# -*- coding: utf-8 -*-
"""The energy terms of each EDA scheme, and how they map onto common terms.
Each scheme keeps its own ("native") terms, with the names the code uses. A few
*common* terms let results from different schemes be put side by side, but only
where the physics really is the same:
* SAPT's induction contains both polarization and charge transfer, so it maps to
ALMO's polarization **plus** charge transfer ("induction" here). Only schemes
that split induction apart (ALMO-EDA) fill "polarization" and "charge
transfer"; SAPT never does. Treating SAPT induction as polarization is the
lumping that hides charge-transfer problems, e.g. for Li⁺.
* "frozen" is ALMO's frozen term (electrostatics + Pauli + dispersion). SAPT has
no such term and leaves it empty.
* SAPT's electrostatics is the Coulomb interaction of the isolated monomers'
densities, which is ALMO's *classical* electrostatic term (Q-Chem's CLS ELEC).
ALMO's own "electrostatic" and "pauli" come from an orthogonal decomposition of
the frozen wavefunction (Horn, Mao and Head-Gordon 2016; Q-Chem's ELEC and
PAULI) and are not comparable with SAPT: for PF6⁻–EC each differs from SAPT by
36 kJ/mol. So the common "electrostatics" is the classical term and the common
"Pauli" is frozen − classical electrostatic − dispersion (Q-Chem's MOD PAULI),
within 2 kJ/mol of SAPT exchange. frozen = electrostatics + Pauli + dispersion
holds in both sets, and the common ≥3-body electrostatics is exactly 0.
All energies are in kJ/mol.
"""
from dataclasses import dataclass, field
COMMON_TERMS = (
"electrostatics",
"Pauli",
"dispersion",
"frozen",
"polarization",
"charge transfer",
"induction",
"total",
)
[docs]
@dataclass(frozen=True)
class Scheme:
"""An EDA scheme: its native terms, identities, and common-term map.
Attributes
----------
name : str
e.g. "ALMO-EDA2".
terms : (str, ...)
The native terms, in the code's names and print order.
common : {str: (str, ...)}
Each common term as the sum of native terms; a name starting with "-"
is subtracted.
identities : ((str, (str, ...)), ...)
Native term = sum of other native terms, which hold exactly.
pairwise_additive : (str, ...)
Native terms that are exactly pairwise additive (no ≥3-body part).
max_fragments : int or None
The most fragments one calculation can have; None for no limit.
notes : (str, ...)
What the terms mean, for the output and the extxyz labels.
"""
name: str
terms: tuple
common: dict = field(default_factory=dict)
identities: tuple = ()
pairwise_additive: tuple = ()
max_fragments: int = None
notes: tuple = ()
[docs]
def to_common(self, energies):
"""The common terms of one result.
Parameters
----------
energies : {str: float}
Native terms, kJ/mol.
Returns
-------
{str: float}
The common terms this scheme defines.
"""
out = {}
for name, parts in self.common.items():
signed = [(-1, p[1:]) if p.startswith("-") else (1, p) for p in parts]
if all(p in energies for _, p in signed):
out[name] = sum(sign * energies[p] for sign, p in signed)
return out
[docs]
def check(self, energies, tolerance=1.0e-6):
"""The identities that do not hold, as (term, value, sum of parts).
Parameters
----------
energies : {str: float}
Native terms, kJ/mol.
tolerance : float
kJ/mol.
Returns
-------
[(str, float, float)]
Empty when everything is consistent.
"""
bad = []
for name, parts in self.identities:
if name in energies and all(p in energies for p in parts):
total = sum(energies[p] for p in parts)
if abs(energies[name] - total) > tolerance:
bad.append((name, energies[name], total))
return bad
ALMO_EDA2 = Scheme(
name="ALMO-EDA2",
terms=(
"electrostatic",
"classical electrostatic",
"pauli",
"dispersion",
"frozen",
"polarization",
"charge transfer",
"total",
),
common={
"electrostatics": ("classical electrostatic",),
"Pauli": ("frozen", "-classical electrostatic", "-dispersion"),
"dispersion": ("dispersion",),
"frozen": ("frozen",),
"polarization": ("polarization",),
"charge transfer": ("charge transfer",),
"induction": ("polarization", "charge transfer"),
"total": ("total",),
},
identities=(
("frozen", ("electrostatic", "pauli", "dispersion")),
("total", ("frozen", "polarization", "charge transfer")),
),
pairwise_additive=("classical electrostatic",),
notes=(
"Second-generation ALMO-EDA (Horn and Head-Gordon): frozen = electrostatic"
" + Pauli + dispersion; polarization from fragment electric-response"
" functions (FERF); charge transfer is the rest of the SCF relaxation.",
"The fragments are at their geometry in the cluster: there is no"
" preparation (distortion) term.",
"Charge transfer carries the basis-set superposition error; polarization"
" does not.",
"Dispersion is defined against a dispersion-free partner functional (HF)."
" With a -D3/-D4 functional it also contains the empirical dispersion,"
" including the D4 three-body (ATM) term, which then appears in the"
" ≥3-body dispersion.",
"Two electrostatic terms: 'classical electrostatic' (Q-Chem CLS ELEC) is the"
" Coulomb interaction of the isolated fragments' densities, comparable to"
" SAPT electrostatics and pairwise additive; 'electrostatic' and 'pauli'"
" (Q-Chem ELEC, PAULI) come from the orthogonal decomposition of the frozen"
" wavefunction (Horn, Mao and Head-Gordon 2016) and are NOT comparable to"
" SAPT.",
"The common terms use the SAPT-comparable pair: electrostatics = classical"
" electrostatic; Pauli = frozen - classical electrostatic - dispersion"
" (Q-Chem MOD PAULI). frozen = electrostatics + Pauli + dispersion holds"
" in both sets; the common >=3-body electrostatics is exactly 0.",
"'induction' = polarization + charge transfer, comparable to SAPT"
" induction.",
),
)
SCHEMES = {s.name: s for s in (ALMO_EDA2,)}
