr_terms[i,j,k, q,r-1,0, im+1]
))
if j:
vrr_terms[i,j,k, q,r+1,0, im] += (
j/2./(zeta+eta)*vrr_terms[i,j-1,k,q,r,0,im+1]
)
for s in range(nc):
for r in range(mc+1):
for q in range(lc+1):
for k in range(na+1):
for j in range(ma+1):
for i in range(la+1):
for im in range(mtot-i-j-k-q-r-s):
vrr_terms[i,j,k,q,r,s+1,im] = (
(qz-zc)*vrr_terms[i,j,k,q,r,s,im]
+ (wz-qz)*vrr_terms[i,j,k,q,r,s,im+1]
)
if s:
vrr_terms[i,j,k,q,r,s+1,im] += (
s/2./eta*(vrr_terms[i,j,k,q,r,s-1,im]
- zeta/(zeta+eta)
*vrr_terms[i,j,k,q,r,s-1,im+1]
))
if k:
vrr_terms[i,j,k,q,r,s+1,im] += (
k/2./(zeta+eta)*vrr_terms[i,j,k-1,q,r,s,im+1]
)
return vrr_terms[la,ma,na,lc,mc,nc,M]
def vrr_array(xyza,lmna,alphaa,xyzb,alphab,
xyzc,lmnc,alphac,xyzd,alphad):
la,ma,na = lmna
lc,mc,nc = lmnc
xa,ya,za = xyza
xb,yb,zb = xyzb
xc,yc,zc = xyzc
xd,yd,zd = xyzd
px,py,pz = xyzp = gaussian_product_center(alphaa,xyza,alphab,xyzb)
qx,qy,qz = xyzq = gaussian_product_center(alphac,xyzc,alphad,xyzd)
zeta,eta = float(alphaa+alphab),float(alphac+alphad)
wx,wy,wz = xyzw = gaussian_product_center(zeta,xyzp,eta,xyzq)
zpe = zeta+eta
rab2 = norm2(xyza-xyzb)
Kab = sqrt(2)*pow(pi,1.25)/(alphaa+alphab)\
*exp(-alphaa*alphab/(alphaa+alphab)*rab2)
rcd2 = norm2(xyzc-xyzd)
Kcd = sqrt(2)*pow(pi,1.25)/(alphac+alphad)\
*exp(-alphac*alphad/(alphac+alphad)*rcd2)
rpq2 = norm2(xyzp-xyzq)
T = zeta*eta/zpe*rpq2
mtot = sum(lmna)+sum(lmnc)
vrr_terms = {}#zeros((la+1,ma+1,na+1,lc+1,mc+1,nc+1,mtot+1),'d')
for m in xrange(mtot+1):
vrr_terms[0,0,0,0,0,0,m] = Fgamma(m,T)*Kab*Kcd/sqrt(zpe)
for i in xrange(la):
for m in xrange(mtot-i):
vrr_terms[i+1,0,0, 0,0,0, m] = (px-xa)*vrr_terms[i,0,0, 0,0,0, m] +\
(wx-px)*vrr_terms[i,0,0, 0,0,0, m+1]
if i>0:
vrr_terms[i+1,0,0, 0,0,0, m] += i/2./zeta*(
vrr_terms[i-1,0,0, 0,0,0, m]
- eta/zpe*vrr_terms[i-1,0,0, 0,0,0, m+1] )
for i,j in product(xrange(la+1),xrange(ma)):
for m in range(mtot-i-j):
vrr_terms[i,j+1,0, 0,0,0, m] = (py-ya)*vrr_terms[i,j,0, 0,0,0, m] +\
(wy-py)*vrr_terms[i,j,0, 0,0,0, m+1]
if j>0:
vrr_terms[i,j+1,0, 0,0,0, m] += j/2./zeta*(
vrr_terms[i,j-1,0, 0,0,0, m]
- eta/zpe*vrr_terms[i,j-1,0, 0,0,0, m+1] )
for i,j,k in product(xrange(la+1),xrange(ma+1),xrange(na)):
for m in range(mtot-i-j-k):
vrr_terms[i,j,k+1, 0,0,0, m] = (pz-za)*vrr_terms[i,j,k, 0,0,0, m] +\
(wz-pz)*vrr_terms[i,j,k, 0,0,0, m+1]
if k>0:
vrr_terms[i,j,k+1, 0,0,0, m] += k/2./zeta*(
vrr_terms[i,j,k-1, 0,0,0, m]
- eta/zpe*vrr_terms[i,j,k-1, 0,0,0, m+1])
for i,j,k, q in product(xrange(la+1),xrange(ma+1),xrange(na+1),xrange(lc)):
for m in range(mtot-i-j-k-q):
vrr_terms[i,j,k, q+1,0,0, m] = (qx-xc)*vrr_terms[i,j,k, q,0,0, m] +\
(wx-qx)*vrr_terms[i,j,k, q,0,0, m+1]
if q>0:
vrr_terms[i,j,k, q+1,0,0, m] += q/2./eta*(
vrr_terms[i,j,k, q-1,0,0, m]
- zeta/zpe*vrr_terms[i,j,k, q-1,0,0, m+1])
if i>0:
vrr_terms[i,j,k, q+1,0,0, m] += i/2./zpe*vrr_terms[i-1,j,k, q,0,0, m+1]
for i,j,k, q,r in product(xrange(la+1),xrange(ma+1),xrange(na+1),
xrange(lc+1),xrange(mc)):
for m in range(mtot-i-j-k-q-r):
vrr_terms[i,j,k, q,r+1,0, m] = (qy-yc)*vrr_terms[i,j,k, q,r,0, m] +\
(wy-qy)*vrr_terms[i,j,k, q,r,0, m+1]
if r>0:
vrr_terms[i,j,k, q,r+1,0, m] += r/2./eta*(
vrr_terms[i,j,k, q,r-1,0, m]
- zeta/zpe*vrr_terms[i,j,k, q,r-1,0, m+1])
if j>0:
vrr_terms[i,j,k, q,r+1,0, m] += j/2./zpe*vrr_terms[i,j-1,k,q,r,0,m+1]
for i,j,k, q,r,s in product(xrange(la+1),xrange(ma+1),xrange(na+1),
xrange(lc+1),xrange(mc+1),xrange(nc)):
for m in range(mtot-i-j-k-q-r-s):
vrr_terms[i,j,k,q,r,s+1,m] = (qz-zc)*vrr_terms[i,j,k,q,r,s,m] +\
(wz-qz)*vrr_terms[i,j,k,q,r,s,m+1]
if s>0:
vrr_terms[i,j,k,q,r,s+1,m] += s/2./eta*(
vrr_terms[i,j,k,q,r,s-1,m]
- zeta/zpe*vrr_terms[i,j,k,q,r,s-1,m+1])
if k>0:
vrr_terms[i,j,k,q,r,s+1,m] += k/2./zpe*vrr_terms[i,j,k-1,q,r,s,m+1]
return vrr_terms
def vrr_shell_2(aexpn,xyza,bexpn,xyzb,cexpn,xyzc,dexpn,xyzd,maxa,maxc):
# This uses a more intelligent method of looping over the am's to
# generate the powers required
import copy
xyzp = gaussian_product_center(aexpn,xyza,bexpn,xyzb)
xyzq = gaussian_product_center(cexpn,xyzc,dexpn,xyzd)
zeta,eta = float(aexpn+bexpn),float(cexpn+dexpn)
xyzw = gaussian_product_center(zeta,xyzp,eta,xyzq)
zpe = zeta+eta
mtot = 3*maxa+3*maxc
# Don't need all of these terms:
#terms = zeros((maxa+1,maxa+1,maxa+1,maxc+1,maxc+1,maxc+1,mtot+1),'d')
terms = {}
# Do ama=amc=0 term first:
ama,amc = 0,0
for m,t in enumerate(term0(aexpn,xyza,bexpn,xyzb,cexpn,xyzc,dexpn,xyzd,mtot)):
terms[0,0,0, 0,0,0, m] = t
#end m
pqac = (xyzp[0]-xyza[0],xyzp[1]-xyza[1],xyzp[2]-xyza[2],
xyzq[0]-xyzc[0],xyzq[1]-xyzc[1],xyzq[2]-xyzc[2])
wpq = (xyzw[0]-xyzp[0],xyzw[1]-xyzp[1],xyzw[2]-xyzp[2],
xyzw[0]-xyzq[0],xyzw[1]-xyzq[1],xyzw[2]-xyzq[2])
ze = (eta,eta,eta,zeta,zeta,zeta)
zezpe = [zei/zpe for zei in ze]
#ama>0, amc=0
for ama in xrange(1,maxa+1):
for aI,aJ,aK in shell_iterator(ama):
l = [aI,aJ,aK, 0,0,0]
ind = indmax(l)
val = l[ind]
r1,r2,r3,r4,r5,r6 = copy_and_decrement(l,ind)
s1,s2,s3,s4,s5,s6 = copy_and_decrement(l,ind,ind)
for m in xrange(mtot-aI-aJ-aK):
terms[aI,aJ,aK, 0,0,0, m] = pqac[ind]*terms[r1,r2,r3, r4,r5,r6,m] +\
wpq[ind]*terms[r1,r2,r3, r4,r5,r6,m+1]
if val>1:
terms[aI,aJ,aK, 0,0,0, m] += 0.5*(val-1)/ze[ind]*(
terms[s1,s2,s3, s4,s5,s6,m] -\
zezpe[ind]*terms[s1,s2,s3, s4,s5,s6,m+1])
#end m
#end cijk
#end ama
# ama=0, amc>0 here:
for amc in xrange(1,maxc+1):
for cI,cJ,cK in shell_iterator(amc):
l = [0,0,0, cI,cJ,cK]
ind = indmax(l)
val = l[ind]
r1,r2,r3,r4,r5,r6 = copy_and_decrement(l,ind)
s1,s2,s3,s4,s5,s6 = copy_and_decrement(l,ind,ind)
for m in xrange(mtot-cI-cJ-cK):
terms[0,0,0, cI,cJ,cK, m] = pqac[ind]*terms[r1,r2,r3, r4,r5,r6,m] +\
wpq[ind]*terms[r1,r2,r3, r4,r5,r6,m+1]
if val>1:
terms[0,0,0, cI,cJ,cK, m] += 0.5*(val-1)/ze[ind]*(
terms[s1,s2,s3, s4,s5,s6,m] -\
zezpe[ind]*terms[s1,s2,s3, s4,s5,s6,m+1])
#end m
#end cIJK
#end amc
# ama>0, amc>0
for ama in xrange(1,maxa+1):
for amc in xrange(1,maxc+1):
for aI,aJ,aK in shell_iterator(ama):
for cI,cJ,cK in shell_iterator(amc):
l = [aI,aJ,aK, cI,cJ,cK]
ind = indmax(l)
val = l[ind]
cind = (ind+3)%6
cval = l[cind]
r1,r2,r3,r4,r5,r6 = copy_and_decrement(l,ind)
s1,s2,s3,s4,s5,s6 = copy_and_decrement(l,ind,ind)
t1,t2,t3,t4,t5,t6 = copy_and_decrement(l,ind,cind)
for m in xrange(mtot-aI-aJ-aK-cI-cJ-cK):
terms[aI,aJ,aK, cI,cJ,cK, m] = pqac[ind]*terms[r1,r2,r3, r4,r5,r6,m] +\
wpq[ind]*terms[r1,r2,r3, r4,r5,r6,m+1]
# should this be ...0.5*(val-1)/... ?
if val>1:
terms[aI,aJ,aK, cI,cJ,cK, m] += 0.5*(val-1)/ze[ind]*(
terms[s1,s2,s3, s4,s5,s6,m] -\
zezpe[ind]*terms[s1,s2,s3, s4,s5,s6,m+1])
#print 'c',(aI,aJ,aK,cI,cJ,cK,m),terms[aI,aJ,aK,cI,cJ,cK,m]
if cval>0:
terms[aI,aJ,aK, cI,cJ,cK, m] += 0.5*cval/zpe*terms[t1,t2,t3,t4,t5,t6,m+1]
#end m
#end bijk
#end aijk
#end amc
#end ama
return pack_full(terms,maxa,maxc) # and unpack later
def vrr(xyza, norma, lmna, alphaa, xyzb, normb, alphab, xyzc, normc, lmnc,
alphac, xyzd, normd, alphad, M):
la, ma, na = lmna
lc, mc, nc = lmnc
xa, ya, za = xyza
xb, yb, zb = xyzb
xc, yc, zc = xyzc
xd, yd, zd = xyzd
px, py, pz = xyzp = gaussian_product_center(alphaa, xyza, alphab, xyzb)
qx, qy, qz = xyzq = gaussian_product_center(alphac, xyzc, alphad, xyzd)
zeta, eta = float(alphaa + alphab), float(alphac + alphad)
wx, wy, wz = xyzw = gaussian_product_center(zeta, xyzp, eta, xyzq)
rab2 = pow(xa - xb, 2) + pow(ya - yb, 2) + pow(za - zb, 2)
Kab = sqrt(2)*pow(pi,1.25)/(alphaa+alphab)\
*exp(-alphaa*alphab/(alphaa+alphab)*rab2)
rcd2 = pow(xc - xd, 2) + pow(yc - yd, 2) + pow(zc - zd, 2)
Kcd = sqrt(2)*pow(pi,1.25)/(alphac+alphad)\
*exp(-alphac*alphad/(alphac+alphad)*rcd2)
rpq2 = pow(px - qx, 2) + pow(py - qy, 2) + pow(pz - qz, 2)
T = zeta * eta / (zeta + eta) * rpq2
mtot = la + ma + na + lc + mc + nc + M
Fgterms = [0] * (mtot + 1)
Fgterms[mtot] = Fgamma(mtot, T)
for im in range(mtot - 1, -1, -1):
Fgterms[im] = (2. * T * Fgterms[im + 1] + exp(-T)) / (2. * im + 1)
# Todo: setup this as a regular array
# Store the vrr values as a 7 dimensional array
# vrr_terms[la,ma,na,lc,mc,nc,m]
vrr_terms = {}
for im in range(mtot + 1):
vrr_terms[0, 0, 0, 0, 0, 0,
im] = (norma * normb * normc * normd * Kab * Kcd /
sqrt(zeta + eta) * Fgterms[im])
# Todo: use itertools.product() for the nested for loops
for i in range(la):
for im in range(mtot - i):
vrr_terms[i + 1, 0, 0, 0, 0, 0,
im] = ((px - xa) * vrr_terms[i, 0, 0, 0, 0, 0, im] +
(wx - px) * vrr_terms[i, 0, 0, 0, 0, 0, im + 1])
if i:
vrr_terms[i + 1, 0, 0, 0, 0, 0, im] += (
i / 2. / zeta *
(vrr_terms[i - 1, 0, 0, 0, 0, 0, im] - eta /
(zeta + eta) * vrr_terms[i - 1, 0, 0, 0, 0, 0, im + 1]))
for j in range(ma):
for i in range(la + 1):
for im in range(mtot - i - j):
vrr_terms[i, j + 1, 0, 0, 0, 0, im] = (
(py - ya) * vrr_terms[i, j, 0, 0, 0, 0, im] +
(wy - py) * vrr_terms[i, j, 0, 0, 0, 0, im + 1])
if j:
vrr_terms[i, j + 1, 0, 0, 0, 0, im] += (j / 2. / zeta * (
vrr_terms[i, j - 1, 0, 0, 0, 0, im] - eta /
(zeta + eta) * vrr_terms[i, j - 1, 0, 0, 0, 0, im + 1])
)
for k in range(na):
for j in range(ma + 1):
for i in range(la + 1):
for im in range(mtot - i - j - k):
vrr_terms[i, j, k + 1, 0, 0, 0, im] = (
(pz - za) * vrr_terms[i, j, k, 0, 0, 0, im] +
(wz - pz) * vrr_terms[i, j, k, 0, 0, 0, im + 1])
if k:
vrr_terms[i, j, k + 1, 0, 0, 0, im] += (
k / 2. / zeta *
(vrr_terms[i, j, k - 1, 0, 0, 0, im] - eta /
(zeta + eta) *
vrr_terms[i, j, k - 1, 0, 0, 0, im + 1]))
for q in range(lc):
for k in range(na + 1):
for j in range(ma + 1):
for i in range(la + 1):
for im in range(mtot - i - j - k - q):
vrr_terms[i, j, k, q + 1, 0, 0, im] = (
(qx - xc) * vrr_terms[i, j, k, q, 0, 0, im] +
(wx - qx) * vrr_terms[i, j, k, q, 0, 0, im + 1])
if q:
vrr_terms[i, j, k, q + 1, 0, 0, im] += (
q / 2. / eta *
(vrr_terms[i, j, k, q - 1, 0, 0, im] - zeta /
(zeta + eta) *
vrr_terms[i, j, k, q - 1, 0, 0, im + 1]))
if i:
vrr_terms[i, j, k, q + 1, 0, 0, im] += (
i / 2. / (zeta + eta) *
vrr_terms[i - 1, j, k, q, 0, 0, im + 1])
for r in range(mc):
for q in range(lc + 1):
for k in range(na + 1):
for j in range(ma + 1):
for i in range(la + 1):
for im in range(mtot - i - j - k - q - r):
vrr_terms[i, j, k, q, r + 1, 0, im] = (
(qy - yc) * vrr_terms[i, j, k, q, r, 0, im] +
(wy - qy) *
vrr_terms[i, j, k, q, r, 0, im + 1])
if r:
vrr_terms[i, j, k, q, r + 1, 0, im] += (
r / 2. / eta *
(vrr_terms[i, j, k, q, r - 1, 0, im] -
zeta / (zeta + eta) *
vrr_terms[i, j, k, q, r - 1, 0, im + 1]))
if j:
vrr_terms[i, j, k, q, r + 1, 0, im] += (
j / 2. / (zeta + eta) *
vrr_terms[i, j - 1, k, q, r, 0, im + 1])
for s in range(nc):
for r in range(mc + 1):
for q in range(lc + 1):
for k in range(na + 1):
for j in range(ma + 1):
for i in range(la + 1):
for im in range(mtot - i - j - k - q - r - s):
vrr_terms[i, j, k, q, r, s + 1, im] = (
(qz - zc) * vrr_terms[i, j, k, q, r, s, im]
+ (wz - qz) *
vrr_terms[i, j, k, q, r, s, im + 1])
if s:
vrr_terms[i, j, k, q, r, s + 1, im] += (
s / 2. / eta *
(vrr_terms[i, j, k, q, r, s - 1, im] -
zeta / (zeta + eta) * vrr_terms[
i, j, k, q, r, s - 1, im + 1]))
if k:
vrr_terms[i, j, k, q, r, s + 1,
im] += (k / 2. / (zeta + eta) *
vrr_terms[i, j, k - 1, q,
r, s, im + 1])
return vrr_terms[la, ma, na, lc, mc, nc, M]
def vrr_array(xyza, lmna, alphaa, xyzb, alphab, xyzc, lmnc, alphac, xyzd,
alphad):
la, ma, na = lmna
lc, mc, nc = lmnc
xa, ya, za = xyza
xb, yb, zb = xyzb
xc, yc, zc = xyzc
xd, yd, zd = xyzd
px, py, pz = xyzp = gaussian_product_center(alphaa, xyza, alphab, xyzb)
qx, qy, qz = xyzq = gaussian_product_center(alphac, xyzc, alphad, xyzd)
zeta, eta = float(alphaa + alphab), float(alphac + alphad)
wx, wy, wz = xyzw = gaussian_product_center(zeta, xyzp, eta, xyzq)
zpe = zeta + eta
rab2 = norm2(xyza - xyzb)
Kab = sqrt(2)*pow(pi,1.25)/(alphaa+alphab)\
*exp(-alphaa*alphab/(alphaa+alphab)*rab2)
rcd2 = norm2(xyzc - xyzd)
Kcd = sqrt(2)*pow(pi,1.25)/(alphac+alphad)\
*exp(-alphac*alphad/(alphac+alphad)*rcd2)
rpq2 = norm2(xyzp - xyzq)
T = zeta * eta / zpe * rpq2
mtot = sum(lmna) + sum(lmnc)
vrr_terms = {} #zeros((la+1,ma+1,na+1,lc+1,mc+1,nc+1,mtot+1),'d')
for m in xrange(mtot + 1):
vrr_terms[0, 0, 0, 0, 0, 0, m] = Fgamma(m, T) * Kab * Kcd / sqrt(zpe)
for i in xrange(la):
for m in xrange(mtot - i):
vrr_terms[i+1,0,0, 0,0,0, m] = (px-xa)*vrr_terms[i,0,0, 0,0,0, m] +\
(wx-px)*vrr_terms[i,0,0, 0,0,0, m+1]
if i > 0:
vrr_terms[i + 1, 0, 0, 0, 0, 0, m] += i / 2. / zeta * (
vrr_terms[i - 1, 0, 0, 0, 0, 0, m] -
eta / zpe * vrr_terms[i - 1, 0, 0, 0, 0, 0, m + 1])
for i, j in product(xrange(la + 1), xrange(ma)):
for m in range(mtot - i - j):
vrr_terms[i,j+1,0, 0,0,0, m] = (py-ya)*vrr_terms[i,j,0, 0,0,0, m] +\
(wy-py)*vrr_terms[i,j,0, 0,0,0, m+1]
if j > 0:
vrr_terms[i, j + 1, 0, 0, 0, 0, m] += j / 2. / zeta * (
vrr_terms[i, j - 1, 0, 0, 0, 0, m] -
eta / zpe * vrr_terms[i, j - 1, 0, 0, 0, 0, m + 1])
for i, j, k in product(xrange(la + 1), xrange(ma + 1), xrange(na)):
for m in range(mtot - i - j - k):
vrr_terms[i,j,k+1, 0,0,0, m] = (pz-za)*vrr_terms[i,j,k, 0,0,0, m] +\
(wz-pz)*vrr_terms[i,j,k, 0,0,0, m+1]
if k > 0:
vrr_terms[i, j, k + 1, 0, 0, 0, m] += k / 2. / zeta * (
vrr_terms[i, j, k - 1, 0, 0, 0, m] -
eta / zpe * vrr_terms[i, j, k - 1, 0, 0, 0, m + 1])
for i, j, k, q in product(xrange(la + 1), xrange(ma + 1), xrange(na + 1),
xrange(lc)):
for m in range(mtot - i - j - k - q):
vrr_terms[i,j,k, q+1,0,0, m] = (qx-xc)*vrr_terms[i,j,k, q,0,0, m] +\
(wx-qx)*vrr_terms[i,j,k, q,0,0, m+1]
if q > 0:
vrr_terms[i, j, k, q + 1, 0, 0, m] += q / 2. / eta * (
vrr_terms[i, j, k, q - 1, 0, 0, m] -
zeta / zpe * vrr_terms[i, j, k, q - 1, 0, 0, m + 1])
if i > 0:
vrr_terms[i, j, k, q + 1, 0, 0,
m] += i / 2. / zpe * vrr_terms[i - 1, j, k, q, 0, 0,
m + 1]
for i, j, k, q, r in product(xrange(la + 1), xrange(ma + 1),
xrange(na + 1), xrange(lc + 1), xrange(mc)):
for m in range(mtot - i - j - k - q - r):
vrr_terms[i,j,k, q,r+1,0, m] = (qy-yc)*vrr_terms[i,j,k, q,r,0, m] +\
(wy-qy)*vrr_terms[i,j,k, q,r,0, m+1]
if r > 0:
vrr_terms[i, j, k, q, r + 1, 0, m] += r / 2. / eta * (
vrr_terms[i, j, k, q, r - 1, 0, m] -
zeta / zpe * vrr_terms[i, j, k, q, r - 1, 0, m + 1])
if j > 0:
vrr_terms[i, j, k, q, r + 1, 0,
m] += j / 2. / zpe * vrr_terms[i, j - 1, k, q, r, 0,
m + 1]
for i, j, k, q, r, s in product(xrange(la + 1), xrange(ma + 1),
xrange(na + 1), xrange(lc + 1),
xrange(mc + 1), xrange(nc)):
for m in range(mtot - i - j - k - q - r - s):
vrr_terms[i,j,k,q,r,s+1,m] = (qz-zc)*vrr_terms[i,j,k,q,r,s,m] +\
(wz-qz)*vrr_terms[i,j,k,q,r,s,m+1]
if s > 0:
vrr_terms[i, j, k, q, r, s + 1, m] += s / 2. / eta * (
vrr_terms[i, j, k, q, r, s - 1, m] -
zeta / zpe * vrr_terms[i, j, k, q, r, s - 1, m + 1])
if k > 0:
vrr_terms[i, j, k, q, r, s + 1,
m] += k / 2. / zpe * vrr_terms[i, j, k - 1, q, r, s,
m + 1]
return vrr_terms
def vrr_shell_2(aexpn, xyza, bexpn, xyzb, cexpn, xyzc, dexpn, xyzd, maxa,
maxc):
# This uses a more intelligent method of looping over the am's to
# generate the powers required
import copy
xyzp = gaussian_product_center(aexpn, xyza, bexpn, xyzb)
xyzq = gaussian_product_center(cexpn, xyzc, dexpn, xyzd)
zeta, eta = float(aexpn + bexpn), float(cexpn + dexpn)
xyzw = gaussian_product_center(zeta, xyzp, eta, xyzq)
zpe = zeta + eta
mtot = 3 * maxa + 3 * maxc
# Don't need all of these terms:
#terms = zeros((maxa+1,maxa+1,maxa+1,maxc+1,maxc+1,maxc+1,mtot+1),'d')
terms = {}
# Do ama=amc=0 term first:
ama, amc = 0, 0
for m, t in enumerate(
term0(aexpn, xyza, bexpn, xyzb, cexpn, xyzc, dexpn, xyzd, mtot)):
terms[0, 0, 0, 0, 0, 0, m] = t
#end m
pqac = (xyzp[0] - xyza[0], xyzp[1] - xyza[1], xyzp[2] - xyza[2],
xyzq[0] - xyzc[0], xyzq[1] - xyzc[1], xyzq[2] - xyzc[2])
wpq = (xyzw[0] - xyzp[0], xyzw[1] - xyzp[1], xyzw[2] - xyzp[2],
xyzw[0] - xyzq[0], xyzw[1] - xyzq[1], xyzw[2] - xyzq[2])
ze = (eta, eta, eta, zeta, zeta, zeta)
zezpe = [zei / zpe for zei in ze]
#ama>0, amc=0
for ama in xrange(1, maxa + 1):
for aI, aJ, aK in shell_iterator(ama):
l = [aI, aJ, aK, 0, 0, 0]
ind = indmax(l)
val = l[ind]
r1, r2, r3, r4, r5, r6 = copy_and_decrement(l, ind)
s1, s2, s3, s4, s5, s6 = copy_and_decrement(l, ind, ind)
for m in xrange(mtot - aI - aJ - aK):
terms[aI,aJ,aK, 0,0,0, m] = pqac[ind]*terms[r1,r2,r3, r4,r5,r6,m] +\
wpq[ind]*terms[r1,r2,r3, r4,r5,r6,m+1]
if val > 1:
terms[aI,aJ,aK, 0,0,0, m] += 0.5*(val-1)/ze[ind]*(
terms[s1,s2,s3, s4,s5,s6,m] -\
zezpe[ind]*terms[s1,s2,s3, s4,s5,s6,m+1])
#end m
#end cijk
#end ama
# ama=0, amc>0 here:
for amc in xrange(1, maxc + 1):
for cI, cJ, cK in shell_iterator(amc):
l = [0, 0, 0, cI, cJ, cK]
ind = indmax(l)
val = l[ind]
r1, r2, r3, r4, r5, r6 = copy_and_decrement(l, ind)
s1, s2, s3, s4, s5, s6 = copy_and_decrement(l, ind, ind)
for m in xrange(mtot - cI - cJ - cK):
terms[0,0,0, cI,cJ,cK, m] = pqac[ind]*terms[r1,r2,r3, r4,r5,r6,m] +\
wpq[ind]*terms[r1,r2,r3, r4,r5,r6,m+1]
if val > 1:
terms[0,0,0, cI,cJ,cK, m] += 0.5*(val-1)/ze[ind]*(
terms[s1,s2,s3, s4,s5,s6,m] -\
zezpe[ind]*terms[s1,s2,s3, s4,s5,s6,m+1])
#end m
#end cIJK
#end amc
# ama>0, amc>0
for ama in xrange(1, maxa + 1):
for amc in xrange(1, maxc + 1):
for aI, aJ, aK in shell_iterator(ama):
for cI, cJ, cK in shell_iterator(amc):
l = [aI, aJ, aK, cI, cJ, cK]
ind = indmax(l)
val = l[ind]
cind = (ind + 3) % 6
cval = l[cind]
r1, r2, r3, r4, r5, r6 = copy_and_decrement(l, ind)
s1, s2, s3, s4, s5, s6 = copy_and_decrement(l, ind, ind)
t1, t2, t3, t4, t5, t6 = copy_and_decrement(l, ind, cind)
for m in xrange(mtot - aI - aJ - aK - cI - cJ - cK):
terms[aI,aJ,aK, cI,cJ,cK, m] = pqac[ind]*terms[r1,r2,r3, r4,r5,r6,m] +\
wpq[ind]*terms[r1,r2,r3, r4,r5,r6,m+1]
# should this be ...0.5*(val-1)/... ?
if val > 1:
terms[aI,aJ,aK, cI,cJ,cK, m] += 0.5*(val-1)/ze[ind]*(
terms[s1,s2,s3, s4,s5,s6,m] -\
zezpe[ind]*terms[s1,s2,s3, s4,s5,s6,m+1])
#print 'c',(aI,aJ,aK,cI,cJ,cK,m),terms[aI,aJ,aK,cI,cJ,cK,m]
if cval > 0:
terms[aI, aJ, aK, cI, cJ, cK,
m] += 0.5 * cval / zpe * terms[t1, t2, t3,
t4, t5, t6,
m + 1]
#end m
#end bijk
#end aijk
#end amc
#end ama
return pack_full(terms, maxa, maxc) # and unpack later
