def SxyzRecur(a,
b,
a_array,
b_array,
la=0,
ma=0,
na=0,
lb=0,
mb=0,
nb=0,
Norm=False):
Na = 1
Nb = 1
if la < 0 or ma < 0 or na < 0 or lb < 0 or mb < 0 or nb < 0:
return 0
if not Norm:
Na = norm_GTO(a, la, ma, na)
Nb = norm_GTO(b, lb, mb, nb)
dAB_2 = ((a_array - b_array)**2).sum()
K = K_GTO(a, b, dAB_2)
p_array = b / (a + b) * b_array + a / (a + b) * a_array
PA_array = p_array - a_array
PB_array = p_array - b_array
Ix = _Sij(a, b, PA_array[0], PB_array[0], la, lb)
Iy = _Sij(a, b, PA_array[1], PB_array[1], ma, mb)
Iz = _Sij(a, b, PA_array[2], PB_array[2], na, nb)
return Na * Nb * K * Ix * Iy * Iz
def phi_2c1e(i, j, k, l, m, n, a, b, Kab, rPA, rPB, rPC, PC2, Norm=False):
p = a + b
Na = 1
Nb = 1
if not Norm:
Na = norm_GTO(a, i, j, k)
Nb = norm_GTO(b, l, m, n)
return Na * Nb * phi_2c1e_nNorm(0, 0, 0, i, j, k, l, m, n, p, Kab, rPA,
rPB, rPC, PC2)
def gabcd(la,
lb,
lc,
ld,
ma,
mb,
mc,
md,
na,
nb,
nc,
nd,
a,
b,
c,
d,
rA,
rB,
rC,
rD,
Norm=False):
Na = 1
Nb = 1
Nc = 1
Nd = 1
p = a + b
q = c + d
rP = (a * rA + b * rB) / p
rQ = (c * rC + d * rD) / q
rPA = rP - rA
rPB = rP - rB
rQC = rQ - rC
rQD = rQ - rD
rAB = rA - rB
rCD = rC - rD
rPQ = rP - rQ
AB2 = (rAB**2).sum()
CD2 = (rCD**2).sum()
PQ2 = (rPQ**2).sum()
Kab_Kcd = K_GTO(a, b, AB2) * K_GTO(c, d, CD2)
if not Norm:
Na = norm_GTO(a, la, ma, na)
Nb = norm_GTO(b, lb, mb, nb)
Nc = norm_GTO(c, lc, mc, nc)
Nd = norm_GTO(d, ld, md, nd)
return Na * Nb * Nc * Nd * gabcd_nNorm(la, lb, lc, ld, ma, mb, mc, md, na,
nb, nc, nd, a, b, c, d, Kab_Kcd,
rPA, rPB, rQC, rQD, rPQ, PQ2)
def phi_2c1e(i, j, k, l, m, n, a, b, rA, rB, rC, Norm=False):
p = a + b
Na = 1
Nb = 1
rP = (a * rA + b * rB) / p
rPA = rP - rA
rPB = rP - rB
rPC = rP - rC
AB2 = ((rA - rB)**2).sum()
PC2 = (rPC**2).sum()
Kab = K_GTO(a, b, AB2)
if not Norm:
Na = norm_GTO(a, i, j, k)
Nb = norm_GTO(b, l, m, n)
return Na * Nb * phi_2c1e_nNorm(0, 0, 0, i, l, j, m, k, n, p, Kab, rPA,
rPB, rPC, PC2)
def kinetDefold(a, b, a_array, b_array, la, ma, na, lb, mb, nb, Norm=False):
"""
Return Kinetic Integrate of GTO A |aAl_a m_a n_a> and B |bBl_b m_b n_b>
:param a:
:param b:
:param a_array: numpy.array
:param b_array: numpy.array
:param la:
:param ma:
:param na:
:param lb:
:param mb:
:param nb:
:return:
"""
Na = 1
Nb = 1
if la < 0 or ma < 0 or na < 0 or lb < 0 or mb < 0 or nb < 0:
return 0
if not Norm:
Na = norm_GTO(a, la, ma, na)
Nb = norm_GTO(b, lb, mb, nb)
dAB_2 = ((a_array - b_array)**2).sum()
K = K_GTO(a, b, dAB_2)
p_array = b / (a + b) * b_array + a / (a + b) * a_array
PA_array = p_array - a_array
PB_array = p_array - b_array
Kl = _Tij(a, b, PA_array[0], PB_array[0], la, lb) * _Sij(
a, b, PA_array[1], PB_array[1], ma, mb) * _Sij(a, b, PA_array[2],
PB_array[2], na, nb)
Km = _Sij(a, b, PA_array[0], PB_array[0], la, lb) * _Tij(
a, b, PA_array[1], PB_array[1], ma, mb) * _Sij(a, b, PA_array[2],
PB_array[2], na, nb)
Kn = _Sij(a, b, PA_array[0], PB_array[0], la, lb) * _Sij(
a, b, PA_array[1], PB_array[1], ma, mb) * _Tij(a, b, PA_array[2],
PB_array[2], na, nb)
return Na * Nb * K * (Kl + Km + Kn)