15 research outputs found
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(3Î 0
+) and A(3Î 1) of
ClF, A′(3Π2u)
of Cl2, and the
ground state \hbox{} 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 Fe<sub>2</sub>(CO)<sub>9</sub> with 3-chloro-2-(chloromethyl)Âpropene
is known to give the stable iron tricarbonyl complex [η<sup>4</sup>-(CH<sub>2</sub>)<sub>3</sub>C]ÂFeÂ(CO)<sub>3</sub>, containing
the umbrella-shaped trimethylenemethane ligand. The mononuclear complexes
(CH<sub>2</sub>)<sub>3</sub>CFeÂ(CO)<sub><i>n</i></sub> (<i>n</i> = 1–4) and the binuclear complexes [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub><i>n</i></sub> (<i>n</i> = 3–5) of this trimethylenemethane
ligand have been studied here. The lowest energy [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>5</sub> structure has
one bridging CO group and an Fe–Fe single bond but is disfavored
with respect to dissociation into the mononuclear fragments [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>3</sub> +
[(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>2</sub>. The lowest energy [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>4</sub> structure has two semibridging CO
groups and an Feî—»Fe double bond but is disfavored with respect
to disproportionation into [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>5</sub> + [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>3</sub>. In contrast to [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>5</sub> and [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>4</sub>, the tricarbonyl [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>3</sub> 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 [(CH<sub>2</sub>)<sub>3</sub>C]<sub>2</sub>Fe<sub>2</sub>(CO)<sub>3</sub> 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 η<sup>2</sup>-trimethylenemethane
ligand was found in the mononuclear tetracarbonyl [η<sup>2</sup>-CH<sub>2</sub>î—»CÂ(CH<sub>2</sub>)<sub>2</sub>]ÂFeÂ(CO)<sub>4</sub>, having a novel FeC<sub>3</sub> four-membered ring. However, this
structure is disfavored with respect to CO loss to give the known
iron tricarbonyl complex [η<sup>4</sup>-(CH<sub>2</sub>)<sub>3</sub>C]ÂFeÂ(CO)<sub>3</sub>
First-Row Transition Metals in Binuclear Cyclopentadienylmetal Derivatives of Tetramethyleneethane: η<sup>3</sup>,η<sup>3</sup> versus η<sup>4</sup>,η<sup>4</sup> Ligand–Metal Bonding Related to Spin State and Metal–Metal Bonds
The tetramethyleneethane (TME) ligand
is found in the η<sup>3</sup>,η<sup>3</sup> complex <i>tran</i>s<i>-</i>(η<sup>3</sup>,η<sup>3</sup>-TME)ÂNi<sub>2</sub>Cp<sub>2</sub> and the η<sup>4</sup>,η<sup>4</sup> complex <i>tran</i>s<i>-</i>(η<sup>4</sup>,η<sup>4</sup>-TME)ÂCo<sub>2</sub>Cp<sub>2</sub>, which have both been synthesized
and structurally characterized by X-ray crystallography. The structures
of the complete series of (TME)ÂM<sub>2</sub>Cp<sub>2</sub> 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>-(η<sup>4</sup>,η<sup>4</sup>-TME)ÂFe<sub>2</sub>Cp<sub>2</sub> structure with geometry
similar to that of the lowest energy cobalt structure. All of the
low-energy (TME)ÂM<sub>2</sub>Cp<sub>2</sub> structures for manganese
and the first-row transition metals to the left of manganese (Cr,
V, and Ti) exhibit <i>cis</i>-(η<sup>4</sup>,η<sup>4</sup>-TME)ÂM<sub>2</sub>Cp<sub>2</sub> 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)ÂM<sub>2</sub>Cp<sub>2</sub> 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>-(η<sup>4</sup>,η<sup>4</sup>-TME)ÂM<sub>2</sub>Cp<sub>2</sub> systems have been examined in order to provide insight
regarding metal–metal bonding. Thus, low-energy <i>cis-</i>(η<sup>4</sup>,η<sup>4</sup>-TME)ÂMn<sub>2</sub>Cp<sub>2</sub> structures are found in both quintet and triplet spin states
with formal Mnî—»Mn double bonds. The lowest energy <i>cis</i>-(η<sup>4</sup>,η<sup>4</sup>-TME)ÂCr<sub>2</sub>Cp<sub>2</sub> and <i>cis</i>-(η<sup>4</sup>,η<sup>4</sup>-TME)ÂTi<sub>2</sub>Cp<sub>2</sub> structures have triplet
spin states with a formal Crî—¼Cr triple bond and a formal Tiî—»Ti
double bond, respectively. The lowest energy <i>cis</i>-(η<sup>4</sup>,η<sup>4</sup>-TME)ÂV<sub>2</sub>Cp<sub>2</sub> structure
is a singlet structure with a formal Vî—¼V triple bond
Flyover Compounds and Bridging Bent Benzene Derivatives as Intermediates in the Cobalt Carbonyl Cyclotrimerization of Alkynes
The so-called flyover complexes (η<sup>3,1</sup>,η<sup>3,1</sup>-μ-R<sub>3</sub>R′<sub>3</sub>C<sub>6</sub>)ÂCo<sub>2</sub>(CO)<sub>4</sub> 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 [C<sub>6</sub>(CF<sub>3</sub>)<sub>6</sub>]ÂCo<sub>2</sub>(CO)<sub>4</sub> and [1,3,6-<i>t</i>Bu<sub>3</sub>C<sub>6</sub>H<sub>3</sub>]ÂCo<sub>2</sub>(CO)<sub>4</sub> with bulky CF<sub>3</sub> 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 (C<sub>6</sub>R<sub>6</sub>)ÂCo<sub>2</sub>(CO)<sub>4</sub> (R = H, CH<sub>3</sub>) and 1,3,6-(CF<sub>3</sub>)<sub>3</sub>C<sub>6</sub>H<sub>3</sub>]ÂCo<sub>2</sub>(CO)<sub>4</sub> 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<sup>3,1</sup>,η<sup>3,1</sup>-μ-R<sub>3</sub>R′<sub>3</sub>C<sub>6</sub>)ÂCo<sub>2</sub>(CO)<sub>4</sub> 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 [C<sub>6</sub>(CF<sub>3</sub>)<sub>6</sub>]ÂCo<sub>2</sub>(CO)<sub>4</sub> and [1,3,6-<i>t</i>Bu<sub>3</sub>C<sub>6</sub>H<sub>3</sub>]ÂCo<sub>2</sub>(CO)<sub>4</sub> with bulky CF<sub>3</sub> 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 (C<sub>6</sub>R<sub>6</sub>)ÂCo<sub>2</sub>(CO)<sub>4</sub> (R = H, CH<sub>3</sub>) and 1,3,6-(CF<sub>3</sub>)<sub>3</sub>C<sub>6</sub>H<sub>3</sub>]ÂCo<sub>2</sub>(CO)<sub>4</sub> 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 (η<sup>4</sup>-C<sub>7</sub>H<sub>6</sub>CH<sub>2</sub>)ÂFeÂ(CO)<sub>3</sub> as well as the binuclear (C<sub>7</sub>H<sub>6</sub>CH<sub>2</sub>)<sub>2</sub>Fe<sub>2</sub>(CO)<sub>6</sub>.
Density functional theory shows that structures of the mononuclear
(C<sub>7</sub>H<sub>6</sub>CH<sub>2</sub>)ÂFeÂ(CO)<sub>3</sub> with
trimethylenemethane and butadiene subunits of the heptafulvene ligand
bonded to the FeÂ(CO)<sub>3</sub> moiety have nearly equal energies
within ∼3 kcal/mol, consistent with the experimental observation
of two isomers depending upon the synthetic method. For (C<sub>7</sub>H<sub>6</sub>CH<sub>2</sub>)ÂFe<sub>2</sub>(CO)<sub>6</sub> a <i>trans</i>-η<sup>4</sup>:η<sup>4</sup> structure
with no iron–iron bond and a <i>cis</i>-η<sup>3</sup>:η<sup>3</sup> allylic structure with an iron–iron
bond are predicted to have energies within ∼3.0 kcal/mol. Comparison
of the predicted νÂ(CO) frequencies for these two structures
with the experimental νÂ(CO) frequencies for the structurally
uncharacterized (C<sub>7</sub>H<sub>6</sub>CH<sub>2</sub>)ÂFe<sub>2</sub>(CO)<sub>6</sub> suggests the <i>cis</i>-η<sup>3</sup>:η<sup>3</sup> allylic structure for the latter
Experimental Determination of the Rotational Constants of High-Lying Vibrational Levels of Ultracold Cs<sub>2</sub> in the 0<sub>g</sub><sup>–</sup> 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