Large Basis Set Superposition Errors Research Articles

Predicting lattice energy and structure of molecular crystals by first-principles method: Role of dispersive interactions

The accurate calculation of lattice energy and structure of molecular crystals represent a test of the ability of first-principles periodic density functional method to model the relatively weak intermolecular interactions found in molecular crystals. The weak intermolecular dispersion interactions need to be considered for the accurate prediction of crystal structure and lattice energy of molecular crystals. In this paper, we report the calculation of lattice energies and structure of a set of eight molecular crystals at the ab initio level of theory. Hartree–Fock and density functional theory with and without dispersion correction potential were employed. Our results clearly show with application of triple zeta polarization (TZP) basis set, the lattice parameters obtained using B3LYP functional with dispersion interactions give better agreement with the experimental results. On the other hand, the lattice energies obtained using B3LYP-D/TZP method is severely underestimated. The lattice energies calculated at B3LYP-D/6-31G(d,p) level of theory are in close agreement with the corresponding experimental results because of smaller size of basis sets provide large basis set superposition errors which compensate the missing dispersion energies.

Basis set effects on Cu(I) coordination in Cu-ZSM-5: a computational study

DFT calculations on the coordination of Cu+ to the framework oxygen atoms of Al-substituted ZSM-5 were performed by using combinations of different basis sets in order to investigate the dependence of the results on the adopted computational level. With low-end basis sets, a large basis set superposition error (BSSE) favors the coordination of Cu+ to three to four oxygen atoms of the framework, only two of which belong to the AlO4 tetrahedron corresponding to the investigated T-site. More extended basis sets considerably lower the BSSE and favor the coordination of Cu+ to only two oxygen atoms of the AlO4 tetrahedron. Upon interaction with NO, the Cu+ ion is always coordinated by two oxygen atoms of the AlO4 tetrahedron, independently of the basis set adopted and of the coordination number before NO adsorption. The shift from three- to twofold coordination caused by the Cu+–NO interaction requires a deformation energy that lowers the final adsorption energy. Such an effect is relevant with low-end basis sets, whereas it is substantially absent with more extended basis sets, which favor the twofold coordination of Cu+ even before NO adsorption. As a result, high-end basis sets increase the NO interaction energy with respect to that calculated by low-end basis sets, in agreement with experiments and suggesting a possible re-interpretation of the catalytic properties of the investigated sites. Provided suitable scale factors are employed, the N–O stretching frequencies of adsorbed nitrogen oxide calculated by sufficiently extended basis sets turned out in fair agreement with experimental findings.

Communication: Efficient counterpoise corrections by a perturbative approach

We investigate the use of Hartree-Fock and density functional perturbative corrections for estimating the counterpoise correction (CPC) for interaction energies at the self-consistent field level. We test our approach using several popular basis sets on the S22 set of weakly bound systems, which can exhibit large basis set superposition errors. Our results show that the perturbative approaches typically recover over 95% of the CPC and can be up to twelve times faster to compute than the conventional methods and therefore provide an attractive alternative to calculating CPCs in the conventional way.

Gas-Phase Folding of a Two-Residue Model Peptide Chain: On the Importance of an Interplay between Experiment and Theory

In order to assess the ability of theory to describe properly the dispersive interactions that are ubiquitous in peptide and protein systems, an isolated short peptide chain has been studied using both gas-phase laser spectroscopy and quantum chemistry. The experimentally observed coexistence of an extended form and a folded form in the supersonic expansion was found to result from comparable Gibbs free energies for the two species under the high-temperature conditions (< or = 320 K) resulting from the laser desorption technique used to vaporize the molecules. These data have been compared to results obtained using a series of quantum chemistry methods, including DFT, DFT-D, and post-Hartree-Fock methods, which give rise to a wide range of relative stabilities predicted for these two forms. The experimental observation was best reproduced by an empirically dispersion-corrected functional (B97-D) and a hybrid functional with a significant Hartree-Fock exchange term (M06-2X). In contrast, the popular post-Hartree-Fock method MP2, which is often used for benchmarking these systems, had to be discarded because of a very large basis-set superposition error. The applicability of the atomic counterpoise correction (ACP) is also discussed. This work also introduces the mandatory theoretical examination of experimental abundances. DeltaH(0 K) predictions are clearly not sufficient for discussion of folding, as the conformation inversion temperature is crucial to the conformation determination and requires taking into account thermodynamical corrections (DeltaG) in order to computationally isolate the most stable conformation.

Correlation and basis set superposition effects on three body ion-water-water interactions

Ab initio SCF and second order Moller-Plesset electronic calculations using a point charge (PC) model as well as standard basis sets for the ions (Li+, Mg++) have been performed for several different water-water geometries and distances. The PC model yields acceptable ion-water potential curves. The ab initio curves calculated with and without Basis Set Superposition Error and electron correlation corrections as well as via a classical model are compared for various water dimer orientations. Certain geometries (particularly those appropriate to the interaction of hydrated ions) gave large Basis Set Superposition Errors and large correlation effects (˜20%) even with the large basis set (Clementi – (11,7,1/6,1) [4,3,1/2,1]) used. For attractive potentials this lead to some cancellation but it is compounded for repulsive curves. The classical model used was able to predict qualitative trends in most cases indicating the nonadditivity arises primarily from an inductive effect; however, geometries with strong hydrogen-hydrogen repulsions show an attractive three body potential at short distances which cannot be understood in terms of this classic model.

Effect of Basis Set Superposition Error on the MP2 Relative Energies of Gold Cluster Au6

We have studied the structures and stabilities of Au6 to explore the origin of the large discrepancy between relative energies obtained from the density functional theory (DFT) and ab initio correlated levels of theory. The MP2 methods significantly overestimate the stability of the non-planar isomer when the double-<TEX>$\zeta$</TEX> polarization quality of basis sets, such as LANL2DZ+1f and CEP31G+1f, are used. However, we show that such preference for the non-planar structure at the MP2 level mainly originates from the large basis set superposition error.

Basis Set Superposition Error Effects Cause the Apparent Nonexistence of the Ethene/Benzenium Ion Complex on the MP2 Potential Energy Surface

In a recent Letter (J. Phys. Chem. A 2008, 112, 6399) Kolboe and Svelle reported that the ethene/benzenium ion complex found by B3LYP transforms into an ethylbenzenium ion when MP2 with a large basis set is used. We find that the failure of MP2 to locate the ethene/benzenium ion complex is due to large basis set superposition errors.

Absolutely Local Excited Orbitals in the Higher Order Perturbation Expansion for the Molecular Interaction

Based on the locally projected molecular orbitals, the third and fourth order perturbation corrections for the molecular interaction within the single excitations are evaluated, and the calculated interaction energies are compared with the counterpoise (CP) corrected interaction energy of the Hartree-Fock level of theory. It is demonstrated that the third order calculation is a practical and powerful method to obtain the binding energy almost equal to the CP corrected energy. It requires only one more two-electron integral handling after the LP MO calculation, which is faster than a usual supermolecule HF calculation. For the perturbation expansion, the absolutely local excited orbitals are determined. For small basis sets, it is shown that the partial delocalization of the absolutely local excited orbitals is a compromizing technique to take into account the charge-transfer contribution without reintroducing a large basis set superposition error.

Insufficient description of dispersion in B3LYP and large basis set superposition errors in MP2 calculations can hide peptide conformers

B3LYP/6-31+G(d) and MP2/6-31+G(d) calculations predict markedly different structures for one Tyr–Gly conformer. Calculation of the energy profile for rotation around the glycine C α–N bond reveals one minimum in the B3LYP profile ( ϕ gly = 180°) and two in the MP2 profile (∼75° and 280°). Large intramolecular BSSE values are responsible for masking the 180°-minimum in the MP2 profile: approximate elimination of BSSE in the MP2 calculations – by (1) correction using BSSE values from complexes of phenol and N-formylglycine, (2) the application of local MP2, or (3) employing large basis sets (aug-cc-pVTZ/QZ) and density fitting – yields an unambiguous triple-well potential.

Intermolecular self-interaction energies of magic clusters MAu4 (M=Ti and Zr)

Two TiAu4 (or ZrAu4) clusters are known to bind to each other with unusually high (∼5–7eV) interaction energies at the Møller–Plesset second-order perturbation theory (MP2) level [T. K. Ghanty et al., J. Chem. Phys.120, 11363 (2004)]. Our MP2 calculations also show very high interaction energies of about 8eV for (TiAu4)2 and (ZrAu4)2. However, the strong MP2 bindings are found to be partly ascribable to large basis set superposition error (BSSE). The BSSE-corrected interaction energies are 4.63 and 4.25eV for (TiAu4)2 and (ZrAu4)2, respectively. We also found that there are Hartree–Fock wave function instabilities for the systems, implying that the restricted MP2 descriptions are potentially inadequate. High-level calculations are needed to draw clear conclusions.

Molecular Orbital Study of Crystalline p-Benzoquinone

The interaction energies for the crystal of p-benzoquinone and aggregates from two to seven molecules have been calculated using Hartree−Fock and density functional theory methods with different basis sets at the experimental (crystallographic) geometries. After correction for basis set superposition error, all methods predict similar interaction energies. Periodic calculations using CRYSTAL92 and CRYSTAL 95 at the HF/6-21G** level produced values of −5.30 kcal/mol for the interaction energy of a two-dimensional slab. The calculation of the crystalline interaction energy is hampered by the inability of HF calculations to reproduce stacking interactions and the large basis set superposition errors associated with the HF/6-21G** molecular orbital method. The cooperative contributions to the interaction energies calculated for the aggregates imply that roughly half the crystalline interaction energy is due to cooperativity.

Intermolecular interaction potential of the carbon dioxide dimer

The energy profile of the lowest energy path connecting the slipped parallel (C2h) and T-shaped (C2v) dimers of carbon dioxide was investigated using a reasonably large 6-311+G(2df) basis set with the MP2 level electron correlation correction and with the counterpoise correction. There was no inversion barrier and the T-shaped dimer was a transition state connecting the two slipped parallel dimers. The calculated interaction energies of the two dimers (−1.290 and −1.072 kcal/mol) were larger than those reported previously. The calculated energy difference of the two dimers (0.218 kcal/mol) was also larger than the previous values (less than 0.1 kcal/mol). The effects of basis set, electron correlation, and basis set superposition error were studied in detail. The second-order Mo/ller–Plesset (MP2) interaction energies of the two dimers were close to the coupled cluster calculations using single and double substitutions including noniteratively triple excitations [CCSD(T)] ones. The choice of the basis set greatly affected the calculated interaction energies. Small basis sets underestimated the attractive interaction energies. Diffuse polarization functions were essential to evaluate the attractive interaction. The calculated MP2 interaction energies of the two dimers with the counterpoise correction increased by the augmentation of the diffuse polarization functions to the 6-311G* basis set. These values were close to the estimated MP2 interaction energies at the complete basis set (−1.362 and −1.140 kcal/mol). The 6-311+G(2df) basis set was reasonably large to evaluate the attractive interactions. Although the basis set augmented with diffuse polarization functions had large basis set superposition error (BSSE), the calculated interaction energies with the counterpoise correction were close to those calculated with the nearly BSSE free cc-pV5Z and aug-cc-pVQZ basis sets and to the expected values at the complete basis set.

On the energetics of the dimerization of boron trifluoride

The energetic pathways for the formation of a number of dimers of boron trifluoride, of symmetry D 2 h , C 2 h and C s , have been followed by means of a series of molecular orbital calculations at the ab initio level. It is concluded that the large amount of energy required to distort a boron trifluoride monomer, by lengthening one of the BF bonds or by changing the values of the FBF angles of the monomer, in order to react with a similarly distorted monomer to form either of the D 2 h structures, mitigates against these structures being the preferred configuration. In contrast, the distortion of a monomer unit to form the non-planar cyclic C 2 h species, or the bent or linear C s dimers, is minimal, and the energy recovered on the reaction of two such distorted monomers is sufficient in these cases to cause the process to be exothermic overall. In the case of the planar C 2 h dimer, while the balance of the distortion energy and the recombination energy of the monomers leads to an exothermic process overall, the large basis set superposition error contribution more than compensates for this, resulting in an endothermic reaction pathway.

An extended basis set ab initio study of Li+(H2O)n, n=1–6

The structures, binding energies, and enthalpies of small molecular clusters incorporating a single lithium cation and up through six waters have been determined with extended Gaussian basis sets using Hartree–Fock and post-Hartree–Fock methods. The resulting properties are analyzed with respect to both basis set completeness and degree of correlation recovery, including core–core and core–valence effects. Although the lithium–water interaction is largely electrostatic in nature, small basis sets, lacking in polarization and near-valence diffuse functions, drastically overestimate the strength of the bond (by 20 kcal/mol or more) and underestimate the Li+...O distance by up to 0.1 Å. Their poor performance is attributable to inherent errors in describing the electric moments and polarizability of water and to large basis set superposition errors. Thus, the accuracy with which the fundamental lithium–water interaction could be modeled was primarily dependent on the quality of the Gaussian basis set and not upon the level of correlation recovery. Basis set enlargement and correlation effects both tend to reduce the strength of the Li+(H2O) bond, but produce corrections of opposite sign for the Li+...O bond length. Although correlation effects play a minor role in describing the lithium–water interaction, as the size of the cluster increases and the number of waters involved in multiple hydrogen bonds grows, correlation recovery can become significant.

Basis sets for molecular interactions. 2. Application to H3NHF, H3NHOH, H2OHF, (NH3)2, and H3CHOH2

AbstractModifications of the standard 6‐31G** basis set as recommended in the accompanying paper are found to markedly lower the basis set superposition error (BSSE) in the title complexes, in contrast to enlargement to a triple‐ζ scheme or by addition of a diffuse sp shell or a second set of d‐functions without prior optimization, all of which lead to BSSE increase. After appropriate correction for correlation and superposition effects, all basis sets (with the exception of the standard 6‐31G** and 6‐311G** with their very large BSSE) predict the cyclic geometry of NH3 dimer to be more stable than the linear arrangement. Correlation and BSSE can shift the equilibrium intermolecular distance in H3CH‐OH2 by up to 0.4 Å. Failure to correct for superposition error leads to a drastic exaggeration of both the SCF and MP2 components of the interaction energy in this complex. Much better estimates are furnished by our recommended basis sets with their smaller superposition errors.

Intermolecular interactions using small basis sets: Perturbation theory calculations avoiding basis set superposition error

As preliminary numerical examples, we report some calculations on intermolecular interactions using a new method of perturbation theory introduced recently. The He…He, LiH…LiH and water—water interactions are studied with small basis sets. The essential feature of the method is that it eliminates basis set superposition errors without any a posteriori collection. Within the range of applicability of the perturbational treatment, the results may be superior to standard vibrational calculations which suffer from large basis set superposition errors.