Basis Set

Density functional theory calculations of the electronic structure of graphane and stoichiometrically halogenated graphene derivatives (fluorographene and other analogous graphene halides) show: (i) localized orbital basis sets can be successfully and effectively used for such two-dimensional materials; (ii) several functionals predict that the band gap of graphane is greater than that of fluorographene, whereas HSE06 gives the opposite trend; (iii) HSE06 functional predicts quite good values of band gaps with respect to benchmark theoretical and experimental data; (iv) the zero band gap of graphene is opened by hydrogenation and halogenation and strongly depends on the chemical composition of mixed graphene halides; (v) the stability of graphene halides decreases sharply with increasing size of the halogen atom - fluorographene is stable, whereas graphene iodide spontaneously decomposes. In terms of band gap and stability, the C2FBr and C2HBr derivatives seem to be promising materials, e.g., for (opto)electronics applications, because their band gaps are similar to those of conventional semiconductors, and they are expected to be stable under ambient conditions. The results indicate that other fluorinated compounds (C a H b F c  and C a F b Y c , Y = Cl, Br, I) are stable insulators.

The carbon–carbon indirect nuclear spin–spin coupling constants in cyclopropane, aziridine and oxirane were investigated by means of ab initio calculations at the RPA, SOPPA and DFT/B3LYP levels. We found that the carbon–carbon couplings are by far dominated by the Fermi contact term. Our best SOPPA and DFT results are in a very good agreement with each other and with the experimental values, whereas calculations at the RPA level of theory strongly overestimate the carbon–carbon couplings. Significant differences in the basis set dependence of the calculated carbon–carbon coupling constants obtained with either wavefunction method, RPA or SOPPA, or the density functional method, DFT/B3LYP, are observed. The SOPPA results depend much more strongly on the quality of the basis set than the results of DFT/B3LYP calculations. The medium-sized core-valence basis sets cc-pCVTZ and even cc-pCVDZ were found to perform fairly well at the SOPPA level for the one-bond carbon–carbon couplings investigated here. Copyright © 2002 John Wiley & Sons, Ltd.

Carbon–carbon and carbon–hydrogen spin–spin coupling constants were calculated in the series of the first six monocycloalkanes using SOPPA and SOPPA(CCSD) methods, and very good agreement with the available experimental data was achieved, with the latter method showing slightly better results in most cases, at least in those involving calculations of J(C,C). Benchmark calculations of all possible 21 coupling constants J(C,C), J(C,H) and J(H,H) in chair cyclohexane revealed the importance of using the appropriate level of theory and adequate quality of the basis sets. Many unknown couplings in this series were predicted with high confidence and several interesting structural trends (hybridization effects, multipath coupling transmission mechanisms, hyperconjugative interactions) were elucidated and are discussed based on the present calculations of spin–spin couplings. Copyright © 2004 John Wiley & Sons, Ltd.

Accurate Gaussian basis sets for atoms from H to
Ba were obtained by means of the generator coordinate
Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations
(GWHF). The discretization of the GWHF equations in this
procedure is based on a mesh of points not equally distributed
in contrast with the original GCHF method. The results of
atomic Hartree-Fock energies demonstrate the capability of
these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the
maximum error found when compared to numerical values
is only 0.788 mHartree for indium. Some test calculations
with the B3LYP exchange-correlation functional for N2, F2,
CO, NO, HF, and HCN show that total energies within 1.0 to
2.4 mHartree compared to the cc-pV5Z basis sets are attained
with our contracted bases with a much smaller number of
polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required
only a tiny fraction of the computational time when compared
to B3LYP/cc-pV5Z calculations

In this article, we present the so far most extended investigation of the calculation of the coupling constant polarizability of a molecule. The components of the coupling constant polarizability are derivatives of the nuclear magnetic resonance (NMR) indirect nuclear spin–spin coupling constant with respect to an external electric field and play an important role for both chiral discrimination and solvation effects on NMR coupling constants. In this study, we illustrate the effects of one-electron basis sets and electron correlation both at the level of density functional theory as well as second-order polarization propagator approximation for the small molecule hydrogen peroxide, which allowed us to perform calculations with the largest available basis sets optimized for the calculation of NMR coupling constants. We find a systematic but rather slow convergence with the one-electron basis set and that augmentation functions are required. We observe also large and nonsystematic correlation effects with significant differences between the density functional and wave function theory methods. © 2012 Wiley Periodicals, Inc.