The T-shape in benzene dimer (and similar compounds in protein structures)
is a consequence of quadrupole - quadrupole long-range electrostatics of
benzene dimer. Benzene rings have zero molecular dipole
and large quadrupole. This electrostatics does not like the undisplaced
stack. It prefers either the T-shape or parallel-displaced, under the vdW
- electrostatics compensation. Classic (original) papers are e.g.,
POTENTIAL-ENERGY SURFACE OF THE BENZENE DIMER - AB INITIO
THEORETICAL-STUDY HOBZA, P; SELZLE, HL; SCHLAG, EW, JACS, 116, 3500-3506,
1994
STRUCTURE AND PROPERTIES OF BENZENE-CONTAINING MOLECULAR CLUSTERS -
NONEMPIRICAL AB-INITIO CALCULATIONS AND EXPERIMENTS By: HOBZA, P; SELZLE,
HL; SCHLAG, EW CHEM. REV., 94, 1767-1785, 1994
Nucleobases have dipolar ESP, so they prefer various variants of flat
stacking, depending on whether these are homodimers (face to back is not
the same as face to face stacking) or heterodimers
Nature of nucleic acid-base stacking: Nonempirical ab initio and empirical
potential characterization of 10 stacked base dimers. Comparison of
stacked and H-bonded base pairs Sponer, J; Leszczynski, J; Hobza, P J PHYS
CHEM, 100, 5590-5596, 1996
Structure, energetics, and dynamics of the nucleic acid base pairs:
Nonempirical ab initio calculations
By: Hobza, P; Sponer, J CHEM REV, 99, 3247-3276, 1999
It all is explainable/describable by ESP-based electrostatics + van der
Waals MM interactions in the first approximation to a reasonable extent.
That is why in proteins we have T-shapes and so-called cation-pi
arrangements while these are absent in nucleic acids (cations interact
with base edges, mainly lone pair regions and not with nucleobase rings,
the ion position above the nucleobase ring is intrinsically unstable). I
think in the Biopolymers 2013 minireview I have discussed many of these
differences.
Nature and Magnitude of Aromatic Base Stacking in DNA and RNA: Quantum
Chemistry, Molecular Mechanics, and Experiment, BIOPOLYMERS, 99, 978-988,
2013
Obviously, there are many finer effects modulating the simple description
which lead to certain deviations for the simplest MM. For example, the r^-12
term of the LJ potential deviates from the supposed to be exponential
exchange-repulsion (and also charge penetration, this short-range part of
QM electrostatics is included effectively in the LJ term of MM.). These
sometimes lead, e.g., to wrong apparent "atom radii", excessive steric
clashes, etc. When trying to capture details you would obviously need to go to
finer details of the QM theory of intermolecular forces, concerning atom
radii we have for example this recent paper on lone-pair pi stacking.
Atoms are not constant-radius spheres.
Short but Weak: The Z-DNA Lone-Pair center dot center dot center dot pi
Conundrum Challenges Standard Carbon Van der Waals Radii Kruse et al.
ANGEW CHEM-INT. EDITION , 59, 16553-16560, 2020
Some systematic QM vs MM component analysis is e.g. here,
Large-scale compensation of errors in pairwise-additive empirical force
fields: comparison of AMBER intermolecular terms with rigorous DFT-SAPT
calculations Zgarbova et al. PHYS. CHEM. CHEM. PHYS.12, 10476-10493,
2010:
Of course, there are other minor-to-moderate deviationsn, including also
some non-additivity in stacking, etc., etc.
In summary, there are some nonsystematic deviations between MM and
rigorous QM PESs, but not fundamental ones. Thus, in the first approximation to a
reasonable extent, these "aromatic stacking" systems can be quite well
described by the standard MM AMBER approximation with no need to any
special "pi-pi" terms. The QM-MM(LJ+ESP charges) diferential PESs show no
visible "pi-pi" effects.
Errors in the intrinsic description of H-bonds are inevitably larger than
for stacking, as polarization and already orbital effects (there is no
clear border between these two, it is definition-dependent) start to play
a bigger role.
Best wishes, Jiri
On Tue, 11 May 2021, Matias Machado wrote:
> Date: Tue, 11 May 2021 12:40:20 -0300 (UYT)
> From: Matias Machado <mmachado.pasteur.edu.uy>
> Reply-To: AMBER Mailing List <amber.ambermd.org>
> To: AMBER Mailing List <amber.ambermd.org>
> Subject: Re: [AMBER] stacking interactions represented by force field
> equation?
>
> This is a very interesting topic to discuss!
>
> I would argue that the normal DNA staking may be just one possible case found in proteins...
>
> Besides the "Sandwich" orientation, there are "Parallel-displaced" and "T-shaped" staking interactions among others...
> https://doi.org/10.1021/ct800471b
>
> I think those arrangements may be more difficult to represent with a standard FF... any comment is welcome...
>
> On the other hand, the "zombie" pi-pi interactions seems to be statistically relevant in the PDB...
> https://doi.org/10.7554/eLife.31486.001
>
> All the best,
>
> Matías
>
> ----- Mensaje original -----
> De: "Jiri Sponer" <sponer.ncbr.muni.cz>
> Para: "AMBER Mailing List" <amber.ambermd.org>
> Enviados: Lunes, 10 de Mayo 2021 13:02:38
> Asunto: Re: [AMBER] stacking interactions represented by force field equation?
>
> I agree. In the first approximation, intrinsic stacking interactions
> between two aromatic rings are suprisingly well described by the van der
> Waals potential + point charge electrostatics.
> So, there is no need for an explicit term for stacking interactions in the
> ffs, it would just complicate.
>
> Atom-centered point
> charges provide enough flexibility for the electrostatic potential.
> That means, the charges should reproduce reasonably well the ESP
> of the monomers. As aromatic rings are rigid, the fixed charges work
> well for all conformations. As AMBER force fields use ESP charges, they
> are good for stacking,
> which was the fundemental decision by P.A. Kollman long time ago.
>
> The so-called "pi-pi effects" (something making aromatic stacking
> special and different from "common" stacking and thus requiring
> a specific force-field term) are in fact marginal.
> These "zombie" effects are still popular in part of the literature but in
> reality do not exist.
> We have never detected them in rigorous QM calculations to be important,
> despite that we have been trying to find them. Actually,
> when we run the first electron correlation calcs on stacking around
> ~1995, we were looking forward to demonstrate how force fields
> fail on stacking. Instead, we have got reasonable semiquantitative
> agreement between QM and MM, which was a surprise for us.
>
> One of the more recent reviews is
> https://onlinelibrary.wiley.com/doi/abs/10.1002/bip.22322
> older is
> https://pubs.acs.org/doi/10.1021/cr9800255
>
> What may be a concern in simulations is the balance with hydration, i.e.,
> solvation energies, but this is not directly related to the description of
> the intrinsic (direct) stacking interactions.
>
> Best wishes, Jiri
>
> n Mon, 10 May 2021, Carlos Simmerling wrote:
>
>> Date: Mon, 10 May 2021 10:52:55 -0400
>> From: Carlos Simmerling <carlos.simmerling.gmail.com>
>> Reply-To: AMBER Mailing List <amber.ambermd.org>
>> To: AMBER Mailing List <amber.ambermd.org>
>> Subject: Re: [AMBER] stacking interactions represented by force field
>> equation?
>>
>> this might be useful:
>>
>> https://pubs.acs.org/doi/10.1021/acs.jctc.8b00643
>> Investigations of Stacked DNA Base-Pair Steps: Highly Accurate Stacking
>> Interaction Energies, Energy Decomposition, and Many-Body Stacking Effects
>> Holger Kruse*, Pavel Banáš, and Jiřı́ Šponer
>> J. Chem. Theory Comput. 2019, 15, 1, 95–115
>>
>> On Mon, May 10, 2021 at 10:31 AM Martin Rosellen <
>> martinrosellen.googlemail.com> wrote:
>>
>>> Dear Amber community,
>>>
>>> if I am right there is no explicit term for stacking interactions in
>>> protein force fields such as ff14SB. I was wondering if force fields
>>> somehow incorporate stacking interactions in the calculation of
>>> non-covalent bonds?
>>>
>>> best
>>> Martin
>>> _______________________________________________
>>> AMBER mailing list
>>> AMBER.ambermd.org
>>> http://lists.ambermd.org/mailman/listinfo/amber
>>>
>> _______________________________________________
>> AMBER mailing list
>> AMBER.ambermd.org
>> http://lists.ambermd.org/mailman/listinfo/amber
>>
>>
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Received on Tue May 11 2021 - 10:30:02 PDT
