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Deriving the CCSDT equations

In this notebook I seek to optimize the code by the use of intermediates, and experiment with ways of letting CCAlgebra decide which factorizations that will be the most beneficial.





In [15]:



    


from IPython.display import display, Math, Latex 
%matplotlib inline  
%cd 'E:\Dropbox\Dropbox\Master Thesis Audun Skau Hansen\Pythonscripts'
%run CCAlgebra_mk4.py



    


















    






E:\Dropbox\Dropbox\Master Thesis Audun Skau Hansen\Pythonscripts

















In [16]:



    


H = normal_ordered_hamiltonian() #Including one- and two-particle interactions
T_1 = Operator([],[1,-1])  #The T_1 cluster operator
T_2 = Operator([],[1,1,-1,-1]) #The T_2 operator; all lists must be normal ordered
T_3 = Operator([],[1,1,1,-1,-1,-1])
expT = expand_ansatz([[T_1],[T_2], [T_3]],4)  #Taylor expand a list of lists to the 3rd order



    











In [17]:



    


tx = combine_to_excitation(H,expT,0, [1,0,0,0])
s = "0 ="
for t in tx:
    s += "+" + t + "\n"
Math(s)



    


















    
Out[17]:







$$0 =+\frac{1}{1} \sum_{ck} \langle k || c \rangle t_{k}^{c}
+\frac{1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{kl}^{cd}
+\frac{1}{2} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{l}^{d}
$$
















In [7]:



    


tx = combine_to_excitation(H,expT,1, [1,0,0,0])
s = "0 ="
for t in tx:
    s += "+" + t + "\n"
Math(s)



    


















    
Out[7]:







$$0 =+\frac{1}{1} \sum_{c} \langle a || c \rangle t_{i}^{c}
+\frac{-1}{1} \sum_{k} \langle k || i \rangle t_{k}^{a}
+\frac{1}{1} \sum_{ck} \langle k || c \rangle t_{ik}^{ca}
+\frac{1}{1} \sum_{ck} \langle k || c \rangle t_{i}^{c} t_{k}^{a}
+\frac{-1}{1} \sum_{ck} \langle ak || ci \rangle t_{k}^{c}
+\frac{1}{2} \sum_{cdk} \langle ak || cd \rangle t_{ik}^{cd}
+\frac{1}{1} \sum_{ckd} \langle ak || cd \rangle t_{k}^{c} t_{i}^{d}
+\frac{-1}{2} \sum_{ckl} \langle kl || ci \rangle t_{kl}^{ca}
+\frac{-1}{1} \sum_{ckl} \langle kl || ci \rangle t_{k}^{c} t_{l}^{a}
+\frac{1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{ikl}^{cda}
+\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{il}^{da}
+\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{kl}^{da}
+\frac{1}{2} \sum_{kcdl} \langle kl || cd \rangle t_{k}^{a} t_{il}^{cd}
+\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ik}^{cd} t_{l}^{a}
+\frac{1}{2} \sum_{ckld} \langle kl || cd \rangle t_{kl}^{ca} t_{i}^{d}
+\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ik}^{ca} t_{l}^{d}
+\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{i}^{d} t_{l}^{a}
+\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{i}^{c} t_{k}^{a} t_{l}^{d}
+\frac{1}{1} \sum_{kcld} \langle kl || cd \rangle t_{k}^{a} t_{l}^{c} t_{i}^{d}
$$
















In [8]:



    


tx = combine_to_excitation(H,expT,2, [1,0,0,0])
s = "0 ="
for t in tx:
    s += "+" + t + "\n"
Math(s)



    


















    
Out[8]:







$$0 =+P(ba)\frac{-1}{1} \sum_{c} \langle a || c \rangle t_{ij}^{cb}
+P(ij)\frac{1}{1} \sum_{k} \langle k || j \rangle t_{ik}^{ab}
+\frac{1}{1} \sum_{ck} \langle k || c \rangle t_{ijk}^{cab}
+P(ij)\frac{-1}{1} \sum_{ck} \langle k || c \rangle t_{i}^{c} t_{jk}^{ab}
+P(ab)\frac{-1}{1} \sum_{kc} \langle k || c \rangle t_{k}^{a} t_{ij}^{cb}
+P(ab)\frac{-1}{1} \sum_{ck} \langle k || c \rangle t_{ij}^{ca} t_{k}^{b}
+P(ij)\frac{-1}{1} \sum_{kc} \langle k || c \rangle t_{ik}^{ab} t_{j}^{c}
+\frac{1}{2} \sum_{cd} \langle ab || cd \rangle t_{ij}^{cd}
+P(ij)\frac{-1}{2} \sum_{cd} \langle ab || cd \rangle t_{i}^{c} t_{j}^{d}
+\frac{1}{2} \sum_{kl} \langle kl || ij \rangle t_{kl}^{ab}
+P(ab)\frac{-1}{2} \sum_{kl} \langle kl || ij \rangle t_{k}^{a} t_{l}^{b}
+P(ba)P(ij)\frac{-1}{1} \sum_{ck} \langle ak || cj \rangle t_{ik}^{cb}
+P(ij)P(ba)\frac{-1}{1} \sum_{ck} \langle ak || cj \rangle t_{i}^{c} t_{k}^{b}
+P(ij)\frac{1}{1} \sum_{c} \langle a || c \rangle t_{i}^{c}
+P(ba)\frac{-1}{2} \sum_{cdk} \langle ak || cd \rangle t_{ijk}^{cdb}
+P(ba)\frac{-1}{1} \sum_{ckd} \langle ak || cd \rangle t_{k}^{c} t_{ij}^{db}
+P(ij)P(ba)\frac{1}{1} \sum_{cdk} \langle ak || cd \rangle t_{i}^{c} t_{jk}^{db}
+P(ab)\frac{-1}{2} \sum_{kcd} \langle kb || cd \rangle t_{k}^{a} t_{ij}^{cd}
+P(ba)\frac{-1}{2} \sum_{cdk} \langle ak || cd \rangle t_{ij}^{cd} t_{k}^{b}
+P(ba)P(ij)\frac{1}{1} \sum_{ckd} \langle ak || cd \rangle t_{ik}^{cb} t_{j}^{d}
+P(ba)\frac{-1}{1} \sum_{cdk} \langle ak || cd \rangle t_{ij}^{cb} t_{k}^{d}
+P(ij)P(ba)\frac{1}{2} \sum_{cdk} \langle ak || cd \rangle t_{i}^{c} t_{j}^{d} t_{k}^{b}
+P(ab)\frac{-1}{1} \sum_{k} \langle k || i \rangle t_{k}^{a}
+P(ij)\frac{1}{2} \sum_{ckl} \langle kl || cj \rangle t_{ikl}^{cab}
+P(ji)\frac{1}{1} \sum_{ckl} \langle kl || ci \rangle t_{k}^{c} t_{jl}^{ab}
+P(ij)\frac{1}{2} \sum_{ckl} \langle kl || cj \rangle t_{i}^{c} t_{kl}^{ab}
+P(ab)P(ji)\frac{-1}{1} \sum_{kcl} \langle kl || ic \rangle t_{k}^{a} t_{jl}^{cb}
+P(ab)P(ij)\frac{-1}{1} \sum_{ckl} \langle kl || cj \rangle t_{ik}^{ca} t_{l}^{b}
+P(ji)\frac{1}{2} \sum_{klc} \langle kl || ic \rangle t_{kl}^{ab} t_{j}^{c}
+P(ij)\frac{1}{1} \sum_{kcl} \langle kl || jc \rangle t_{ik}^{ab} t_{l}^{c}
+P(ij)P(ab)\frac{-1}{2} \sum_{ckl} \langle kl || cj \rangle t_{i}^{c} t_{k}^{a} t_{l}^{b}
+\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{ijl}^{dab}
+P(ij)\frac{-1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{jkl}^{dab}
+P(ab)\frac{-1}{2} \sum_{kcdl} \langle kl || cd \rangle t_{k}^{a} t_{ijl}^{cdb}
+P(ij)\frac{-1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ik}^{cd} t_{jl}^{ab}
+\frac{1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{cd} t_{kl}^{ab}
+P(ab)\frac{-1}{2} \sum_{ckld} \langle kl || cd \rangle t_{kl}^{ca} t_{ij}^{db}
+P(ab)P(ij)\frac{1}{2} \sum_{ckdl} \langle kl || cd \rangle t_{ik}^{ca} t_{jl}^{db}
+P(ab)\frac{-1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ijk}^{cda} t_{l}^{b}
+P(ij)\frac{-1}{2} \sum_{ckld} \langle kl || cd \rangle t_{ikl}^{cab} t_{j}^{d}
+\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ijk}^{cab} t_{l}^{d}
+P(ij)\frac{-1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{i}^{d} t_{jl}^{ab}
+P(ab)\frac{-1}{1} \sum_{ckld} \langle kl || cd \rangle t_{k}^{c} t_{l}^{a} t_{ij}^{db}
+P(ij)\frac{-1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{j}^{d} t_{kl}^{ab}
+P(ij)P(ab)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{i}^{c} t_{k}^{a} t_{jl}^{db}
+P(ab)\frac{-1}{4} \sum_{klcd} \langle kl || cd \rangle t_{k}^{a} t_{l}^{b} t_{ij}^{cd}
+P(ab)\frac{-1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{ij}^{da} t_{l}^{b}
+P(ij)\frac{-1}{1} \sum_{ckld} \langle kl || cd \rangle t_{k}^{c} t_{il}^{ab} t_{j}^{d}
+P(ij)P(ab)\frac{1}{1} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{jk}^{da} t_{l}^{b}
+P(ij)\frac{-1}{4} \sum_{ckld} \langle kl || cd \rangle t_{i}^{c} t_{kl}^{ab} t_{j}^{d}
+P(ab)\frac{-1}{4} \sum_{kcdl} \langle kl || cd \rangle t_{k}^{a} t_{ij}^{cd} t_{l}^{b}
+P(ab)\frac{-1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{cd} t_{k}^{a} t_{l}^{b}
+P(ab)P(ij)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ik}^{ca} t_{j}^{d} t_{l}^{b}
+P(ab)\frac{-1}{1} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{ca} t_{k}^{d} t_{l}^{b}
+P(ij)\frac{-1}{4} \sum_{klcd} \langle kl || cd \rangle t_{kl}^{ab} t_{i}^{c} t_{j}^{d}
+P(ij)\frac{-1}{1} \sum_{kcld} \langle kl || cd \rangle t_{ik}^{ab} t_{l}^{c} t_{j}^{d}
+P(ij)P(ab)\frac{1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{j}^{d} t_{k}^{a} t_{l}^{b}
+P(ab)P(ij)\frac{1}{4} \sum_{klcd} \langle kl || cd \rangle t_{k}^{a} t_{l}^{b} t_{i}^{c} t_{j}^{d}
$$
















In [6]:



    


tx = combine_to_excitation(H,expT,3, [1,0,0,0])
s = "0 ="
for t in tx:
    s += "+" + t + "\n"
Math(s)



    


















    
Out[6]:







$$0 =+P(ba)P(za)\frac{1}{1} \sum_{c} \langle a || c \rangle t_{ijw}^{cbz}
+P(iw)P(jw)\frac{-1}{1} \sum_{k} \langle k || w \rangle t_{ijk}^{abz}
+P(ij)P(iw)\frac{1}{1} \sum_{ck} \langle k || c \rangle t_{i}^{c} t_{jwk}^{abz}
+P(ab)P(az)\frac{1}{1} \sum_{kc} \langle k || c \rangle t_{k}^{a} t_{ijw}^{cbz}
+P(ab)P(az)P(iw)P(jw)\frac{1}{1} \sum_{ck} \langle k || c \rangle t_{ij}^{ca} t_{wk}^{bz}
+P(az)P(bz)\frac{1}{1} \sum_{ck} \langle k || c \rangle t_{ijw}^{cab} t_{k}^{z}
+P(iw)P(jw)\frac{1}{1} \sum_{kc} \langle k || c \rangle t_{ijk}^{abz} t_{w}^{c}
+P(za)P(zb)\frac{1}{2} \sum_{cd} \langle ab || cd \rangle t_{ijw}^{cdz}
+P(ij)P(iw)P(za)P(zb)\frac{1}{1} \sum_{cd} \langle ab || cd \rangle t_{i}^{c} t_{jw}^{dz}
+P(ba)P(bz)P(iw)P(jw)\frac{1}{1} \sum_{cd} \langle az || cd \rangle t_{ij}^{cb} t_{w}^{d}
+P(iw)P(ij)\frac{1}{2} \sum_{kl} \langle kl || jw \rangle t_{ikl}^{abz}
+P(ab)P(az)P(ji)P(jw)\frac{1}{1} \sum_{kl} \langle kl || iw \rangle t_{k}^{a} t_{jl}^{bz}
+P(az)P(bz)P(ij)P(iw)\frac{1}{1} \sum_{kl} \langle kl || jw \rangle t_{ik}^{ab} t_{l}^{z}
+P(ba)P(za)P(iw)P(jw)\frac{-1}{1} \sum_{ck} \langle ak || cw \rangle t_{ijk}^{cbz}
+P(ij)P(iw)P(ba)P(za)P(jw)\frac{1}{1} \sum_{ck} \langle ak || cw \rangle t_{i}^{c} t_{jk}^{bz}
+P(az)P(ab)P(zb)P(ji)P(wi)\frac{1}{1} \sum_{kc} \langle kb || ic \rangle t_{k}^{a} t_{jw}^{cz}
+P(bz)P(ba)P(iw)P(jw)P(za)\frac{1}{1} \sum_{ck} \langle ak || cw \rangle t_{ij}^{cb} t_{k}^{z}
+P(az)P(bz)P(iw)P(ij)P(wj)\frac{1}{1} \sum_{kc} \langle kz || jc \rangle t_{ik}^{ab} t_{w}^{c}
+P(ba)P(bz)P(iw)P(jw)\frac{-1}{1} \sum_{c} \langle a || c \rangle t_{ij}^{cb}
+P(ba)P(za)\frac{1}{1} \sum_{ckd} \langle ak || cd \rangle t_{k}^{c} t_{ijw}^{dbz}
+P(ij)P(iw)P(ba)P(za)\frac{1}{1} \sum_{cdk} \langle ak || cd \rangle t_{i}^{c} t_{jwk}^{dbz}
+P(az)P(ab)P(zb)\frac{-1}{2} \sum_{kcd} \langle kb || cd \rangle t_{k}^{a} t_{ijw}^{cdz}
+P(iw)P(jw)P(ba)P(za)\frac{1}{2} \sum_{cdk} \langle ak || cd \rangle t_{ij}^{cd} t_{wk}^{bz}
+P(bz)P(ba)P(ij)P(iw)P(za)\frac{-1}{1} \sum_{ckd} \langle ak || cd \rangle t_{ik}^{cb} t_{jw}^{dz}
+P(bz)P(ba)P(za)\frac{-1}{2} \sum_{cdk} \langle ak || cd \rangle t_{ijw}^{cdb} t_{k}^{z}
+P(ba)P(za)P(iw)P(jw)\frac{1}{1} \sum_{ckd} \langle ak || cd \rangle t_{ijk}^{cbz} t_{w}^{d}
+P(ba)P(za)\frac{1}{1} \sum_{cdk} \langle ak || cd \rangle t_{ijw}^{cbz} t_{k}^{d}
+P(ij)P(iw)P(jw)P(ba)P(za)\frac{-1}{2} \sum_{cdk} \langle ak || cd \rangle t_{i}^{c} t_{j}^{d} t_{wk}^{bz}
+P(ij)P(iw)P(bz)P(ba)P(za)\frac{-1}{1} \sum_{ckd} \langle ak || cd \rangle t_{i}^{c} t_{k}^{b} t_{jw}^{dz}
+P(ij)P(iw)P(bz)P(ba)P(za)\frac{-1}{1} \sum_{cdk} \langle ak || cd \rangle t_{i}^{c} t_{jw}^{db} t_{k}^{z}
+P(ij)P(iw)P(ba)P(za)P(jw)\frac{-1}{2} \sum_{ckd} \langle ak || cd \rangle t_{i}^{c} t_{jk}^{bz} t_{w}^{d}
+P(bz)P(ba)P(iw)P(jw)P(za)\frac{-1}{1} \sum_{cdk} \langle ak || cd \rangle t_{ij}^{cb} t_{w}^{d} t_{k}^{z}
+P(az)P(bz)P(ij)P(iw)P(jw)\frac{-1}{2} \sum_{kcd} \langle kz || cd \rangle t_{ik}^{ab} t_{j}^{c} t_{w}^{d}
+P(az)P(bz)P(ij)P(iw)\frac{1}{1} \sum_{k} \langle k || j \rangle t_{ik}^{ab}
+P(ji)P(wi)\frac{-1}{1} \sum_{ckl} \langle kl || ci \rangle t_{k}^{c} t_{jwl}^{abz}
+P(ij)P(iw)P(jw)\frac{1}{2} \sum_{ckl} \langle kl || cw \rangle t_{i}^{c} t_{jkl}^{abz}
+P(ab)P(az)P(ji)P(wi)\frac{-1}{1} \sum_{kcl} \langle kl || ic \rangle t_{k}^{a} t_{jwl}^{cbz}
+P(ab)P(az)P(iw)P(ij)P(wj)\frac{1}{1} \sum_{ckl} \langle kl || cj \rangle t_{ik}^{ca} t_{wl}^{bz}
+P(ab)P(az)P(iw)P(jw)\frac{-1}{2} \sum_{ckl} \langle kl || cw \rangle t_{ij}^{ca} t_{kl}^{bz}
+P(az)P(bz)P(iw)P(jw)\frac{-1}{1} \sum_{ckl} \langle kl || cw \rangle t_{ijk}^{cab} t_{l}^{z}
+P(iw)P(ij)P(wj)\frac{1}{2} \sum_{klc} \langle kl || jc \rangle t_{ikl}^{abz} t_{w}^{c}
+P(iw)P(jw)\frac{-1}{1} \sum_{kcl} \langle kl || wc \rangle t_{ijk}^{abz} t_{l}^{c}
+P(iw)P(ij)P(ab)P(az)P(wj)\frac{1}{1} \sum_{ckl} \langle kl || cj \rangle t_{i}^{c} t_{k}^{a} t_{wl}^{bz}
+P(ab)P(az)P(bz)P(ji)P(wi)\frac{1}{2} \sum_{klc} \langle kl || ic \rangle t_{k}^{a} t_{l}^{b} t_{jw}^{cz}
+P(ij)P(iw)P(az)P(bz)P(jw)\frac{1}{1} \sum_{ckl} \langle kl || cw \rangle t_{i}^{c} t_{jk}^{ab} t_{l}^{z}
+P(ab)P(az)P(bz)P(ji)P(wi)\frac{1}{2} \sum_{kcl} \langle kl || ic \rangle t_{k}^{a} t_{jw}^{cb} t_{l}^{z}
+P(ab)P(az)P(iw)P(jw)P(bz)\frac{1}{2} \sum_{ckl} \langle kl || cw \rangle t_{ij}^{ca} t_{k}^{b} t_{l}^{z}
+P(az)P(bz)P(iw)P(ij)P(wj)\frac{1}{1} \sum_{kcl} \langle kl || jc \rangle t_{ik}^{ab} t_{w}^{c} t_{l}^{z}
+P(ij)P(iw)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ik}^{cd} t_{jwl}^{abz}
+P(iw)P(jw)\frac{1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{cd} t_{wkl}^{abz}
+P(ab)P(az)\frac{1}{2} \sum_{ckld} \langle kl || cd \rangle t_{kl}^{ca} t_{ijw}^{dbz}
+P(ab)P(az)P(ij)P(iw)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ik}^{ca} t_{jwl}^{dbz}
+P(ab)P(az)P(iw)P(jw)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{ca} t_{wkl}^{dbz}
+P(az)P(bz)\frac{1}{4} \sum_{klcd} \langle kl || cd \rangle t_{kl}^{ab} t_{ijw}^{cdz}
+P(az)P(bz)P(ij)P(iw)\frac{1}{2} \sum_{kcdl} \langle kl || cd \rangle t_{ik}^{ab} t_{jwl}^{cdz}
+P(ab)P(az)P(iw)P(jw)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ijk}^{cda} t_{wl}^{bz}
+P(ab)P(az)\frac{1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{ijw}^{cda} t_{kl}^{bz}
+P(az)P(bz)P(ij)P(iw)\frac{1}{2} \sum_{ckld} \langle kl || cd \rangle t_{ikl}^{cab} t_{jw}^{dz}
+P(az)P(bz)P(iw)P(jw)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ijk}^{cab} t_{wl}^{dz}
+P(az)P(bz)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ijw}^{cab} t_{kl}^{dz}
+P(ij)P(iw)\frac{1}{4} \sum_{klcd} \langle kl || cd \rangle t_{ikl}^{abz} t_{jw}^{cd}
+P(iw)P(jw)\frac{1}{2} \sum_{kcdl} \langle kl || cd \rangle t_{ijk}^{abz} t_{wl}^{cd}
+P(ij)P(iw)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{i}^{d} t_{jwl}^{abz}
+P(ab)P(az)\frac{1}{1} \sum_{ckld} \langle kl || cd \rangle t_{k}^{c} t_{l}^{a} t_{ijw}^{dbz}
+P(ij)P(iw)P(jw)\frac{-1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{j}^{d} t_{wkl}^{abz}
+P(ij)P(iw)P(ab)P(az)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{i}^{c} t_{k}^{a} t_{jwl}^{dbz}
+P(ab)P(az)P(bz)\frac{-1}{4} \sum_{klcd} \langle kl || cd \rangle t_{k}^{a} t_{l}^{b} t_{ijw}^{cdz}
+P(ab)P(az)P(iw)P(jw)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{ij}^{da} t_{wl}^{bz}
+P(ij)P(iw)P(ab)P(az)P(jw)\frac{-1}{1} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{jk}^{da} t_{wl}^{bz}
+P(ij)P(iw)P(ab)P(az)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{jw}^{da} t_{kl}^{bz}
+P(ab)P(az)P(iw)P(jw)\frac{1}{2} \sum_{kcdl} \langle kl || cd \rangle t_{k}^{a} t_{ij}^{cd} t_{wl}^{bz}
+P(ab)P(az)P(bz)P(ij)P(iw)\frac{-1}{1} \sum_{kcld} \langle kl || cd \rangle t_{k}^{a} t_{il}^{cb} t_{jw}^{dz}
+P(az)P(bz)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{k}^{c} t_{ijw}^{dab} t_{l}^{z}
+P(iw)P(jw)\frac{1}{1} \sum_{ckld} \langle kl || cd \rangle t_{k}^{c} t_{ijl}^{abz} t_{w}^{d}
+P(ij)P(iw)P(az)P(bz)\frac{1}{1} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{jwk}^{dab} t_{l}^{z}
+P(ij)P(iw)P(jw)\frac{-1}{4} \sum_{ckld} \langle kl || cd \rangle t_{i}^{c} t_{jkl}^{abz} t_{w}^{d}
+P(ab)P(az)P(bz)\frac{-1}{4} \sum_{kcdl} \langle kl || cd \rangle t_{k}^{a} t_{ijw}^{cdb} t_{l}^{z}
+P(iw)P(jw)P(ab)P(az)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{cd} t_{k}^{a} t_{wl}^{bz}
+P(ab)P(az)P(ij)P(iw)P(jw)\frac{-1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ik}^{ca} t_{j}^{d} t_{wl}^{bz}
+P(ab)P(az)P(ij)P(iw)P(bz)\frac{-1}{1} \sum_{ckld} \langle kl || cd \rangle t_{ik}^{ca} t_{l}^{b} t_{jw}^{dz}
+P(ab)P(az)P(iw)P(jw)\frac{1}{1} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{ca} t_{k}^{d} t_{wl}^{bz}
+P(ab)P(az)P(iw)P(jw)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{ca} t_{w}^{d} t_{kl}^{bz}
+P(iw)P(jw)P(az)P(bz)\frac{1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{cd} t_{wk}^{ab} t_{l}^{z}
+P(ab)P(az)P(ij)P(iw)P(bz)\frac{-1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ik}^{ca} t_{jw}^{db} t_{l}^{z}
+P(ab)P(az)P(ij)P(iw)P(jw)\frac{-1}{1} \sum_{ckld} \langle kl || cd \rangle t_{ik}^{ca} t_{jl}^{bz} t_{w}^{d}
+P(ab)P(az)P(iw)P(jw)\frac{1}{2} \sum_{ckld} \langle kl || cd \rangle t_{ij}^{ca} t_{kl}^{bz} t_{w}^{d}
+P(ab)P(az)P(iw)P(jw)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ij}^{ca} t_{wk}^{bz} t_{l}^{d}
+P(ab)P(az)P(bz)\frac{-1}{4} \sum_{cdkl} \langle kl || cd \rangle t_{ijw}^{cda} t_{k}^{b} t_{l}^{z}
+P(az)P(bz)P(iw)P(jw)\frac{1}{1} \sum_{ckdl} \langle kl || cd \rangle t_{ijk}^{cab} t_{w}^{d} t_{l}^{z}
+P(az)P(bz)\frac{1}{1} \sum_{cdkl} \langle kl || cd \rangle t_{ijw}^{cab} t_{k}^{d} t_{l}^{z}
+P(ij)P(iw)P(jw)\frac{-1}{4} \sum_{klcd} \langle kl || cd \rangle t_{ikl}^{abz} t_{j}^{c} t_{w}^{d}
+P(iw)P(jw)\frac{1}{1} \sum_{kcld} \langle kl || cd \rangle t_{ijk}^{abz} t_{l}^{c} t_{w}^{d}
+P(ij)P(iw)P(jw)P(ab)P(az)\frac{-1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{j}^{d} t_{k}^{a} t_{wl}^{bz}
+P(ij)P(iw)P(ab)P(az)P(bz)\frac{-1}{2} \sum_{ckld} \langle kl || cd \rangle t_{i}^{c} t_{k}^{a} t_{l}^{b} t_{jw}^{dz}
+P(ij)P(iw)P(jw)P(az)P(bz)\frac{-1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{j}^{d} t_{wk}^{ab} t_{l}^{z}
+P(ij)P(iw)P(ab)P(az)P(bz)\frac{-1}{2} \sum_{ckdl} \langle kl || cd \rangle t_{i}^{c} t_{k}^{a} t_{jw}^{db} t_{l}^{z}
+P(ij)P(iw)P(ab)P(az)P(bz)\frac{-1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{i}^{c} t_{jw}^{da} t_{k}^{b} t_{l}^{z}
+P(ij)P(iw)P(az)P(bz)P(jw)\frac{-1}{2} \sum_{ckdl} \langle kl || cd \rangle t_{i}^{c} t_{jk}^{ab} t_{w}^{d} t_{l}^{z}
+P(ab)P(az)P(iw)P(jw)P(bz)\frac{-1}{2} \sum_{cdkl} \langle kl || cd \rangle t_{ij}^{ca} t_{w}^{d} t_{k}^{b} t_{l}^{z}
+P(az)P(bz)P(ij)P(iw)P(jw)\frac{-1}{2} \sum_{kcdl} \langle kl || cd \rangle t_{ik}^{ab} t_{j}^{c} t_{w}^{d} t_{l}^{z}
$$
















In [ ]:

Content source: CompPhysics/ThesisProjects

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