Evaluation of Orbital- and Ground State Energies of Some Open- and Closed-Shell Atoms over Integer and Noninteger Slater Type Orbitals

Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.     

Elektronenlokalisierung im Grundzustand und in angeregten Zuständen Pars-Orbital-Methode, 12. Mitt

UsingGleason's theorem the pars orbital concept is developed for excited states of conjugated systems described by CI-methods. A significance index is introduced to evaluate different patterns of fragmentation. The usefulness of this approach is illustrated for butadiene, biphenyl, naphthalene, and azulene.

11. Mitt.:H. Karpf, O. E. Polansky undM. Zander, Tetrahedron Lett.1978, 2069.     

Improved third-order Møller-Plesset perturbation theory

Based on a partitioning of the total correlation energy into contributions from parallel‐ and antiparallel‐spin pairs of electrons, a modified third‐order Møller–Plesset (MP) perturbation theory is developed. The method, termed SCS–MP3 (SCS for spin‐component‐scaled) continues previous work on an improved version of MP2 (S. Grimme, J Chem Phys 2003, 118, 9095). A benchmark set of 32 isogyric reaction energies, 11 atomization energies, and 11 stretched geometries is used to assess to performance of the model in comparison to the standard quantum chemical approaches MP2, MP3, and QCISD(T). It is found, that the new method performs significantly better than usual MP2/MP3 and even outperforms the more costly QCISD method. Opposite to the usual MP series, the SCS third‐order correction uniformly improves the results. Dramatic enhancements are especially observed for the more difficult atomization energies, some of the stretched geometries, and reaction and ionization energies involving transition metal compounds where the method seems to be competitive or even superior to the widely used density functional approaches. Further tests performed for other complex systems (biradicals, C₂₀ isomers, transition states) demonstrate that the SCS–MP3 model yields often results of QCISD(T) accuracy. The uniformity with which the new approach improves for very different correlation problems indicates significant robustness, and suggests it as a valuable quantum chemical method of general use. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1529–1537, 2003     

Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.     

Disordered ground states for classical discrete-state problems in one dimension

It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs.     

The Effect of cis-trans Isomerism on the Electronic-vibrational Structure of the Ground and Excited States and Reactivity of 2-(2-Furyl)- and 2-(2-Thienyl)oxazole

The fluorescent properties, structure, and electronic structure of the ground and excited singlet and triplet electronic states of the cis and trans forms of 4,5-dihydro-2-(2-furyl)oxazole, 4,4-dihydro-2-(2-thienyl)oxazole, 2-(2-furyl)oxazole (FO), and 2-(2-thienyl)oxazole (TO) have been studied. The orbital nature of the lower excited singlet and triplet states has been studied by the semiempirical INDO/S (valence approximation) and PPP/S ( approximation) methods. It was shown that for FO and TO molecules the lower triplet state is of the * type, for which delocalization of the electronic excitation on atoms is characteristic. In the singlet excitation state inversion was observed of the energy levels of the delocalized * states and n* states localized over several bonds (for the free TO and FO molecules the lower excited singlet states S₁* were assigned to * and n* types respectively). Owing to the low position of the T * and T _n* levels relative to the singlet level of * type, the rate constant for intercombination conversion is greater than the rate constant for radiative decay. Consequently an efficient population of the triplet states of the molecules occurs under conditions of electronic-vibrational excitation. The direction of reactions during synthesis was compared with the localization indices in the ground state for electrophilic, nucleophilic, and radical substitution, and also with the excitation localization numbers L for a wide selection of electronically excited states. It was concluded that the change in the structure of the azole molecule on replacing an O atom by an S atom, or on changing from a partially hydrogenated to a heteroaromatic system, was the main reason for the change of all the spectral parameters characterizing the electronic-vibrational or the spin-orbital interaction of the most reactive groups of atoms in the molecular structure.     

First principles study of the structure,electronic state,and stability of CmN2 clusters

Geometric and electronic properties of C_mN₂ (m = 1–14) clusters have been investigated by density functional theory using the hybrid B3LYP functional and the 6‐311G(d) basis set. Harmonic frequencies for these clusters are given to aid in the characterization of the ground states. These results show that C_mN₂ (m = 1–14) clusters form linear structures with D_∞h symmetry. Two N atoms favor to bond at ends in linear isomers. The chains with odd m have triplet ground states whereas the ones with even m have singlet ground states. The calculated HOMO–LUMO gaps and ionization potentials all show that the C_mN₂ (m = 1–14) clusters with even m are more stable than those with odd m, which is consistent with the observed even–odd alternation of the time‐of‐flight signal intensities. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

New Ni(II)Cu(II)Ni(II) trinuclear complexes with an 5=3/2 high-spin ground

Four new heterotrinuclear complexes have been synthesized and characterized, namely {[Ni(L)₂]₂[Cu(opba)]}(ClO₄)₂, where opba denotes o-phenylenebis(oxamato) and L stands for 1,10-phenanthroline(phen) (1), 5-nitro-l,10-phenanthroline(NO₂-phen) (2), 2,2′-bipyridyl(bpy) (S) and 4,4′-dimethyl-2,2′-bipyridyl(Me₂bpy) (4). The temperature dependence of the magnetic susceptibility of {[Ni(phen)₂]₂[Cu(opba)]}(ClO₄)₂3H₂O has been studied in the 4–300 K range, giving the exchange integral J—109 cm^?1. The HMT vs. T plot exhibits a minimum at about 100 K, characteristic of this kind of coupled polymetallic complex with an irregular spin-state structure.     

One-dimensional Ising chain with competing interactions: Exact results and connection with other statistical models

We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ ₁, and akth neighboranti-ferromagnetic interactionJ _k . WhenJ _k/J₁=–1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k–1)th term in a generalized Fibonacci sequence defined by,F _N ^(k) =F _N–1 ^(k) +F _N–k ^(k) . In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2× strip of the square lattice, and (c) directed self-avoiding walks on finite lattice strips.Work partially supported by grants from AFOSR and ARO.