This paper presents the first rigorous analysis of the MP2 and MP3 supermolecular treatments in terms of the perturbation theory of intermolecular forces. In order to connect the two formalisms the MP energies are first expanded in terms of an auxiliary double-perturbation theory in spirit similar to the one proposed by Sadlej (1980, Molec. Phys., 39, 1249). In the next step, each term of this expansion is related to the perturbation theory of intermolecular interactions in the formulation of Szalewicz and Jeziorski (1979, Molec. Phys., 38, 191). Although the formal analysis neglects intermolecular exchange effects, a generalization of the final results is proposed so as to accommodate exchange effects. The supermolecular MP2 interaction energy contains the second-order intrasystem correlation correction to the Coulomb energy, in addition to the UCHF dispersion. The supermolecular MP3 term additionally involves the following: first-order intrasystem (apparent) correlation correction to the second-order UCHF dispersion, third-order UCHF dispersion, and third-order intramolecular correlation correction to the Coulomb energy. All terms should be accompanied by their exchange counterparts. Numerical illustration of this decomposition is provided by calculations of interaction energies in the He₂ and (HF)₂ systems. The correction of supermolecular values by the full counterpose procedure is shown to be essential.

The H bonds in H2O–HF and H2O–HCl are studied and compared using ab initio molecular orbital methods and the results compared to experimental data. Basis sets used are: (i) triple valence 6-311G** and (ii) double ζ with two sets of polarization functions. Electron correlation, included via second- and third-order Mo/ller–Plesset perturbation theory, is found to have profound effects on both systems, particularly H2O–HCl. Both H bonds are strengthened substantially with a concomitant reduction in length. H-bond energies and geometries calculated at correlated levels are in excellent accord with available experimental information. In both systems, all levels of theory indicate the equilibrium geometry contains a pyramidal arrangement about the oxygen atom. However, the difference in energy between this structure and a C2v planar arrangement is found to be small enough that consideration of probability amplitudes in the ground vibrational level leads to nearly equal likelihood of observing either geometry. Agreement between experimental vibrational frequencies in H2O–HF and those calculated at correlated levels and involving quadratic, cubic, and quartic force constants is quite good. An explanation is offered for the increase in HX bond length which occurs at SCF and correlated levels upon H-bond formation based upon nearly linear relationships between this length on one hand and subunit dipole moment and polarizability on the other. The dispersion energy is found to be a very sensitive, almost exactly linear function of the increase of H–X bond length. This energy contributes substantially to the weakening of the HX bond upon complexation.

Absorption UV spectra of gold clusters Au_n (n = 4, 6, 8, 12, 20) are investigated using the time-dependent density functional theory (TDDFT). The calculations employ several long-range corrected xc functionals: ωB97X, LC-ωPBEh, CAM-B3LYP* (where * denotes a variant with corrected asymptote of CAM-B3LYP), and LC-ωPBE. The latter two are subject to first-principle tuning according to a prescription of Stein et al. [Phys. Rev. Lett. 105, 266802 (2010)] by varying the range separation parameter. TDDFT results are validated for Au₄ and Au₈ against the equation-of-motion coupled cluster singles and doubles results and the experiment. Both long-range correction and the inclusion of a fixed portion of the exact exchange in the short-range are essential for the proper description of the optical spectra of gold. The ωB97X functional performs well across all studied cluster sizes. LC-ωPBEh, with parameters recommended by Rohrdanz et al. [J. Chem. Phys. 130, 054112 (2009)], affords the best performance for clusters of n > 4. The optimally tuned CAM-B3LYP* features the range separation parameter of 0.33 for Au₄ and 0.25 for all the larger clusters. For LC-ωPBE the tuning procedure resulted in incorrect transition energies and oscillator strengths despite the fact that the optimized functional showed the accurate linear dependence on fractional electron numbers. Au_n (n = 4, 6, 8) feature optical gaps above of 3 eV and Au₂₀ of ∼2.9 eV. In Au₁₂ this gap narrows to ∼2.1 eV. The calculated spectrum for Au₂₀ involves intensity being concentrated in only a few transitions with the absorption maximum at 3.5 eV. The intense 3.5 eV absorption is present in all cluster sizes of n > 4. The calculated HOMO-LUMO gaps for all cluster sizes are within 0.5 eV of the difference between the vertical ionization potential and electron affinity. The reasons for this and for the failure of conventional xc functionals for optical spectra of gold are discussed.