[Work in progress] LNOCC

[hongzhouye]

This PR adds the molecular and periodic LNO-CCSD/CCSD(T). The LNO method was originally introduced by Kállay and co-workers:

• J. Chem. Phys. 139, 094105 (2013) (link)
• J. Chem. Phys. 135, 104111 (2011) (link)

And this PR is particularly based on a recent extension:

• J. Chem. Theory Comput. 2024, 20, 20, 8948–8959 (link)

for spin-restricted molecular & periodic LNO-CC and an unpublished work for spin-unrestricted references (@fishjojo, @MoleOrbitalHybridAnalyst).

The PR is still work in progress with the following to-do's:

• add examples and more unit tests (me and @tberkel)
• make the C library pyscf-forge/pyscf/lib/lno compatible with regular pyscf (@fishjojo)
• remove redundant functions in lno/lnoccsd.py for precomputation (perhaps need to slightly refactor pyscf's CCSD code) (@fishjojo )
• add support for spin-unrestricted references (@fishjojo, @MoleOrbitalHybridAnalyst)

[tberkel]

I'm working on adding examples, but frozen seems broken with unrestricted LNO. @fishjojo or @MoleOrbitalHybridAnalyst have you tested frozen orbitals? Skimming the code suggests that you did, but I get a correlation energy of 0 when I freeze orbitals. Example is below. Works fine when frozen = 0.

from pyscf import gto, scf, mp, lo
from pyscf.data import elements
from pyscf import lno

mol = gto.Mole()
mol.atom = '''
    O   -1.485163346097   -0.114724564047    0.000000000000
    H   -1.868415346097    0.762298435953    0.000000000000
    H   -0.533833346097    0.040507435953    0.000000000000
    O    1.416468653903    0.111264435953    0.000000000000
    H    1.746241653903   -0.373945564047   -0.758561000000
    H    1.746241653903   -0.373945564047    0.758561000000
'''
mol.basis = 'ccpvdz'
mol.verbose = 7
mol.spin = 0
mol.build()

mf = scf.UHF(mol).density_fit()
mf.kernel()

frozen = elements.chemcore(mol)
# frozen = 0

mymp = mp.MP2(mf, frozen=frozen)
mymp.kernel(with_t2=False)

thresh = [1e-4] * 2

nocca, noccb = mymp.get_nocc()
moidxa, moidxb = mymp.get_frozen_mask()
mo_coeff = mf.mo_coeff[0][:, moidxa], mf.mo_coeff[1][:, moidxb]
orbocca = mo_coeff[0][:, :nocca]
lo_coeff_a = lo.PipekMezey(mf.mol, orbocca).kernel()
orboccb = mo_coeff[1][:, :noccb]
lo_coeff_b = lo.PipekMezey(mf.mol, orboccb).kernel()
lo_coeff = [lo_coeff_a, lo_coeff_b]

frag_lolist_a = [[[i], []] for i in range(nocca)]
frag_lolist_b = [[[], [i]] for i in range(noccb)]
frag_lolist = frag_lolist_a + frag_lolist_b

mlcc = lno.ULNOCCSD(mf, lo_coeff, frag_lolist, frozen=frozen,
                    lno_thresh=thresh)
mlcc.kernel()
# E(LNOMP2) = -152.062490646908  E_corr = 0
# E(LNOCCSD) = -152.062490646908  E_corr = 0

[tberkel]

I fixed the ULNO frozen orbitals problem (help from @hczhai) and cleaned up the unittest for ULNO.

[tberkel]

Another question for @fishjojo and/or @MoleOrbitalHybridAnalyst - I notice that the results for ULNO and (R)LNO are different for the same thresholds, even when the reference doesn't break spin symmetry. Did you observe the same? I guess the issue is that the orbital-specific DMs treat up and down differently (e.g., commonly a different number of up and down orbitals are included in the active space). I wonder if there's a way to spin average, so that the results agree in the limit of no spin symmetry breaking.

[fishjojo]

@tberkel, thanks for the fix for frozen orbitals. The ULNO results match those of RLNO from the old implementation. I notice there are some changes to the RLNO code for determining the LNOs, and I’m not sure the default is still the original ‘ie’ flavor for building the LNOs. Currently, ULNO only works for ‘ie’, as there is difficulty matching the RLNO results using other flavors. Maybe Hongzhou could provide some insights of this. Timothy Berkelbach ***@***.***>于2025年5月6日 周二上午6:18写道：

…

*tberkel* left a comment (pyscf/pyscf-forge#115) <#115 (comment)> Another question for @fishjojo <https://github.com/fishjojo> and/or @MoleOrbitalHybridAnalyst <https://github.com/MoleOrbitalHybridAnalyst> - I notice that the results for ULNO and (R)LNO are different for the same thresholds, even when the reference doesn't break spin symmetry. Did you observe the same? I guess the issue is that the orbital-specific DMs treat up and down differently (e.g., commonly a different number of up and down orbitals are included in the active space). I wonder if there's a way to spin average, so that the results agree in the limit of no spin symmetry breaking. — Reply to this email directly, view it on GitHub <#115 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACCZ6FRLAEPZ6D7G2VSY74L25CZD7AVCNFSM6AAAAABX3R2U7SVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDQNJUGU2TKMBSGU> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[hongzhouye]

@fishjojo @tberkel Could it be related to this line? I had updated the local MP2 DM definition at some point to better align with the canonical MP2 DM definition, which is twice the value of what the earlier version produced. I’m okay with defaulting to either convention.