In the multiplicative integral approximation (MIA), two-electron integrals are evaluated using an expansion of a product of two Gaussians in terms of auxiliary functions. An estimator of the error introduced by the approximation is incorporated in the self-consistent field (SCF) calculations and the integrals for which the error estimate is larger than a preset value are systematically corrected. In this way the results of a MIA-assisted calculation have the same accuracy as a conventional calculation. The full exploitation of the expansion technique while constructing the Fock-matrix allows important time savings.
Van Alsenoy, C. J. Comp. Chem. 1988, 9, 620-626.
The geometrical structure and vibrational spectrum of urea were studied in the gas phase as well as in the crystal phase. Experimental frequencies for urea in the crystal phase were determined for eight isotopomers. Using calculations at the RHF/6-31++G** level, the equilibrium geometry and harmonic force field for both the gas phase and the crystal phase were determined. The crystal phase is modeled using a 15-molecule cluster surrounded by 5312 point charges. Calculated structure and frequencies are in excellent agreement with the experiment. Shifts in frequencies for the above-mentioned isotopomers are reproduced with a root-mean-square deviation and largest difference of 15 and 43 wave numbers, respectively. Shifts in frequencies upon going from the gas phase to the crystal phase for the parent and deuterated isotopomers are reproduced with a root-mean-square deviation and largest difference of 14 and 31 wave number, respectively.
Rousseau, B.; Van Alsenoy, C.; Keuleers, R.; Desseyn, H.O. J. Phys. Chem. A 1998, 102, 6540-6548
Hirshfeld Partitioning Scheme
Bond orders calculated using the Mayer, Wiberg or NAO methodologies are incompatible with the observed bond lengths in chalcogen-nitrogen systems. To study this discrepancy four types of bond orders and three types of (scaled) overlap populations have been used to determine the bonding in these systems. A new overlap population based on the Hirshfeld partitioning of the electron density is compared to the Mayer, Wiberg, NAO and Fuzzy bond order schemes and the Mulliken and Fuzzy overlap population schemes. The correlation between the investigated bond orders and overlap populations is excellent for common organic molecules, but the (scaled) Hirshfeld and Fuzzy overlap population schemes produce the best results for a series of chalcogen-nitrogen systems.
Oláh, J.; Blockhuys, F.; Veszprémi, T.; Van Alsenoy, C. Eur. J. Inorg. Chem. 2006, 69-77.
A correlation between delocalization indices (DIs) and proton spin-spin coupling constants, previously observed for DIs calculated within the QTAIM scheme, is examined using Hirshfeld and Mulliken schemes. The original set of molecules has been extended with a number of five- and six-membered heteroaromatics containing nitrogen, oxygen, sulfur and selenium. QTAIM DIs are found to correlate well with the experimental values, even those containing the electronegative nitrogen and oxygen atoms. In contrast, an acceptable correlation with the Hirshfeld DIs is found only for polybenzenoids, whereas no correlation is found for the Mulliken DIs with any of the systems.
Mandado, M.; Blockhuys, F.; Van Alsenoy, C. Chem. Phys. Lett. 2006, 430, 454-458.
In this work, a new partitioning method is presented which allows one to calculate properties of radicals, in particular, atomic spin populations. The method can be seen as an extension of the Hirshfeld-I method [Bultinck, P. et al. J. Chem. Phys. 2007, 126, 144111], in which the atomic weight functions, defining the atoms-in-molecules, are constructed by means of an iterative scheme in which the charges of the atoms-in-molecules are altered but the spin remains fixed. The Hirshfeld-I method is therefore not suitable for the calculation of atomic spin populations of open-shell systems. The new fractional occupation Hirshfeld-I (FOHI) uses an iterative scheme in which both the atomic charge and spin are optimized, resulting in a self-consistent method for the calculation of atomic spin populations. The results obtained with the FOHI method are compared with experimental results obtained using polarized neutron diffraction, thus serving as a validation of the FOHI method as well as the Hirshfeld definition of atoms-in-molecules in general.
Geldof, D.; Krishtal, A.; Blockhuys, F.; Van Alsenoy, C. J. Chem. Theory Comput. 2011, 7, 1328-1335.
A quantum chemical study was performed on ten different self-doping PPV oligomers. The geometry and the different weak intramolecular interactions were studied. The atomic spin populations were calculated using the FOHI method and related to the calculated EPR parameters. The effects of the removal of methoxy groups, the introduction of nitrogen atoms, and the relocation of the self-doping sidechain on the geometry, the spin distribution, and the EPR parameters have been described.
Geldof, D.; Krishtal, A.; Blockhuys, F.; Van Alsenoy, C. Theor. Chem. Acc. 2012, 131, 1243.