This paper is published as part of a PCCP
themed issue series on biophysics and
biophysical chemistry:
Biomolecular Structures: From Isolated
Molecules to Living Cells
Guest Editors: Seong Keun Kim,
Jean-Pierre Schermann and
Taekjip Ha
Editorial
Biomolecular Structures: From Isolated Molecules to the
Cell Crowded Medium
Seong Keun Kim, Jean-Pierre Schermann, Taekjip Ha, Phys.
Chem. Chem. Phys., 2010
DOI: 10.1039/c004156b
Perspectives
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Stepwise hydration and evaporation of adenosine
monophosphate nucleotide anions: a multiscale
theoretical study
F. Calvo and J. Douady, Phys. Chem. Chem. Phys., 2010
DOI: 10.1039/b923972c
Communications
Reference MP2/CBS and CCSD(T) quantum-chemical
calculations on stacked adenine dimers. Comparison with
DFT-D, MP2.5, SCS(MI)-MP2, M06-2X, CBS(SCS-D) and
force field descriptions
Claudio A. Morgado, Petr Jure ka, Daniel Svozil, Pavel Hobza
and Jiří Šponer, Phys. Chem. Chem. Phys., 2010
DOI: 10.1039/b924461a
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DOI: 10.1039/b919039b
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Kathleen B. Hall and Martin Gruebele, Phys. Chem. Chem.
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DOI: 10.1039/b925033f
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Al ona Furmanchuk, Olexandr Isayev, Oleg V. Shishkin,
Leonid Gorb and Jerzy Leszczynski, Phys. Chem. Chem.
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DOI: 10.1039/b923930h
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Hui Zhu, Martine Blom, Isabel Compagnon, Anouk M. Rijs,
Santanu Roy, Gert von Helden and Burkhard Schmidt, Phys.
Chem. Chem. Phys., 2010
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Peptide fragmentation by keV ion-induced dissociation
Sadia Bari, Ronnie Hoekstra and Thomas Schlathölter, Phys.
Chem. Chem. Phys., 2010
DOI: 10.1039/b924145k
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Clemens Glaubitz, Ernst Bamberg and Bernd Brutschy, Phys.
Chem. Chem. Phys., 2010
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Sub-microsecond photodissociation pathways of gas
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B. Rahbek, J. Rajput, P. Dugourd and L. H. Andersen, Phys.
Chem. Chem. Phys., 2010
DOI: 10.1039/b921038e
DFT-MD and vibrational anharmonicities of a
phosphorylated amino acid. Success and failure
Alvaro Cimas and Marie-Pierre Gaigeot, Phys. Chem. Chem.
Phys., 2010
DOI: 10.1039/b924025j
Infrared vibrational spectra as a structural probe of
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Richard A. Marta, Ronghu Wu, Kris R. Eldridge, Jonathan K.
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Laser spectroscopic study on (dibenzo-24-crown-8-ether)–
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Satoshi Kokubu, Ryoji Kusaka, Yoshiya Inokuchi, Takeharu
Haino and Takayuki Ebata, Phys. Chem. Chem. Phys., 2010
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Investigations of the water clusters of the protected amino
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Probing the specific interactions and structures of gasphase vancomycin antibiotics with cell-wall precursor
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Bruno Manil, Jean Pierre Schermann, Charles Desfrançois,
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Electronic coupling between cytosine bases in DNA single
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Vrønning Hoffmann and Steen Brøndsted Nielsen, Phys.
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Two-dimensional network stability of nucleobases and
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Subramani, Mingdong Dong, Chen Wang, Wael Mamdouh,
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Grégoire, C. Desfrançois, G. A. Garcia, L. Nahon, D. Nandi, L.
Poisson and M. Hochlaf, Phys. Chem. Chem. Phys., 2010
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Insulin dimer dissociation and unfolding revealed by
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Structural diversity of dimers of the Alzheimer Amyloid(25-35) peptide and polymorphism of the resulting fibrils
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PAPER
www.rsc.org/pccp | Physical Chemistry Chemical Physics
Reference MP2/CBS and CCSD(T) quantum-chemical calculations
on stacked adenine dimers. Comparison with DFT-D, MP2.5,
SCS(MI)-MP2, M06-2X, CBS(SCS-D) and force field descriptionsw
Claudio A. Morgado,ab Petr Jurečka,ac Daniel Svozil,ad Pavel Hobzace and
Jiřı́ Šponer*ae
Received 20th November 2009, Accepted 15th January 2010
First published as an Advance Article on the web 12th February 2010
DOI: 10.1039/b924461a
We have performed reference quantum-chemical calculations for about 130 structures of adenine dimers
in stacked conformations, with special attention given to dimers that are either vertically compressed
(parallel structures) or contain close interatomic contacts (non-parallel structures). Such geometries are
sampled during thermal fluctuations of nucleic acids and contribute to the local conformational
variability of these systems. Their theoretical characterization requires a good description of interaction
energies in the short-range repulsion region. The reference calculations have been performed with the
CBS(T) method, i.e., MP2/CBS computations corrected for higher-order electron-correlation effects using
the CCSD(T) method. These benchmark data have been used to examine the performance of the DFT-D,
SCS(MI)-MP2, MP2.5, M06-2X and CBS(SCS-D) quantum-mechanical methods, and of the AMBER
Cornell et al. force field. The present results, as well as those of our previous study on stacked uracil
dimers, confirm that the force field severely exaggerates the repulsion at short intermolecular distances.
This behavior complicates the use of the force field in scans of the stacking-energy dependence on local
conformational parameters in nucleic acids. Compared against the previous results obtained in the uracil
dimer study, the performance of DFT-D to describe stacking at short intermolecular distances has
worsened, showing for the adenine dimers a larger exaggeration of the repulsion, especially for structures
where the monomers are parallel to each other. Despite these deviations, the performance of DFT-D is
still reasonably good and this method provides, for example, a relatively inexpensive way to monitor
stacking energies along molecular dynamics trajectories. The best performers are the MP2.5,
SCS(MI)-MP2, and CBS(SCS-D) methods. In addition, the energy profiles given by the SCS(MI)-MP2
and CBS(SCS-D) methods are the ones that most closely resemble the CBS(T) data. Interestingly, the
performance of the SCS(MI)-MP2 method for stacked adenine dimers is better than for stacked uracil
dimers, indicating that the quality of the description may vary with the nucleobase composition. Even
though the SCS(MI)-MP2 method cannot match the speed of DFT-D, the results so far render it a
promising tool to study intrinsic interactions in systems of moderate size. In general, for most
applications all the QM methods tested here are of sufficient accuracy.
Introduction
It is well established that intermolecular interactions, like
hydrogen bonding and base stacking, contribute substantially
a
Institute of Biophysics, Academy of Sciences of the Czech Republic,
Královopolská 135, 612 65 Brno, Czech Republic.
E-mail: sponer@ncbr.chemi.muni.cz
b
Universidad Técnica Federico Santa Marı´a, Departamento de
Quı´mica, Casilla 110-V, Valparaı´so, Chile
c
Department of Physical Chemistry, Palacky University, tr. Svobody
26, 771 46, Olomouc, Czech Republic
d
Institute of Chemical Technology, Laboratory of Informatics and
Chemistry, Technická 3, 166 28, Prague, Czech Republic
e
Institute of Organic Chemistry and Biochemistry, Academy of
Sciences of the Czech Republic and Center of Biomolecules and
Complex Molecular Systems, Flemingovo nam. 2, 166 10 Prague 6,
Czech Republic
w Electronic supplementary information (ESI) available: The studied
geometries (xyz coordinates); additional technical details for the
computational methods; interaction-energy Tables; plots of energy
gradients; plots of DFT-SAPT energy contributions. See DOI:
10.1039/b924461a
3522 | Phys. Chem. Chem. Phys., 2010, 12, 3522–3534
to the structure, dynamics and, ultimately, function of nucleic
acids. Despite years of studies, there are many aspects of these
interactions that are not satisfactorily understood. For example,
the sequence-dependence of the thermodynamics, structure
and dynamics of even small RNA motifs has not been fully
elucidated, a knowledge of which would contribute to the
prediction of RNA secondary and three-dimensional structures.1
In order to tackle such questions, experiments are starting to
be combined with theoretical methods in an effort to better
understand the relative magnitude and nature of the intermolecular interactions that take place in these biological
systems.2–5 The theoretical methods used for this purpose
comprise both calculations in the gas phase as well as in the
condensed-phase media.
The study of biologically relevant molecules in isolation is
often criticized due to the neglect of a real chemical environment.
However, studies of complexes of nucleic-acid bases in the gas
phase are important for several reasons. First, it is the only
way to unambiguously evaluate the nature and magnitude of
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the interactions which are due to direct (intrinsic) forces.
Second, this knowledge is indispensable for a proper
parameterization of other theoretical methods such as force
fields, which can be used to study larger systems. Finally, the
description of intrinsic interactions is important for the
discrimination between intrinsic and externally imposed
properties. Experiments do not offer any unambiguous ways
to separate the intrinsic forces from the environmental effects.
The study of complexes of increasing size can then simulate the
transition from the isolated molecule to the condensed
medium, and the analysis of the differences between the gas- and
condensed-phase behavior can help in the identification of the
environmental influences on the building blocks of nucleic-acids.6
Also, gas-phase quantum-mechanical (QM) calculations can
be compared to gas-phase experiments, which allows for a
direct testing and calibration of the theory, thus increasing our
confidence on the latter. Along these lines, we have studied the
potential-energy surface (PES) of the adenine dimer in stacked
conformations with a set of QM and empirical methods.
The stacking of adenine bases can be seen in the majority of
nucleic-acid architectures, and definitely the largest variability of
geometries of adenine stacks can be found in ribosomes.7,8
The only experimental data on the stabilization energy of
nucleic-acid bases in vacuo can be found in the work of
Yanson et al.,9 who employed mass-field spectrometry to
measure the stabilization enthalpy of several complexes of
nucleic-acid bases. At the experimental conditions the partial
pressure of 9-methyladenine was not enough for the formation
of its dimer. Had these authors reported a stabilization
enthalpy for the 9-methyladenine dimer, the experimental
value would have had to be compared against the weighted
average of theoretical stabilization enthalpies of all populated
structures at the experimental conditions.10 Such populated
structures should be determined theoretically, since those
experiments did not reveal any structural information.
On the theoretical side, the stacking interactions between
the building blocks of biomacromolecules have been extensively studied with QM methods,11–35 and in several studies the
authors have reported interaction energies for stacked conformations of the adenine dimer, either as independent dimer
or as structural component of a DNA base-pair step.11–22 The
first electron-correlation characterization of a stacked
adenine dimer was reported by Šponer et al.11 using the
MP236/6-31G*(0.25)37,38 method. The main conclusion of
their study was that the stability of stacking comes from the
dispersion attraction, and that the electrostatic interactions
determine the orientation between the monomers. The study
demonstrated the applicability of the Coulombic term with
atom-center point charges to describe the electrostatic component
of base stacking. Reference calculations extrapolated to the
complete basis set (CBS) limit and including higher-order
electron-correlation effects using the CCSD(T)39,40 method
became available only recently and were reported, e.g., for
base stacking in B-DNA base-pair steps.13 Such calculations
are quantitatively more accurate than the MP2/6-31G*(0.25)
computations, however both methods reveal the same qualitative
picture of stacking. For examples of other relevant work
involving stacked adenine dimers, the reader is referred to
the references given above.
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In the present work we report an analysis of interaction
energies in stacked adenine dimers, both in parallel and nonparallel (tilted) geometries. The reference data are obtained
with the CBS(T)41–43 method and serve as a benchmark for
several other computational techniques: we have primarily
tested the AMBER44 force field, DFT-D,45 SCS(MI)-MP2,46
and the newly developed MP2.547 method. This portfolio of
methods includes the leading force field for nucleic acids, a fast
inexpensive DFT method with a specifically parameterized
empirical dispersion term, and two QM methods that are
assumed to be of almost comparable quality to the CBS(T)
technique. These methods were selected in order to represent a
broad set of techniques with varying computer requirements
and accuracy, to demonstrate the range of options currently
available for stacking calculations. After this initial testing was
completed, we carried out calculations with the M06-2X48 and
CBS(SCS-D) methods. The former represents an advanced
DFT method that does not utilize any empirical dispersion
term, while the latter is based on the SCS-CCSD49 method and
is a possible replacement for the CBS(T) method. Although it
has been shown that the AMBER force field provides a very
good description of stacking,11,13 molecular-mechanics (MM)
force fields are known to have limitations, and they should
always be subjected to critical evaluation against QM data in
order to establish their applicability. In a study of uracil
dimers in stacked conformations we have recently found that
the non-bonded empirical potential of the AMBER force field
severely exaggerates the repulsion at relatively short intermolecular distances, i.e., when close interatomic contacts
occur due to mutual inclination between the bases in the
stack.50 Regions of intermolecular contacts are linked to
interaction energy gradients, and the incorrect description of
these gradients might affect the outcome of molecular
dynamics (MD) simulations and potential energy scans carried
out with the force field. Even though in an MD simulation the
sampling of a large amount of degrees of freedom should ease
the impact of the incorrect description of the forces, some
conformations might be insufficiently populated in certain
cases. With the aim of further evaluating the AMBER nonbonded potential we now study its performance to compute
stacking energies in adenine dimers, a system where the
monomers have a relatively low dipolar moment and where
the attractive part of the interaction energy is expected to be
dominated by dispersion interactions (included in the LennardJones term of the force field). In line with our previous work
we have also chosen to test the DFT-D and the SCS(MI)-MP2
methods. These methods gave a very good account of stacking
in uracil dimers albeit, mainly for DFT-D, the performance
for geometries with close interatomic contacts in tilted
geometries was not perfect.50 The recently developed MP2.5
method (not tested in our preceding work on the uracil dimer)
has also been selected for the benchmarking since the method
has been proposed as an accurate and computationally feasible
alternative to CCSD(T) or CBS(T) for the study of noncovalent systems.47 The accuracy assessment of QM methods
is particularly relevant for studying local conformational
variations51–54 in B-DNA, which are essential for B-DNA
interactions with proteins and ligands. Since local variations
are associated with very subtle energy changes, the study of
Phys. Chem. Chem. Phys., 2010, 12, 3522–3534 | 3523
these systems demands a very high level of accuracy in the
computation of interaction energies (mainly the dispersion/
repulsion balance), as well as a proper inclusion of solvation
effects.13 Therefore it would be very useful to have a method
capable of reaching CCSD(T) accuracy in any nucleic-acid
system but at a fraction of its computational cost. This would
allow the increase of the sampling and size of the studied
systems. Equipped with such a method, meticulous analyses of
the PES of nucleic-acid base complexes combined with MD
simulations and other computational techniques would help us
to shed light on the sequence dependence of nucleic-acid
structures.55–63
Local variations are frequently associated with interactions
involving non-parallel bases, where close contacts and local
unstacking can commonly be observed in the base-pair steps,
and such geometries have been deliberately included in the set
of structures studied in this work. Such geometries are typically
not included in reference QM calculations. It should be noted,
when compared to our preceding study on stacked uracil
dimers,50 that stacked adenine dimers show a considerably
larger effect of higher-order electron-correlation contributions
to base stacking (i.e., the correction when passing from the
MP2 to the CCSD(T) level). From this point of view the
present study is a significant extension of the earlier stacking
analysis of uracil dimers. We have also performed DFTSAPT64 energy decompositions for all of the structures with
the intention of gaining some insight into the nature of the
interaction.
Computational details
Geometries
The structures have been obtained as follows. First, an adenine
monomer is optimized using the RI-MP265–67 method along
with the cc-pVTZ68 basis set. Then, it is placed in the xy plane
(z = 0) with the center of mass coinciding with the origin. The
N9–H9 bond is parallel to the y-axis and is pointing to the
direction of negative y values, and the amino group is oriented
towards the direction of positive y values (Fig. 1). This first
monomer is always fixed, and the second monomer is initially
superimposed on the first one. Then the relative position of the
second monomer is determined via 6 independent parameters.
Firstly, three angles are set by applying rotational matrices
consecutively and in a counterclockwise manner: rotation
around the x axis (g), rotation around the y axis (a) and
rotation around the z axis (o). Then, the second monomer is
shifted along the x and y axes by the parameters Dx and Dy.
Finally, the vertical distance is adjusted by Dz. In what
follows, we define Dz r for the PES scans. Following this
procedure we obtain structures where r equals the distance
between the center of mass of the second monomer and the
xy plane.
The structures are grouped into two different sets, P and NP
(Fig. 2). The set P contains 9 different adenine dimers
(P1, P2,. . .,P9), in conformations where the planes of the rings
are parallel (P) to each other, whereas the set NP contains
3 different dimers (NP1, NP2, and NP3) in conformations in
which the monomers are not parallel (NP) to each other. The
3524 | Phys. Chem. Chem. Phys., 2010, 12, 3522–3534
Fig. 1
Orientation of the first adenine monomer in the xy plane.
geometry of these dimers can be described in terms of the
position of the amino group of the second monomer (in white
in Fig. 2) relative to a region in the first monomer (in gray in
Fig. 2). In NP1 the amino group is above the N9–H9 region, in
NP2 the amino group is over the C4–C5 region, and in NP3
the amino group is above the N3 edge. By varying a free
structural parameter while the rest are kept fixed, we have built
a potential-energy curve (PEC) for each dimer. This way we
have generated a subset of structures for each dimer, and these
subsets add up to a total of 131 distinct geometries. With one
exception (P9, for which we have scanned the twist angle in
increments of 301) we have determined the dependence of the
stacking energy on r for a fixed combination of the other
five geometrical parameters, scanning the r parameter in
increments of 0.1 Å. For the vertical scans of the parallel
structures r ranges from 2.9 to 4.0 Å, whereas for the nonparallel ones the range goes from 3.6 to 4.5 Å, except for NP1
for which r ranges from 3.5 to 4.4 Å.
The three non-parallel dimers have been selected by visual
inspection of a number of a, g, o, Dx, and Dy combinations in
order to obtain three vertical scans with diverse close interatomic contacts. There are of course many structures that
would be worthy of study, but given that the high-level
ab initio calculations on these systems are expensive, we have
limited the study of stacking to the structures described above.
The Cartesian coordinates of all structures are given in the
ESI.w
Interaction energies
The interaction energies have been calculated following the
supermolecular approach. According to this approach the
interaction energy DEAB of a stacked dimer is calculated as
the difference in electronic energy between the dimer and the
isolated monomers (see equation below).69,70 We have used
only rigid monomers, and therefore we do not consider the
energies associated with the deformation of the monomers. In
the case of the SCS(MI)-MP2, MP2.5 and CBS(T) methods,
all of the interaction energies have been corrected for the basis
set superposition error (BSSE) using the counterpoise71,72
(CP) technique. This correction is not applied within the
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Fig. 2 Top and side views of the parallel and non-parallel structures of the adenine dimer, respectively. The first adenine monomer is shown in
gray. Some atoms have been labeled in order to aid in the visualization. The description of the structures is as follows: P1: untwisted undisplaced;
P2, P3: untwisted displaced; P4: antiparallel undisplaced; P5, P6, P7, P8: antiparallel displaced; P9: variation of twist at r = 3.3 Å.
DFT-D formalism as this method was parameterized against
BSSE-corrected data.45
DEAB = EAB
EA
EB
The supermolecular approach is applied for all of the methods
used in the present work, except for DFT-SAPT, where
the interaction energy is expressed as the sum of selected
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perturbation contributions. In an intermolecular perturbation
theory like DFT-SAPT the BSSE occurs only in the dHF term.
Methods
The theoretical methods used in the present study are
described in the following. Additional technical details are
provided in the ESI.w
Phys. Chem. Chem. Phys., 2010, 12, 3522–3534 | 3525
MP2/CBS calculations corrected by the CCSD(T) method
with a small basis set (abbreviated as CBS(T)). The MP2/CBS
and CCSD(T) calculations have been performed with the
Molpro73 2006.1 software package, applying the frozen-core
approximation. In the case of MP2, we have also applied the
density-fitting74,75 approximation. The Helgaker et al.76,77
extrapolation scheme has been used to extrapolate the
Hartree–Fock (HF) and the correlation energies. Herein we
have used the aug-cc-pVDZ - aug-cc-pVTZ extrapolation.
The correction for higher-order electron-correlation effects
(DCCSD(T)) has been computed with the cc-pVDZ basis set.
MP2/CBS plus MP3 corrections (MP2.5). The MP2/CBS
calculations have been performed with the Molpro73
2006.1 software package, applying the frozen-core and the
density-fitting74,75 approximations, whereas the calculations
needed for the third-order correction have been performed
with a recently developed module103 of the MOLCAS104
7 software package, taking advantage of the Cholesky
decomposition of the two-electron integrals.105 This correction
has been computed with the aug-cc-pVDZ basis set, and has
been damped by 50%.
Data analysis
AMBER non-bonded empirical potential. The empiricalpotential calculations have been performed with a local code,
employing the van der Waals (vdW) and Coulombic terms of
the AMBER force field.44 The atom-centered point charges
were obtained by an electrostatic potential (ESP) fitting at the
MP2/aug-cc-pVDZ68,78 level of theory using the Merz–
Kollman79,80 approach as implemented in the Gaussian81 03
software package. The reasons why this level of theory has
been chosen for the derivation of point charges can be found
in the literature.50
DFT augmented with an empirical dispersion term (DFT-D).
The DFT-D calculations have been performed with the
TurboMole82 5.8 software package in combination with a
local code that computes the empirical dispersion correction,
following the approach developed by Jurečka et al.,45 who
parameterized the method by a fitting procedure against the
CCSD(T) interaction-energy data for the S2283 training set.
For the DFT part of the calculation we have used the
TPSS84/6-311++G(3df,3pd)37 level of theory and the RI
approximation,85–88 also known as density fitting. This level
of theory augmented with the dispersion correction will
hereafter be referred to as DFT-D. When discussing the
performance of the DFT-D method we refer exclusively to the
approach of Jurečka et al.,45 without claiming that the results
are valid for other methods that also combine DFT with an
empirical correction for dispersion interactions.12,17,89–97
SCS-MP2 for molecular interactions (SCS(MI)-MP2). The
SCS(MI)-MP246 calculations have been performed with the
Molpro73 2006.1 software package, applying the frozen-core
and density-fitting74,75 approximations. This method has also
been parameterized by a fitting procedure against the
CCSD(T) interaction-energy data for the S2283 training set.
Here we calculate the SCS(MI)-MP2 interaction energies using
the cc-pVDZ - cc-pVTZ extrapolation scheme.
DFT-symmetry adapted perturbation theory (DFT-SAPT).
The DFT-SAPT98–101 calculations have been performed with
the Molpro73 2006.1 software package. The decomposition has
been carried out using the LPBE0AC101 XC potential with the
pure ALDA kernel for both the static and dynamic response,
in combination with the aug-cc-pVDZ basis set. The
density-fitting101 approximation has also been used. The
ionization potential (IP) of the monomer and the energy of
the highest occupied molecular orbital (HOMO) have been
calculated at the PBE0102/aug-cc-pVDZ level of theory with
the Gaussian81 03 software package.
3526 | Phys. Chem. Chem. Phys., 2010, 12, 3522–3534
The data have been analyzed in terms of root-mean-squared
(RMS) errors, maximum absolute deviations (MAX), and xy
plots. In the case of the plots we have plotted not only the
interaction energies but also their gradients. RMS errors are
calculated using the standard formula. For the calculation of
the MAX values we have defined a deviation as the difference
between the value obtained with a given method (AMBER,
DFT-D, SCS(MI)-MP2, or MP2.5) and the value obtained
with CBS(T), and the MAX value for a given dimer merely
corresponds to the absolute value of the largest deviation. We
have not included the DFT-SAPT method in this analysis
because of the relatively small basis set used in the energy
decompositions, which leads to underestimation of the
strength of the interaction in all cases. However, the basis
set used is enough to obtain qualitatively correct information
about the relative magnitude of the energy components. With
a larger basis set the DFT-SAPT method was shown to
provide very accurate total interaction energies in good
agreement with CCSD(T) data.101 All of the plots have
been generated with the Matplotlib106 graphics package in
combination with the SciPy107 and NumPy108 packages. The
interaction-energy data and the plots of interaction-energy
gradients and of DFT-SAPT energy decompositions are given
in the ESI.w
Results and discussion
Interaction energies and interaction-energy gradients for the
AMBER, DFT-D, SCS(MI)-MP2 and MP2.5 methods
The vertical scans of the parallel structures (P1–P8) show that
in general the QM methods systematically underestimate the
strength of the interaction, except for SCS(MI)-MP2, which
slightly overestimates it for the P2, P6 and P8 dimers. For all
of the tested QM methods the differences with respect to
the reference data increase as the intermolecular distance
decreases, and given the resolution used in the scans (0.1 Å)
all of the methods predict the same optimal intermonomer
distance as CBS(T) does, except for DFT-D that overestimates
this parameter for P5 (see Fig. 3). Overall, the performance of
the QM methods is very good, as can be seen from Fig. 3 and
the RMS errors and MAX values reported in Table 1. The
SCS(MI)-MP2 method clearly stands out, producing interaction-energy curves with shapes that closely resemble those of
the corresponding CBS(T) ones, making this method the one
providing the most reliable energy gradients. Furthermore,
this method exhibits RMSD and MAX values of only 0.19 and
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0.65 kcal mol 1, respectively. MP2.5 also performs very
well, with RMSD values somewhat larger than those of
SCS(MI)-MP2 and energy profiles that deviate from the
CBS(T) ones to some degree. Among the QM methods
DFT-D exhibits the largest RMS errors (Table 1) and the
PECs generated with this method reveal that the interaction
energies at short intermolecular distances are being underestimated to a greater extent. Such underestimation could be
the consequence of short-range correlation effects that are
neither completely described by the density functional used,
nor compensated for by the empirical correction. However,
the RMS error of DFT-D for the parallel structures is
0.99 kcal mol 1, which is a reasonably good result. Note also
that DFT-D, among the tested QM methods, is definitely the
most economical one, being the only method that would be
applicable to really routine massive scans of potential-energy
surfaces of base stacking in B-DNA. Contrary to the good
performance shown by the QM methods, the AMBER force
field shows substantial deviations from the CBS(T) data,
giving PECs that overestimate the strength of the interaction
at long distances and underestimate it at short ones, with the
exception of P1, for which the method overestimates the
strength of the interaction energy in a wide range of intermolecular distances (3.2–4.0 Å). The AMBER curves exhibit
an excessively steep slope in the short-range repulsion region,
overestimating the optimal intermonomer distance by about
0.1 Å in several cases. The little overestimated stabilization at
larger distances does not pose any problem in computations
of base stacking. However, the substantially exaggerated
repulsion for short interatomic distances is significant and may
affect studies of local conformational variations significantly.
The most stable structure is P4 (antiparallel undisplaced) at
r = 3.3 Å, with a CBS(T) stacking energy of 8.29 kcal mol 1.
The highest stability of this structure can easily be explained
by the large dispersion overlap combined with favorable
electrostatics, which is typical for antiparallel stacks.
The dependence of the stacking energy on twist at r = 3.3 Å
(P9) is shown in Fig. 4. The DFT-D and MP2.5 methods
underestimate the interaction energy (the stabilization) across
the entire range of twist angles, whereas SCS(MI)-MP2
slightly underestimates it for angles approximately between
01 and 551. All of the QM methods show PECs with shapes
that more or less match that of the CBS(T) curve. Among
these methods SCS(MI)-MP2 is again the best performer, with
RMSD and MAX values of 0.10 and 0.20 kcal mol 1,
respectively. The AMBER force field mostly underestimates
the strength of the interaction, and the shape of its PEC
somewhat deviates from the shape of the CBS(T) one. On
the contrary, the twist-dependence of the stacking energy in
the uracil dimer shows that the force field is more stabilizing
than CBS(T),50 indicating that the force field does not perform
evenly across different nucleic-acid base complexes. However,
the effect is not dramatic. For the twist dependencies that do
not lead to close atomic contacts, the force field performance
is, considering its simplicity, quite amazing. It again justifies
the use of the ESP atom-centered point-charge model in the
description of base stacking and supports suggestions that
base stacking is the best approximated contribution in classical
nucleic-acid simulations.109,110 For the non-parallel structures
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the situation is a little bit different from what has been found
for the parallel ones (Fig. 5). The SCS(MI)-MP2 and MP2.5
methods underestimate the strength of the interaction energy
for all of the dimers in this group, although the underestimation
is not very significant. These methods show a similar
performance in terms of RMS errors, and both give PECs
similar to the reference curve. DFT-D shows deviations from
the reference data that in average are larger than the deviations
seen for the other two QM methods. For the NP2 and NP3
dimers DFT-D overestimates the strength of the interaction at
long intermolecular distances and underestimates it at short
ones, and exaggerates the short-range repulsion to some
extent. Although not as good as in the case of the parallel
dimers, the performance of the SCS(MI)-MP2 method for the
non-parallel structures is still remarkable, with RMSD and
MAX values of 0.32 and 0.59 kcal mol 1, respectively. On the
force-field side the AMBER method exhibits the same
behavior previously seen for the parallel dimers, that is, the
method overestimates the strength of the interaction at long
intermolecular distances and underestimates it in the shortrange repulsion region, with energy gradients in the latter
region whose magnitudes are larger than those produced by
the CBS(T) reference method. Both the AMBER and the
tested QM methods agree with CBS(T) when predicting
the optimal intermolecular separation of the monomers, with
the only exception of DFT-D, which overestimates this
distance for NP2.
The dashed curves in Fig. 3–5 represent the stacking-energy
profiles calculated at the MP2/CBS level of theory. The
adenine dimer stacking stabilization energy would be seriously
overestimated without the inclusion of the DCCSD(T) correction.
Evidently, higher-order electron-correlation effects cannot be
neglected for aromatic stacking. Note that, contrary to the
previously analyzed uracil dimer,50 the adenine dimer is a
system with a very large DCCSD(T) correction. Thus, the close
match between the tested methods and the CBS(T) data is very
satisfactory and demonstrates that even the force field is better
suited for the description of stacking than pure MP2/CBS
computations. For the most stable antiparallel undisplaced
adenine dimer, the DCCSD(T) correction amounts to
3.01 kcal mol 1, while the correction was 1.14 kcal mol 1
for the most stable uracil dimer structure studied in our
previous work.
Very good performance is obtained with the SCS(MI)-MP2
method when calculating interaction-energy gradients. Looking at the shapes of the PECs in Fig. 3 and 5 one can see that
the SCS(MI)-MP2 method is clearly the best performer, when
compared with the reference CBS(T) data. Thus, the method
should produce reliable interaction-energy differences for
studies of stacked conformations of adenine monomers. In
addition, this method has also been shown to give interactionenergy gradients in good agreement with CBS(T) data for
several uracil dimers in stacked conformations, which makes
one believe that a similar performance might be observed
if different nucleic-acid base systems are studied with this
method. In the case of the AMBER force field the greatest
disagreements with the reference data occur at short intermolecular distances, where the force field exaggerates the
short-range repulsion. An example of this is given in Fig. 6,
Phys. Chem. Chem. Phys., 2010, 12, 3522–3534 | 3527
Fig. 3 Potential energy curves for P1 through P8, calculated with the AMBER, DFT-D, SCS(MI)-MP2, MP2.5 and CBS(T) methods
(the MP2/CBS curve is also given).
where it can be seen that at r = 3.1 Å (only 0.2 Å away from
the CBS(T) minimum) the magnitude of the force-field energy
gradient is approximately three times larger than the CBS(T)
one. Note that for this distance the CBS(T) energy is about
7.4 kcal mol 1, and the associated structure is indeed
accessible on the CBS(T) PEC. As we have explained in our
3528 | Phys. Chem. Chem. Phys., 2010, 12, 3522–3534
uracil dimer study, such geometries would be penalized when
performing a force-field calculation.50
The AMBER force field has also been used in the past to
study the potential and free energy surfaces of base pairs in the
gas phase, in order to estimate the populations of distinct
structures in eventual gas-phase experiments.111,112 Our study
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Table 1 Root-mean-squared deviations (RMSD, kcal mol 1) and maximum absolute deviations (MAX, kcal mol 1) of the AMBER, DFT-D,
SCS(MI)-MP2, and MP2.5 interaction energies with respect to the CBS(T) reference dataa
AMBER
DFT-D
SCS(MI)-MP2
MP2.5
Dimer
RMSD
MAX
RMSD
MAX
RMSD
MAX
RMSD
MAX
P1
P2
P3
P4
P5
P6
P7
P8
P9
All Pb
NP1
NP2
NP3
All NP
1.82
2.31
2.69
3.97
2.42
1.70
2.16
2.35
0.65
2.51
1.73
2.02
1.69
1.82
5.34
6.67
7.63
11.07
7.05
4.72
6.28
6.86
1.22
11.07
4.79
5.66
4.62
5.66
0.92
1.03
0.88
1.20
1.21
0.94
0.79
0.83
0.69
0.99
0.56
0.64
0.51
0.58
2.14
2.49
2.07
2.64
2.61
2.06
1.68
1.96
0.92
2.64
1.26
1.40
1.23
1.40
0.27
0.07
0.10
0.04
0.21
0.17
0.32
0.12
0.10
0.19
0.39
0.19
0.36
0.32
0.65
0.16
0.13
0.06
0.30
0.37
0.53
0.21
0.20
0.65
0.57
0.25
0.59
0.59
0.52
0.46
0.60
0.65
0.70
0.44
0.61
0.42
0.61
0.56
0.54
0.26
0.31
0.39
0.85
0.71
0.98
1.06
1.20
0.68
1.01
0.76
0.69
1.20
0.81
0.34
0.46
0.81
a
Some extreme MAX values are not visualized in the figures because they are out of the range of intermolecular distances in those figures. b ,P9
not included in the calculation of RMSD and MAX values, i.e., the values in this row correspond to the group of dimers for which vertical scans
have been performed.
Performance of the M06-2X and CBS(SCS-D) methods
Fig. 4 Potential energy curves for P9, calculated with the AMBER,
DFT-D, SCS(MI)-MP2, MP2.5 and CBS(T) methods (the MP2/CBS
curve is also given). The vertical separation between the monomers is
3.3 Å.
indicates that the force field is rather well suited for this
purpose, and we would recommend using its variant with
gas-phase atom-centered point charges, as used in the present
paper. (Note that condensed-phase simulations utilize HF
charges which overestimate the polarity of the monomers.)
On the other hand we have to exercise caution, because the
evaluation of populations of co-existing structures may be
very sensitive to even small errors in the energy description and
it is unlikely that the force field achieves a true quantitative
accuracy, especially in the case of co-existence of H-bonded,
T-shaped and stacked structures. It would be thus advisable to
combine force-field calculations with highest-quality QM
calculations for the key structures in their respective local
and global minima. It is usually assumed that the most
accurate contemporary gas-phase benchmark calculations
may have an accuracy of around 0.5 kcal mol 1 for the
individual structures. The force field certainly cannot achieve
such accuracy.
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Obviously, the above-examined DFT-D, MP2.5 and
SCS(MI)-MP2 methods represent only a fraction of the
recently introduced techniques capable to describe well base
stacking. During the review process we finished testing two
additional techniques: M06-2X and CBS(SCS-D). The former
method is a hybrid meta exchange–correlation density
functional that does not require an additional empirical
dispersion term, and the latter method makes use of the
SCS-CCSD method to evaluate a DSCS-CCSD difference
DESCS-CCSD), which is then added
(DSCS-CCSD=DEMP2
to the MP2/CBS energy. The CBS(SCS-D) method therefore
aims to offer a viable alternative for accurate calculations of
large systems when the CBS(T) method is already inapplicable.
In the present work the DSCS-CCSD difference has been
calculated with the cc-pVDZ basis set. The results of the
M06-2X and CBS(SCS-D) calculations are summarized in
Fig. S24–S35 in the ESI.w Both methods perform well, but
the latter is a much better performer. For the parallel
structures the RMS error and MAX value obtained with
CBS(SCS-D) are 0.31 and 0.68 kcal mol 1, respectively while
for the non-parallel structures these quantities amount to 0.20
and 0.41 kcal mol 1, respectively. In terms of RMS errors, for
the parallel structures the performance of SCS(MI)-MP2 is
better than that of CBS(SCS-D), but the converse is true in the
case of the non-parallel ones. Nevertheless, we would rank
both methods as highly accurate and entirely comparable to
each other. On the DFT side and also taking as performance
parameter the RMS error, DFT-D is better than M06-2X in
both cases. Fig. S24–S32 show that for the parallel structures
the shapes of the CBS(SCS-D) PECs would ensure very good
gradients at all intermolecular distances, whereas M06-2X
tends to produce good gradients at short and long intermolecular distances, while showing deviations from the CBS(T)
PECs when approaching the minimum. The M06-2X method
considerably underestimates the strength of the interaction at
long distances, and predicts in most cases a location of the
Phys. Chem. Chem. Phys., 2010, 12, 3522–3534 | 3529
Fig. 6 Estimate of the interaction-energy gradient for P4, calculated
with the AMBER and CBS(T) methods.
Fig. 5 Potential energy curves for NP1, NP2 and NP3, calculated
with the AMBER, DFT-D, SCS(MI)-MP2, MP2.5 and CBS(T)
methods (the MP2/CBS curve is also given).
minimum that is 0.1 Å too short when compared to the
CBS(T) data.
DFT-SAPT interaction-energy decompositions
The plots of the DFT-SAPT interaction-energy terms of all
dimers are given in Fig. S11–S23 in the ESI.w In all of the
structures the dispersion term is the most important stabilizing
contribution, followed by the electrostatic term, and in none of
them is the magnitude of the electrostatic interaction close to
that of the dispersion term, which can be explained in terms
of the lower polarity of adenine when compared to other
nucleic-acid bases. On the contrary, for dimers of more polar
3530 | Phys. Chem. Chem. Phys., 2010, 12, 3522–3534
bases like uracil there exist conformations for which the
difference between the magnitudes of the dispersion and
electrostatic terms is not as large, with the latter term also
providing a very significant part of the binding. The contributions
of the induction and dHF terms are also stabilizing in all cases,
but not as significant as the contributions of the dispersion and
electrostatic terms. The fact that the induction term is not
significant in this case should not be interpreted as polarization
effects not being important for nucleic-acid systems. Such
effects are relevant for macromolecular simulations in condensed
media, and many efforts are currently being devoted to the
development of polarizable force fields in order to perform
more realistic MD simulations.113 As is usual for vdW
complexes, the dispersion and exchange terms tend to cancel
each other in the region around the minimum.
Similar to what has been found for different stacked
conformations of the uracil dimer, in the case of stacked
adenine dimers the AMBER electrostatic component is in
many cases repulsive, and the magnitude of the repulsion
increases as the intermolecular distance decreases. This
description is physically incorrect and is in disagreement with
DFT-SAPT calculations which show that the electrostatic
component becomes more stabilizing at short intermolecular
separations (see for instance the electrostatic component of P1
in Fig. 7). This penetration effect is not taken into account in
the AMBER electrostatic term, but it is implicitly (effectively)
included in the vdW part of the force field,50 at least to some
extent. This is sufficient for overall reasonable balance of the
force field. For some structures like P6 one can see that the
force field is sometimes able to produce electrostatic-energy
profiles that show that the contribution is more stabilizing at
short intermolecular separations, but the distance dependence
of the AMBER electrostatic term is weak when compared
against the DFT-SAPT method. This of course does not mean
that the force field is able to capture penetration effects in
some situations. It is well known that most of the force fields
neglect such effects, but several approaches have been explored
in order to take them into account.114
One interesting feature of P1 is the behavior of its
DFT-SAPT electrostatic term, being the most repulsive, except
at very short intermolecular distances where this term becomes
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Fig. 7
Comparison between DFT-SAPT and AMBER electrostatic energies for P1, P3, P6, and P9.
more stabilizing than in the case of P2 and P3 (see Fig. S23 in
the ESIw). This indicates that electrostatic penetration effects
are more favorable for the P1 geometry at very short
distances, compared to the other two geometries.
For the angular variations of the electrostatic energy one
can see for P9 in Fig. 7 that the AMBER energy profile
basically matches the DFT-SAPT one, giving in this case a
correct physical description. The horizontal twist scan of P9
shows that the electrostatic and exchange terms clearly depend
on the twist angle o, and that the dispersion term is basically
constant across the entire range of twist angles.
Summary and conclusions
We have studied about 130 structures of adenine dimers in
stacked conformations in order to assess the performance of
the AMBER force field and the DFT-D, SCS(MI)-MP2, and
MP2.5 QM methods against CBS(T) data. The PECs reported
herein can also serve as reference data for the examination
or parameterization of other theoretical methods. Specific
attention was paid to structures where short-range repulsion
is important, either due to vertical compression of the dimers
or the presence of close interatomic contacts due to mutual
tilting of the bases. Note that these geometries are not pure
artificial constructs, but they appear e.g. in time-averaged
nucleic-acid structures (mainly those with tilted bases) or are
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commonly sampled due to thermal fluctuations. Such structures
are not included very often in reference datasets. The present
study thus brings a considerable extension of the currently
available reference data for base stacking.
Similar to what has been found in the study of stacked uracil
dimers,50 large differences between the CBS(T) method and
the AMBER force field can be seen in the PECs for geometries
where the dimers are either vertically compressed or contain
close interatomic contacts. The description of such geometries
suffers clearly from a sharply exaggerated repulsion by the
force field.
The reported differences in the interaction energies are large
enough to influence the description of the fine structure of
nucleic acids, like local conformational variations in B-DNA.
Perhaps, this exaggerated repulsion should not affect MD
simulations dramatically, since the sampling of all the other
degrees of freedom should effectively alleviate the effects of the
excessive repulsion. Nevertheless, thermal fluctuations of
stacked systems could be influenced to certain extent. On the
other hand, there are likely to be major artifacts in calculations
where the empirical force field is used for scanning the
dependence of stacking energy on local conformational
parameters that can lead to steric clashes, such as propeller
twist and base-pair roll. Note that such contacts are supposed
to be one of the very driving forces for the sequence dependence
of B-DNA geometry.51,53,115 The exaggerated repulsion of the
Phys. Chem. Chem. Phys., 2010, 12, 3522–3534 | 3531
force field upon compression and formation of interatomic
contacts is primarily due to the simplicity of the van der Waals
Lennard-Jones part of the force field. Its repulsive r 12 term
may be too hard and could be eventually replaced by some
softer term, such as an exponential function.
Compared to previous results on stacked uracil dimers,50
the agreement between CBS(T) and DFT-D at short intermolecular distances has worsened. For the adenine dimers the
amplification of the repulsion shown by DFT-D is larger than
in the case of the uracil dimers. The largest deviations of the
DFT-D interaction energies occur for the parallel structures at
intermolecular distances below the optimum. Despite the
deviations of the DFT-D interaction-energy profile in the
short-range repulsion region the performance of the method
is still satisfactory (considering also the speed of DFT-D), with
RMS errors of 0.99 and 0.58 kcal mol 1 for the parallel and
non-parallel dimers, respectively. Given the reasonably good
performance of the method to describe stacking profiles in
different conformations of uracil and adenine dimers, we
believe that DFT-D could also perform well for other
nucleic-acid base complexes, in line with other tests
available in the literature. Since DFT-D calculations are not
computationally expensive, they could even be used for the
monitoring of stacking interactions along MD simulation
trajectories, which involves the computation of stacking
energies for massive amounts of structures.
The best results, as compared to the reference CBS(T)
calculations, were obtained with the MP2.5 and SCS(MI)-MP2
methods. Both methods yield RMS errors basically lower than
0.5 kcal mol 1 and the shape of their interaction-energy
profiles are more similar to the CBS(T) ones. The performance
of SCS(MI)-MP2 is remarkable, with RMS errors of 0.19 and
0.32 kcal mol 1 for the parallel and non-parallel dimers,
respectively. The MAX values did not exceed 0.65 kcal mol 1
and they were below 0.30 kcal mol 1 for many scans. In
addition, this method is the one providing the profiles that
most closely match the CBS(T) ones, which means that the
SCS(MI)-MP2 would also outperform the rest of the methods
when calculating differences of interaction energies. Interestingly,
however, the SCS(MI)-MP2 method was a little less satisfactory
for the stacked uracil dimers than for the stacked adenine
dimers. This indicates that the performance of the methods for
base stacking can modestly vary with the nucleobase composition.
Thus, additional studies of some carefully chosen stacked
systems would improve our understanding of this phenomenon
(work in progress). Nevertheless, even the SCS(MI)-MP2
performance achieved earlier for the uracil dimer would be
excellent for the majority of possible applications. It should be
mentioned here that the SCS(MI)-MP2 method was parameterized against the interaction-energy data of the S22
dataset, which does not contain adenine dimers. The
SCS(MI)-MP2 method is more economical than MP2.5, at
least with the method, setup, codes and computers used in our
study. However, neither method is sufficiently fast for massive
computations and, therefore, they cannot compete with the
speed of DFT-D or the force field.
Considering all the results, the CBS(T) method will continue
to be the gold standard for QM calculations on nucleic-acid
systems. However, having an accurate method that would
3532 | Phys. Chem. Chem. Phys., 2010, 12, 3522–3534
allow routine calculations on base-pair steps is highly desirable.
It seems that the SCS(MI)-MP2 method would perform very
well in cases where more geometries and larger systems need to
be studied. Regarding SCS(MI)-MP2 and CBS(T) there is still
room for accuracy improvements because larger extrapolation
schemes can be used. For the former method we have used the
cc-pVDZ - cc-pVTZ extrapolation, while the use of the
cc-pVTZ - cc-pVQZ extrapolation could still bring some
quantitative changes. In the case of CBS(T), the performance
of the method can be improved by using larger basis sets for
the DCCSD(T) correction. For most applications, however,
the expected improvement would be insignificant. Concerning the
need for massive QM computations on stacking systems, the
DFT-D method seems to be suitable for the task. Finally,
although having several limitations, the force field remains a
choice for the qualitative description of base stacking forces.
Nevertheless, when assessing base stacking in nucleic acids all
QM methods have one disadvantage, which is not easy to
overcome. They include full gas-phase electrostatics and
do not allow its exclusion. Due to the presence of solvent
screening effects in nucleic acids, the energy contribution of
gas-phase electrostatics to the stacking stability is known to be
overwhelmingly suppressed.116 For example, a recent QM
investigation of twist-dependence of stacking in B-DNA
predicts optimal helical-twist values that are far away from
the observed range for most base-pair steps, scattered in a
wide range of values between less than 201 and almost 501.117
Thus, unless the studied system is appropriately solvated,
calculations with the pure vdW term of the force field (retaining
the dispersion overlap of the stacked bases and their steric
shape while switching off the electrostatics) may achieve better
relevance to assess the stability of experimental stacks than
calculations with full inclusion of electrostatics.
Acknowledgements
This work was supported by the Grant Agency of the
Academy of Sciences of the Czech Republic (grant
IAA400040802), Grant Agency of the Czech Republic
(203/09/1476), Ministry of Education of the Czech Republic
(LC06030, LC512, MSM6198959216 and MSM0021622413)
and Academy of Sciences of the Czech Republic
(AV0Z50040507, AV0Z50040702 and Z40550506). A portion
of the research described in this paper was carried out on the
high-performance computer system of the Environmental
Molecular Sciences Laboratory (EMSL), a scientific user
facility at the Pacific Northwest National Laboratory. The
support of Praemium Academiae, Academy of Sciences of the
Czech Republic, awarded to PH in 2007 is also acknowledged.
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