Analytical potential energy functions for some interhalogen diatomic electronic states

The studies of vibrational energies and analytical potential energy functions (APEFs) have been carried out for four interhalogen diatomic electronic states B(3Π0 +) and A(3Π1) of ClF, A′(3Π2u) of Cl2, and the ground state \hbox{$X^{1}\Sigma _{g}^{+}$} of Br2 by using an improved variational algebraic energy-consistent method (VAECM(4)). The full vibrational energies, the vibrational spectroscopic constants, the force constants fn, and the expansion coefficients an of the ECM (energy-consistent method) potential are tabulated. The VAECM(4) APEF with adjustable variational parameter λ for each electronic state is determined, and is shown to be in excellent agreement with available experimental data and has no any artificial barrier in all the calculation ranges that may appear in some other analytical potentials

Analytical potential curves of some hydride molecules using algebraic and energy-consistent method

Based on the algebraic method (AM) and the energy consistent method (ECM), an AM-ECM protocol for analytical potential energy curves of stable diatomic electronic states is proposed as functions of the internuclear distance. Applications of the AM-ECM to the 6 hydride electronic states of HF-X1Σ+, DF-X1Σ+, D35Cl-X1Σ+, 6LiH-X1Σ+, 7LiH-X1Σ+, and 7LiD-X1Σ+ show that the AM-ECM potentials are in excellent agreement with the experimental RKR data and the full AM-RKR data, and that the AM-ECM can obtain reliable analytical potential energies in the molecular asymptotic and dissociation region for these molecular electronic states

The Umbrella-Shaped Trimethylenemethane Ligand in Iron Carbonyl Chemistry: Comparison with Butadiene and Cyclobutadiene Analogues

Reaction of Fe₂(CO)₉ with 3-chloro-2-(chloromethyl)­propene is known to give the stable iron tricarbonyl complex [η⁴-(CH₂)₃C]­Fe­(CO)₃, containing the umbrella-shaped trimethylenemethane ligand. The mononuclear complexes (CH₂)₃CFe­(CO)_<i>n</i> (<i>n</i> = 1–4) and the binuclear complexes [(CH₂)₃C]₂Fe₂(CO)_<i>n</i> (<i>n</i> = 3–5) of this trimethylenemethane ligand have been studied here. The lowest energy [(CH₂)₃C]₂Fe₂(CO)₅ structure has one bridging CO group and an Fe–Fe single bond but is disfavored with respect to dissociation into the mononuclear fragments [(CH₂)₃C]₂Fe₂(CO)₃ + [(CH₂)₃C]₂Fe₂(CO)₂. The lowest energy [(CH₂)₃C]₂Fe₂(CO)₄ structure has two semibridging CO groups and an FeFe double bond but is disfavored with respect to disproportionation into [(CH₂)₃C]₂Fe₂(CO)₅ + [(CH₂)₃C]₂Fe₂(CO)₃. In contrast to [(CH₂)₃C]₂Fe₂(CO)₅ and [(CH₂)₃C]₂Fe₂(CO)₄, the tricarbonyl [(CH₂)₃C]₂Fe₂(CO)₃ appears to be a reasonable synthetic objective. The lowest energy structure has one terminal CO group, one semibridging CO group, one symmetrical bridging CO group, and a short FeFe distance of ∼2.2 Å consistent with the formal triple bond required to give both iron atoms the favored 18-electron configuration. However, a second [(CH₂)₃C]₂Fe₂(CO)₃ structure having two semibridging CO groups and one symmetrical bridging CO group was found at only ∼3 kcal/mol above this global minimum. The Wiberg bond indices in these binuclear derivatives support the metal–metal bond order assignments suggested by metal–metal distances and electron counting. The only example of a η²-trimethylenemethane ligand was found in the mononuclear tetracarbonyl [η²-CH₂C­(CH₂)₂]­Fe­(CO)₄, having a novel FeC₃ four-membered ring. However, this structure is disfavored with respect to CO loss to give the known iron tricarbonyl complex [η⁴-(CH₂)₃C]­Fe­(CO)₃

First-Row Transition Metals in Binuclear Cyclopentadienylmetal Derivatives of Tetramethyleneethane: η³,η³ versus η⁴,η⁴ Ligand–Metal Bonding Related to Spin State and Metal–Metal Bonds

The tetramethyleneethane (TME) ligand is found in the η³,η³ complex <i>tran</i>s<i>-</i>(η³,η³-TME)­Ni₂Cp₂ and the η⁴,η⁴ complex <i>tran</i>s<i>-</i>(η⁴,η⁴-TME)­Co₂Cp₂, which have both been synthesized and structurally characterized by X-ray crystallography. The structures of the complete series of (TME)­M₂Cp₂ derivatives of the first-row transition metals from Ti to Ni have now been investigated by density functional theory. The experimentally known nickel and cobalt complexes are found to have closed-shell electronic ground states. The lowest energy structure for the iron complex is the triplet spin state <i>trans</i>-(η⁴,η⁴-TME)­Fe₂Cp₂ structure with geometry similar to that of the lowest energy cobalt structure. All of the low-energy (TME)­M₂Cp₂ structures for manganese and the first-row transition metals to the left of manganese (Cr, V, and Ti) exhibit <i>cis</i>-(η⁴,η⁴-TME)­M₂Cp₂ stereochemistry, thereby providing the possibility for direct metal–metal interactions. Vanadium is the only first-row transition metal to the left of cobalt where the lowest energy (TME)­M₂Cp₂ structure is a singlet spin state, suggesting limited applicability of the 18-electron rule in these systems. The frontier molecular orbitals of these <i>cis</i>-(η⁴,η⁴-TME)­M₂Cp₂ systems have been examined in order to provide insight regarding metal–metal bonding. Thus, low-energy <i>cis-</i>(η⁴,η⁴-TME)­Mn₂Cp₂ structures are found in both quintet and triplet spin states with formal MnMn double bonds. The lowest energy <i>cis</i>-(η⁴,η⁴-TME)­Cr₂Cp₂ and <i>cis</i>-(η⁴,η⁴-TME)­Ti₂Cp₂ structures have triplet spin states with a formal CrCr triple bond and a formal TiTi double bond, respectively. The lowest energy <i>cis</i>-(η⁴,η⁴-TME)­V₂Cp₂ structure is a singlet structure with a formal VV triple bond

Flyover Compounds and Bridging Bent Benzene Derivatives as Intermediates in the Cobalt Carbonyl Cyclotrimerization of Alkynes

The so-called flyover complexes (η^3,1,η^3,1-μ-R₃R′₃C₆)­Co₂(CO)₄ are important because of their role as intermediates in the cobalt carbonyl-catalyzed cyclotrimerization of alkynes. A density functional study of such flyover complexes has led to the discovery of isomers with bent benzene rings bridging a pair of cobalt atoms. Such complexes are likely to be involved in the process of forming a carbon–carbon bond in closing the six-carbon chain in the flyover complexes to give the corresponding arene derivatives. The relative energies of the flyover complexes and the bridging bent benzene derivatives depend on the substituents on the six-carbon chain. Thus, for [C₆(CF₃)₆]­Co₂(CO)₄ and [1,3,6-<i>t</i>Bu₃C₆H₃]­Co₂(CO)₄ with bulky CF₃ and <i>tert</i>-butyl substituents at the ends of the six-carbon chain, the experimentally known flyover complexes are preferred energetically over the isomeric bridging bent benzene ring structure by 23.3 and 1.1 kcal/mol, respectively. However, for the less sterically hindered (C₆R₆)­Co₂(CO)₄ (R = H, CH₃) and 1,3,6-(CF₃)₃C₆H₃]­Co₂(CO)₄ derivatives the bridging bent benzene ring structures are preferred energetically over the flyover structures by 3.6 to 14.3 kcal/mol, respectively

Flyover Compounds and Bridging Bent Benzene Derivatives as Intermediates in the Cobalt Carbonyl Cyclotrimerization of Alkynes

The so-called flyover complexes (η^3,1,η^3,1-μ-R₃R′₃C₆)­Co₂(CO)₄ are important because of their role as intermediates in the cobalt carbonyl-catalyzed cyclotrimerization of alkynes. A density functional study of such flyover complexes has led to the discovery of isomers with bent benzene rings bridging a pair of cobalt atoms. Such complexes are likely to be involved in the process of forming a carbon–carbon bond in closing the six-carbon chain in the flyover complexes to give the corresponding arene derivatives. The relative energies of the flyover complexes and the bridging bent benzene derivatives depend on the substituents on the six-carbon chain. Thus, for [C₆(CF₃)₆]­Co₂(CO)₄ and [1,3,6-<i>t</i>Bu₃C₆H₃]­Co₂(CO)₄ with bulky CF₃ and <i>tert</i>-butyl substituents at the ends of the six-carbon chain, the experimentally known flyover complexes are preferred energetically over the isomeric bridging bent benzene ring structure by 23.3 and 1.1 kcal/mol, respectively. However, for the less sterically hindered (C₆R₆)­Co₂(CO)₄ (R = H, CH₃) and 1,3,6-(CF₃)₃C₆H₃]­Co₂(CO)₄ derivatives the bridging bent benzene ring structures are preferred energetically over the flyover structures by 3.6 to 14.3 kcal/mol, respectively

Bonding of Iron Tricarbonyl Units to Heptafulvene: Trimethylenemethane, Butadiene, and Allylic Coordination Modes

Complexation of the very unstable free heptafulvene with iron carbonyls is known experimentally to lead to stable complexes, including two isomers of (η⁴-C₇H₆CH₂)­Fe­(CO)₃ as well as the binuclear (C₇H₆CH₂)₂Fe₂(CO)₆. Density functional theory shows that structures of the mononuclear (C₇H₆CH₂)­Fe­(CO)₃ with trimethylenemethane and butadiene subunits of the heptafulvene ligand bonded to the Fe­(CO)₃ moiety have nearly equal energies within ∼3 kcal/mol, consistent with the experimental observation of two isomers depending upon the synthetic method. For (C₇H₆CH₂)­Fe₂(CO)₆ a <i>trans</i>-η⁴:η⁴ structure with no iron–iron bond and a <i>cis</i>-η³:η³ allylic structure with an iron–iron bond are predicted to have energies within ∼3.0 kcal/mol. Comparison of the predicted ν­(CO) frequencies for these two structures with the experimental ν­(CO) frequencies for the structurally uncharacterized (C₇H₆CH₂)­Fe₂(CO)₆ suggests the <i>cis</i>-η³:η³ allylic structure for the latter

Experimental Determination of the Rotational Constants of High-Lying Vibrational Levels of Ultracold Cs₂ in the 0_g^– Purely Long-Range State

We report on a quantitative experimental determination of the rotational constants for the high-lying vibrational levels of the ultracold pure long-range Cesium molecules formed via photoassociation. The scheme relies on a precise reference of frequency difference in a double photoassociation spectroscopy, which is induced by two laser beams based on an acoustic-optical modulator. The rotational constants are obtained by fitting a nonrigid rotor model into the frequency intervals of the neighboring rotational levels deduced from the reference