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#!/usr/bin/env python
"""
Calculates the Coupled-Cluster energy- and amplitude equations
See 'An Introduction to Coupled Cluster Theory' by
T. Daniel Crawford and Henry F. Schaefer III.
http://www.ccc.uga.edu/lec_top/cc/html/review.html
"""
from sympy.physics.secondquant import (AntiSymmetricTensor, wicks,
F, Fd, NO, evaluate_deltas, substitute_dummies, Commutator,
simplify_index_permutations, PermutationOperator)
from sympy import (
symbols, expand, pprint, Rational, latex, Dummy
)
pretty_dummies_dict = {
'above': 'cdefgh',
'below': 'klmno',
'general': 'pqrstu'
}
def get_CC_operators():
"""
Returns a tuple (T1,T2) of unique operators.
"""
i = symbols('i', below_fermi=True, cls=Dummy)
a = symbols('a', above_fermi=True, cls=Dummy)
t_ai = AntiSymmetricTensor('t', (a,), (i,))
ai = NO(Fd(a)*F(i))
i, j = symbols('i,j', below_fermi=True, cls=Dummy)
a, b = symbols('a,b', above_fermi=True, cls=Dummy)
t_abij = AntiSymmetricTensor('t', (a, b), (i, j))
abji = NO(Fd(a)*Fd(b)*F(j)*F(i))
T1 = t_ai*ai
T2 = Rational(1, 4)*t_abij*abji
return (T1, T2)
def main():
print()
print("Calculates the Coupled-Cluster energy- and amplitude equations")
print("See 'An Introduction to Coupled Cluster Theory' by")
print("T. Daniel Crawford and Henry F. Schaefer III")
print("http://www.ccc.uga.edu/lec_top/cc/html/review.html")
print()
# setup hamiltonian
p, q, r, s = symbols('p,q,r,s', cls=Dummy)
f = AntiSymmetricTensor('f', (p,), (q,))
pr = NO((Fd(p)*F(q)))
v = AntiSymmetricTensor('v', (p, q), (r, s))
pqsr = NO(Fd(p)*Fd(q)*F(s)*F(r))
H = f*pr + Rational(1, 4)*v*pqsr
print("Using the hamiltonian:", latex(H))
print("Calculating 4 nested commutators")
C = Commutator
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 1...")
comm1 = wicks(C(H, T))
comm1 = evaluate_deltas(comm1)
comm1 = substitute_dummies(comm1)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 2...")
comm2 = wicks(C(comm1, T))
comm2 = evaluate_deltas(comm2)
comm2 = substitute_dummies(comm2)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 3...")
comm3 = wicks(C(comm2, T))
comm3 = evaluate_deltas(comm3)
comm3 = substitute_dummies(comm3)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 4...")
comm4 = wicks(C(comm3, T))
comm4 = evaluate_deltas(comm4)
comm4 = substitute_dummies(comm4)
print("construct Hausdoff expansion...")
eq = H + comm1 + comm2/2 + comm3/6 + comm4/24
eq = eq.expand()
eq = evaluate_deltas(eq)
eq = substitute_dummies(eq, new_indices=True,
pretty_indices=pretty_dummies_dict)
print("*********************")
print()
print("extracting CC equations from full Hbar")
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
print()
print("CC Energy:")
print(latex(wicks(eq, simplify_dummies=True,
keep_only_fully_contracted=True)))
print()
print("CC T1:")
eqT1 = wicks(NO(Fd(i)*F(a))*eq, simplify_kronecker_deltas=True, keep_only_fully_contracted=True)
eqT1 = substitute_dummies(eqT1)
print(latex(eqT1))
print()
print("CC T2:")
eqT2 = wicks(NO(Fd(i)*Fd(j)*F(b)*F(a))*eq, simplify_dummies=True, keep_only_fully_contracted=True, simplify_kronecker_deltas=True)
P = PermutationOperator
eqT2 = simplify_index_permutations(eqT2, [P(a, b), P(i, j)])
print(latex(eqT2))
if __name__ == "__main__":
main()
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