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A study is conducted to describe the reference ad initio structures and interaction energies of hydrogen-bonded nucleic acid base pairs with binding energies ranging from 5 to 47 kcal/mol. The molecular structures are obtained using the RI-MP2 (resolution of identity MP2) method with extended cc-pVTZ basis set of atomic orbitals.

The evaluation of the stabilization energies and stabilization enthalpies of the most favorable H-bonded and stacked structure of the guanine... cytosine (G...C), adenine...thymine(A...T), 9-methylguanine...1-methylcytosine (mG...mC), and 9-methyladenine...1-methylmine (mA...mT) NA base pairs is given. The convergency of the MP2 interaction energy for the present complexes is rather slow, and it is found to be essential to include the extrapolation to the complete basis set limit.

The spectroscopic and computational studies about the effect of the base sequences on stacked (S) versus B-type (B) conformational heterogeneity caused by the major dG adduct derived from the model carcinogen 7-fluoro-2-aminofluorene (FAF) is reported. The findings show that FAF-modified DNA duplexes balanced between S and B conformations and interconverted slowly at room temperature.

Aromatic ring-peptide bond interactions are analyzed by using advanced computational chemistry methods. Decomposition of interaction energy by the density functional theory (DFT)-symmetry-adapted perturbation treatment (SAPT) method has shown that the parallel and T-shaped arrangements have differed significantly in the proportion of electrostatic and dispersion terms.

Resolution of identity standard density functional theory augmented with a damped empirical dispersion term (RI-DFT-D) calculations are used to study the lowest energy minima of tryptophyl-glycine (Trp-Gly) and tryptophyl-glycyl-glycine (Trp-Gly-Gly) peptides. RI-DFT-D theory is found to be a promising method for analyzing oligopeptides with accuracy comparable to ab initio quantum chemical calculations.

The complete basis set (CBS) limit of the MP2 interaction energy and the CCSD(T) correction term, determined as the difference between the CCSD(T) and MP2 interaction energies, were evaluated for 17 stacked and 4 H-bonded structures of the cytosine dimer. The new reference values are compared with AMBER empirical force field to highlight the nature of base stacking and to estimate the accuracy of force fields used for molecular modeling.

The intermolecular interaction energy components for several molecular complexes were calculated using force fields available in the AMBER suite of programs and compared with Density Functional Theory-Symmetry Adapted Perturbation Theory (DFT-SAPT) values. The extent to which such comparison is meaningful is discussed. The comparability is shown to depend strongly on the intermolecular distance, which means that comparisons made at one distance only are of limited value. At large distances the coulombic and van der Waals 1/r(6) empirical terms correspond fairly well with the DFT-SAPT electrostatics and dispersion terms, respectively. At the onset of electronic overlap the empirical values deviate from the reference values considerably. However, the errors in the force fields tend to cancel out in a systematic manner at equilibrium distances. Thus, the overall performance of the force fields displays errors an order of magnitude smaller than those of the individual interaction energy components. The repulsive 1/r(12) component of the van der Waals expression seems to be responsible for a significant part of the deviation of the force field results from the reference values. We suggest that further improvement of the force fields for intermolecular interactions would require replacement of the nonphysical 1/r(12) term by an exponential function. Dispersion anisotropy and its effects are discussed. Our analysis is intended to show that although comparing the empirical and non-empirical interaction energy components is in general problematic, it might bring insights useful for the construction of new force fields. Our results are relevant to often performed force-field-based interaction energy decompositions.

The reliability of the AMBER force field is tested by comparing the total interaction energy and dispersion energy with the reference data obtained at the density functional theory-symmetry-adapted perturbation treatment (DFT-SAPT)/aug-cc-pVDZ level. The comparison is made for 194 different geometries of noncovalent complexes (H-bonded, stacked, mixed, and dispersion-bound), at the equilibrium distances as well as at longer distances (up to a relative distance of two). The total interaction energies agree very well with the reference data and only the strength of H-bonded complexes is slightly underestimated. In the case of dispersion energy, the overall agreement is even better, with the exception of the stacked aromatic systems, where the empirical dispersion energy is overestimated. The use of AMBER interaction energy and AMBER dispersion energy for different types of noncovalent complexes at equilibrium as well as at longer distances is thus justified, except for a few cases, such as the water molecule, where the dispersion energy is highly inaccurate.

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.

Hybrid QM/MM methods combine the rigor of quantum mechanical (QM) calculations with the low computational cost of empirical molecular mechanical (MM) treatment allowing to capture dynamic properties to probe critical atomistic details of enzyme reactions. Catalysis by RNA enzymes (ribozymes) has only recently begun to be addressed with QM/MM approaches and is thus still a field under development. This review surveys methodology as well as recent advances in QM/MM applications to RNA mechanisms, including those of the HDV, hairpin, and hammerhead ribozymes, as well as the ribosome. We compare and correlate QM/MM results with those from QM and/or molecular dynamics (MD) simulations, and discuss scope and limitations with a critical eye on current shortcomings in available methodologies and computer resources. We thus hope to foster mutual appreciation and facilitate collaboration between experimentalists and theorists to jointly advance our understanding of RNA catalysis at an atomistic level.

Recently, two computational approaches that supply a density-functional-based quantum-chemical method with an empirical term accounting for London dispersion were introduced and found use in the studies of biomolecular systems, namely, DFT-D and SCC-DFTB-D. Here, we examine the performance and usability of these combined techniques for dealing with several tasks typically occurring in the research of biomolecules. The interaction energy of small biomolecular complexes agrees very well with the reference data yielded by correlated ab initio quantum chemical methods. In real-life studies aimed at interaction energy, structure, and infrared spectra, the mentioned methods provide results in good agreement with each other and with experiment (where available). The very favorable time demands of these approaches are discussed, and for each of them, a suitable area of use is proposed on the basis of the results of our analysis.

Interactions involving aromatic rings are important in molecular/biomolecular assembly and engineering. As a consequence, there have been a number of investigations on dimers involving benzene or other substituted pi systems. In this Feature Article, we examine the relevance of the magnitudes of their attractive and repulsive interaction energy components in governing the geometries of several pi-pi systems. The geometries and the associated binding energies were evaluated at the complete basis set (CBS) limit of coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] using a least biased scheme for the given data set. The results for the benzene dimer indicate that the floppy T-shaped structure (center-to-center distance: 4.96 A, with an axial benzene off-centered above the facial benzene) is isoenergetic in zero-point-energy (ZPE) corrected binding energy (D0) to the displaced-stacked structure (vertical interplanar distance: 3.54 A). However, the T-shaped structure is likely to be slightly more stable (D0 approximately equal to 2.4-2.5 kcal/mol) if quadruple excitations are included in the coupled cluster calculations. The presence of substituents on the aromatic ring, irrespective of their electron withdrawing or donating nature, leads to an increase in the binding energy, and the displaced-stacked conformations are more stabilized than the T-shaped conformers. This explains the wide prevalence of displaced stacked structures in organic crystals. Despite that the dispersion energy is dominating, the substituent as well as the conformational effects are correlated to the electrostatic interaction. This electrostatic origin implies that the substituent effect would be reduced in polar solution, but important in apolar media, in particular, for assembling processes.

Stabilisation energies of stacked structures of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, CN) complexes were determined at the CCSD(T) complete basis set (CBS) limit level. These energies were constructed from MP2/CBS stabilisation energies and a CCSD(T) correction term determined with a medium basis set (6-31G**). The former energies were extrapolated using the two-point formula of Helgaker et al. from aug-cc-pVDZ and aug-cc-pVTZ Hartree-Fock energies and MP2 correlation energies. The CCSD(T) correction term is systematically repulsive. The final CCSD(T)/CBS stabilisation energies are large, considerably larger than previously calculated and increase in the series as follows: hexafluorobenzene (6.3 kcal mol(-1)), hexachlorobenzene (8.8 kcal mol(-1)), hexabromobenzene (8.1 kcal mol(-1)) and hexacyanobenzene (11.0 kcal mol(-1)). MP2/SDD** relativistic calculations performed for all complexes mentioned and also for benzene[dot dot dot]hexaiodobenzene have clearly shown that due to relativistic effects the stabilisation energy of the hexaiodobenzene complex is lower than that of hexabromobenzene complex. The decomposition of the total interaction energy to physically defined energy components was made by using the symmetry adapted perturbation treatment (SAPT). The main stabilisation contribution for all complexes investigated is due to London dispersion energy, with the induction term being smaller. Electrostatic and induction terms which are attractive are compensated by their exchange counterparts. The stacked motif in the complexes studied is very stable and might thus be valuable as a supramolecular synthon.

Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high-level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated-B-LYP, B3-LYP, PBE, TPSS, TPSSh, and BH-LYP-and even surpass the MP2/cc-pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, s(R), scaling globally the vdW radii. For good results, a basis set of at least triple-zeta quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen-bonded and stacked complexes considered, respectively.

MP2 and CCSD(T) complete basis set (CBS) limit interaction energies and geometries for more than 100 DNA base pairs, amino acid pairs and model complexes are for the first time presented together. Extrapolation to the CBS limit is done by using two-point extrapolation methods and different basis sets (aug-cc-pVDZ - aug-cc-pVTZ, aug-cc-pVTZ - aug-cc-pVQZ, cc-pVTZ - cc-pVQZ) are utilized. The CCSD(T) correction term, determined as a difference between CCSD(T) and MP2 interaction energies, is evaluated with smaller basis sets (6-31G** and cc-pVDZ). Two sets of complex geometries were used, optimized or experimental ones. The JSCH-2005 benchmark set, which is now available to the chemical community, can be used for testing lower-level computational methods. For the first screening the smaller training set (S22) containing 22 model complexes can be recommended. In this case larger basis sets were used for extrapolation to the CBS limit and also CCSD(T) and counterpoise-corrected MP2 optimized geometries were sometimes adopted.

Base-stacking energies in ten unique B-DNA base-pair steps and some other arrangements were evaluated by the second-order Møller-Plesset (MP2) method, complete basis set (CBS) extrapolation, and correction for triple (T) electron-correlation contributions. The CBS(T) calculations were compared with decade-old MP2/6-31G*(0.25) reference data and AMBER force field. The new calculations show modest increases in stacking stabilization compared to the MP2/6-31G*(0.25) data and surprisingly large sequence-dependent variation of stacking energies. The absolute force-field values are in better agreement with the new reference data, while relative discrepancies between quantum-chemical (QM) and force-field values increase modestly. Nevertheless, the force field provides good qualitative description of stacking, and there is no need to introduce additional pair-additive electrostatic terms, such as distributed multipoles or out-of-plane charges. There is a rather surprising difference of about 0.1 A between the vertical separation of base pairs predicted by quantum chemistry and derived from crystal structures. Evaluations of different local arrangements of the 5'-CG-3' step indicate a sensitivity of the relative stacking energies to the level of calculation. Thus, describing quantitative relations between local DNA geometrical variations and stacking may be more complicated than usually assumed. The reference calculations are complemented by continuum-solvent assessment of solvent-screening effects.

The intrinsic stability of Watson-Crick d(AT) and r(AU) hydrogen bonds was analyzed by employing a variety of quantum-mechanical techniques, such as energy calculations, determination of reactivity indexes, and analysis of electron density topology. The analyses were performed not only for equilibrium gas-phase geometries, but also on hundreds of conformations derived from molecular dynamics (MD) and database analysis. None of our results support the idea that r(AU) hydrogen bonds are intrinsically more stable than those of d(AT). Instead, our data are in accordance with the traditional view that the greater stability of RNA relative to DNA is attributable to a variety of effects (e.g., stacking, sugar puckering, solvation) rather than to a significant difference in the hydrogen bonding of DNA and RNA base pairs.

The geometries and interaction energies of stacked and hydrogen-bonded uracil dimers and a stacked adeninecdots, three dots, centeredthymine pair were studied by means of high-level quantum chemical calculations. Specifically, standard as well as counterpoise-corrected optimizations were performed at second-order Moller-Plesset (MP2) and coupled cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)] levels with various basis sets up to the complete basis set limit. The results can be summarized as follows: (i) standard geometry optimization with small basis set (e.g., 6-31G(*)) provides fairly reasonable intermolecular separation; (ii) geometry optimization with extended basis sets at the MP2 level underestimates the intermolecular distances compared to the reference CCSD(T) results, whereas the MP2/cc-pVTZ counterpoise-corrected optimization agrees well with the reference geometries and, therefore, is recommended as a next step for improving MP2/cc-pVTZ geometries; (iii) the stabilization energy of stacked nucleic acids base pairs depends considerably on the method used for geometry optimization, so the use of reliable geometries, such as counterpoise-corrected MP2/cc-pVTZ ones, is recommended; (iv) the density functional theory methods fail completely in locating the energy minima for stacked structures and when the geometries from MP2 calculations are used, the resulting stabilization energies are strongly underestimated; (v) the self-consistent charges-density functional tight binding method, with inclusion of the empirical dispersion energy, accurately reproduces interaction energies and geometries of dispersion-bonded (stacked) complexes; this method can thus be recommended for prescanning the potential energy surfaces of van der Waals complexes.

Twenty two hydrogen-bonded and improper blue-shifting hydrogen-bonded complexes were studied by means of the HF, MP2 and B3LYP methods using the 6-31G(d,p) and 6--311 ++G(d,p) basis sets. In contrast to the standard H bonding, the origin of the improper blue-shifting H bonding is still not fully understood. Contrary to a frequently presented idea, the electric field of the proton acceptor cannot solely explain the different behavior of the H-bonded and improper blue-shifting H-bonded complexes. Compression of the hydrogen bond due to different attractive forces-dispersion or electrostatics--makes an important contribution as well. The symmetry-adapted perturbation theory (SAPT) has been utilized to decompose the total interaction energy into physically meaningful contributions. In the red-shifting complexes, the induction energy is mostly larger than the dispersion energy while, in the case of blue-shifting complexes, the situation is opposite. Dispersion as an attractive force increases the blue shift in the blue-shifting complexes as it compresses the H bond and, therefore, it increases the Pauli repulsion. On the other hand, dispersion in the red-shifting complexes increases their red shift.

Stabilization energies of the H-bonded and stacked structures of a DNA base pair were studied in the crystal structures of adenine-thymine, cytosine-guanine, and adenine-cytosine steps as well as in the 5'-d(GCGAAGC)-3' hairpin (utilizing the NMR geometry). Stabilization energies were determined as the sum of the complete basis set (CBS) limit of MP2 stabilization energies and the Delta E(CCSD(T)) - Delta E(MP2) correction term evaluated with the 6-31G*(0.25) basis set. The CBS limit was determined by a two-point extrapolation using the aug-cc-pVXZ basis sets for X = D and T. While the H-bonding energies are comparable to those of base pairs in a crystal and a vacuum, the stacking energies are considerably smaller in a crystal. Despite this, the stacking is still important and accounts for a significant part of the overall stabilization. It contributes equally to the stability of DNA as does H-bonding for AT-rich DNAs, while in the case of GC-rich DNAs it forms about one-third of the total stabilization. Interstrand stacking reaches surprisingly large values, well comparable to the intrastrand ones, and thus contributes significantly to the overall stabilization. The hairpin structure is characterized by significant stacking, and both guanine...cytosine pairs possess stacking energies larger than 11.5 kcal/mol. A high portion of stabilization in the studied hairpin comes from stacking (similar to that found for AT-rich DNAs) despite the fact that it contains two GC Watson-Crick pairs having very large H-bonding stabilization. The DFT/B3LYP/6-31G** method yields satisfactory values of interaction energies for H-bonded structures, while it fails completely for stacking.