# CEPA(0) Singles

I’m unclear on how the CEPA(0) implementation considers singles. Is it analogous to Szabo’s MBPT equations:

-B^\dagger D B = E_{corr}
B = \braket{\Psi_0|H|\Psi_{ij}^{ab}}
D = \braket{\Psi_{kl}^{cd}|H|\Psi_{ij}^{ab}}

but with D including single/single and single/double terms and with B including single terms? The Wennmohs & Neese paper mentions an ambiguity in the treatment of singles, but I believe that ambiguity should go away if all the shifts are 0 anyway, right?

The implementation of CEPA(0) with singles in the FNOCC module should be equivalent to linearized CCSD, which I think is what you’re describing with zero shift for the singles. A long time ago I verified that implementation against the CEPA code in Molpro for CEPA-0,1, and 3, so I believe the singles are handled in a consistent way with that code.

Does that mean that LCCD should be equivalent to using the CEPA_NO_SINGLES flag? (I ask because I’m getting different numbers for these, and I’m not sure if it’s an input issue on my end, a misunderstanding of the theory, or a bug with psi4.) Computed energies:

LCCD:
-460.2612756198385

LCCSD:
-460.26183389044934

CEPA(0)D:
-460.26183389045053

CEPA(0)SD:
-460.26183389045025

Code input:

import numpy as np

molecule = {
0 1
H 0 0 0
Cl 0 0 1
}

psi4.core.be_quiet()
set basis cc-pvdz
set reference rhf

print(‘LCCD’)
print(psi4.optimize(‘lccd’))

print(‘LCCSD’)
print(psi4.optimize(‘lccsd’))

print(‘CEPA(0)D’)
print(psi4.optimize(‘cepa(0)’, CEPA_NO_SINGLES = True))

print(‘CEPA(0)SD’)
print(psi4.optimize(‘cepa(0)’, CEPA_NO_SINGLES = False))

Hmm I thought that was the case. Hold on, looking into this

it looks to me like the cepa_no_singles flag isn’t working.

energy(‘lccsd’)
energy(‘cepa(0)’)
set cepa_no_singles true
energy(‘cepa(0)’)

all give the same energy for me, too.

From psi4/psi4/driver/procrouting/proc.py it looks like CEPA_NO_SINGLES is set to false for the method ‘cepa(0)’. I am not sure why - perhaps for consistency with the DCFT and DFOCC modules, which I think also can run cepa0. Maybe @loriab knows why the procedure is defined that way and if it is possible to override that procedure from within the input file?

Thank you for the assistance in either case!

Here’s the history. I’m still reading it myself. But it’s almost certainly for consistency with other modules.

If I just use LCCD will I get the same answer that CEPA(0) with no singles would have given?

Ok, I think all is working as expected. Consistent with the table, cepa(0) includes singles and is equivalent to lccsd. lccd is equivalent to cepa(0) without singles. By declaring method ocepa(0), you’re entering into a contract that overrides keywords, so no-singles doesn’t work (@hrgrimsl, you were setting as a kwarg, not a keyword anyways).

So the below is what I get, and I think it’s sane. Yes, use lccd.

molecule {
Ne
}

e = energy('lccsd/cc-pvdz')
print(e)
e = energy('lccd/cc-pvdz')
print(e)
e = energy('cepa(0)/cc-pvdz')
print(e)

-128.68046437265727
-128.6802140889028
-128.68046437265727


This is fine, and I understand what is going on now ,but I had originally intended for CEPA_NO_SINGLES to control whether or not singles were used in any CEPA-n generated through FNOCC. it seems weird that that option will work for CEPA-1/3 but not for CEPA-0.

Although, looking back at the previous conversation, it seems I was fine with this scheme 3.5 years ago. I’ll try not to forget if it comes up again!

Thank you both for the help!