CCM.ccDgrams¶

Provides functions for all of the coupled cluster diagrams

Functions

`dgram_acik_bcjk`(v_ppph_res, t2)	Calculates - P(ij)P(ab)X^{ac}_{ij}t^{bc}_{jk}
`dgram_akci_ck`(v_phph, t1)	Calculates -V^{ak}_{ci}t^{c}_{k}
`dgram_bijk_ak1`(v_ppph_res, t1)	Calculates 0.5 * P(ab)X^{bi}_{jk}t^{a}_{k}
`dgram_bijk_ak2`(v_ppph_res, t1)	Calculates 0.5 * P(ij)P(ab)X^{bi}_{jk}t^{a}_{k}
`dgram_bijk_bj`(v_phhh, t1)	Calculates -V^{bi}_{jk}t^{b}_{j}
`dgram_bkci_ak_cj`(v_phph, t1)	Calculates - P(ij)P(ab)V^{bk}_{ci}t^{a}_{k}t^{c}_{j}
`dgram_bkcj_acik`(v_phph, t2)	Calculates -P(ij)P(ab)V^{bk}_{cj}t^{cb}_{ik}
`dgram_bkij_ak`(v_phhh, t1)	Calculates P(ab)V^{bk}_{ij}t^{a}_{k}
`dgram_cdkl_acik_dblj`(v_pphh, t2)	Calculates 0.5 * P(ij)P(ab)V^{cd}_{kl}t^{ac}_{ik}t^{db}_{lj}
`dgram_cdkl_ak_bl_cdij`(v_pphh, t1, t2)	Calculates 0.25 * P(ab)V^{cd}_{kl}t^{a}_{k}t^{b}_{l}t^{cd}_{ij}
`dgram_cdkl_bdkl`(v_pphh, t2)	Calculates -0.5 * V^{cd}_{kl}t^{bd}_{kl}
`dgram_cdkl_cdij_abkl`(v_pphh, t2)	Calculates 0.25 * P(ab)V^{cd}_{kl}t^{cd}_{ij}t^{ab}_{kl}
`dgram_cdkl_cdjl`(v_pphh, t2)	Calculates -0.5 * V^{cd}_{kl}t^{cd}_{jl}
`dgram_cdkl_ci_ak_dj_bl`(v_pphh, t1)	Calculates 0.25 * P(ij)P(ab)V^{cd}_{kl}t^{c}_{i}t^{a}_{k}t^{d}_{j}t^{b}_{l}
`dgram_cdkl_ci_bl_adkj`(v_pphh, t1, t2)	Calculates P(ij)P(ab)V^{cd}_{kl}t^{c}_{i}t^{b}_{l}t^{ad}_{kj}
`dgram_cdkl_ci_dj_abkl`(v_pphh, t1, t2)	Calculates 0.25 * P(ij)V^{cd}_{kl}t^{c}_{i}t^{d}_{j}t^{ab}_{kl}
`dgram_cdkl_ck_dali`(v_pphh, t1, t2)	Calculates V^{cd}_{kl}t^{c}_{k}t^{da}_{li}
`dgram_cdkl_dk_al`(v_pphh, t1)	Calculates 0.5 * V^{cd}_{kl}t^{d}_{k}t^{a}_{l}
`dgram_cdlk_cdli`(v_pphh, t2)	Calculates -0.5 * V^{cd}_{lk}t^{cd}_{li}
`dgram_cdlk_cl_di`(v_pphh, t1)	Calculates -0.5 * V^{cd}_{lk}t^{c}_{l}t^{d}_{i}
`dgram_cdlk_cl_dj`(v_pphh, t1)	Calculates -V^{cd}_{kl}t^{c}_{l}t^{d}_{j}
`dgram_cdlk_dk_bl`(v_pphh, t1)	Calculates -V^{cd}_{kl}t^{d}_{k}t^{b}_{l}
`dgram_cikl_al_bcjk`(v_phhh, t1, t2)	Calculates - P(ij)P(ab)V^{ci}_{kl}t^{a}_{l}t^{bc}_{jk}
`dgram_cikl_cakl`(v_phhh, t2)	Calculates -0.5 * V^{ci}_{kl}t^{ca}_{kl}
`dgram_cikl_ck_ablj`(v_phhh, t1, t2)	Calculates - P(ij)V^{ci}_{kl}t^{c}_{k}t^{ab}_{lj}
`dgram_cjkl_ci_abkl`(v_phhh, t1, t2)	Calculates 0.5 * P(ij)V^{cj}_{kl}t^{c}_{i}t^{ab}_{kl}
`dgram_cjkl_ci_ak_bl`(v_phhh, t1)	Calculates 0.5 * P(ij)P(ab)V^{cj}_{kl}t^{c}_{i}t^{a}_{k}t^{b}_{l}
`dgram_ck_acik`(f_ph, t2)	Calculates f^{c}_{k}t^{ac}_{ik}
`dgram_ck_ak`(f_ph, t1)	Calculates -0.5 * f^{c}_{k}t^{a}_{k}
`dgram_ck_bk`(f_ph, t1)	Calculates - * f^{c}_{k}t^{b}_{k}
`dgram_ck_ci`(f_ph, t1)	Calculates -0.5 * f^{c}_{k}t^{c}_{i}
`dgram_ck_cj`(f_ph, t1)	Calculates - * f^{c}_{k}t^{c}_{j}
`dgram_da_dbij`(v_ppph_res, t2)	Calculates - P(ab)X^d_at^{db}_{ij}
`dgram_dckl_dakl`(v_pphh, t2)	Calculates -0.5 * V^{dc}_{kl}t^{da}_{kl}
`dgram_klij_abkl`(v_hhhh, t2)	Calculates 0.5 * V^{kl}_{ij}t^{ab}_{kl}
`dgram_klij_ak_bl`(v_hhhh, t1)	Calculates - 0.5 * P(ab)V^{kl}_{ij}t^{a}_{k}t^{b}_{l}
`pAB`(val)	Permutator for ab
`pIJ`(val)	Permutator for ij
`v_ppph_dgrams`(v_ppph, t1, t2)	Calculates all 6 of the diagrams that use v_pppp using the fact that it is sparse
`v_pppp_dgrams`(v_pppp, t1, t2)	Calculates both of the diagrams that use v_pppp using the fact that it is sparse

CCM.ccDgrams.v_ppph_dgrams(v_ppph, t1, t2)¶

Calculates all 6 of the diagrams that use v_pppp using the fact that it is sparse

Parameters:

v_ppph (list[(int, int, int, int, float)]) – nonzeroes of the two body interaction matrix V^{ab}_{ck}
t1 (numpy array) – T1 matrix t_i^a
t2 (numpy array) – T2 matrix t_{ij}^{ab}

Returns:

The result of the 6 diagrams that contribute to t1 and t2

Return type:

list[numpy array]

CCM.ccDgrams.dgram_akci_ck(v_phph, t1)¶

Calculates -V^{ak}_{ci}t^{c}_{k}

Parameters:

v_phph (numpy array) – two body interaction matrix V^{ai}_{bj}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_ck_acik(f_ph, t2)¶

Calculates f^{c}_{k}t^{ac}_{ik}

Parameters:

f_ph (numpy array) – Fock matrix f^{a}_{i}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cikl_cakl(v_phhh, t2)¶

Calculates -0.5 * V^{ci}_{kl}t^{ca}_{kl}

Parameters:

v_phhh (numpy array) – two body interaction matrix V^{ai}_{jk}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_ck_dali(v_pphh, t1, t2)¶

Calculates V^{cd}_{kl}t^{c}_{k}t^{da}_{li}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{ij}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_ck_ci(f_ph, t1)¶

Calculates -0.5 * f^{c}_{k}t^{c}_{i}

Parameters:

f_ph (numpy array) – Fock matrix f^{a}_{i}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_ck_ak(f_ph, t1)¶

Calculates -0.5 * f^{c}_{k}t^{a}_{k}

Parameters:

f_ph (numpy array) – Fock matrix f^{a}_{i}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_bijk_bj(v_phhh, t1)¶

Calculates -V^{bi}_{jk}t^{b}_{j}

Parameters:

v_phhh (numpy array) – two body interaction matrix V^{bi}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdlk_cdli(v_pphh, t2)¶

Calculates -0.5 * V^{cd}_{lk}t^{cd}_{li}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{ij}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_dckl_dakl(v_pphh, t2)¶

Calculates -0.5 * V^{dc}_{kl}t^{da}_{kl}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{ij}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdlk_cl_di(v_pphh, t1)¶

Calculates -0.5 * V^{cd}_{lk}t^{c}_{l}t^{d}_{i}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{ij}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_dk_al(v_pphh, t1)¶

Calculates 0.5 * V^{cd}_{kl}t^{d}_{k}t^{a}_{l}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{ij}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.pAB(val)¶

Permutator for ab

Parameters:: val (numpy array) – array to be permutated over
Returns:: val^{ab}_{ij} - val^{ba}_{ij}
Return type:: numpy array

CCM.ccDgrams.pIJ(val)¶

Permutator for ij

Parameters:: val (numpy array) – array to be permutated over
Returns:: val^{ab}_{ij} - val^{ab}_{ji}
Return type:: numpy array

CCM.ccDgrams.v_pppp_dgrams(v_pppp, t1, t2)¶

Calculates both of the diagrams that use v_pppp using the fact that it is sparse

Parameters:

v_pppp (list[(int, int, int, int, float)]) – nonzeroes of the two body interaction matrix V^{ab}_{cd}
t1 (numpy array) – T1 matrix t_i^a
t2 (numpy array) – T2 matrix t_{ij}^{ab}

Returns:

The result of the two diagrams that contribute to t2

Return type:

numpy array, numpy array

CCM.ccDgrams.dgram_klij_abkl(v_hhhh, t2)¶

Calculates 0.5 * V^{kl}_{ij}t^{ab}_{kl}

Parameters:

v_hhhh (numpy array) – two body interaction matrix V^{kl}_{ij}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_bkcj_acik(v_phph, t2)¶

Calculates -P(ij)P(ab)V^{bk}_{cj}t^{cb}_{ik}

Parameters:

v_phph (numpy array) – two body interaction matrix V^{bk}_{cj}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_bkij_ak(v_phhh, t1)¶

Calculates P(ab)V^{bk}_{ij}t^{a}_{k}

Parameters:

v_phhh (numpy array) – two body interaction matrix V^{bk}_{ij}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_acik_dblj(v_pphh, t2)¶

Calculates 0.5 * P(ij)P(ab)V^{cd}_{kl}t^{ac}_{ik}t^{db}_{lj}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{ij}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_cdij_abkl(v_pphh, t2)¶

Calculates 0.25 * P(ab)V^{cd}_{kl}t^{cd}_{ij}t^{ab}_{kl}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{ij}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_klij_ak_bl(v_hhhh, t1)¶

Calculates - 0.5 * P(ab)V^{kl}_{ij}t^{a}_{k}t^{b}_{l}

Parameters:

v_hhhh (numpy array) – two body interaction matrix V^{kl}_{ij}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_bkci_ak_cj(v_phph, t1)¶

Calculates - P(ij)P(ab)V^{bk}_{ci}t^{a}_{k}t^{c}_{j}

Parameters:

v_phph (numpy array) – two body interaction matrix V^{ai}_{bj}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cikl_ck_ablj(v_phhh, t1, t2)¶

Calculates - P(ij)V^{ci}_{kl}t^{c}_{k}t^{ab}_{lj}

Parameters:

v_phhh (numpy array) – two body interaction matrix V^{ai}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_da_dbij(v_ppph_res, t2)¶

Calculates - P(ab)X^d_at^{db}_{ij}

Parameters:

v_ppph_res (numpy array) – intermediate result 3 from v_ppph_dgrams()
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_acik_bcjk(v_ppph_res, t2)¶

Calculates - P(ij)P(ab)X^{ac}_{ij}t^{bc}_{jk}

Parameters:

v_ppph_res (numpy array) – intermediate result 4 from v_ppph_dgrams()
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cikl_al_bcjk(v_phhh, t1, t2)¶

Calculates - P(ij)P(ab)V^{ci}_{kl}t^{a}_{l}t^{bc}_{jk}

Parameters:

v_phhh (numpy array) – two body interaction matrix V^{ai}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cjkl_ci_abkl(v_phhh, t1, t2)¶

Calculates 0.5 * P(ij)V^{cj}_{kl}t^{c}_{i}t^{ab}_{kl}

Parameters:

v_phhh (numpy array) – two body interaction matrix V^{ai}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_bijk_ak1(v_ppph_res, t1)¶

Calculates 0.5 * P(ab)X^{bi}_{jk}t^{a}_{k}

Parameters:

v_ppph_res (numpy array) – intermediate result 5 from v_ppph_dgrams()
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_bijk_ak2(v_ppph_res, t1)¶

Calculates 0.5 * P(ij)P(ab)X^{bi}_{jk}t^{a}_{k}

Parameters:

v_ppph_res (numpy array) – intermediate result 6 from v_ppph_dgrams()
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cjkl_ci_ak_bl(v_phhh, t1)¶

Calculates 0.5 * P(ij)P(ab)V^{cj}_{kl}t^{c}_{i}t^{a}_{k}t^{b}_{l}

Parameters:

v_phhh (numpy array) – two body interaction matrix V^{ai}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_ci_dj_abkl(v_pphh, t1, t2)¶

Calculates 0.25 * P(ij)V^{cd}_{kl}t^{c}_{i}t^{d}_{j}t^{ab}_{kl}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_ak_bl_cdij(v_pphh, t1, t2)¶

Calculates 0.25 * P(ab)V^{cd}_{kl}t^{a}_{k}t^{b}_{l}t^{cd}_{ij}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_ci_bl_adkj(v_pphh, t1, t2)¶

Calculates P(ij)P(ab)V^{cd}_{kl}t^{c}_{i}t^{b}_{l}t^{ad}_{kj}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_ci_ak_dj_bl(v_pphh, t1)¶

Calculates 0.25 * P(ij)P(ab)V^{cd}_{kl}t^{c}_{i}t^{a}_{k}t^{d}_{j}t^{b}_{l}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_bdkl(v_pphh, t2)¶

Calculates -0.5 * V^{cd}_{kl}t^{bd}_{kl}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdkl_cdjl(v_pphh, t2)¶

Calculates -0.5 * V^{cd}_{kl}t^{cd}_{jl}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t2 (numpy array) – T^{ab}_{ij} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_ck_bk(f_ph, t1)¶

Calculates - * f^{c}_{k}t^{b}_{k}

Parameters:

f_ph (numpy array) – Fock matrix f^{a}_{i}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_ck_cj(f_ph, t1)¶

Calculates - * f^{c}_{k}t^{c}_{j}

Parameters:

f_ph (numpy array) – Fock matrix f^{a}_{i}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdlk_cl_dj(v_pphh, t1)¶

Calculates -V^{cd}_{kl}t^{c}_{l}t^{d}_{j}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams.dgram_cdlk_dk_bl(v_pphh, t1)¶

Calculates -V^{cd}_{kl}t^{d}_{k}t^{b}_{l}

Parameters:

v_pphh (numpy array) – two body interaction matrix V^{ab}_{jk}
t1 (numpy array) – T^{a}_{i} from the coupled cluster equations

Returns:

result of the contraction

Return type:

numpy array

CCM.ccDgrams¶

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