MP2 Complete Basis Set Limit Research Articles

Benchmark Study of the Interaction Energy for an (H2O)16 Cluster: Quantum Monte Carlo and Complete Basis Set Limit MP2 Results

The quantum Monte Carlo method is used to calculate the binding energy of an (H2O)16 cluster that has been the subject of several recent theoretical studies. The resulting interaction energy, -165.1(8) kcal/mol, is very close to our MP2 complete basis set limit interaction energy of -164.1 kcal/mol. Comparison of these results with those for the one-, two-, three-, and four-body interaction energies leads us to conclude that the five- and higher-body interactions are attractive, contributing over 2 kcal/mol to the net interaction energy of this (H2O)16 isomer.

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH2 O, H2 O, HF, F2 , HCN, SiH4 and H2 S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS-2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization-consistent pcS-n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS-2 and aug-cc-pVTZ-J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS-2, MP2/pcS-2 and DFT/CBS calculations with pcS-n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts.

Calculation of boron-isotope fractionation between B(OH)3(aq) and

Abstract Density functional and correlated molecular orbital calculations (MP2) are carried out on B(OH) 3 · n H 2 O clusters ( n = 0, 6, 32), and B ( OH ) 4 - · n H 2 O ( n = 0, 8, 11, 32) to estimate the equilibrium distribution of 10 B and 11 B isotopes between boric acid and borate in aqueous solution. For the large 32-water clusters, multiple conformations are generated from ab initio molecular dynamics simulations to account for the effect of solvent fluctuations on the isotopic fractionation. We provide an extrapolated value of the equilibrium constant α 34 for the isotope exchange reaction 10 B(OH) 3 (aq) + 11 B ( OH ) 4 - (aq) = 11 B(OH) 3 (aq) + 11 B ( OH ) 4 - (aq) of 1.026–1.028 near the MP2 complete basis set limit with 32 explicit waters of solvation. With some exchange-correlation functionals we find potentially important contributions from a tetrahedral neutral B(OH) 3 ·H 2 O Lewis acid–base complex. The extrapolations presented here suggest that DFT calculations give a value for 10 3 ln α 34 about 15% higher than the MP2 calculations.

CCSD(T) Complete Basis Set Limit Relative Energies for Low-Lying Water Hexamer Structures

MP2 and CCSD(T) complete basis set (CBS) limit relative electronic energies (DeltaE(e)) have been determined for eight low-lying structures of the water hexamer by combining explicitly correlated MP2-R12 computations with higher-order correlation corrections from CCSD(T) calculations. Higher-order correlation effects are quite substantial and increase DeltaE(e) by at least +0.19 kcal mol(-1) and as much as +0.59 kcal mol(-1). The effects from zero-point vibrational energy (ZPVE) have been assessed from unscaled harmonic vibrational frequencies computed at the MP2 level with a correlation consistent triple-zeta basis set (cc-pVTZ for H and aug-cc-pVTZ for O). ZPVE effects are even more significant than higher-order correlation effects and are uniformly negative, decreasing the relative energies by -0.16 kcal mol(-1) to -1.61 kcal mol(-1). Although it has been widely accepted that the cage becomes the lowest-energy structure after ZPVE effects are included [Nature 1996, 381, 501-503], the prism is consistently the most stable structure in this work, lying 0.06 kcal mol(-1) below the nearly isoenergetic cage isomer at the electronic MP2 CBS limit, 0.25 kcal mol(-1) below at the electronic CCSD(T) CBS limit, and 0.09 kcal mol(-1) below at the harmonic ZPVE corrected CCSD(T) CBS limit. Moreover, application of any uniform scaling factor less than unity to correct for anharmonicity further stabilizes the prism and increases the relative energies of the other structures.

Basis-set convergence of nuclear magnetic shielding constants in molecular HF and MP2 calculations

Recently, segmented contracted basis sets of double, triple, quadruple and quintuple zeta valence quality plus polarization functions (XZP, X = D, T, Q and 5) for the atoms from H to Ar were presented by Jorge et al. We report a systematic study of basis sets required to obtain accurate values for nuclear magnetic shielding tensors for 20 molecules at their experimental equilibrium geometries. Two methods were examined: Hartree–Fock (HF) and second-order Møller–Plesset perturbation theory (MP2). Gauge-invariant atomic orbitals were used to guarantee origin-independent values of magnetic properties. By direct calculations or by fitting the directly calculated values through two extrapolation schemes, estimates of the HF and MP2 complete basis-set limit have been obtained. Comparison with experiment and benchmark results reported in the literature is made.

Geometrical and Electronic Structure Variability of the Sugar−phosphate Backbone in Nucleic Acids

The anionic sugar-phosphate backbone of nucleic acids substantially contributes to their structural flexibility. To model nucleic acid structure and dynamics correctly, the potentially sampled substates of the sugar-phosphate backbone must be properly described. However, because of the complexity of the electronic distribution in the nucleic acid backbone, its representation by classical force fields is very challenging. In this work, the three-dimensional potential energy surfaces with two independent variables corresponding to rotations around the alpha and gamma backbone torsions are studied by means of high-level ab initio methods (B3LYP/6-31+G*, MP2/6-31+G*, and MP2 complete basis set limit levels). The ability of the AMBER ff99 [Wang, J. M.; Cieplak, P.; Kollman, P. A. J. Comput. Chem. 2000, 21, 1049-1074] and parmbsc0 [Perez, A.; Marchan, I.; Svozil, D.; Sponer, J.; Cheatham, T. E.; Laughten, C. A.; Orozco, M. Biophys. J. 2007, 92, 3817-3829] force fields to describe the various alpha/gamma conformations of the DNA backbone accurately is assessed by comparing the results with those of ab initio quantum chemical calculations. Two model systems differing in structural complexity were used to describe the alpha/gamma energetics. The simpler one, SPM, consisting of a sugar and methyl group linked through a phosphodiester bond was used to determine higher-order correlation effects covered by the CCSD(T) method. The second, more complex model system, SPSOM, includes two deoxyribose residues (without the bases) connected via a phosphodiester bond. It has been shown by means of a natural bond orbital analysis that the SPSOM model provides a more realistic representation of the hyperconjugation network along the C5'-O5'-P-O3'-C3' linkage. However, we have also shown that quantum mechanical investigations of this model system are nontrivial because of the complexity of the SPSOM conformational space. A comparison of the ab initio data with the ff99 potential energy surface clearly reveals an incorrect ff99 force-field description in the regions where the gamma torsion is in the trans conformation. An explanation is proposed for why the alpha/gamma flips are eliminated so successfully when the parmbsc0 force-field modification is used.

The Limitations of Certain Density Functionals in Modeling Neutral Water Clusters

We have used density functional theory (DFT) with four different functionals and with basis sets optimized for studying water clusters to calculate the structures and energies for selected water dimer, trimer, tetramer, pentamer, hexamer, and octamer structures. We compare the results to the CBS‐APNO and G3 model chemistry methods, and with highly accurate MP2 complete basis set limit energies. We find that while all the DFT methods capture the minimum energy structures for tetramers and pentamers, and reproduce the interaction energies well, they fail to find certain structures where London dispersion forces are critical to the interaction. Specifically structures that are not composed of cyclic rings, such as the tetramer pyramid and the pentamer cage structures, are not minima on the DFT potential energy hypersurfaces.

Complete basis set limit ofAb initiobinding energies and geometrical parameters for various typical types of complexes

Using basis-set extrapolation schemes for a given data set, we evaluated the binding energies and geometries at the complete basis set (CBS) limit at the levels of the second order Møller-Plesset perturbation theory (MP2) and the coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)]. The systems include the hydrogen bonding (water dimer), aromatic interaction (benzene dimer), pi-H interaction (benzene-water), cation-water, anion-water, pi-cation interaction (cation-benzene), and pi-anion interaction (anion-triazine). One extrapolation method is to exploit both BSSE-corrected and BSSE-uncorrected binding energies for the aug-cc-pVNZ (N = 2, 3, 4, ...) basis set in consideration that both binding energies give the same CBS limit (CBS(B)). Another CBS limit (CBS(C)) is to use the commonly known extrapolation approach to exploit that the electron correlation energy is proportional to N(-3). Since both methods are complementary, they are useful for estimating the errors and trend of the asymptotic values. There is no significant difference between both methods. Overall, the values of CBS(C) are found to be robust because of their consistency. However, for small N (in particular, for N = 2, 3), CBS(N)(B) is found to be slightly better for water-water interactions and cation-water and cation-benzene interactions, whereas CBS(N)(C) is found to be more reliable for bezene-water and anion-water interactions. We also note that the MP2 CBS limit value based on N = 2 and 3 combined with the difference between CCSD(T) and MP2 at N = 2 would be exploited to obtain a CCSD(T)/CBS value for aromatic-aromatic interactions and anion-pi interactions, but not for cationic complexes.

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.

An ab Initio Benchmark Study of Hydrogen Bonded Formamide Dimers

The five singly and doubly hydrogen bonded dimers of formamide are calculated at the correlated level by using resolution of identity Møller-Plesset second-order perturbation theory (RIMP2) and the coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] method. All structures are optimized with the Dunning aug-cc-pVTZ and aug-cc-pVQZ basis sets. The binding energies are extrapolated to the complete basis set (CBS) limit by using the aug-cc-pVXZ (X = D, T, Q) basis set series. The effect of extending the basis set to aug-cc-pV5Z on the geometries and binding energies is studied for the centrosymmetric doubly N-H...O bonded dimer FA1 and the doubly C-H...O bonded dimer FA5. The MP2 CBS limits range from -5.19 kcal/mol for FA5 to -14.80 kcal/mol for the FA1 dimer. The DeltaCCSD(T) corrections to the MP2 CBS limit binding energies calculated with the 6-31+G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are mutually consistent to within < or =0.03 kcal/mol. The DeltaCCSD(T) correction increases the binding energy of the C-H...O bonded FA5 dimer by 0.4 kcal/mol or approximately 9% over the distance range +/-0.5 Angstrom relative to the potential minimum. This implies that the ubiquitous long-range C-H...O interactions in proteins are stronger than hitherto calculated.

Potential Energy Surface of the Cytosine Dimer: MP2 Complete Basis Set Limit Interaction Energies, CCSD(T) Correction Term, and Comparison with the AMBER Force Field

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. 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. Extrapolation to the CBS limit is essential in all parts of the potential energy surface and affects mainly the absolute MP2 stabilization energy. The effect on the relative stability is smaller but not negligible. The CCSD(T) correction term is for stacked structures with large overlaps of the monomers substantially repulsive but not uniform. Thus, when comparing the final estimate (abbreviated as CBS(T)) with previously used medium-level MP2/6-31G*(0.25) data, the CCSD(T) correction partially compensates for the enhanced absolute MP2 CBS stabilization but further increases the relative ...

A Journey from Generalized Valence Bond Theory to the Full CI Complete Basis Set Limit

A qualitative examination of generalized valence bond pair correlation energies leads us to a quantitative relationship (interference effect) between basis set truncation errors in MP2 energies and basis set truncation errors in CCSD(T) energies. Thus, a knowledge of the MP2 complete basis set limit can be combined (for example) with CCSD(T)/[5s4p3d2f/4s3p2d] calculations to estimate the CCSD(T) limit to within ±0.46 kcal/mol. Explicit MP2−R12 calculations are then compared to three extrapolation schemes employing cc-pVnZ correlation consistent basis sets in an attempt to find an inexpensive route to the required MP2 limit. The first employs the N-1 asymptotic convergence of pair natural orbital (PNO) expansions to extrapolate to the complete basis set (CBS2) limit. The second employs (&#x1d4c1; + 1/2)-3 extrapolations of more than one MP2/cc-pVnZ calculation to estimate this MP2 limit. The third method combines the PNO extrapolations with a linear and thus size-consistent (&#x1d4c1; + 1/2)-3 extrapolation. This linear (...