Augmented basis set

Basis sets can be extended indefinitely. The highest MOs in anions and weakly bound lone pairs, for instance, are very diffuse maybe more so than the most diffuse basis functions in a spht valence basis set. In this case, extra diffuse functions must be added to give a diffuse augmented basis set. An early example of such a basis set is 6-31+G [26]. Basis sets may also be split more than once and have many sets of polarization functions. 

A reliable calculation of polarizabilities requires an adequate description of the outer part of the electron density. For this reason Kassimi and Lin [98JPC(A)9906] used augmented basis sets of triple- quality to study polarizabilities and dipole moments of thiazoles and thiadiazoles. They expect their results to be reliable within 5%. In addition, the authors provide MP2/6-31G geometries for most of their structures. Hyperpolarizabilities for substituted thiazoles obtained from calculations at lower levels are also provided [99MI2]. 

Let us now consider the errors in the CC3 S( — 2) Cauchy moment (the static polarizability). From the monotonic convergence of the CCSD doubly augmented basis-set calculations of S( — 2) in Table 1 it appears that the difference between the 5Z and 6Z results should give a good estimate of the CCSD basis-set error at the 6Z level. CC3/d-aug-pV5Z 5 ( —2) Cauchy moment is 2.670 a.u. Using the... 

Diffuse augmented basis sets were also developed for both the NR and DK cases by simple even tempered extensions. Valence electrons correlated CCSD(T) dipole polarizabilities calculated with the inclusion of DK scalar relativity are 35.08 and 35.07 a.u. for aug-cc-pVQZ-DK and aug-cc-pV5Z-DK, respectively. These values are about 0.3 a.u. larger than the PP values and therefore somewhat further away from experiment. 

Efficient Diffuse Function-Augmented Basis Sets for Anion Calculations. III. The 3-21+G Basis Set for First-Row Elements, Lithium to Fluorine. 

Overall, it seems that - similar to the calculation of hyperpolarizabilities -(doubly) augmented basis sets of at least triple- or better quadruple- quality are required to obtain reasonable results, as the use of non-augmented basis sets might even lead to qualitatively wrong results, i.e., a wrong sign of / (w). Eor N,... 

In linear variational problems, one way of satisfying Hurley s conditions is to make the basis set closed with respect to the differential operators d/dp. Such a basis set is in principle infinite. Practically, however, the Hellmann-Feynman theorem will be approximately satisfied if, for each significantly populated basis function x, its derivatives with respect to the orbital centers, X, x are included in the basis set (Pulay, 1969). The use of augmented basis sets in conjunction with the Hellmann-Feynman theorem was considered by Pulay (1969, 1977) but dismissed as expensive. Recently, Nakatsuji et al. (1982) have recommended such a procedure. However, an analysis of their procedure (Pulay, 1983c Nakatsuji et al., 1983) reveals that it is not competitive with the traditional gradient technique. Much of the error in the Hellmann-Feynman forces is due to core orbitals. Therefore, methods based on the Hellmann-Feynman theorem presumably work better for effective core... 

W.J. Hehre, R. Ditchfield, J.A. Pople, Self—Consistent Molecular Orbital Methods. Xll. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules, J. Chem. Phys. 56 (1972) 2257 T. Qark, J. Chandrasekhar, P.V.R. Schleyer, Efficient diffuse function-augmented basis sets for anion calculations. 111. The 3-21+G basis set for flrst-row elements, Li-F, J. Comput. Chem. 4 (1983) 294. 

T Clark, J Chandrasekhar, GW Spitznagel, PR Schleyer. Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21 + G basis set for first-row elements, lithium to fluorine. J Comput Chem 4 294-301, 1983. 

Kamada et al.165 166 have studied the effect of heavy atoms on the second hyperpolarizability of furan, thiophene, selenophene and tetrahydrofuran by a HF calculation with augmented basis sets. The heavier atoms are found to enhance the hyperpolarizability but -conjugation no longer contributes to its value in the presence of the heavier heteroatoms. 

It is interesting that the position of Zc is strongly dependent on the basis set. In the case of F if the cc-pVDZ basis, which lacks the dilfiise functions of the augmented basis sets, is used instead, then the singularity on the negative real axis seems to disappear [5,7,20]. Apparently, difliise functions are needed to describe the autoionization. 

Papajak, E., and Truhlar, D. G. (2011). Convergent partially augmented basis sets for post-Hartree-Fock calculations of molecular properties and reaction barrier heights, 7. Chem. Theory Comput. 7, pp. 10-18, doi 10,1021/ctl005533. 

For the monomer units one can directly compare values of 2nd hyperpolarizability obtained in a -electron approximation and ab inito methods with augmented basis set, 6-31 -l-+G(d,p). We carried out calculations for monomer units of considered (in the Sect. 3.3.3.3) polyfulvenes at MP2 level of theory. Results are presented in the Table 3.1. 

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