Non-covalent ALMO-EDA charge transfer term

Questions
#1

I ran non-bonded ALMO-EDA on a He2 system with 2 He fragments. To my surprise, the charge transfer term (CT) was quite large despite the fragments being the same. The polarization term was much smaller by comparison. I would expect the opposite trend due to equal electronegativity between the fragments. This trend is agnostic to use of FERFs or not. Is there something wrong either my input file or understanding of these energy terms?
Input file for a single point:

$molecule
   0 1
--  An alpha spin H atom
   0 1
   He1
--  Another alpha spin H atom. Bonded ALMO-EDA does not need the multiplicities to sum to that of the molecule
   0 1
He2 He1 1.5000
$end

$rem
JOBTYPE eda
EDA2 2
METHOD wb97x-v
BASIS cc-pvtz-full
SCF_CONVERGENCE 6
THRESH 14
DISP_FREE_X HF
DISP_FREE_C None
EDA_BSSE false

FRZ_RELAX true
FRZ_RELAX_METHOD 2
FRZ_ORTHO_DECOMP -1

CHILD_MP true
CHILD_MP_ORDERS 232
$end

Output file:

================================
        Results of EDA2         
================================
Basic EDA Quantities
--------------------
Fragment Energies (Ha):
1   -2.9027828841
2   -2.9027828841
--------------------
  E_prp (kJ/mol) = 0.0000
  E_frz (kJ/mol) = 55.5769
  E_pol (kJ/mol) = -0.0003
  E_vct (kJ/mol) = -7.0288
  E_int (kJ/mol) = 48.5479
--------------------


Initial Wavefunction Relaxation
--------------------
  Energy lowering from initial wavefunction relaxation (kJ/mol) = -0.0000
--------------------


Decomposition of frozen interaction energy
--------------------
  --------------------
  Classical Frozen Decomposition:
  --------------------
     E_cls_elec  (CLS ELEC)  (kJ/mol) = -14.2725
     E_cls_pauli (CLS PAULI) (kJ/mol) = 69.8494
  --------------------
--------------------

Simplified EDA Summary (kJ/mol)
--------------------
 PREPARATION      0.0000
 FROZEN           55.5769 (ELEC + PAULI + DISP)
 POLARIZATION    -0.0003
 CHARGE TRANSFER -7.0288
 TOTAL           48.5479     (PRP + FRZ + POL + CT)
--------------------
#2

There is nothing wrong here. The ALMO-based CT describes energy lowering due to delocalization of the fragment wavefunctions. For the cases where the two fragments are identical, there will be both A->B and B->A charge transfer, which both contribute to energy lowering despite that there will be no net charge flow in this case.

See https://doi.org/10.1021/acs.jctc.7b01256 for a detailed discussion of this matter.

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#3

The other point to notice is that the He atoms are quite close together, and therefore the whole analysis is a bit artificial, not representing an actual vdW complex.

Overall the interaction is strongly repulsive. There is a slightly attractive CT term, but it is strongly overshadowed by Pauli repulsion.

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#4

Thanks, these are helpful explanations regarding the CT term.

Iā€™m still somewhat surprised that the polarization is nearly 0, despite the small distance of the He atoms. My expectation was that the atomic environment experienced by each He atom would cause some distortion that would be captured by the multipoles.

#5

To properly describe the interaction between two He atoms, you will need diffuse functions, otherwise the electronic structure is too compact.

With eda2 = 1, basis = aug-cc-pvtz, the polarization energy is about -0.35 kJ/mol.

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