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dipole.f90
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module mdipole
use constants
implicit none
contains
function dipole(n1,i1,j1,a1,k1,n2,i2,j2,a2,k2) result(ans)
integer, intent(in) :: n1,i1,j1,n2,i2,j2
real(quad), intent(in) :: a1,a2,k1,k2
real(quad) :: ans
! - - - - - - - - - - - - - - - - - -
integer :: key
real(quad) :: ap, spp
real(quad) :: p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13
real(quad) :: e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13
! - - - - - - - - - - - - - - - - - -
key = n1 + 2*i1 + 4*j1 + 8*n2 + 16*i2 + 32*j2
select case (key)
case (0)
ans = 0
case (1)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
ans = (p1*spp)/2.
case (2)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p7 = k1**2
e7 = exp(-(p1*p7)/4.)
ans = (e7*k1*p1*spp)/2.
case (3)
ans = 0
case (4)
ans = 0
case (5)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p7 = k1**2
p10 = ap**(-2)
e7 = exp(-(p1*p7)/4.)
ans = (e7*p10*(2*ap - p7)*spp)/4.
case (6)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p7 = k1**2
e8 = exp(-(p1*p7))
ans = (e8*k1*p1*spp)/2.
case (7)
ans = 0
case (8)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
ans = (p1*spp)/2.
case (9)
ans = 0
case (10)
ans = 0
case (11)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p7 = k1**2
p11 = ap**(-3)
p13 = k1**3
e7 = exp(-(p1*p7)/4.)
ans = (e7*p11*(6*ap*k1 - p13)*spp)/8.
case (12)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p7 = k1**2
p10 = ap**(-2)
e7 = exp(-(p1*p7)/4.)
ans = (e7*p10*(2*ap - p7)*spp)/4.
case (13)
ans = 0
case (14)
ans = 0
case (15)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p7 = k1**2
p11 = ap**(-3)
p13 = k1**3
e8 = exp(-(p1*p7))
ans = (e8*p11*(3*ap*k1 - 2*p13)*spp)/4.
case (16)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p2 = k2**2
e1 = exp(-(p1*p2)/4.)
ans = (e1*k2*p1*spp)/2.
case (17)
ans = 0
case (18)
ans = 0
case (19)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p10 = ap**(-2)
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = (p10*(e3*(2*ap - p3) + e4*(-2*ap + p4))*spp)/8.
case (20)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = ((e3*(-k1 + k2) + e4*(k1 + k2))*p1*spp)/4.
case (21)
ans = 0
case (22)
ans = 0
case (23)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p8 = (-2*k1 + k2)**2
p9 = (2*k1 + k2)**2
p10 = ap**(-2)
e9 = exp(-(p1*p8)/4.)
e10 = exp(-(p1*p9)/4.)
ans = (p10*(e9*(2*ap - p8) + e10*(-2*ap + p9))*spp)/16.
case (24)
ans = 0
case (25)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p2 = k2**2
p11 = ap**(-3)
p12 = k2**3
e1 = exp(-(p1*p2)/4.)
ans = (e1*p11*(6*ap*k2 - p12)*spp)/8.
case (26)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p10 = ap**(-2)
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = (p10*(e3*(2*ap - p3) + e4*(-2*ap + p4))*spp)/8.
case (27)
ans = 0
case (28)
ans = 0
case (29)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p11 = ap**(-3)
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = (p11*(e3*(k1 - k2)*(-6*ap + p3) + e4*(k1 + k2)*(6*ap - p4))*spp)/16.
case (30)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p8 = (-2*k1 + k2)**2
p9 = (2*k1 + k2)**2
p10 = ap**(-2)
e9 = exp(-(p1*p8)/4.)
e10 = exp(-(p1*p9)/4.)
ans = (p10*(e9*(2*ap - p8) + e10*(-2*ap + p9))*spp)/16.
case (31)
ans = 0
case (32)
ans = 0
case (33)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p2 = k2**2
p10 = ap**(-2)
e1 = exp(-(p1*p2)/4.)
ans = (e1*p10*(2*ap - p2)*spp)/4.
case (34)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = ((e3*(k1 - k2) + e4*(k1 + k2))*p1*spp)/4.
case (35)
ans = 0
case (36)
ans = 0
case (37)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p10 = ap**(-2)
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = (p10*(2*ap*(e3 + e4) - e3*p3 - e4*p4)*spp)/8.
case (38)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p8 = (-2*k1 + k2)**2
p9 = (2*k1 + k2)**2
e9 = exp(-(p1*p8)/4.)
e10 = exp(-(p1*p9)/4.)
ans = ((2*(e10 + e9)*k1 + (e10 - e9)*k2)*p1*spp)/8.
case (39)
ans = 0
case (40)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p2 = k2**2
p10 = ap**(-2)
e1 = exp(-(p1*p2)/4.)
ans = (e1*p10*(2*ap - p2)*spp)/4.
case (41)
ans = 0
case (42)
ans = 0
case (43)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p11 = ap**(-3)
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = (p11*(e3*(k1 - k2)*(6*ap - p3) + e4*(k1 + k2)*(6*ap - p4))*spp)/16.
case (44)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p10 = ap**(-2)
e3 = exp(-(p1*p3)/4.)
e4 = exp(-(p1*p4)/4.)
ans = (p10*(2*ap*(e3 + e4) - e3*p3 - e4*p4)*spp)/8.
case (45)
ans = 0
case (46)
ans = 0
case (47)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p2 = k2**2
p7 = k1**2
p11 = ap**(-3)
e13 = exp(-(p1*(p2 + 4*p7))/4.)
ans = (e13*p11*spp*(2*k1*(6*ap - 3*p2 - 4*p7)*Cosh(k1*k2*p1) + &
& k2*(-6*ap + p2 + 12*p7)*Sinh(k1*k2*p1)))/16.
case (48)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p2 = k2**2
e2 = exp(-(p1*p2))
ans = (e2*k2*p1*spp)/2.
case (49)
ans = 0
case (50)
ans = 0
case (51)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p5 = (k1 - 2*k2)**2
p6 = (k1 + 2*k2)**2
p10 = ap**(-2)
e5 = exp(-(p1*p5)/4.)
e6 = exp(-(p1*p6)/4.)
ans = (p10*(e5*(2*ap - p5) + e6*(-2*ap + p6))*spp)/16.
case (52)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p5 = (k1 - 2*k2)**2
p6 = (k1 + 2*k2)**2
e5 = exp(-(p1*p5)/4.)
e6 = exp(-(p1*p6)/4.)
ans = (((-e5 + e6)*k1 + 2*(e5 + e6)*k2)*p1*spp)/8.
case (53)
ans = 0
case (54)
ans = 0
case (55)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p10 = ap**(-2)
e11 = exp(-(p1*p3))
e12 = exp(-(p1*p4))
ans = (p10*(e11*(ap - 2*p3) - e12*(ap - 2*p4))*spp)/16.
case (56)
ans = 0
case (57)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p2 = k2**2
p11 = ap**(-3)
p12 = k2**3
e2 = exp(-(p1*p2))
ans = (e2*p11*(3*ap*k2 - 2*p12)*spp)/4.
case (58)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p5 = (k1 - 2*k2)**2
p6 = (k1 + 2*k2)**2
p10 = ap**(-2)
e5 = exp(-(p1*p5)/4.)
e6 = exp(-(p1*p6)/4.)
ans = (p10*(e5*(2*ap - p5) + e6*(-2*ap + p6))*spp)/16.
case (59)
ans = 0
case (60)
ans = 0
case (61)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p5 = (k1 - 2*k2)**2
p6 = (k1 + 2*k2)**2
p11 = ap**(-3)
e5 = exp(-(p1*p5)/4.)
e6 = exp(-(p1*p6)/4.)
ans = (p11*(e5*(k1 - 2*k2)*(-6*ap + p5) + e6*(k1 + 2*k2)*(6*ap - p6))*spp)/&
& 32.
case (62)
ap = a1 + a2
spp = sqrt(q_pi/ap)
p1 = 1/ap
p3 = (k1 - k2)**2
p4 = (k1 + k2)**2
p10 = ap**(-2)
e11 = exp(-(p1*p3))
e12 = exp(-(p1*p4))
ans = (p10*(e11*(ap - 2*p3) - e12*(ap - 2*p4))*spp)/16.
case (63)
ans = 0
end select
end function dipole
end module mdipole