Two-component Fermi systems: II. Superfluid coupled cluster theory

In this second paper of a series the coupled cluster method (CCM) or exp(S) formalism is applied to two-component Fermi superfluids using a Bardeen-Cooper-Schrieffer (BCS) ground state as a zeroth-order approximation. We concentrate on developing the formalism necessary for carrying out eventual numerical calculations on realistic superconducting systems. We do this by generalising the one-component formalism in an appropriate manner and by using the results in the first paper of this series, where we studied two-component Fermi fluids. We stress the previous successes of the CCM, both from the point of view of analytic and numerical results, and we further indicate its potential for studying superconductivity. We restrict ourselves here to a so-called ring plus single particle energy (RING+SPE) approximation for general potentials and show how it can be formulated as a set of four coupled, bilinear integral equations for the cluster-integrated amplitudes. These latter amplitudes are themselves derived from the four-point functions of the system which provide a measure of the two-particle/two-hole component in the true ground-state wavefunction with respect to the BCS model state. We indicate how to obtain possible analytic solutions.     

Geometrical effects on the intramolecular quenching of pi,pi* aromatic ketones by phenols and indoles

Laser flash photolysis of a series of bichromophoric compounds 1-12 containing the 2-benzoylthiophene (BT) and phenol (PhOH) or indole (InH) moieties has been used to determine the possible geometrical effects in the intramolecular quenching of triplet excited ketones, resulting in formal hydrogen abstraction. The results are compared with those obtained in the intermolecular process. In both cases, substitution either at the thienyl or the phenyl moiety has a marked influence on the photoreactivity. Time-resolved experiments showed that the rate constants for bimolecular quenching by phenol and indole of 2-benzoylthiophene substituted at the thienyl 5-position were lower than those for BT substituted at the phenyl p-position, which agrees with the higher energy found for the excited triplet state of the latter compounds. However, the rate constant for hydrogen abstraction in the bichromophoric compounds by the pi,pi* triplet state of the derivatives with the spacer linked to the thienyl 5-position are higher than those of their regioisomers. These results indicate a possible geometry-dependence in the intramolecular quenching process. Theoretical DFT studies have been carried out in order to estimate the optimum conformation for hydrogen abstraction in two pairs of phenolic and indolic bichromophoric regioisomers. The energy profile for photoactivation/deactivation of the aromatic ketone and the structures of the triplet states and biradicals involved in the process have been determined. The observed regiodifferentiation in the experimental studies is consistent with a dependence of the rate constant on orbital overlap between the carbonyl oxygen and the X-H bonds.     

Stereoselective oxidative additions of iodoalkanes and activated alkynes to a sulfido-bridged heterotrinuclear early-late (TiIr2) complex

The reactions of the early-late trinuclear complex [Cp(acac)Ti(mu(3)-S)(2)Ir(2)(CO)(4)] (1) with electrophiles have been found to occur on the iridium atoms with no other involvement of the early metal than in electronic effects. The reaction with iodine gave two isomers of the diiridium(II) complex [Cp(acac)Ti(mu(3)-S)(2)Ir(2)I(2)(CO)(4)] differentiated by the relative positions of the iodo ligands on the iridium atoms. The reactions with iodoalkanes are highly stereoselective to give one sole isomer of formula [Cp(acac)Ti(mu(3)-S)(2)Ir(2)(R)(I)(CO)(4)] (R = CH(3), CH(2)I, CHI(2)) with a carbonyl and the iodo ligand trans to the metal-metal bond. The structures of the symmetrical isomer with the iodo ligands trans to the metal-metal bond and that of the compound with R = CHI(2) have been solved by X-ray diffraction methods. The stereoselectivity of the oxidative-addition reactions can be rationalized assuming the influence of steric effects of the groups on the titanium center and a radical-like mechanism. Reactions of 1 with the activated acetylenes, dimethylacetylenedicarboxylate and methylacetylenecarboxylate, gave the complexes [Cp(acac)Ti(mu(3)-S)(2)Ir(2)(mu-eta(1)-RC=CCO(2)Me)(CO)(4)] (R = CO(2)Me, H), with the alkyne bridging the two iridium centers as a cis-dimetalated olefin and the C=C bond parallel to the Ir-Ir axis. Two isomers resulting from the disposition of the alkyne along the Ir-Ir vector were observed in solution for the compound with the nonsymmetrical alkyne (R = H), while only one was observed for the compound with R = CO(2)Me. An exchange, fast in the NMR time scale, of the apical with the equatorial carbonyls occured in the complexes [Cp(acac)Ti(mu(3)-S)(2)Ir(2)(mu-eta(1)-RC=CCO(2)Me)(CO)(4)], producing their equivalence in the (13)C((1)H) NMR spectra.     

Crescent-shaped rhodium(I) complexes with bis(o-carboxymethylphenyl)triazenide

Reaction of [[Rh(mu-Cl)(CO)2]2] with the triazene ArNNNHAr (Ar = o-CO2MeC6H4) produced the mononuclear complex [RhCl(ArNNNHAr)(CO)2] (1). Complex 1 reacted with KOH in methanol to give the dinuclear compound [[Rh(mu-ArNNNAr)(CO)2]2] (2), which showed a "mu-(1kappaN1,2kappaN3)-ArNNNAr" coordination mode for both bridging ligands. The dinuclear complex [[Rh(mu-ArNNNAr)(CO)2]2] (2) easily undergoes redistribution reactions in which the eight-membered "Rh2(NNN)2" core is broken. Thus, reaction of 2 with the anionic complex (NHEt3)[RhCl2(CO)2] gave the single-bridged complex (NHEt3)[Rh2(mu-ArNNNAr)Cl2(CO)4] (4), while the trinuclear complexes [Rh3(mu-ArNNNAr)(mu-Cl)(mu-CO)Cl(CO)4] (5) and [Rh3(mu-ArNNNAr)2(mu-Cl)(mu-CO)(CO)3] (6) were isolated by addition of the neutral compound [[Rh(mu-Cl)(CO)2]2] to 2, depending on the molar ratio employed. The formation of 5 and 6 involved the loss of carbonyl groups and the coordination of the oxygen atoms of the CO2Me groups. The structures of 4, 5, and 6 have been determined by X-ray diffraction methods, which show the ability of bis(o-carboxymethylphenyl)triazenide to act as bi-, tri-, and tetra-dentate ligand-spanning dinuclear moieties in trinuclear complexes.     

Key factors determining the course of methyl iodide oxidative addition to diamidonaphthalene-bridged diiridium(I) and dirhodium(I) complexes

The course of methyl iodide oxidative addition to various nucleophilic complexes, [Ir2(mu-1,8-(NH)2naphth)(CO)2(PiPr3)2] (1), [IrRh(mu-1,8-(NH)2naphth)(CO)2(PiPr3)2] (2), and [Rh2(mu-1,8-(NH)2naphth)(CO)2(PR3)2] (R = iPr, 3; Ph, 4; p-tolyl, 5; Me, 6), has been investigated. The CH3I addition to complex 1 readily affords the diiridium(II) complex [Ir2(mu-1,8-(NH)2naphth)I(CH3)(CO)2(PiPr3)2] (7), which undergoes slow rearrangement to give a thermodynamically stable stereoisomer, 8. The reaction of the Ir-Rh complex 2 gives the ionic compound [IrRh(mu-1,8-(NH)2naphth)(CH3)(CO)2(PiPr3)2]I (10). The dirhodium compounds, 3-5, undergo one-center additions to yield acyl complexes of the formula (Rh2(mu-1,8-(NH)2naphth)I(COCH3)(CO)(PR3)2] (R = iPr, 12; Ph, 13; p-tolyl, 14). The structure of 12 has been determined by X-ray diffraction. Further reactions of these Rh(III)-Rh(I) acyl derivatives with CH3I are productive only for the p-tolylphosphine derivative, which affords the bis-acyl complex [Rh2(mu-1,8-(NH)2naphth)(CH3CO)2I2(P(p-tolyl)3)2] (15). The reaction of the PMe3 derivative, 6, allows the isolation of the bis-methyl complex [Rh2(mu-1,8-(NH)2naphth)(mu-I)(CH3)2(CO)2(PMe3)2]I (16a), which emanates from a double one-center addition. Upon reaction with methyl triflate, the starting materials, 1, 2, 3, and 6, give the isostructural cationic methyl complexes 9, 11, 17, and 18, respectively. The behavior of these cationic methyl compounds toward CH3I, CH3OSO2CF3, and tetrabutylamonium iodide is consistent with the role of these species as intermediates in the SN2 addition of CH3I. Compounds 18 and 17 react with an excess of methyl triflate to give [Rh2(mu-1,8-(NH)2naphth)(mu-OSO2CF3)(CH3)2(CO)2(PMe3)2][CF3SO3] (19) and [Rh2(mu-1,8-(NH)2naphth)(OSO2CF3)(COCH3)(CH3)(CO)(PiPr3)2][CF3SO3] (20), respectively. Upon treatment with acetonitrile, complexes 17 and 18 give the isostructural cationic acyl complexes [Rh2(mu-1,8-(NH)2naphth)(COCH3)(NCCH3)(CO)(PR3)2][CF3SO3] (R = iPr, 21; Me, 22). A kinetic study of the reaction leading to 21 shows that formation of these complexes involves a slow insertion step followed by the fast coordination of the acetonitrile. The variety of reactions found in this system can be rationalized in terms of three alternative reaction pathways, which are determined by the effectiveness of the interactions between the two metal centers of the dinuclear complex and by the steric constraints due to the phosphine ligands.     

Synthesis, characterization, and crystal structure of the Pd(phen)(bdt) complex. A DFT and TDDFT study of its ground electronic and excited states compared to those of analogous complexes

The synthesis and characterization of Pd(phen)(bdt) (1) (phen = 1,10-phenanthroline, bdt = 1,2-benzenedithiolate) is presented. 1 crystallizes in the monoclinic space group P2(1)/c, alpha = 11.281(4) A, b = 20.498(8) A, c = 8.374(3) A, beta = 90.234(8), V = 1936.5(13) A(3), Z = 4, and is isostructural with its previously reported related complexes. The ground and low lying excited electronic states in 1 and in the related complexes Pd(bpy)(bdt) (2), Pt(bpy)(bdt) (3), Pt(bpy)(mnt) (4), and Pt(bpy)(edt) (5) [where bpy = 2,2'-bipyridine, edt = ethylene-1,2-dithiolate, and mnt = maleonitriledithiolate] are studied using density functional theory techniques. The electronic properties of 1-5 are studied using the B3LYP functional. Optimized geometries are compared to experimentally observed structures. Time dependent density functional theory (TDDFT) is employed to investigate the excited singlet and triplet states. The calculated energies of the lowest singlet state and the lowest triplet state in all five complexes are in considerable agreement with experimental data. It is shown that variation of both metal and dithiolate-ligand going from 1 and 2 to 3, 4, and 5 has a substantial impact on the spectroscopic and excited-state properties, indicating at the same time the mixed metal/dithiolate character of the HOMO orbital. All the low-lying transitions are categorized as MMLL'CT transitions. The emissive state of all complexes is assigned as a triplet dithiolate/metal to diimine charge transfer with differences in the structures of the emissions resulting from differences in the pi dithiolate orbital of the mnt, bdt, and edt as well as from differences in metal.