Calculating stacking interactions in nucleic acid base-pair steps using spin-component scaling and local second order Møller-Plesset perturbation theory

Stacking interaction energies for ten B-DNA base-pair steps are computed with density fitted local second-order M?ller-Plesset perturbation theory (DF-LMP2), and with the spin-component scaled (SCS) and spin-component scaled for nucleobases (SCSN) variants of DF-LMP2. Comparison with existing CBS(T) reference data indicates larger than expected energy differences for both SCS variants. After an analysis of the errors involved, an alternative method of producing reference data is proposed where DF-LMP2/aug-cc-pVTZ and DF-LMP2/aug-cc-pVQZ energies for the whole complex are extrapolated to produce interaction energies that do not require many-body correction and show reduced error in estimation of the basis set limit. A literature correction term from coupled cluster theory with perturbative triples is then added to the DF-LMP2 estimated basis set limit. These new reference data are consistently around 1 kcal mol(-1) less than previous literature data. DF-SCSN-LMP2/aug-cc-pVTZ is found to reproduce the new reference interaction energies with a root mean square error (RMSE) of 0.71 kcal mol(-1), while SCS consistently underestimates the binding energy.     

Coupled-cluster, Möller Plesset (MP2), density fitted local MP2, and density functional theory examination of the energetic and structural features of hydrophobic solvation: water and pentane

The interaction potentials between immiscible polar and non-polar solvents are a major driving force behind the formation of liquid:liquid interfaces. In this work, the interaction energy of water-pentane dimer has been determined using coupled-cluster theory with single double (triple) excitations [CCSD(T)], 2nd order M?ller Plesset perturbation theory (MP2), density fitted local MP2 (DF-LMP2), as well as density functional theory using a wide variety of density functionals and several different basis sets. The M05-2X exchange correlation functionals exhibit excellent agreement with CCSD(T) and DF-LMP2 after taking into account basis set superposition error. The gas phase water-pentane interaction energy is found to be quite sensitive to the specific pentane isomer (2,2-dimethylpropane vs. n-pentane) and relative orientation of the monomeric constituents. Subsequent solution phase cluster calculations of 2,2-dimethylpropane and n-pentane solvated by water indicate a positive free energy of solvation that is in good agreement with available experimental data. Structural parameters are quite sensitive to the density functional employed and reflect differences in the two-body interaction energy calculated by each method. In contrast, cluster calculations of pentane solvation of H(2)O solute are found to be inadequate for describing the organic solvent, likely due to limitations associated with the functionals employed (B3LYP, BHandH, and M05-2X).     

Electron correlation contribution to the physisorption of CO on MgF2(110)

We have performed CCSD(T), MP2, and DF-LMP2 calculations of the interaction energy of CO on the MgF(2)(110) surface by applying the method of increments and an embedded cluster model. In addition, we performed periodic HF, B3LYP, and DF-LMP2 calculations and compare them to the cluster results. The incremental CCSD(T) calculations predict an interaction energy of E(int) = -0.37?eV with a C-down orientation of CO above a Mg(2+) ion at the surface with a basis set of VTZ quality. We find that electron correlation constitutes about 50% of the binding energy and a detailed evaluation of the increments shows that the largest contribution to the correlation energy originates from the CO interaction with the closest F ions on the second layer.     

Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor

The recently introduced MP2-R122*A(loc) and LMP2-R122*A(loc) methods are modified to use a short-range correlation factor expanded as a fixed linear combination of Gaussian geminals. Density fitting is used to reduce the effort for integral evaluation, and local approximations are introduced to improve the scaling of the computational resources with molecular size. The MP2-F122*A(loc) correlation energies converge very rapidly with respect to the atomic orbital basis set size. Already with the aug-cc-pVTZ basis the correlation energies computed for a set of 21 small molecules are found to be within 0.5% of the MP2 basis set limit. Furthermore the short-range correlation factor leads to an improved convergence of the resolution of the identity, and eliminates problems with long-range errors in density fitting caused by the linear r12 factor. The DF-LMP2-F122*A(loc) method is applied to compute second-order correlation energies for molecules with up to 49 atoms and more than 1600 basis functions.     

High-level ab initio computations of structures and interaction energies of naphthalene dimers: origin of attraction and its directionality

The intermolecular interaction energies of naphthalene dimers have been calculated by using an aromatic intermolecular interaction model (a model chemistry for the evaluation of intermolecular interactions between aromatic molecules). The CCSD(T) (coupled cluster calculations with single and double substitutions with noniterative triple excitations) interaction energy at the basis set limit has been estimated from the second-order M?ller-Plesset perturbation interaction energy near saturation and the CCSD(T) correction term obtained using a medium-size basis set. The estimated interaction energies of the set of geometries explored in this work show that two structures emerge as being the lowest energy, and may effectively be considered as isoenergetic on the basis of the errors inherent in out extrapolation procedure. These structures are the slipped-parallel (Ci) structure (-5.73 kcal/mol) and the cross (D2d) structure (-5.28 kcal/mol). The T-shaped (C2v) and sandwich (D2h) dimers are substantially less stable (-4.34 and -3.78 kcal/mol, respectively). The dispersion interaction is found to be the major source of attraction in the naphthalene dimer. The electrostatic interaction is substantially smaller than the dispersion interaction. The large dispersion interaction is the cause of the large binding energies of the cross and slipped-parallel dimers.     

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.     

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.     

Ab initio study of AmCl(+): f-f spectroscopy and chemical binding

A valence full configuration interaction study with a polarized double-zeta quality basis set has been carried out for the lowest 49 electronic states of AmCl(+). The calculations use a pseudopotential treatment for the core electrons and incorporate a one-electron spin-orbit interaction operator. Electrons in the valence s, p, d, and f subshells were included in the active space. The resulting electronic potential energy curves are largely repulsive. The chemical bonding is ionic in character with negligible participation of 5f electrons. The molecular f-f spectroscopy of AmCl(+) arises essentially from an in situ Am(2+) core with states slightly redshifted by the presence of chloride ion. Am(+)+Cl asymptotes which give rise to the few attractive potential energy curves can be predicted by analysis of the f-f spectroscopy of isolated Am(+) and Am(2+). The attractive curves have substantial binding energies, on the order of 75-80 kcal/mol, and are noticeably lower than recent indirect measurements on the isovalent EuCl(+). An independent empirical correlation supports the predicted reduction in AmCl(+) binding energy. The energies of the repulsive curves are strongly dependent on the selection of the underlying atomic orbitals while the energies of the attractive curves do not display this sensitivity. The calculations were carried out using our recently developed parallel spin-orbit configuration interaction software.     

Hydrogen-bonded nucleic acid base pairs containing unusual base tautomers: complete basis set calculations at the MP2 and CCSD(T) levels

The total interaction energies of altogether 15 hydrogen-bonded nucleic acid base pairs containing unusual base tautomers were calculated. The geometry properties of all selected adenine-thymine and guanine-cytosine hydrogen-bonded base pairs enable their incorporation into DNA. Unusual base pairing patterns were compared with Watson-Crick H-bonded structures of the adenine-thymine and guanine-cytosine pairs. 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, was evaluated. Extrapolation to the MP2 CBS limit was done using the aug-cc-pVDZ and aug-cc-pVTZ results, and the CCSD(T) correction term was determined with the 6-31G*(0.25) basis set. Final interaction energies were corrected while taking into account both tautomeric penalization determined at the CBS level and solvation/desolvation free energies. The situation for the adenine-thymine pairs is straightforward, and tautomeric pairs are significantly less stable than the Watson-Crick pair consisting of the canonical forms. In the case of the guanine-cytosine pair, the Watson-Crick structure made by canonical forms is again the most stable. The other two structures are, however, energetically rather similar (by 5 and 6 kcal/mol), which provides a very small but non-negligible chance of detecting these structures in the DNA double helix (1:5000). Due to the fact that DNA bases and base pairs incorporated into DNA are solvated less favorably than in isolated systems, this probability represents the very upper limit. The results clearly show how precisely the canonical building blocks of DNA molecules were chosen and how well their stability is maintained.     

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.     

Interactions of M(z)-X complexes (M = Cu, Ag, and Au; X = He, Ne, and Ar; and z = ±1)

The coupled cluster singles and doubles method with perturbative treatment of triple excitations is applied to calculate the potentials of M(z)-X complexes (M = Cu, Ag, and Au; X = He, Ne, and Ar; and z = ±1). The bond functions and the basis set superposition errors are considered to obtain accurate interaction energies. The potential energy curves of all complexes are obtained. The vibrational energy levels and the spectroscopic parameters for these complexes are determined. The analytical potential energy functions are also fitted based on the potential energies.     

Basis set effects on the intermolecular interaction of the H2-H2 system obtained using ab initio molecular orbital calculations with the Møller-Plesset perturbation correction

The intermolecular interaction potential of the H₂-H₂ system was calculated by an ab initio molecular orbital method using several basis sets (up to 6-31 lG(3pd)) with inclusion of the electron correlation correction of the Møller-Plesset perturbation method and the basis set superposition error (BSSE) correction of the counterpoise method in order to evaluate the basis set effect. The calculated interaction energies depend strongly on the basis set used. Whereas the interaction energies of the repulsive and coulombic energy components calculated at the Hartree-Fock level are not affected by a change of basis set, the dispersion energy component depends strongly on the basis set used. Parameters of an exp-6-1 type non-bonding interaction potential were optimized on the basis of the MP4(SDTQ)/6-311G(3p) level intermolecular interaction energies of the H₂-H₂ system.     

Ne-CO2的从头算势能面及微波光谱

采用三重激发校正的耦合簇[CCSD(T)]方法和大基组计算了范德华复合物Ne-CO2的分子间势能面. 分子间相互作用能的计算采用考虑了基组重叠误差修正的超分子方法. 计算结果表明, 该势能面有两个极小值点, 分别对应T形构型和线性Ne-OCO构型. 采用离散变量表象(DVR)方法及Lanczos算法计算了Ne-CO2的振转能级. 计算结果表明, 体系势能面支持22个振动束缚态. 计算得到的微波光谱的跃迁频率与实验值吻合得很好.     

Ab initio and analytic intermolecular potentials for Ar-CF4

Ab initio calculations at the CCSD(T) level of theory were performed to characterize the Ar + CF4 intermolecular potential. Potential energy curves were calculated with the aug-cc-pVTZ basis set, and with and without a correction for basis set superposition error (BSSE). Additional calculations were performed with other correlation consistent basis sets to extrapolate the Ar-CF4 potential energy minimum to the complete basis set (CBS) limit. Both the size of the basis set and BSSE have substantial effects on the Ar + CF4 potential. Calculations with the aug-cc-pVTZ basis set, and with a BSSE correction, appear to give a good representation of the BSSE corrected potential at the CBS limit. In addition, MP2 theory is found to give potential energies in very good agreement with those determined by the much higher level CCSD(T) theory. Two model analytic potential energy functions were determined for Ar + CF4. One is a fit to the aug-cc-pVTZ calculations with a BSSE correction. The second was derived by fitting an average BSSE corrected potential, which is an average of the CCSD(T)/aug-cc-pVTZ potentials with and without a BSSE correction. These analytic functions are written as a sum of two-body potentials and excellent fits to the ab initio potentials are obtained by representing each two-body interaction as a Buckingham potential.     

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.     

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.     

Physical nature of ethidium and proflavine interactions with nucleic acid bases in the intercalation plane

On the basis of the crystallographic structures of three nucleic acid intercalation complexes involving ethidium and proflavine, we have analyzed the interaction energies between intercalator chromophores and their four nearest bases, using a hybrid variation-perturbation method at the second-order M?ller-Plesset theory level (MP2) with a 6-31G(d,p) basis set. A total MP2 interaction energy minimum precisely reproduces the crystallographic position of the ethidium chromophore in the intercalation plane between UA/AU bases. The electrostatic component constitutes the same fraction of the total energy for all three studied structures. The multipole electrostatic interaction energy, calculated from cumulative atomic multipole moments (CAMMs), was found to converge only after including components above the fifth order. CAMM interaction surfaces, calculated on grids in the intercalation planes of these structures, reasonably reproduce the alignment of intercalators in crystal structures; they exhibit additional minima in the direction of the DNA grooves, however, which also need to be examined at higher theory levels if no crystallographic data are given.     

Perturbative ab initio calculations of intermolecular energies. III. The water dimer

The interaction energy between two water molecules A and B is calculated by the method described in Paper I [1], previously applied for the interaction between two helium atoms (Paper II) [2]. This interaction energy is obtained as the difference between the energies of the complex (A + B) and the monomers (A) and (B), obtained by a perturbation method. The results obtained with the perturbation developed up to the second order in a minimal atomic basis set are decomposed into classical contributions and contributions linked to the exchange possibility. Charge transfer contributions are important and the localized character of the hydrogen bond is examined. It is pointed out that the definition of the set of excited configurations for the calculation of the energies of the isolated monomers is important, especially when one tries to use a small atomic basis set. A similar effect in SCF -type calculations is evaluated. The contribution of higher orders is evaluated by the CIPSI method.