Basis sets, diffuse superposition error

Ethynyllithium is one of the very first organometallic compounds to be computed at a reasonable ab initio level. This calculation involved Slater functions rather than Gaussian-lype orbitals because ethynyllithium is a linear molecule and the integrals for Slater functions on a line all have analytical solutions. The compound was found to be highly ionic, as expected. The formally sp-hybrid character of the carbon orbital of the C-Li bond also results in a bond length about 0.1 A shorter than in methyllithium. The electron density function of ethynyllithium was used to study the effect of basis set on superposition errors diffuse functions were found to be more important than d-orbitals in this regard. ... 

Diffuse functions are those functions with small Gaussian exponents, thus describing the wave function far from the nucleus. It is common to add additional diffuse functions to a basis. The most frequent reason for doing this is to describe orbitals with a large spatial extent, such as the HOMO of an anion or Rydberg orbitals. Adding diffuse functions can also result in a greater tendency to develop basis set superposition error (BSSE), as described later in this chapter. 

As it is well known, the Basis Set Superposition Error (BSSE) affects calculations involving hydrogen bonds [1] and, more generally, intermolecular interaction investigations [2,3], This issue of consistency, as first pointed out in 1968 [4], arises from the use of an incomplete basis set but it does not correspond to the basis set truncation error and it is due to the use of diffuse functions on neighbouring interacting particles, which leads to a non physical contribution to the interaction energy within the complex. 

H-bonded systems may require additional diffuse or polarization functions. For example, the 6-311++G(d,p) basis set had been found to be suitable for H-bonded systems [78-81], It may be necessary to include Basis Set Superposition Errors (BSSE) [82] and Zero-Point-Energy (ZPE) corrections in evaluating the relative stabilities. Such corrections are often of the same magnitude as the energy differences among the dominant conformers. Moreover, the relative conformer energies may also differ noticeably with the basis sets used. All these factors will affect the Boltzmann factors predicted for different conformers and therefore the appearance of the population weighted VA and VCD spectra. Thus, an appropriate selection of DFT functionals and basis sets is very important for VCD simulations. A scale factor of 0.97-0.98 is usually applied to the calculated harmonic frequencies to account for the fact that the observed frequencies arise from an anharmonic force field instead of a harmonic one. A Lorentzian line shape is typically used in simulations of VA and VCD spectra. The full-width at half maximum (FWHM) used in the spectral simulation is usually based on the experimental VA line widths. 

The geometries of the isolated bases and base pairs were optimized at the HF/6-31G level and were taken from our paper [11] the non-planarity of bases [38] and base pairs [39] was taken into consideration. The interaction energies [11] of base pairs were constructed as the sum of the HF/6-31G (0.25] interaction energy, MP2/6-31G (0.25) correlation interaction energy and respective deformation energy of bases determined at the HF/6-31G level. Abbreviation 6-3IG (0.25) means that the standard polarization functions in the 6-31G basis set were replaced by more diffuse ones, with an exponent of 0.25. The HF and MP2 interaction energies were corrected for the basis set superposition error. The harmonic vibrational frequencies were determined at the HF/6-31G level [27] and no scaling factors were utilized. 

Alagona G, Ghio C (1990) The effect of diffuse functions on minimal basis set superposition errors for Id-bonded dimers. J Comput Chem 11 930-942... 

The basis sets used in the CEPA calculations were large. For example with H2HF, the F atom basis was a (10s,6p) contracted to [6s,4p] augmented with extra diffuse s and p orbitals, and 3d and 4f orbitals optimised to produce the dipole and quadrupole polarisabilities of HF. The results reported here for ArHCN did not include f orbitals in the basis set, although the sensitivity of the results to these functions is currently being examined. The CEPA potential for ArOH was calculated by Esposti and Wemer. In all cases, basis set superposition errors were accounted for. 

The choice of the appropriate level of approximation usually results from a compromise between accuracy and availability in CPU. In fact, to avoid excessive computational time, the limit consisting in the use of a complete basis set is seldom reached [15]. However, the overlap of incomplete basis sets between two neighboring atoms leads to the basis set superposition error (BSSE) [16], thus resulting in a lowering of the energy. The extent of this mathematical artifact actually depends on the level of approximation and the computed property. Validation of calculations is thus a very important issue. The use of an inappropriate basis set can actually lead to important discrepancies with experimental data. For instance, if the studied system contains an anion, diffuse functions must be added to the basis set in order to account for the occurrence of longer range interactions [17]. 

An ionic model for methyllithium divides the molecule into two closed shells in juxtaposition. This aspect probably accounts for the fact that even relatively small basis sets give a good account of the structure. High ionic character, however, results in an imbalance in the usual computations. As mentioned before, lithium, with only a small valence density, is nevertheless usually given the same number of basis functions as other first-row atoms for which these functions must treat much greater electron density that is, the electron density near these first-row atoms will tend to use diffuse parts of mathematical functions centered on lithium to aid in their description. This type of basis set superposition error can occur whenever an electron poor-function rich atom is near an electron rich-function poor atom, a description that fits polar organometallic bonds generally. 

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