Stabilization energies of the hydrogen-bonded and stacked structures of nucleic acid base pairs in the crystal geometries of CG, AT, and AC DNA steps and in the NMR geometry of the 5'-d(GCGAAGC)-3' hairpin: Complete basis set calculations at the MP2 and CCSD(T) levels

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.     

Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs

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.     

Toward a less costly but accurate calculation of the CCSD(T)/CBS noncovalent interaction energy

The popular method of calculating the noncovalent interaction energies at the coupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] theory level in the complete basis set (CBS) limit was to add a CCSD(T) correction term to the CBS second-order Møller-Plesset perturbation theory (MP2). The CCSD(T) correction term is the difference between the CCSD(T) and MP2 interaction energies evaluated in a medium basis set. However, the CCSD(T) calculations with the medium basis sets are still very expensive for systems with more than 30 atoms. Comparatively, the domain-based local pair natural orbital coupled-cluster method [DLPNO-CCSD(T)] can be applied to large systems with over 1,000 atoms. Considering both the computational accuracy and efficiency, in this work, we propose a new scheme to calculate the CCSD(T)/CBS interaction energies. In this scheme, the MP2/CBS term keeps intact and the CCSD(T) correction term is replaced by a DLPNO-CCSD(T) correction term which is the difference between the DLPNO-CCSD(T) and DLPNO-MP2 interaction energies evaluated in a medium basis set. The interaction energies of the noncovalent systems in the S22, HSG, HBC6, NBC10, and S66 databases were recalculated employing this new scheme. The consistent and tight settings of the truncation parameters for DLPNO-CCSD(T) and DLPNO-MP2 in this noncanonical CCSD(T)/CBS calculations lead to the maximum absolute deviation and root-mean-square deviation from the canonical CCSD(T)/CBS interaction energies of less than or equal to 0.28 kcal/mol and 0.09 kcal/mol, respectively. The high accuracy and low cost of this new computational scheme make it an excellent candidate for the study of large noncovalent systems.     

A study of nucleic acid base-stacking by the Monte Carlo method: Extended cluster approach

The adenine-thymine (AT), adenine-uracil (AU) and guanine-cytosine (GC) base associates in clusters containing 400 water molecules were studied using a newly implemented Metropolis Monte Carlo algorithm based on the extended cluster approach. Starting from the hydrogen-bonded Watson-Crick geometries, all three base pairs are transformed into more favorable stacked configurations during the simulation. The obtained results show, for the first time, the transition from planar base pairs to stacked base associates in the Monte Carlo framework. Analysis of the interaction energies shows that, in the water cluster, the stacked dimers are energetically preferable compared to the corresponding Watson-Crick base pairs. This is due to the larger base-water interaction in the stacked structures. The water-water interaction is one of the main factors promoting the formation of stacked dimers, and the obtained data confirm the crucial role of the water-water interactions in base stacking.     

Semi-empirical molecular orbital methods including dispersion corrections for the accurate prediction of the full range of intermolecular interactions in biomolecules

Semi-empirical calculations including an empirical dispersive correction are used to calculate intermolecular interaction energies and structures for a large database containing 156 biologically relevant molecules (hydrogen-bonded DNA base pairs, interstrand base pairs, stacked base pairs and amino acid base pairs) for which MP2 and CCSD(T) complete basis set (CBS) limit estimates of the interaction energies are available. The dispersion corrected semi-empirical methods are parameterised against a small training set of 22 complexes having a range of biologically important non-covalent interactions. For the full molecule set (156 complexes), compared to the high-level ab initio database, the mean unsigned errors of the interaction energies at the corrected semi-empirical level are 1.1 (AM1-D) and 1.2 (PM3-D) kcal mol(-1), being a significant improvement over existing AM1 and PM3 methods (8.6 and 8.2 kcal mol(-1)). Importantly, the new semi-empirical methods are capable of describing the diverse range of biological interactions, most notably stacking interactions, which are poorly described by both current AM1 and PM3 methods and by many DFT functionals. The new methods require no more computer time than existing semi-empirical methods and therefore represent an important advance in the study of important biological interactions.     

Effective fragment potential study of the interaction of DNA bases

Hydrogen-bonded and stacked structures of adenine-thymine and guanine-cytosine nucleotide base pairs, along with their methylated analogues, are examined with the ab inito based general effective fragment potential (EFP2) method. A comparison of coupled cluster with single, double, and perturbative triple (CCSD(T)) energies is presented, along with an EFP2 energy decomposition to illustrate the components of the interaction energy.     

Accurate interaction energies of hydrogen-bonded nucleic acid base pairs

Hydrogen-bonded nucleic acids base pairs substantially contribute to the structure and stability of nucleic acids. The study presents reference ab initio structures and interaction energies of selected 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 RI-MP2 method provides results essentially identical with the standard MP2 method. The interaction energies are calculated using the Complete Basis Set (CBS) extrapolation at the RI-MP2 level. For some base pairs, Coupled-Cluster corrections with inclusion of noniterative triple contributions (CCSD(T)) are given. The calculations are compared with selected medium quality methods. The PW91 DFT functional with the 6-31G basis set matches well the RI-MP2/CBS absolute interaction energies and reproduces the relative values of base pairing energies with a maximum relative error of 2.6 kcal/mol when applied with Becke3LYP-optimized geometries. The Becke3LYP DFT functional underestimates the interaction energies by few kcal/mol with relative error of 2.2 kcal/mol. Very good performance of nonpolarizable Cornell et al. force field is confirmed and this indirectly supports the view that H-bonded base pairs are primarily stabilized by electrostatic interactions.     

Probing phenylalanine/adenine pi-stacking interactions in protein complexes with explicitly correlated and CCSD(T) computations

To examine the effects of pi-stacking interactions between aromatic amino acid side chains and adenine bearing ligands in crystalline protein structures, 26 toluene/(N9-methyl)adenine model configurations have been constructed from protein/ligand crystal structures. Full geometry optimizations with the MP2 method cause the 26 crystal structures to collapse to six unique structures. The complete basis set (CBS) limit of the CCSD(T) interaction energies has been determined for all 32 structures by combining explicitly correlated MP2-R12 computations with a correction for higher-order correlation effects from CCSD(T) calculations. The CCSD(T) CBS limit interaction energies of the 26 crystal structures range from -3.19 to -6.77 kcal mol (-1) and average -5.01 kcal mol (-1). The CCSD(T) CBS limit interaction energies of the optimized complexes increase by roughly 1.5 kcal mol (-1) on average to -6.54 kcal mol (-1) (ranging from -5.93 to -7.05 kcal mol (-1)). Corrections for higher-order correlation effects are extremely important for both sets of structures and are responsible for the modest increase in the interaction energy after optimization. The MP2 method overbinds the crystal structures by 2.31 kcal mol (-1) on average compared to 4.50 kcal mol (-1) for the optimized structures.     

True stabilization energies for the optimal planar hydrogen-bonded and stacked structures of guanine...cytosine, adenine...thymine, and their 9- and 1-methyl derivatives: complete basis set calculations at the MP2 and CCSD(T) levels and comparison with experiment

Planar H-bonded and stacked structures of guanine...cytosine (G.C), adenine...thymine (A...T), 9-methylguanine...1-methylcytosine (mG...mC), and 9-methyladenine...1-methylthymine (mA...mT) were optimized at the RI-MP2 level using the TZVPP ([5s3p2d1f/3s2p1d]) basis set. Planar H-bonded structures of G...C, mG...mC, and A...T correspond to the Watson-Crick (WC) arrangement, in contrast to mA...mT for which the Hoogsteen (H) structure is found. Stabilization energies for all structures were determined as the sum of the complete basis set limit of MP2 energies and a (DeltaE(CCSD(T)) - DeltaE(MP2)) correction term evaluated with the cc-pVDZ(0.25,0.15) basis set. The complete basis set limit of MP2 energies was determined by two-point extrapolation using the aug-cc-pVXZ basis sets for X = D and T and X = T and Q. This procedure is required since the convergency of the MP2 interaction energy for the present complexes is rather slow, and it is thus important to include the extrapolation to the complete basis set limit. For the MP2/aug-cc-pVQZ level of theory, stabilization energies for all complexes studied are already very close to the complete basis set limit. The much cheaper D-->T extrapolation provided a complete basis set limit close (by less than 0.7 kcal/mol) to the more accurate T-->Q term, and the D-->T extrapolation can be recommended for evaluation of complete basis set limits of more extended complexes (e.g. larger motifs of DNA). The convergency of the (DeltaE(CCSD(T)) - DeltaE(MP2)) term is known to be faster than that of the MP2 or CCSD(T) correlation energy itself, and the cc-pVDZ(0.25,0.15) basis set provides reasonable values for planar H-bonded as well as stacked structures. Inclusion of the CCSD(T) correction is essential for obtaining reliable relative values for planar H-bonding and stacking interactions; neglecting the CCSD(T) correction results in very considerable errors between 2.5 and 3.4 kcal/mol. Final stabilization energies (kcal/mol) for the base pairs studied are very substantial (A...T WC, 15.4; mA...mT H, 16.3; A...T stacked, 11.6; mA...mT stacked, 13.1; G...C WC, 28.8; mG...mC WC, 28.5; G...C stacked, 16.9; mG...mC stacked, 18.0), much larger than published previously. On the basis of comparison with experimental data, we conclude that our values represent the lower boundary of the true stabilization energies. On the basis of error analysis, we expect the present H-bonding energies to be fairly close to the true values, while stacked energies are still expected to be about 10% too low. The stacking energy for the mG...mC pair is considerably lower than the respective H-bonding energy, but it is larger than the mA...mT H-bonding energy. This conclusion could significantly change the present view on the importance of specific H-bonding interactions and nonspecific stacking interactions in nature, for instance, in DNA. Present stabilization energies for H-bonding and stacking energies represent the most accurate and reliable values and can be considered as new reference data.     

On geometries of stacked and H-bonded nucleic acid base pairs determined at various DFT, MP2, and CCSD(T) levels up to the CCSD(T)/complete basis set limit level

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.     

Structure of 2,4-diaminopyrimidine-theobromine alternate base pairs

We report the structure of clusters of 2,4-diaminopyrimidine with 3,7-dimethylxanthine (theobromine) in the gas phase determined by IR-UV double resonance spectroscopy in both the near-IR and mid-IR regions in combination with ab initio computations. These clusters represent potential alternate nucleobase pairs, geometrically equivalent to guanine-cytosine. We have found the four lowest energy structures, which include the Watson-Crick base pairing motif. This Watson-Crick structure has not been observed by resonant two-photon ionization (R2PI) in the gas phase for the canonical DNA base pairs.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Stabilisation energy of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, I, CN) complexes: complete basis set limit calculations at MP2 and CCSD(T) levels

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.     

Toward true DNA base-stacking energies: MP2, CCSD(T), and complete basis set calculations

Stacking energies in low-energy geometries of pyrimidine, uracil, cytosine, and guanine homodimers were determined by the MP2 and CCSD(T) calculations utilizing a wide range of split-valence, correlation-consistent, and bond-functions basis sets. Complete basis set MP2 (CBS MP2) stacking energies extrapolated using aug-cc-pVXZ (X = D, T, and for pyrimidine dimer Q) basis sets equal to -5.3, -12.3, and -11.2 kcal/mol for the first three dimers, respectively. Higher-order correlation corrections estimated as the difference between MP2 and CCSD(T) stacking energies amount to 2.0, 0.7, and 0.9 kcal/mol and lead to final estimates of the genuine stacking energies for the three dimers of -3.4, -11.6, and -10.4 kcal/mol. The CBS MP2 stacking-energy estimate for guanine dimer (-14.8 kcal/mol) was based on the 6-31G(0.25) and aug-cc-pVDZ calculations. This simplified extrapolation can be routinely used with a meaningful accuracy around 1 kcal/mol for large aromatic stacking clusters. The final estimate of the guanine stacking energy after the CCSD(T) correction amounts to -12.9 kcal/mol. The MP2/6-31G(0.25) method previously used as the standard level to calculate aromatic stacking in hundreds of geometries of nucleobase dimers systematically underestimates the base stacking by ca. 1.0-2.5 kcal/mol per stacked dimer, covering 75-90% of the intermolecular correlation stabilization. We suggest that this correction is to be considered in calibration of force fields and other cheaper computational methods. The quality of the MP2/6-31G(0.25) predictions is nevertheless considerably better than suggested on the basis of monomer polarizability calculations. Fast and very accurate estimates of the MP2 aromatic stacking energies can be achieved using the RI-MP2 method. The CBS MP2 calculations and the CCSD(T) correction, when taken together, bring only marginal changes to the relative stability of H-bonded and stacked base pairs, with a slight shift of ca. 1 kcal/mol in favor of H-bonding. We suggest that the present values are very close to ultimate predictions of the strength of aromatic base stacking of DNA and RNA bases.     

Explicit correlation and basis set superposition error: the structure and energy of carbon dioxide dimer

We have investigated the slipped parallel and t-shaped structures of carbon dioxide dimer [(CO(2))(2)] using both conventional and explicitly correlated coupled cluster methods, inclusive and exclusive of counterpoise (CP) correction. We have determined the geometry of both structures with conventional coupled cluster singles doubles and perturbative triples theory [CCSD(T)] and explicitly correlated cluster singles doubles and perturbative triples theory [CCSD(T)-F12b] at the complete basis set (CBS) limits using custom optimization routines. Consistent with previous investigations, we find that the slipped parallel structure corresponds to the global minimum and is 1.09 kJ mol(-1) lower in energy. For a given cardinal number, the optimized geometries and interaction energies of (CO(2))(2) obtained with the explicitly correlated CCSD(T)-F12b method are closer to the CBS limit than the corresponding conventional CCSD(T) results. Furthermore, the magnitude of basis set superposition error (BSSE) in the CCSD(T)-F12b optimized geometries and interaction energies is appreciably smaller than the magnitude of BSSE in the conventional CCSD(T) results. We decompose the CCSD(T) and CCSD(T)-F12b interaction energies into the constituent HF or HF CABS, CCSD or CCSD-F12b, and (T) contributions. We find that the complementary auxiliary basis set (CABS) singles correction and the F12b approximation significantly reduce the magnitude of BSSE at the HF and CCSD levels of theory, respectively. For a given cardinal number, we find that non-CP corrected, unscaled triples CCSD(T)-F12b/VXZ-F12 interaction energies are in overall best agreement with the CBS limit.     

Scaled MP3 Non‐Covalent Interaction Energies Agree Closely with Accurate CCSD(T) Benchmark Data

Scaled MP3 interaction energies calculated as a sum of MP2/CBS (complete basis set limit) interaction energies and scaled third‐order energy contributions obtained in small or medium size basis sets agree very closely with the estimated CCSD(T)/CBS interaction energies for the 22 H‐bonded, dispersion‐controlled and mixed non‐covalent complexes from the S22 data set. Performance of this so‐called MP2.5 (third‐order scaling factor of 0.5) method has also been tested for 33 nucleic acid base pairs and two stacked conformers of porphine dimer. In all the test cases, performance of the MP2.5 method was shown to be superior to the scaled spin‐component MP2 based methods, e.g. SCS–MP2, SCSN–MP2 and SCS(MI)–MP2. In particular, a very balanced treatment of hydrogen‐bonded compared to stacked complexes is achieved with MP2.5. The main advantage of the approach is that it employs only a single empirical parameter and is thus biased by two rigorously defined, asymptotically correct ab‐initio methods, MP2 and MP3. The method is proposed as an accurate but computationally feasible alternative to CCSD(T) for the computation of the properties of various kinds of non‐covalently bound systems.     

Direct assessment of interresidue forces in Watson-Crick base pairs using theoretical compliance constants

This communication presents quantum mechanical calculations of interresidue potential constants for the Watson-Crick base pairs adenine-thymine (AT) and guanine-cytosine (GC), permitting a unique quantification of hydrogen bond strengths. Due to the calculated compliance constants, large differences between individual H bonds were found, while a repulsive character of the C-H...O bond in AT can be excluded.     

Electronic properties of metal-modified DNA base pairs

The electronic properties of several metal-modified Watson-Crick guanine-cytosine base pairs are investigated by means of first-principle density functional theory calculations. Focus is placed on a new structure recently proposed as a plausible model for building an antiparallel duplex with Zn-guanine-cytosine pairs, but we also inspect several other conformations and the incorporation of Ag and Cu ions. We analyze the effects induced by the incorporation of one metal cation per base pair by comparing the structures and the electronic properties of the metalated pairs to those of the natural guanine-cytosine pair, particularly for what concerns the modifications of energy levels and charge density distributions of the frontier orbitals. Our results reveal the establishment of covalent bonding between the metal cation and the nucleobases, identified in the presence of hybrid metal-guanine and metal-cytosine orbitals. Attachment of the cation can occur either at the N1 or the N7 site of guanine and is compatible with altering or not altering the H-bond pattern of the natural pair. Cu(II) strongly contributes to the hybridization of the orbitals around the band gap, whereas Ag(I) and Zn(II) give hybrid states farther from the band gap. Most metalated pairs have smaller band gaps than the natural guanine-cytosine pair. The band gap shrinking along with the metal-base coupling suggests interesting consequences for electron transfer through DNA double helices.