adc-connect/adcc | Build 22406590854 | adcc/adc_pp/state_diffdm_2p.py | Coveralls

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#!/usr/bin/env python3

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## vi: tabstop=4 shiftwidth=4 softtabstop=4 expandtab

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## ---------------------------------------------------------------------

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##

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## Copyright (C) 2026 by the adcc authors

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##

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## This file is part of adcc.

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##

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## adcc is free software: you can redistribute it and/or modify

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## it under the terms of the GNU General Public License as published

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## by the Free Software Foundation, either version 3 of the License, or

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## (at your option) any later version.

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##

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## adcc is distributed in the hope that it will be useful,

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## but WITHOUT ANY WARRANTY; without even the implied warranty of

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## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

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## GNU General Public License for more details.

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##

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## You should have received a copy of the GNU General Public License

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## along with adcc. If not, see <http://www.gnu.org/licenses/>.

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##

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## ---------------------------------------------------------------------

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    # ADC(1) diffdm

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        # N^4: O^4 / N^4: O^4

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        - 4.0 * einsum("il,jk->ijkl", p1_oo, d_oo)

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    ).antisymmetrise(0, 1).antisymmetrise(2, 3)

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        # N^4: O^2V^2 / N^4: O^2V^2

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        - 1.0 * einsum("ja,ib->iajb", u1, u1)

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        # N^4: O^2V^2 / N^4: O^2V^2

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        + 1.0 * einsum("ab,ij->iajb", p1_vv, d_oo)

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    # TODO move to intermediates!

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    # ADC(1) diffdm

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    # ADC(2) ISR intermediate (TODO Move to intermediates)

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    # new ones

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        # N^4: O^2V^2 / N^4: O^2V^2

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        + 4.0 * (

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            einsum("ib,ja->ijab", ru1, u1)

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        ).antisymmetrise(0, 1).antisymmetrise(2, 3)

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        # N^5: O^3V^2 / N^4: O^2V^2

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        + 2.0 * (

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            einsum("ijka,kb->ijab", ru1_ooov, u1)

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        ).antisymmetrise(2, 3)

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        # N^5: O^3V^2 / N^4: O^2V^2

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        - 2.0 * (

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            einsum("jk,ikab->ijab", p1_oo, t2)

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        ).antisymmetrise(0, 1)

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        # N^6: O^4V^2 / N^4: O^2V^2

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        + 2.0 * einsum("ijab,klab->ijkl", u2, u2)

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        # N^6: O^5V^1 / N^4: O^2V^2

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        - 1.0 * einsum("klmc,ijmc->ijkl", einsum("mb,klbc->klmc", u1, t2),

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                       einsum("ma,ijac->ijmc", u1, t2))

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+ (

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            # N^5: O^3V^2 / N^4: O^2V^2

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            - 8.0 * einsum("ik,jl->ijkl", einsum("imab,kmab->ik", u2, u2), d_oo)

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            # N^4: O^4 / N^4: O^4

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            + 4.0 * einsum("il,jk->ijkl", einsum("ia,la->il", u1, u1), p0.oo)

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            # N^6: O^5V^1 / N^4: O^2V^2

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            + 4.0 * einsum("jlmc,ikmc->ijkl", einsum("lb,jmbc->jlmc", u1, t2),

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                           einsum("ia,kmac->ikmc", u1, t2))

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            # N^4: O^2V^2 / N^4: O^2V^2

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            + 4.0 * einsum("il,jk->ijkl",

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                           einsum("lc,ic->il", einsum("nb,lnbc->lc", u1, t2),

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                                  einsum("ma,imac->ic", u1, t2)), d_oo)

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 4.0 * einsum("ik,jl->ijkl", einsum("kmnc,imnc->ik",

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                                                 einsum("nb,kmbc->kmnc", u1, t2),

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                                                 einsum("na,imac->imnc", u1, t2)),

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                           d_oo)

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 2.0 * einsum("ik,jl->ijkl",

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                           einsum("inbc,knbc->ik",

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                                  einsum("mn,imbc->inbc",

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                                         einsum("ia,la->il", u1, u1), t2), t2),

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                           d_oo)

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        ).antisymmetrise(0, 1).antisymmetrise(2, 3)

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+ (

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 4.0 * einsum("iklb,jb->ijkl",

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                           einsum("ic,klbc->iklb", einsum("ma,imac->ic", u1, t2),

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                                  t2), u1)

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            # N^6: O^4V^2 / N^4: O^2V^2

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            + 2.0 * einsum("jklm,im->ijkl",

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                           einsum("jmbc,klbc->jklm", t2, t2),

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                           einsum("ia,la->il", u1, u1))

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        ).antisymmetrise(0, 1).symmetrise([(0, 2), (1, 3)])

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+ (

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            # N^4: O^4 / N^4: O^4

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            + 4.0 * einsum("il,jk->ijkl", einsum("im,lm->il",

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                                                 einsum("ia,la->il", u1, u1),

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                                                 p0.oo), d_oo)

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            # N^4: O^2V^2 / N^4: O^2V^2

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            + 4.0 * einsum("ik,jl->ijkl",

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                           einsum("kb,ib->ik",

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                                  einsum("mc,kmbc->kb",

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                                         einsum("na,mnac->mc", u1, t2), t2), u1),

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                           d_oo)

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        ).antisymmetrise(0, 1).antisymmetrise(2, 3).symmetrise([(0, 2), (1, 3)])

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        # N^5: O^3V^2 / N^4: O^2V^2

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        - 2.0 * einsum("kb,ijab->ijka", u1, u2)

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        # N^6: O^4V^2 / N^4: O^2V^2

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        + 1.0 * einsum("ijkl,la->ijka", einsum("klbc,ijbc->ijkl", u2, t2), u1)

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        # N^5: O^3V^2 / N^4: O^2V^2

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        + 2.0 * einsum("kb,ijab->ijka", einsum("lc,klbc->kb", u1, u2), t2)

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+ (

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            # N^4: O^2V^2 / N^4: O^2V^2

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            - 4.0 * einsum("ja,ik->ijka", einsum("lb,jlab->ja", u1, u2), d_oo)

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 2.0 * einsum("jk,ia->ijka", einsum("klbc,jlbc->jk", u2, t2), u1)

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            # N^6: O^4V^2 / N^4: O^2V^2

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            - 4.0 * einsum("jklb,ilab->ijka", einsum("jc,klbc->jklb", u1, u2), t2)

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 2.0 * einsum("ja,ik->ijka",

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                           einsum("jlmb,lmab->ja",

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                                  einsum("jc,lmbc->jlmb", u1, u2), t2), d_oo)

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            # N^4: O^2V^2 / N^4: O^2V^2

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            - 4.0 * einsum("ia,jk->ijka",

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                           einsum("lb,ilab->ia",

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                                  einsum("mc,lmbc->lb", u1, u2), t2), d_oo)

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 2.0 * einsum("ia,jk->ijka",

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                           einsum("il,la->ia",

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                                  einsum("lmbc,imbc->il", u2, t2), u1), d_oo)

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            # N^4: O^3V^1 / N^4: O^3V^1

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            + 2.0 * einsum("jk,ia->ijka", einsum("kb,jb->jk", u1, p0.ov), u1)

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            # N^4: O^3V^1 / N^4: O^3V^1

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            + 2.0 * einsum("jk,ia->ijka", einsum("jb,kb->jk", u1, u1), p0.ov)

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            # N^4: O^3V^1 / N^4: O^3V^1

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            + 2.0 * einsum("ia,jk->ijka",

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                           einsum("il,la->ia",

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                                  einsum("lb,ib->il", u1, p0.ov), u1), d_oo)

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            # N^4: O^3V^1 / N^4: O^3V^1

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            + 2.0 * einsum("ia,jk->ijka",

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                           einsum("il,la->ia", einsum("ia,la->il", u1, u1),

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                                  p0.ov), d_oo)

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        ).antisymmetrise(0, 1)

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        # N^4: O^2V^2 / N^4: O^2V^2

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        + 4.0 * einsum("ib,ja->ijab",

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                       einsum("kc,ikbc->ib", u1, td2),

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                       u1).antisymmetrise(0, 1).antisymmetrise(2, 3)

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        # N^5: O^3V^2 / N^4: O^2V^2

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        + 2.0 * einsum("ijka,kb->ijab",

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                       einsum("kc,ijac->ijka", u1, td2), u1).antisymmetrise(2, 3)

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        # N^5: O^3V^2 / N^4: O^2V^2

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        + 2.0 * einsum("jk,ikab->ijab", einsum("jc,kc->jk", u1, u1), td2)

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        # N^6: O^3V^3 / N^4: O^2V^2

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        - 4.0 * einsum("jkac,ikbc->iajb", u2, u2)

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        # N^5: O^2V^3 / N^4: O^2V^2

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        + 2.0 * einsum("ab,ij->iajb", einsum("klac,klbc->ab", u2, u2), d_oo)

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        # N^6: O^4V^2 / N^4: O^2V^2

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        + 1.0 * einsum("iklb,jkla->iajb", einsum("ld,ikbd->iklb", u1, t2),

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                       einsum("lc,jkac->jkla", u1, t2))

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        # N^4: O^2V^2 / N^4: O^2V^2

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        + 1.0 * einsum("ab,ij->iajb", einsum("ka,kb->ab", u1, u1), p0.oo)

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        # N^4: O^2V^2 / N^4: O^2V^2

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        - 1.0 * einsum("ij,ab->iajb", einsum("ic,jc->ij", u1, u1), p0.vv)

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        # N^6: O^3V^3 / N^4: O^2V^2

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        + 1.0 * einsum("jlac,ilbc->iajb",

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                       einsum("kl,jkac->jlac", einsum("kd,ld->kl", u1, u1), t2), t2)

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        # N^6: O^4V^2 / N^4: O^2V^2

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        + 0.5 * einsum("ijla,lb->iajb",

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                       einsum("ijkl,ka->ijla",

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                              einsum("ikcd,jlcd->ijkl", t2, t2), u1), u1)

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        # N^6: O^4V^2 / N^4: O^2V^2

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        + 0.5 * einsum("jklb,ikla->iajb",

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                       einsum("jd,klbd->jklb", u1, t2),

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                       einsum("ic,klac->ikla", u1, t2))

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        # N^4: O^2V^2 / N^4: O^2V^2

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        - 1.0 * einsum("ib,ja->iajb",

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                       einsum("kd,ikbd->ib", u1, t2), einsum("lc,jlac->ja", u1, t2))

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        # N^5: O^2V^3 / N^4: O^2V^2

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        + 1.0 * einsum("ab,ij->iajb",

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                       einsum("lmad,lmbd->ab",

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                              einsum("km,klad->lmad",

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                                     einsum("kc,mc->km", u1, u1), t2), t2), d_oo)

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        # N^4: O^2V^2 / N^4: O^2V^2

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        - 1.0 * einsum("ab,ij->iajb",

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                       einsum("lb,la->ab",

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                              einsum("kd,klbd->lb", u1, t2),

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                              einsum("mc,lmac->la", u1, t2)), d_oo)

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        # N^5: O^3V^2 / N^4: O^2V^2

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        - 0.5 * einsum("ab,ij->iajb",

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                       einsum("klmb,klma->ab",

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                              einsum("md,klbd->klmb", u1, t2),

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                              einsum("mc,klac->klma", u1, t2)), d_oo)

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+ (

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            # N^4: O^2V^2 / N^4: O^2V^2

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            + 1.0 * einsum("ib,ja->iajb", einsum("ic,bc->ib", u1, p0.vv), u1)

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            # N^4: O^2V^2 / N^4: O^2V^2

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            - 1.0 * einsum("ib,ja->iajb", einsum("kb,ik->ib", u1, p0.oo), u1)

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 2.0 * einsum("ijlb,la->iajb",

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                           einsum("jc,ilbc->ijlb",

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                                  einsum("kd,jkcd->jc", u1, t2), t2), u1)

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            # N^5: O^3V^2 / N^4: O^2V^2

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            + 2.0 * einsum("kb,ijka->iajb",

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                           einsum("ld,klbd->kb", u1, t2),

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                           einsum("ic,jkac->ijka", u1, t2))

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            # N^6: O^4V^2 / N^4: O^2V^2

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            - 2.0 * einsum("ijkb,ka->iajb",

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                           einsum("jklc,ilbc->ijkb",

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                                  einsum("kd,jlcd->jklc", u1, t2), t2), u1)

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            # N^6: O^4V^2 / N^4: O^2V^2

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            - 2.0 * einsum("ijlb,la->iajb",

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                           einsum("ijkc,klbc->ijlb",

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                                  einsum("id,jkcd->ijkc", u1, t2), t2), u1)

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            # N^6: O^3V^3 / N^4: O^2V^2

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            - 2.0 * einsum("ikbc,jkac->iajb",

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                           einsum("il,klbc->ikbc",

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                                  einsum("id,ld->il", u1, u1), t2), t2)

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            # N^4: O^2V^2 / N^4: O^2V^2

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            - 1.0 * einsum("ib,ja->iajb",

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                           einsum("kc,ikbc->ib",

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                                  einsum("ld,klcd->kc", u1, t2), t2), u1)

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            # N^4: O^2V^2 / N^4: O^2V^2

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            - 1.0 * einsum("ab,ij->iajb",

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                           einsum("kb,ka->ab",

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                                  einsum("kc,bc->kb", u1, p0.vv), u1), d_oo)

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            # N^4: O^2V^2 / N^4: O^2V^2

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            - 1.0 * einsum("ab,ij->iajb",

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                           einsum("mb,ma->ab",

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                                  einsum("ld,lmbd->mb",

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                                         einsum("kc,klcd->ld", u1, t2),

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                                         t2), u1), d_oo)

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        ).symmetrise([(0, 2), (1, 3)])

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        # N^5: O^2V^3 / N^4: O^1V^3

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        - 2.0 * einsum("ja,ijbc->iabc", u1, u2)

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        # N^6: O^3V^3 / N^4: O^1V^3

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        + 1.0 * einsum("ijka,jkbc->iabc", einsum("id,jkad->ijka", u1, u2), t2)

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        # N^5: O^2V^3 / N^4: O^1V^3

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        + 2.0 * einsum("ja,ijbc->iabc", einsum("kd,jkad->ja", u1, u2), t2)

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+ (

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            # N^5: O^2V^3 / N^4: O^1V^3

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            + 2.0 * einsum("ac,ib->iabc", einsum("jkad,jkcd->ac", u2, t2), u1)

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            # N^6: O^3V^3 / N^4: O^1V^3

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            - 4.0 * einsum("ikab,kc->iabc", einsum("jkad,ijbd->ikab", u2, t2), u1)

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            # N^4: O^1V^3 / N^4: O^1V^3

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            + 2.0 * einsum("ac,ib->iabc", einsum("ja,jc->ac", u1, p0.ov), u1)

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            # N^4: O^1V^3 / N^4: O^1V^3

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            + 2.0 * einsum("ac,ib->iabc", einsum("ja,jc->ac", u1, u1), p0.ov)

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        ).antisymmetrise(2, 3)

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        # N^6: O^2V^4 / N^4: V^4

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        + 2 * einsum("ijab,ijcd->abcd", u2, u2)

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        # N^6: O^2V^4 / N^4: V^4

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        - 1 * einsum("jkab,jkcd->abcd",

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                     einsum("ij,ikab->jkab", einsum("ie,je->ij", u1, u1), t2), t2)

319

+ (

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            # N^4: V^4 / N^4: V^4

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            + 4.0 * einsum("ac,bd->abcd", einsum("ia,ic->ac", u1, u1), p0.vv)

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            # N^6: O^3V^3 / N^4: V^4

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            + 4.0 * einsum("jabc,jd->abcd",

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                           einsum("ijbc,ia->jabc",

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                                  einsum("jkbe,ikce->ijbc", t2, t2), u1), u1)

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        ).antisymmetrise(0, 1).antisymmetrise(2, 3)

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+ (

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            # N^5: O^1V^4 / N^4: V^4

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            + 4.0 * einsum("ka,kbcd->abcd",

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                           einsum("ie,ikae->ka", u1, t2),

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                           einsum("jb,jkcd->kbcd", u1, t2))

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            # N^6: O^3V^3 / N^4: V^4

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            + 2.0 * einsum("ibcd,ia->abcd",

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                           einsum("ijkb,jkcd->ibcd",

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                                  einsum("ie,jkbe->ijkb", u1, t2), t2), u1)

336

        ).antisymmetrise(0, 1).symmetrise([(0, 2), (1, 3)])

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# dict controlling the dispatch of the state_diffdm function

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    "adc0": diffdm_adc0_2p,

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    "adc1": diffdm_adc1_2p,

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    "adc2": diffdm_adc2_2p,

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    "adc2x": diffdm_adc2_2p,      # same as ADC(2)

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"""

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    Compute the two-particle difference density matrix of an excited state

353

    in the MO basis.

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    Parameters

356

    ----------

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    method : str, AdcMethod

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        The method to use for the computation (e.g. "adc2")

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    ground_state : LazyMp

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        The ground state upon which the excitation was based

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    amplitude : AmplitudeVector

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        The amplitude vector

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    intermediates : adcc.Intermediates

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        Intermediates from the ADC calculation to reuse

365

"""

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                                  f"for {method.name}.")

378

    else:

adc-connect / adcc / 22406590854

Source File
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1	#!/usr/bin/env python3
2	## vi: tabstop=4 shiftwidth=4 softtabstop=4 expandtab
3	## ---------------------------------------------------------------------
4	##
5	## Copyright (C) 2026 by the adcc authors
6	##
7	## This file is part of adcc.
8	##
9	## adcc is free software: you can redistribute it and/or modify
10	## it under the terms of the GNU General Public License as published
11	## by the Free Software Foundation, either version 3 of the License, or
12	## (at your option) any later version.
13	##
14	## adcc is distributed in the hope that it will be useful,
15	## but WITHOUT ANY WARRANTY; without even the implied warranty of
16	## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17	## GNU General Public License for more details.
18	##
19	## You should have received a copy of the GNU General Public License
20	## along with adcc. If not, see <http://www.gnu.org/licenses/>.
21	##
22	## ---------------------------------------------------------------------
23	from adcc import block as b	2✔
24	from adcc.LazyMp import LazyMp	2✔
25	from adcc.AdcMethod import AdcMethod	2✔
26	from adcc.functions import einsum, zeros_like	2✔
27	from adcc.Intermediates import Intermediates	2✔
28	from adcc.AmplitudeVector import AmplitudeVector	2✔
29	from adcc.TwoParticleDensity import TwoParticleDensity	2✔
30	from adcc.NParticleOperator import OperatorSymmetry	2✔
31
32	from .util import check_doubles_amplitudes, check_singles_amplitudes	2✔
33
34
35	def diffdm_adc0_2p(mp, amplitude, intermediates):	2✔
36	check_singles_amplitudes([b.o, b.v], amplitude)	2✔
37	u1 = amplitude.ph	2✔
38
39	hf = mp.reference_state	2✔
40	d_oo = zeros_like(hf.foo)	2✔
41	d_oo.set_mask("ii", 1)	2✔
42
43	dm = TwoParticleDensity(mp, symmetry=OperatorSymmetry.HERMITIAN)	2✔
44
45	# ADC(1) diffdm
46	p1_oo = -einsum("ia,la->il", u1, u1).evaluate()	2✔
47	p1_vv = einsum("ka,kb->ab", u1, u1).evaluate()	2✔
48
49	dm.oooo = (	2✔
50	# N^4: O^4 / N^4: O^4
51	- 4.0 * einsum("il,jk->ijkl", p1_oo, d_oo)
52	).antisymmetrise(0, 1).antisymmetrise(2, 3)
53	dm.ovov = (	2✔
54	# N^4: O^2V^2 / N^4: O^2V^2
55	- 1.0 * einsum("ja,ib->iajb", u1, u1)
56	# N^4: O^2V^2 / N^4: O^2V^2
57	+ 1.0 * einsum("ab,ij->iajb", p1_vv, d_oo)
58	)
59	return dm	2✔
60
61
62	def diffdm_adc1_2p(mp, amplitude, intermediates):	2✔
63	dm = diffdm_adc0_2p(mp, amplitude, intermediates) # Get ADC(0) result	2✔
64	u1 = amplitude.ph	2✔
65
66	hf = mp.reference_state	2✔
67	d_oo = zeros_like(hf.foo)	2✔
68	d_oo.set_mask("ii", 1)	2✔
69
70	t2 = mp.t2(b.oovv)	2✔
71	# TODO move to intermediates!
72	# ADC(1) diffdm
73	p1_oo = -einsum("ia,la->il", u1, u1).evaluate()	2✔
74
75	# ADC(2) ISR intermediate (TODO Move to intermediates)
76	ru1 = einsum("ijab,jb->ia", t2, u1).evaluate()	2✔
77	# new ones
78	ru1_ooov = einsum("kc,ijac->ijka", u1, t2).evaluate()	2✔
79
80	dm.oovv += (	2✔
81	# N^4: O^2V^2 / N^4: O^2V^2
82	+ 4.0 * (
83	einsum("ib,ja->ijab", ru1, u1)
84	).antisymmetrise(0, 1).antisymmetrise(2, 3)
85	# N^5: O^3V^2 / N^4: O^2V^2
86	+ 2.0 * (
87	einsum("ijka,kb->ijab", ru1_ooov, u1)
88	).antisymmetrise(2, 3)
89	# N^5: O^3V^2 / N^4: O^2V^2
90	- 2.0 * (
91	einsum("jk,ikab->ijab", p1_oo, t2)
92	).antisymmetrise(0, 1)
93	)
94	return dm	2✔
95
96
97	def diffdm_adc2_2p(mp, amplitude, intermediates):	2✔
98	dm = diffdm_adc1_2p(mp, amplitude, intermediates) # Get ADC(1) result	2✔
99	check_doubles_amplitudes([b.o, b.o, b.v, b.v], amplitude)	2✔
100	u1, u2 = amplitude.ph, amplitude.pphh	2✔
101	hf = mp.reference_state	2✔
102	d_oo = zeros_like(hf.foo)	2✔
103	d_oo.set_mask("ii", 1)	2✔
104
105	t2 = mp.t2(b.oovv)	2✔
106	td2 = mp.td2(b.oovv)	2✔
107	p0 = mp.mp2_diffdm	2✔
108
109	dm.oooo += (	2✔
110	# N^6: O^4V^2 / N^4: O^2V^2
111	+ 2.0 * einsum("ijab,klab->ijkl", u2, u2)
112	# N^6: O^5V^1 / N^4: O^2V^2
113	- 1.0 * einsum("klmc,ijmc->ijkl", einsum("mb,klbc->klmc", u1, t2),
114	einsum("ma,ijac->ijmc", u1, t2))
115	+ (
116	# N^5: O^3V^2 / N^4: O^2V^2
117	- 8.0 * einsum("ik,jl->ijkl", einsum("imab,kmab->ik", u2, u2), d_oo)
118	# N^4: O^4 / N^4: O^4
119	+ 4.0 * einsum("il,jk->ijkl", einsum("ia,la->il", u1, u1), p0.oo)
120	# N^6: O^5V^1 / N^4: O^2V^2
121	+ 4.0 * einsum("jlmc,ikmc->ijkl", einsum("lb,jmbc->jlmc", u1, t2),
122	einsum("ia,kmac->ikmc", u1, t2))
123	# N^4: O^2V^2 / N^4: O^2V^2
124	+ 4.0 * einsum("il,jk->ijkl",
125	einsum("lc,ic->il", einsum("nb,lnbc->lc", u1, t2),
126	einsum("ma,imac->ic", u1, t2)), d_oo)
127	# N^5: O^3V^2 / N^4: O^2V^2
128	+ 4.0 * einsum("ik,jl->ijkl", einsum("kmnc,imnc->ik",
129	einsum("nb,kmbc->kmnc", u1, t2),
130	einsum("na,imac->imnc", u1, t2)),
131	d_oo)
132	# N^5: O^3V^2 / N^4: O^2V^2
133	+ 2.0 * einsum("ik,jl->ijkl",
134	einsum("inbc,knbc->ik",
135	einsum("mn,imbc->inbc",
136	einsum("ia,la->il", u1, u1), t2), t2),
137	d_oo)
138	).antisymmetrise(0, 1).antisymmetrise(2, 3)
139	+ (
140	# N^5: O^3V^2 / N^4: O^2V^2
141	+ 4.0 * einsum("iklb,jb->ijkl",
142	einsum("ic,klbc->iklb", einsum("ma,imac->ic", u1, t2),
143	t2), u1)
144	# N^6: O^4V^2 / N^4: O^2V^2
145	+ 2.0 * einsum("jklm,im->ijkl",
146	einsum("jmbc,klbc->jklm", t2, t2),
147	einsum("ia,la->il", u1, u1))
148	).antisymmetrise(0, 1).symmetrise([(0, 2), (1, 3)])
149	+ (
150	# N^4: O^4 / N^4: O^4
151	+ 4.0 * einsum("il,jk->ijkl", einsum("im,lm->il",
152	einsum("ia,la->il", u1, u1),
153	p0.oo), d_oo)
154	# N^4: O^2V^2 / N^4: O^2V^2
155	+ 4.0 * einsum("ik,jl->ijkl",
156	einsum("kb,ib->ik",
157	einsum("mc,kmbc->kb",
158	einsum("na,mnac->mc", u1, t2), t2), u1),
159	d_oo)
160	).antisymmetrise(0, 1).antisymmetrise(2, 3).symmetrise([(0, 2), (1, 3)])
161	)
162	dm.ooov += (	2✔
163	# N^5: O^3V^2 / N^4: O^2V^2
164	- 2.0 * einsum("kb,ijab->ijka", u1, u2)
165	# N^6: O^4V^2 / N^4: O^2V^2
166	+ 1.0 * einsum("ijkl,la->ijka", einsum("klbc,ijbc->ijkl", u2, t2), u1)
167	# N^5: O^3V^2 / N^4: O^2V^2
168	+ 2.0 * einsum("kb,ijab->ijka", einsum("lc,klbc->kb", u1, u2), t2)
169	+ (
170	# N^4: O^2V^2 / N^4: O^2V^2
171	- 4.0 * einsum("ja,ik->ijka", einsum("lb,jlab->ja", u1, u2), d_oo)
172	# N^5: O^3V^2 / N^4: O^2V^2
173	+ 2.0 * einsum("jk,ia->ijka", einsum("klbc,jlbc->jk", u2, t2), u1)
174	# N^6: O^4V^2 / N^4: O^2V^2
175	- 4.0 * einsum("jklb,ilab->ijka", einsum("jc,klbc->jklb", u1, u2), t2)
176	# N^5: O^3V^2 / N^4: O^2V^2
177	+ 2.0 * einsum("ja,ik->ijka",
178	einsum("jlmb,lmab->ja",
179	einsum("jc,lmbc->jlmb", u1, u2), t2), d_oo)
180	# N^4: O^2V^2 / N^4: O^2V^2
181	- 4.0 * einsum("ia,jk->ijka",
182	einsum("lb,ilab->ia",
183	einsum("mc,lmbc->lb", u1, u2), t2), d_oo)
184	# N^5: O^3V^2 / N^4: O^2V^2
185	+ 2.0 * einsum("ia,jk->ijka",
186	einsum("il,la->ia",
187	einsum("lmbc,imbc->il", u2, t2), u1), d_oo)
188	# N^4: O^3V^1 / N^4: O^3V^1
189	+ 2.0 * einsum("jk,ia->ijka", einsum("kb,jb->jk", u1, p0.ov), u1)
190	# N^4: O^3V^1 / N^4: O^3V^1
191	+ 2.0 * einsum("jk,ia->ijka", einsum("jb,kb->jk", u1, u1), p0.ov)
192	# N^4: O^3V^1 / N^4: O^3V^1
193	+ 2.0 * einsum("ia,jk->ijka",
194	einsum("il,la->ia",
195	einsum("lb,ib->il", u1, p0.ov), u1), d_oo)
196	# N^4: O^3V^1 / N^4: O^3V^1
197	+ 2.0 * einsum("ia,jk->ijka",
198	einsum("il,la->ia", einsum("ia,la->il", u1, u1),
199	p0.ov), d_oo)
200	).antisymmetrise(0, 1)
201	)
202	dm.oovv += (	2✔
203	# N^4: O^2V^2 / N^4: O^2V^2
204	+ 4.0 * einsum("ib,ja->ijab",
205	einsum("kc,ikbc->ib", u1, td2),
206	u1).antisymmetrise(0, 1).antisymmetrise(2, 3)
207	# N^5: O^3V^2 / N^4: O^2V^2
208	+ 2.0 * einsum("ijka,kb->ijab",
209	einsum("kc,ijac->ijka", u1, td2), u1).antisymmetrise(2, 3)
210	# N^5: O^3V^2 / N^4: O^2V^2
211	+ 2.0 * einsum("jk,ikab->ijab", einsum("jc,kc->jk", u1, u1), td2)
212	)
213	dm.ovov += (	2✔
214	# N^6: O^3V^3 / N^4: O^2V^2
215	- 4.0 * einsum("jkac,ikbc->iajb", u2, u2)
216	# N^5: O^2V^3 / N^4: O^2V^2
217	+ 2.0 * einsum("ab,ij->iajb", einsum("klac,klbc->ab", u2, u2), d_oo)
218	# N^6: O^4V^2 / N^4: O^2V^2
219	+ 1.0 * einsum("iklb,jkla->iajb", einsum("ld,ikbd->iklb", u1, t2),
220	einsum("lc,jkac->jkla", u1, t2))
221	# N^4: O^2V^2 / N^4: O^2V^2
222	+ 1.0 * einsum("ab,ij->iajb", einsum("ka,kb->ab", u1, u1), p0.oo)
223	# N^4: O^2V^2 / N^4: O^2V^2
224	- 1.0 * einsum("ij,ab->iajb", einsum("ic,jc->ij", u1, u1), p0.vv)
225	# N^6: O^3V^3 / N^4: O^2V^2
226	+ 1.0 * einsum("jlac,ilbc->iajb",
227	einsum("kl,jkac->jlac", einsum("kd,ld->kl", u1, u1), t2), t2)
228	# N^6: O^4V^2 / N^4: O^2V^2
229	+ 0.5 * einsum("ijla,lb->iajb",
230	einsum("ijkl,ka->ijla",
231	einsum("ikcd,jlcd->ijkl", t2, t2), u1), u1)
232	# N^6: O^4V^2 / N^4: O^2V^2
233	+ 0.5 * einsum("jklb,ikla->iajb",
234	einsum("jd,klbd->jklb", u1, t2),
235	einsum("ic,klac->ikla", u1, t2))
236	# N^4: O^2V^2 / N^4: O^2V^2
237	- 1.0 * einsum("ib,ja->iajb",
238	einsum("kd,ikbd->ib", u1, t2), einsum("lc,jlac->ja", u1, t2))
239	# N^5: O^2V^3 / N^4: O^2V^2
240	+ 1.0 * einsum("ab,ij->iajb",
241	einsum("lmad,lmbd->ab",
242	einsum("km,klad->lmad",
243	einsum("kc,mc->km", u1, u1), t2), t2), d_oo)
244	# N^4: O^2V^2 / N^4: O^2V^2
245	- 1.0 * einsum("ab,ij->iajb",
246	einsum("lb,la->ab",
247	einsum("kd,klbd->lb", u1, t2),
248	einsum("mc,lmac->la", u1, t2)), d_oo)
249	# N^5: O^3V^2 / N^4: O^2V^2
250	- 0.5 * einsum("ab,ij->iajb",
251	einsum("klmb,klma->ab",
252	einsum("md,klbd->klmb", u1, t2),
253	einsum("mc,klac->klma", u1, t2)), d_oo)
254	+ (
255	# N^4: O^2V^2 / N^4: O^2V^2
256	+ 1.0 * einsum("ib,ja->iajb", einsum("ic,bc->ib", u1, p0.vv), u1)
257	# N^4: O^2V^2 / N^4: O^2V^2
258	- 1.0 * einsum("ib,ja->iajb", einsum("kb,ik->ib", u1, p0.oo), u1)
259	# N^5: O^3V^2 / N^4: O^2V^2
260	+ 2.0 * einsum("ijlb,la->iajb",
261	einsum("jc,ilbc->ijlb",
262	einsum("kd,jkcd->jc", u1, t2), t2), u1)
263	# N^5: O^3V^2 / N^4: O^2V^2
264	+ 2.0 * einsum("kb,ijka->iajb",
265	einsum("ld,klbd->kb", u1, t2),
266	einsum("ic,jkac->ijka", u1, t2))
267	# N^6: O^4V^2 / N^4: O^2V^2
268	- 2.0 * einsum("ijkb,ka->iajb",
269	einsum("jklc,ilbc->ijkb",
270	einsum("kd,jlcd->jklc", u1, t2), t2), u1)
271	# N^6: O^4V^2 / N^4: O^2V^2
272	- 2.0 * einsum("ijlb,la->iajb",
273	einsum("ijkc,klbc->ijlb",
274	einsum("id,jkcd->ijkc", u1, t2), t2), u1)
275	# N^6: O^3V^3 / N^4: O^2V^2
276	- 2.0 * einsum("ikbc,jkac->iajb",
277	einsum("il,klbc->ikbc",
278	einsum("id,ld->il", u1, u1), t2), t2)
279	# N^4: O^2V^2 / N^4: O^2V^2
280	- 1.0 * einsum("ib,ja->iajb",
281	einsum("kc,ikbc->ib",
282	einsum("ld,klcd->kc", u1, t2), t2), u1)
283	# N^4: O^2V^2 / N^4: O^2V^2
284	- 1.0 * einsum("ab,ij->iajb",
285	einsum("kb,ka->ab",
286	einsum("kc,bc->kb", u1, p0.vv), u1), d_oo)
287	# N^4: O^2V^2 / N^4: O^2V^2
288	- 1.0 * einsum("ab,ij->iajb",
289	einsum("mb,ma->ab",
290	einsum("ld,lmbd->mb",
291	einsum("kc,klcd->ld", u1, t2),
292	t2), u1), d_oo)
293	).symmetrise([(0, 2), (1, 3)])
294	)
295	dm.ovvv += (	2✔
296	# N^5: O^2V^3 / N^4: O^1V^3
297	- 2.0 * einsum("ja,ijbc->iabc", u1, u2)
298	# N^6: O^3V^3 / N^4: O^1V^3
299	+ 1.0 * einsum("ijka,jkbc->iabc", einsum("id,jkad->ijka", u1, u2), t2)
300	# N^5: O^2V^3 / N^4: O^1V^3
301	+ 2.0 * einsum("ja,ijbc->iabc", einsum("kd,jkad->ja", u1, u2), t2)
302	+ (
303	# N^5: O^2V^3 / N^4: O^1V^3
304	+ 2.0 * einsum("ac,ib->iabc", einsum("jkad,jkcd->ac", u2, t2), u1)
305	# N^6: O^3V^3 / N^4: O^1V^3
306	- 4.0 * einsum("ikab,kc->iabc", einsum("jkad,ijbd->ikab", u2, t2), u1)
307	# N^4: O^1V^3 / N^4: O^1V^3
308	+ 2.0 * einsum("ac,ib->iabc", einsum("ja,jc->ac", u1, p0.ov), u1)
309	# N^4: O^1V^3 / N^4: O^1V^3
310	+ 2.0 * einsum("ac,ib->iabc", einsum("ja,jc->ac", u1, u1), p0.ov)
311	).antisymmetrise(2, 3)
312	)
313	dm.vvvv += (	2✔
314	# N^6: O^2V^4 / N^4: V^4
315	+ 2 * einsum("ijab,ijcd->abcd", u2, u2)
316	# N^6: O^2V^4 / N^4: V^4
317	- 1 * einsum("jkab,jkcd->abcd",
318	einsum("ij,ikab->jkab", einsum("ie,je->ij", u1, u1), t2), t2)
319	+ (
320	# N^4: V^4 / N^4: V^4
321	+ 4.0 * einsum("ac,bd->abcd", einsum("ia,ic->ac", u1, u1), p0.vv)
322	# N^6: O^3V^3 / N^4: V^4
323	+ 4.0 * einsum("jabc,jd->abcd",
324	einsum("ijbc,ia->jabc",
325	einsum("jkbe,ikce->ijbc", t2, t2), u1), u1)
326	).antisymmetrise(0, 1).antisymmetrise(2, 3)
327	+ (
328	# N^5: O^1V^4 / N^4: V^4
329	+ 4.0 * einsum("ka,kbcd->abcd",
330	einsum("ie,ikae->ka", u1, t2),
331	einsum("jb,jkcd->kbcd", u1, t2))
332	# N^6: O^3V^3 / N^4: V^4
333	+ 2.0 * einsum("ibcd,ia->abcd",
334	einsum("ijkb,jkcd->ibcd",
335	einsum("ie,jkbe->ijkb", u1, t2), t2), u1)
336	).antisymmetrise(0, 1).symmetrise([(0, 2), (1, 3)])
337	)
338	return dm	2✔
339
340
341	# dict controlling the dispatch of the state_diffdm function
342	DISPATCH = {	2✔
343	"adc0": diffdm_adc0_2p,
344	"adc1": diffdm_adc1_2p,
345	"adc2": diffdm_adc2_2p,
346	"adc2x": diffdm_adc2_2p, # same as ADC(2)
347	}
348
349
350	def state_diffdm_2p(method, ground_state, amplitude, intermediates=None):	2✔
351	"""
352	Compute the two-particle difference density matrix of an excited state
353	in the MO basis.
354
355	Parameters
356	----------
357	method : str, AdcMethod
358	The method to use for the computation (e.g. "adc2")
359	ground_state : LazyMp
360	The ground state upon which the excitation was based
361	amplitude : AmplitudeVector
362	The amplitude vector
363	intermediates : adcc.Intermediates
364	Intermediates from the ADC calculation to reuse
365	"""
366	if not isinstance(method, AdcMethod):	2!
NEW 367	method = AdcMethod(method)	×
368	if not isinstance(ground_state, LazyMp):	2!
NEW 369	raise TypeError("ground_state should be a LazyMp object.")	×
370	if not isinstance(amplitude, AmplitudeVector):	2!
NEW 371	raise TypeError("amplitude should be an AmplitudeVector object.")	×
372	if intermediates is None:	2✔
373	intermediates = Intermediates(ground_state)	2✔
374
375	if method.name not in DISPATCH:	2!
NEW 376	raise NotImplementedError("state_diffdm_2p is not implemented "	×
377	f"for {method.name}.")
378	else:
379	ret = DISPATCH[method.name](ground_state, amplitude, intermediates)	2✔
380	return ret.evaluate()	2✔

adc-connect / adcc / 22406590854

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