The sensitivity of B3LYP atomization energies to the basis set and a comparison of basis set requirements for CCSD(T) and B3LYP

The atomization energies of the 55 G2 molecules are computed using the B3LYP approach with a variety of basis sets. The 6–311 + G(3df) basis set is found to yield superior results to those obtained using the augumented-correlation-consistent valence-polarized triple-zeta set. The atomization energy of SO₂ is found to be the most sensitive to basis set and is studied in detail. Including tight d functions is found to be important for obtaining good atomization energies. The results for SO₂ are compared with those obtained using the coupled-cluster singles and doubles approach including a perturbational estimate of the triple excitations.     

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.     

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.     

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.     

Intrinsic conformational preferences of substituted cyclohexanes and tetrahydropyrans evaluated at the CCSD(T) complete basis set limit: implications for the anomeric effect

A series of MP2 and CCSD(T) computations have been carried out with correlation consistent basis sets as large as aug-cc-pV5Z to determine the intrinsic equatorial-axial conformational preference of CH(3)-, F-, OCH(3)-, and OH-substituted cyclohexane and tetrahydropyran rings. The high-accuracy relative electronic energies reported here shed new light on the intrinsic energetics of these cyclic prototypes for the anomeric effect. At the CCSD(T) complete basis set (CBS) limit, the energy of the equatorial conformation relative to the axial position (DeltaE (CBS)(CCSD(T))) is -1.75, -0.20, -0.21, and -0.56 kcal mol(-1) in methyl-, fluoro-, methoxy-, and hydroxycyclohexane, respectively, while DeltaE(CBS)(CCSD(T) is -2.83, +2.45, +1.27, and +0.86 kcal mol(-1) for 2-methyl-, 2-fluoro-, 2-methoxy-, and 2-hydroxytetrahydropyran, respectively. Note that the equatorial and axial conformers are nearly electronically isoenergetic in both fluoro- and methoxycyclohexane. For all eight cyclic species, a zero-point vibrational energy correction decreases Delta by a few tenths of a kilocalorie per mole. Relative energies obtained with popular methods and basis sets are unreliable, including Hartree-Fock theory, the B3LYP density functional, and the 6-31G and 6-311G families of split-valence basis sets. Even with the massive pentuple-zeta basis sets, the HF and B3LYP methods substantially overestimate the stability of the equatorial conformers (by as much as 0.99 and 0.73 kcal mol(-1), respectively, for 2-methoxytetrahydropyran). Only because of a consistent cancellation of errors do these popular approaches sometimes provide reasonable estimates of the anomeric effect.     

Basis set limit CCSD(T) harmonic vibrational frequencies

Benchmark, frozen-core CCSD(T) equilibrium harmonic vibrational frequencies of 12 closed-shell and five open-shell molecules are computed to within 1 cm-1 of the basis set limit using the explicitly correlated CCSD(T)-R12 method. The convergence of the standard CCSD(T) method with the one-particle basis sets of Dunning and co-workers is examined and found to be slow, with mean and maximum absolute errors of 1.3 and 3.5 cm-1 remaining at the cc-pV6Z level. Finite basis set effects do not appear to introduce systematic errors in equilibrium harmonic frequencies, and mean absolute errors reduce by a factor of 2 for each basis set cardinal number increment. The convergence of individual equilibrium harmonic frequencies is not guaranteed to be monotonic due to the associated shift in the equilibrium structure. The inclusion of computed scalar relativistic effects and previously available corrections for core-valence correlation and higher-order excitations in the cluster operator results in an agreement with experimentally derived harmonic frequencies of 0.1, 0.3, and -0.4 cm-1 for HF, N2, and CO, respectively. F2 continues to present a challenge to computational chemistry with an error of 3.2 cm-1, primarily resulting from the high basis set dependence of the quadruples contribution.     

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.     

The convergence of complete active space self-consistent-field energies to the complete basis set limit

Examination of the convergence of full valence complete active space self-consistent-field energies with expansion of the one-electron basis set reveals a pattern very similar to the convergence of single determinant Hartree-Fock energies. Calculations on 26 molecular examples with the sequence of ntuple-zeta augmented polarized (nZaP) basis sets (n=2, 3, 4, 5, and 6) are used to evaluate complete basis set extrapolation schemes. The most effective extrapolation reduces the rms one-electron basis set truncation errors from 3.03, 0.58, and 0.12 mhartree to 0.23, 0.05, and 0.014 mhartree for the 3ZaP, 4ZaP, and 5ZaP basis sets, respectively.     

Structure and spectra of the molecules of manganese, iron, and cobalt trifluorides: A CCSD(T) study in the complete basis set

The coupled-cluster singles and doubles with perturbative triples (CCSD(T)) method in triple-, quadruple-, and quintuple-zeta basis sets with extrapolation to the complete basis set limit is used to analyze the properties of MnF₃, FeF₃, and CoF₃ molecules. The relative energies of low-lying electronic states are determined. The Jahn-Teller effect is investigated in the ground electronic state ⁵ E?? of the MnF₃ molecule and the first excited electronic state ⁵ E?? of the CoF₃ molecule. Geometric parameters, atomization enthalpies, vibrational frequencies, intensities in the infrared and Raman spectra are found with high accuracy. The assignment of the bands observed in the low-frequency region of the IR and Raman spectra of MnF₃ and CoF₃ molecules are revised.     

Molecular structure and spectra of titanium and vanadium trifluorides: Complete basis set CCSD(T) study

Quantum chemical study on TiF₃ and VF₃ molecules was carried out using the CCSD(T) coupled cluster method using the triple-, quadruple-, and quintuple-zeta basis set and an extrapolation to the complete basis set limit. The methods of multireference configuration interaction MRCISD+Q and perturbation theory MCQDPT2 were used also. The symmetry of the ground electronic state was determined: ² A′₁ and ³ E″ in TiF₃ and VF₃, respectively. The adiabatic excitation energies were evaluated: AEE(TiF₃, $\tilde A^2 E'' \leftarrow \tilde X^2 A'_1 $ ) = 5000 cm^?1, AEE(VF₃, $\tilde A^3 A'_2 \leftarrow \tilde X^3 E''$ ) = 1000 cm^?1. The Jahn-Teller effect in $\tilde A^2 E''$ state of TiF₃ and $\tilde X^3 E''$ state of VF₃ was investigated. The computed Jahn-Teller stabilization energy D _3h → C _2v amounts to 555 and 292 cm^?1, respectively. The spin-orbit coupling effect on the VF₃ molecular structure and spectrum of electronic states is shown to be quite significant. The calculated vibrational frequencies of TiF₃ are in excellent agreement with IR spectroscopy data. The atomization enthalpies were evaluated: Δ_at H ₂₉₈ ^pO = 430 kcal/mol (TiF₃), 393 kcal/mol (VF₃).     

Parameterization of a B3LYP specific correction for non-covalent interactions and basis set superposition error on a gigantic dataset of CCSD(T) quality non-covalent interaction energies

A vast number of non-covalent interaction energies at the counterpoise corrected CCSD(T) level have been collected from the literature to build a diverse new dataset. The whole dataset, which consists of 2027 CCSD(T) energies, includes most of the published data at this level. A large subset of the data was then used to train a novel, B3LYP specific, empirical correction scheme for non-covalent interactions and basis set superposition error (abbreviated as B3LYP-MM). Results obtained with our new correction scheme were directly compared to benchmark results obtained with B3LYP-D3(1) and M06-2X(2) (two popular density functions designed specifically to accurately model non-covalent interactions). For non-covalent complexes dominated by dispersion or dipole-dipole interactions all three tested methods give accurate results with the medium size aug-cc-pVDZ(3-6) basis set with MUE's of 0.27 (B3LYP-MM), 0.32 (B3LYP-D3) and 0.47 kcal/mol (M06-2X) (with explicit counterpoise corrections). These results validate both B3LYP-D3 and M06-2X for interactions of this type using a much larger data set than was presented in prior work. However, our new dispersion correction scheme shows some clear advantages for dispersion and dipole-dipole dominated complexes with the small LACVP* basis set, which is very popular in use due to its low associated computational cost: The MUE for B3LYP-MM with the LACVP* basis set for this subset of complexes (without explicit counterpoise corrections) is only 0.28 kcal/mol, compared to 0.65 kcal/mol for M06-2X or 1.16 kcal/mol for B3LYP-D3. Additionally, our new correction scheme also shows major improvements in accuracy for hydrogen-bonded systems and for systems involving ionic interactions, for example cation-π interactions. Compared to B3LYP-D3 and M06-2X, we also find that our new B3LYP-MM correction scheme gives results of higher or equal accuracy for a large dataset of conformer energies of di- and tripeptides, sugars, and cysteine.     

Vibrational energies of PH3 calculated variationally at the complete basis set limit

The potential energy surface for the electronic ground state of PH(3) was calculated at the CCSD(T) level using aug-cc-pV(Q+d)Z and aug-cc-pVQZ basis sets for P and H, respectively, with scalar relativistic corrections included. A parametrized function was fitted through these ab initio points, and one parameter of this function was empirically adjusted. This analytical PES was employed in variational calculations of vibrational energies with the newly developed program TROVE. The convergence of the calculated vibrational energies with increasing vibrational basis set size was improved by means of an extrapolation scheme analogous to the complete basis set limit schemes used in ab initio electronic structure calculations. The resulting theoretical energy values are in excellent agreement with the available experimentally derived values.     

Extrapolation of electron correlation energies to finite and complete basis set targets

The electron correlation energy of two-electron atoms is known to converge asymptotically as approximately (L+1)(-3) to the complete basis set limit, where L is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence approximately X(-3) with the cardinal number X of correlation-consistent basis sets cc-pVXZ for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of X by defining a trial function X(-beta) that for an effective exponent beta=beta(eff)(X,X+1,X+N) provides the correct energy E(X+N), when extrapolating from results for two smaller basis sets, E(X) and E(X+1). This analysis is first applied to "model" expansions available from analytical theory, and then to a large body of finite basis set results (X=D,T,Q,5,6) for 105 molecules containing H, C, N, O, and F, complemented by a smaller set of 14 molecules for which accurate complete basis set limits are available from MP2-R12 and CCSD-R12 calculations. beta(eff) is generally found to vary monotonically with the target of extrapolation, X+N, making results for large but finite basis sets a useful addition to the limited number of cases where complete basis set limits are available. Significant differences in effective convergence behavior are observed between MP2 and CCSD (valence) correlation energies, between hydrogen-rich and hydrogen-free molecules, and, for He, between partial-wave expansions and correlation-consistent basis sets. Deviations from asymptotic convergence behavior tend to get smaller as X increases, but not always monotonically, and are still quite noticeable even for X=5. Finally, correlation contributions to atomization energies (rather than total energies) exhibit a much larger variation of effective convergence behavior, and extrapolations from small basis sets are found to be particularly erratic for molecules containing several electronegative atoms. Observed effects are discussed in the light of results known from analytical theory. A carefully calibrated protocol for extrapolations to the complete basis set limit is presented, based on a single "optimal" exponent beta(opt)(X,X+1,infinity) for the entire set of molecules, and compared to similar approaches reported in the literature.     

Estimated MP2 and CCSD(T) interaction energies of n-alkane dimers at the basis set limit: comparison of the methods of Helgaker et al. and Feller

The MP2 (the second-order M?ller-Plesset calculation) and CCSD(T) (coupled cluster calculation with single and double substitutions with noniterative triple excitations) interaction energies of all-trans n-alkane dimers were calculated using Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation consistent basis sets. The estimated MP2 interaction energies of methane, ethane, and propane dimers at the basis set limit [EMP2(limit)] by the method of Helgaker et al. [J. Chem. Phys. 106, 9639 (1997)] from the MP2/aug-cc-pVXZ (X=D and T) level interaction energies are very close to those estimated from the MP2/aug-cc-pVXZ (X=T and Q) level interaction energies. The estimated EMP2(limit) values of n-butane to n-heptane dimers from the MP2/cc-pVXZ (X=D and T) level interaction energies are very close to those from the MP2/aug-cc-pVXZ (X=D and T) ones. The EMP2(limit) values estimated by Feller's [J. Chem. Phys. 96, 6104 (1992)] method from the MP2/cc-pVXZ (X=D, T, and Q) level interaction energies are close to those estimated by the method of Helgaker et al. from the MP2/cc-pVXZ (X=T and Q) ones. The estimated EMP2(limit) values by the method of Helgaker et al. using the aug-cc-pVXZ (X=D and T) are close to these values. The estimated EMP2(limit) of the methane, ethane, propane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, n-nonane, and n-decane dimers by the method of Helgaker et al. are -0.48, -1.35, -2.08, -2.97, -3.92, -4.91, -5.96, -6.68, -7.75, and -8.75 kcal/mol, respectively. Effects of electron correlation beyond MP2 are not large. The estimated CCSD(T) interaction energies of the methane, ethane, propane, and n-butane dimers at the basis set limit by the method of Helgaker et al. (-0.41, -1.22, -1.87, and -2.74 kcal/mol, respectively) from the CCSD(T)/cc-pVXZ (X=D and T) level interaction energies are close to the EMP2(limit) obtained using the same basis sets. The estimated EMP2(limit) values of the ten dimers were fitted to the form m0+m1X (X is 1 for methane, 2 for ethane, etc.). The obtained m0 and m1 (0.595 and -0.926 kcal/mol) show that the interactions between long n-alkane chains are significant. Analysis of basis set effects shows that cc-pVXZ (X=T, Q, or 5), aug-cc-pVXZ (X=D, T, Q, or 5) basis set, or 6-311G** basis set augmented with diffuse polarization function is necessary for quantitative evaluation of the interaction energies between n-alkane chains.     

On basis set superposition error corrected stabilization energies for large n-body clusters

In this contribution, we propose an approximate basis set superposition error (BSSE) correction scheme for the site-site function counterpoise and for the Valiron-Mayer function counterpoise correction of second order to account for the basis set superposition error in clusters with a large number of subunits. The accuracy of the proposed scheme has been investigated for a water cluster series at the CCSD(T), CCSD, MP2, and self-consistent field levels of theory using Dunning's correlation consistent basis sets. The BSSE corrected stabilization energies for a series of water clusters are presented. A study regarding the possible savings with respect to computational resources has been carried out as well as a monitoring of the basis set dependence of the approximate BSSE corrections.     

Effects of global orbital cutoff value and numerical basis set size on accuracies of theoretical atomization energies

Numerical basis sets are known for their rapid convergence in density functional theory calculations. The selections of global orbital cutoff values and numerical basis set sizes are important to the computational accuracies and efficiencies. In this study, the effects of global orbital cutoff values and numerical basis set sizes on the theoretical atomization energies (D ₀) were investigated using density functional theory with the generalized gradient approximation. Our results on the total energies of seven atoms and D ₀ of a set of 44 molecules demonstrate that the numerical orbital cutoff value should be larger than 6.5 Å to get the converged energetic properties. Through comparing the D ₀ of these 44 molecules obtained by using four kinds of different numerical basis sets, DN, DND, DNP, and TNP, it demonstrates that the DNP basis set is good enough to predict accurate D ₀ with affordable computational cost.     

Basis set convergence of post-CCSD contributions to molecular atomization energies

Basis set convergence of correlation effects on molecular atomization energies beyond the coupled cluster with singles and doubles (CCSD) approximation has been studied near the one-particle basis set limit. Quasiperturbative connected triple excitations, (T), converge more rapidly than L(-3) (where L is the highest angular momentum represented in the basis set), while higher-order connected triples, T3-(T), converge more slowly--empirically, proportional to L(-5/2). Quasiperturbative connected quadruple excitations, (Q), converge smoothly as proportional to L(-3) starting with the cc-pVTZ basis set, while the cc-pVDZ basis set causes overshooting of the contribution in highly polar systems. Higher-order connected quadruples display only weak, but somewhat erratic, basis set dependence. Connected quintuple excitations converge very rapidly with the basis set, to the point where even an unpolarized double-zeta basis set yields useful numbers. In cases where fully iterative coupled cluster up to connected quintuples (CCSDTQ5) calculations are not an option, CCSDTQ(5) (i.e., coupled cluster up to connected quadruples plus a quasiperturbative connected quintuples correction) cannot be relied upon in the presence of significant nondynamical correlation, whereas CCSDTQ(5)(Lambda) represents a viable alternative. Connected quadruples corrections to the core-valence contribution are thermochemically significant in some systems. We propose an additional variant of W4 theory [A. Karton et al., J. Chem. Phys. 125, 144108 (2006)], denoted W4.4 theory, which is shown to yield a rms deviation from experimental atomization energies (active thermochemical tables, ATcT) of only 0.05 kcal/mol for systems for which ATcT values are available. We conclude that "3sigma 相似文献   

Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 Å), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.     

Spectroscopic investigations on AsH(XΣ) radical using CCSD(T) theory in combination with correlation-consistent quintuple basis set

The equilibrium internuclear separations, harmonic frequencies and potential energy curves of the AsH(X³Σ⁻) radical have been calculated using the coupled-cluster singles–doubles–approximate-triples [CCSD(T)] theory in combination with the series of correlation-consistent basis sets in the valence range. The potential energy curves are all fitted to the Murrell–Sorbie function, which are used to reproduce the spectroscopic parameters such as D_e, ω_eχ_e, α_e, B_e and D₀. The present D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e obtained at the cc-pV5Z basis set are of 2.8004 eV, 2.9351 eV, 0.15137 nm, 2194.341 cm⁻¹, 43.1235 cm⁻¹, 0.2031 cm⁻¹ and 7.3980 cm⁻¹, respectively, which almost perfectly conform to the measurements. With the potential obtained at the UCCSD(T)/cc-pV5Z level of theory, a total of 18 vibrational states is predicted when the rotational quantum number J is set to equal zero (J = 0) by numerically solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0 for the first time, which are in excellent agreement with the experiments.     

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.