The recently developed second-order perturbation theory restricted active space (RASPT2) method has been benchmarked versus the well-established complete active space (CASPT2) approach. Vertical excitation energies for valence and Rydberg excited states of different groups of organic (polyenes, acenes, heterocycles, azabenzenes, nucleobases, and free base porphin) and inorganic (nickel atom and copper tetrachloride dianion) molecules have been computed at the RASPT2 and multistate (MS) RASPT2 levels using different reference spaces and compared with CASPT2, CCSD, and experimental data in order to set the accuracy of the approach, which extends the applicability of multiconfigurational perturbation theory to much larger and complex systems than previously. Relevant aspects in multiconfigurational excited state quantum chemistry such as the valence−Rydberg mixing problem in organic molecules or the double d-shell effect for first-row transition metals have also been addressed.

Multiconfigurational second-order perturbation theory based on either a complete active space reference wave function (CASSCF/CASPT2) or a restricted active space reference wave function (RASSCF/RASPT2) has been applied to compute one-electron ionization potentials and vertical electronic energy differences of oligomers of length n formed from ethylene (n = 1-10), acetylene (n = 1-5), and phenylene (n = 1-3) subunits. The RASSCF/RASPT2 approach offers an accuracy similar to CASSCF/CASPT2 at significantly reduced computational expense (both methods show good agreement with experimental data where available). It is shown that RASPT2 extends the range of CASPT2-like approaches by permitting the use of larger active spaces.

Multiconfigurational second-order perturbation theory calculations based on a complete active space reference wave function (CASPT2), employing active spaces of increasing size, are well converged at the level of 12 electrons in 12 orbitals for the singlet−triplet state−energy splittings of three supported copper−dioxygen and two supported copper−oxo complexes. Corresponding calculations using the restricted active space approach (RASPT2) offer similar accuracy with a significantly reduced computational overhead provided an inner (2,2) complete active space is included in the overall RAS space in order to account for strong biradical character in most of the compounds. The effects of the different active space choices and the outer RAS space excitations are examined, and conclusions are drawn with respect to the general applicability of the RASPT2 protocol.

We describe the preparation of a helicate containing four closely spaced, linearly arrayed copper(I) ions. This product may be prepared either directly by mixing copper(I) with a set of precursor amine and aldehyde subcomponents, or indirectly through the dimerization of a dicopper(I) helicate upon addition of 1,2-phenylenediamine. A notable feature of this helicate is that its length is not limited by the lengths of its precursor subcomponents: each of the two ligands wrapped around the four copper(I) centers contains one diamine, two dialdehyde, and two monoamine residues. This work thus paves the way for the preparation of longer oligo- and polymeric structures. DFT calculations and electrochemical measurements indicate a high degree of electronic delocalization among the metal ions forming the cores of the structures described herein, which may therefore be described as "molecular wires".

A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described. This model is particularly effective for cases where a chemical system requires a balanced orbital active space that is too large to be addressed by the complete active space self-consistent field model with or without second-order perturbation theory (CASPT2 or CASSCF, respectively). Rather than permitting all possible electronic configurations of the electrons in the active space to appear in the reference wave function, certain orbitals are sequestered into two subspaces that permit a maximum number of occupations or holes, respectively, in any given configuration, thereby reducing the total number of possible configurations. Subsequent second-order perturbation theory captures additional dynamical correlation effects. Applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented. In the mononuclear case, RASPT2 and CASPT2 provide very similar results. In the binuclear cases, however, only RASPT2 proves quantitatively useful, owing to the very large size of the necessary active space.

The relative energies of side-on versus end-on binding of molecular oxygen to a supported Cu(I) species, and the singlet versus triplet nature of the ground electronic state, are sensitive to the nature of the supporting ligands and, in particular, depend upon their geometric arrangement relative to the O₂ binding site. Highly correlated ab initio and density functional theory electronic structure calculations demonstrate that optimal overlap (and oxidative charge transfer) occurs for the side-on geometry, and this is promoted by ligands that raise the energy, thereby enhancing resonance, of the filled Cu d_xz orbital that hybridizes with the in-plane Ï€* orbital of O₂. Conversely, ligands that raise the energy of the filled Cu d_z² orbital foster a preference for end-on binding as this is the only mode that permits good overlap with the in-plane O₂ Ï€*. Because the overlap of Cu d_z² with O₂ Ï€* is reduced as compared to the overlap of Cu d_xz with the same O₂ orbital, the resonance is also reduced, leading to generally more stable triplet states relative to singlets in the end-on geometry as compared to the side-on geometry, where singlet ground states become more easily accessible once ligands are stronger donors. Biradical Cu(II)-O₂ superoxide character in the electronic structure of the supported complexes leads to significant challenges for accurate quantum chemical calculations that are best addressed by exploiting the spin-purified M06L local density functional, single-reference completely renormalized coupled-cluster theory, or multireference second-order perturbation theory, all of which provide predictions that are qualitatively and quantitatively consistent with one another.

The new bis(pentalene) complex Cr₂(η⁵:η⁵-C₈H₄^1,4-SiiPr₃)₂ has been synthesized and characterized; it is found to exhibit paramagnetism at room temperature, and solid-state magnetic studies show that the dimer is best modeled as containing a pair of antiferromagnetically interacting S = ½ centers with the separation between the singlet ground state and triplet excited state being 2.23 kJ mol^−1. Structural data show a Cr−Cr distance of 2.2514(15) Ã…, consistent with a strong metal−metal interaction. The bonding has been further investigated by density functional, hybrid, and CASPT2 methods. The metal−metal interaction is best described by a double bond with each metal having an 18-electron count. Theory predicts the singlet and triplet states to lie close in energy but puts the triplet state at a slightly lower energy than the singlet. The energy difference predicted by CASPT2 is closest to the experimental value.

The ground and excited electronic state properties of calicene (triapentafulvalene or 5-(cycloprop-2-en-1-ylidene)cyclopenta-1,3-diene) have been studied with a variety of density functional models (mPWPW91, PBE, TPSS, TPSh, B3LYP) and post-Hartree−Fock models based on single (MP2 and CCSD(T)) and multideterminantal (CASPT2) reference wave functions. All methods agree well on the properties of ground-state calicene, which is described as a conjugated double bond system with substantial zwitterionic character deriving from a charge-separated mesomer in which the three- and five-membered rings are both aromatic. Although the two rings are joined by a formal double bond, contributions from the aromatic mesomer reduce its bond order substantially. A rotational barrier of 40−41 kcal mol^-1 is predicted in the gas phase and solvation effects reduce the barrier to 37 and 33 kcal mol^-1 in benzene and water, respectively, because of increased zwitterionic character in the twisted transition-state structure. Multi-state CASPT2 (MS-CASPT2) is used to characterize the first few excited singlet and triplet states and indicates that the most important transition occurs at 4.93 eV (251 nm). A cis−trans photoisomerization about the inter-ring double bond is found to be inefficient.