import numpy as np
from moha.system.integral.differential import D
from moha.system.integral.nuclear_attraction import E
[docs]def Lxyz(a,lmn1,A,b,lmn2,B):
''' Evaluates kinetic energy integral between two Gaussians
Returns a float.
a: orbital exponent on Gaussian 'a' (e.g. alpha in the text)
b: orbital exponent on Gaussian 'b' (e.g. beta in the text)
lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))
for Gaussian 'a'
lmn2: int tuple containing orbital angular momentum for Gaussian 'b'
A: list containing origin of Gaussian 'a', e.g. [1.0, 2.0, 0.0]
B: list containing origin of Gaussian 'b'
'''
i,k,m = lmn1
j,l,n = lmn2
term0 = E(i,j,0,A[0],B[0],a,b)*E(k,l,1,A[1],B[1],a,b)*D(m,n,1,A[2],B[2],a,b)-\
E(i,j,0,A[0],B[0],a,b)*D(k,l,1,A[1],B[1],a,b)*E(m,n,1,A[2],B[2],a,b)
term1 = D(i,j,1,A[0],B[0],a,b)*E(k,l,0,A[1],B[1],a,b)*E(m,n,1,A[2],B[2],a,b)-\
E(i,j,1,A[0],B[0],a,b)*E(k,l,0,A[1],B[1],a,b)*D(m,n,1,A[2],B[2],a,b)
term2 = E(i,j,1,A[0],B[0],a,b)*D(k,l,1,A[1],B[1],a,b)*E(m,n,0,A[2],B[2],a,b)-\
D(i,j,1,A[0],B[0],a,b)*E(k,l,1,A[1],B[1],a,b)*E(m,n,0,A[2],B[2],a,b)
return -1j*np.power(np.pi/(a+b),1.5)*(term0+term1+term2)
[docs]def angular_momentum(a,b):
'''Evaluates kinetic energy between two contracted Gaussians
Returns float.
Arguments:
a: contracted Gaussian 'a', BasisFunction object
b: contracted Gaussian 'b', BasisFunction object
'''
t = 0.0
for ia, ca in enumerate(a.coefs):
for ib, cb in enumerate(b.coefs):
t += a.norm[ia]*b.norm[ib]*ca*cb*\
Lxyz(a.exps[ia],a.shell,a.origin,\
b.exps[ib],b.shell,b.origin)
return t