Application of Lie algebraic method to the calculation of rotational spectra for linear triatomic molecules

The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrational interactions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels of v2 band for transition (02°0-0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm-1, respectively.     

The model U(5) of the triatomic molecule

Rotation-vibration spectra of a triatomic molecule can be classified by the irreducible representations of the group U(5). The dynamical symmetry U(5) ? O(5) ? O(3) is discussed. Its application to the spectrum of HCN is considered.     

Mononuclear to Polynuclear UIV Structural Units: Effects of Reaction Conditions on U-Furoate Phase Formation

Uranium(IV) complexation by 2-furoic acid (2-FA) was examined to better understand the effects of ligand identity and reaction conditions on species formation and stability. Five compounds were isolated: [UCl₂(2-FA)₂(H₂O)₂]_n ( 1 ), [U₄Cl₁₀O₂(THF)₆(2-FA)₂] ⋅ 2 THF ( 2 ), [U₆O₄(OH)₄(H₂O)₃(2-FA)₁₂] ⋅ 7 THF ⋅ H₂O ( 3 ), [U₆O₄(OH)₄(H₂O)₂(2-FA)₁₂] ⋅ 8.76 H₂O ( 4 ), and [U₃₈Cl₄₂O₅₄(OH)₂(H₂O)₂₀] ⋅ m H₂O ⋅ n THF ( 5 ). The structures were determined by single-crystal X-ray diffraction and further characterized by Raman, IR, and optical absorption spectroscopy. The thermal stability and magnetic behavior of the compounds were also examined. Variations in the synthetic conditions led to notable differences in the structural units observed in the solid state. At low H₂O/THF ratios, a tetranuclear oxo-bridged [U₄O₂] core was isolated. Aging of this solution resulted in the formation a U₃₈ oxo cluster capped by chloro and water ligands. However, at increasing water concentrations only hexanuclear units were observed. In all cases, at temperatures of 100–120 °C, UO₂ nanoparticles formed.     

Building [UIV70(OH)36(O)64]4− Oxocluster Frameworks with Sulfate,Transition Metals,and UV

Uranium(IV) oxide clusters, colloids, and materials are designed and studied for 1) nuclear materials applications, 2) understanding the environmental fate and transport of actinides, and 3) exploring the complex bonding behavior of open-shell f-elements. U^IV-oxyhydroxsulfate clusters are particularly relevant in industrial processes and in nature. Recent studies have shown that counter-cations to these polynuclear anions differentiate rich structural topologies in the solid-state. Herein, we present nine different structures with wheel-shaped [U₇₀(OH)₃₆(O)₆₄(SO₄)₆₀]⁴⁻ (U₇₀) linked into one- and two-dimensional frameworks with sulfate, divalent transition metals (Cr^II, Fe^II, Co^II, Ni^II) and U^V. Small-angle X-ray scattering of these phases dissolved in butylamine reveals differing supramolecular assembly of U₇₀ clusters, controlled primarily by sulfates. However, observed trends in transition metal linking guide future design of U₇₀ materials with different topologies. Finally, U₇₀ linking via U^IV-O-U^V-O-U^IV bridges presents a rare example of mixed-oxidation-state uranium oxides without disorder.     

Unitary group approach to general system partitioning. I. Calculation of U(n = n1 + n2): U(n1) × u(n2) reduced matrix elements and reduced wigner coefficients

This paper is the first in a series of two directed toward a unitary calculus for group-function-type approaches to the many-electron correlation problem. In this paper we present a complete derivation of the matrix elements of the U(n = n₁ + n₂) generators, for the representations approapriate to many-electron systems, in a basis symmetry adapted to the subgroup U(n₁) × U(n₂). Explicit formulae for the fundamental U(n):U(n₁) × U(n₂) reduced Wigner coefficients, which are needed for the general multishell problem, are also obtained. The symmetry properties of the reduced Wigner coefficients and reduced matrix elements are investigated, and a suitable phase convention is given.     

On unicyclic conjugated molecules with minimal energies

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let U(k) be the set of all unicyclic graphs with a perfect matching. Let C _g(G) be the unique cycle of G with length g(G), and M(G) be a perfect matching of G. Let U ⁰(k) be the subset of U(k) such that g(G)≡ 0 (mod 4), there are just g/2 independence edges of M(G) in C _g(G) and there are some edges of E(G)\ M(G) in G\ C _g(G) for any G∈U ⁰(k). In this paper, we discuss the graphs with minimal and second minimal energies in U ^*(k) = U(k)\ U ⁰(k), the graph with minimal energy in U ⁰(k), and propose a conjecture on the graph with minimal energy in U(k).      

Nonadiabatic photodissociation dynamics

The photodissociation dynamics of the triatomic (or pseudo‐triatomic) system in the nonadiabatic multiple electronic states is investigated by employing a time‐dependent quantum wave packet method, while the time propagation of the wave packet is carried out using the split‐operator scheme. As a numerical example, the photodissociation dynamics of CH₃I in three electronic states ¹Q₁(A′), ¹Q₁(A″), and ³Q₀₊ is studied and CH₃I is treated as a pseudotriatomic model. The absorption spectra and product vibrational state distributions are calculated and compared with previous theoretical work. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Cation‐Mediated Conversion of the State of Charge in Uranium Arene Inverted‐Sandwich Complexes

Two new arene inverted‐sandwich complexes of uranium supported by siloxide ancillary ligands [K{U(OSi(OtBu)₃)₃}₂(μ‐η⁶:η⁶‐C₇H₈)] ( 3 ) and [K₂{U(OSi(OtBu)₃)₃}₂(μ‐η⁶:η⁶‐C₇H₈)] ( 4 ) were synthesized by the reduction of the parent arene‐bridged complex [{U(OSi(OtBu)₃)₃}₂(μ‐η⁶:η⁶‐C₇H₈)] ( 2 ) with stoichiometric amounts of KC₈ yielding a rare family of inverted‐sandwich complexes in three states of charge. The structural data and computational studies of the electronic structure are in agreement with the presence of high‐valent uranium centers bridged by a reduced tetra‐anionic toluene with the best formulation being U^V–(arene^4?)–U^V, KU^IV–(arene^4?)–U^V, and K₂U^IV–(arene^4?)–U^IV for complexes 2 , 3 , and 4 respectively. The potassium cations in complexes 3 and 4 are coordinated to the siloxide ligands both in the solid state and in solution. The addition of KOTf (OTf=triflate) to the neutral compound 2 promotes its disproportionation to yield complexes 3 and 4 (depending on the stoichiometry) and the U^IV mononuclear complex [U(OSi(OtBu)₃)₃(OTf)(thf)₂] ( 5 ). This unprecedented reactivity demonstrates the key role of potassium for the stability of these complexes.     

Thermal Responsive Ion Selectivity of Uranyl Peroxide Nanocages: An Inorganic Mimic of K+ Ion Channels

An actinyl peroxide cage cluster, Li_48+mK₁₂(OH)_m[UO₂(O₂)(OH)]₆₀ (H₂O)_n (m≈20 and n≈310; U₆₀), discriminates precisely between Na⁺ and K⁺ ions when heated to certain temperatures, a most essential feature for K⁺ selective filters. The U₆₀ clusters demonstrate several other features in common with K⁺ ion channels, including passive transport of K⁺ ions, a high flux rate, and the dehydration of U₆₀ and K⁺ ions. These qualities make U₆₀ (a pure inorganic cluster) a promising ion channel mimic in an aqueous environment. Laser light scattering (LLS) and isothermal titration calorimetry (ITC) studies revealed that the tailorable ion selectivity of U₆₀ clusters is a result of the thermal responsiveness of the U₆₀ hydration shells.     

Three‐Dimensional MOF‐Type Architectures with Tetravalent Uranium Hexanuclear Motifs (U6O8)

Four metal–organic frameworks (MOF) with tetravalent uranium have been solvothermally synthesized by treating UCl₄ with rigid dicarboxylate linkers in N,N‐dimethylfomamide (DMF). The use of the ditopic ligands 4,4′‐biphenyldicarboxylate ( 1 ), 2,6‐naphthalenedicarboxylate ( 2 ), terephthalate ( 3 ), and fumarate ( 4 ) resulted in the formation of three‐dimensional networks based on the hexanuclear uranium‐centered motif [U₆O₄(OH)₄(H₂O)₆]. This motif corresponds to an octahedral configuration of uranium nodes and is also known for thorium in crystalline solids. The atomic arrangement of this specific building unit with organic linkers is similar to that found in the zirconium‐based porous compounds of the UiO‐66/67 series. The structure of [U₆O₄(OH)₄(H₂O)₆(L)₆] ? X (L=dicarboxylate ligand; X=DMF) shows the inorganic hexamers connected in a face‐centered cubic manner through the ditopic linkers to build up a three‐dimensional framework that delimits octahedral (from 5.4 Å for 4 up to 14.0 Å for 1 ) and tetrahedral cavities. The four compounds have been characterized by using single‐crystal X‐ray diffraction analysis (or powder diffraction analysis for 4 ). The tetravalent state of uranium has been examined by using XPS and solid‐state UV/Vis analyses. The measurement of the Brunauer–Emmett–Teller surface area indicated very low values (Langmuir <300 m² g^?1 for 1 , <7 m² g^?1 for 2 – 4 ) and showed that the structures are quite unstable upon removal of the encapsulated DMF solvent.     

Subduction coefficients for 〈2N/2–S, 12S〉 ↓ 〈2, 1〉 ⊗ 〈2, 1〉 of U(n) ↓ U(n1) ⊗ U(n2)

The determination of the subduction coefficients for states of the unitary group U(n) under the restrictions U(n) ↓ U(n₁) ? U(n₂) have been considered for the spin free states of many electron systems. Using the transformation properties of the tensor basis spanning the irreducible representation 〈2^N/2–S, 1^2S〉 of U(n) under the permutations of electron coordinates, a simple programmable procedure has been developed for the determination of these coefficients. The procedure has been illustrated using a simple example.     

The evaluation of matrix elements for non-canonical Weyl tableau basis states adapted toU(n 1+n 2)⊃U(n 1)×U(n 2)

Summary This is the first paper of a series of two, which enables the evaluation ofU(n) generator matrix elements in the non-canonical Weyl tableau basis adapted to subgroupU(n ₁)×U(n ₂). In this paper the explicit closed formulae for subduction coefficients are presented. These formulae will become useful through an inductive method to be presented in the second paper.     

An Application of the Dynamical Lie Algebraic Method to Potential Energy Surface of the Stable Linear Asymmetric Tetratomic Molecules

Potential energy surfaces play an important role in studying theoretical chemistry. In the present paper, we first use the dynamical symmetry group G = U ₁(4) U ₂(4) U ₃(4) to get the expression of the potential energy surface for the stable linear asymmetric tetratomic molecules with the stretching vibration and the dissociation energy. The method can be applied to a number of stable tetratomic molecules. As an example we use the method to calculate the potential energy surface of C₂HD.     

A Local D4h Symmetric Dysprosium(III) Single-Molecule Magnet with an Energy Barrier Exceeding 2000 K**

Three six-coordinate Dy^III single-molecule magnets (SMMs) [Dy(O^tBu)₂(L)₄]⁺ with local D_4h symmetry are obtained by optimizing the equatorial ligands. One of the compounds with L=4-phenylpyridine shows an energy barrier (U_eff) of 2075(11) K, which is the third largest U_eff, and the first U_eff>2000 K for SMMs with axial-type symmetry so far. Ab initio analysis indicates that the exceptional uniaxial magnetic anisotropy is deeply related to the axially compressed octahedral geometry. This work provides a new insight into the local D_4h symmetry for high-performance SMMs.     

A Route to Stabilize Uranium(II) and Uranium(I) Synthons in Multimetallic Complexes

Herein, we report the redox reactivity of a multimetallic uranium complex supported by triphenylsiloxide (−OSiPh₃) ligands, where we show that low valent synthons can be stabilized via an unprecedented mechanism involving intramolecular ligand migration. The two- and three-electron reduction of the oxo-bridged diuranium(IV) complex [{(Ph₃SiO)₃(DME)U}₂(μ-O)], 4 , yields the formal “U^II/U^IV”, 5 , and “U^I/U^IV”, 6 , complexes via ligand migration and formation of uranium-arene δ-bond interactions. Remarkably, complex 5 effects the two-electron reductive coupling of pyridine affording complex 7 , which demonstrates that the electron-transfer is accompanied by ligand migration, restoring the original ligand arrangement found in 4 . This work provides a new method for controlling the redox reactivity in molecular complexes of unstable, low-valent metal centers, and can lead to the further development of f-elements redox reactivity.     

Selective Permeability of Uranyl Peroxide Nanocages to Different Alkali Ions: Influences from Surface Pores and Hydration Shells

The precise guidance to different ions across the biological channels is essential for many biological processes. An artificial nanopore system will facilitate the study of the ion‐transport mechanism through nanosized channels and offer new views for designing nanodevices. Herein we reveal that a 2.5 nm‐sized, fullerene‐shaped molecular cluster Li_48+mK₁₂(OH)_m[UO₂(O₂)(OH)]_60?(H₂O)_n (m≈20 and n≈310) ( U₆₀ ) shows selective permeability to different alkali ions. The subnanometer pores on the water–ligand‐rich surface of U₆₀ are able to block Rb⁺ and Cs⁺ ions from passing through, while allowing Na⁺ and K⁺ ions, which possess larger hydrated sizes, to enter the interior space of U₆₀ . An interestingly high entropy gain during the binding process between U₆₀ and alkali ions suggests that the hydration shells of Na⁺/K⁺ and U₆₀ are damaged during the interaction. The ion selectivity of U₆₀ is greatly influenced by both the morphologies of the surface nanopores and the dynamics of the hydration shells.     

Calculation of SN 1 + N 2 ⊃ SN1 ⊗ sn 2 and U(n1 + n2) ⊃ u (n1) ⊗ u (n2) subduction coefficients by using spin graph

By use of the graphical method of spin algebra, simple, and closed expressions for S_N1+_N2 ? S_N1 ? S_N2 and U(n₁ + n₂) ? U(n₁) ? U(n₂), subduction coefficients are derived.     

The spread of unicyclic graphs with given size of maximum matchings

The spread s(G) of a graph G is defined as s(G) = max _i,j |λ _i − λ _j |, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U ^*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U ^*(n,k), and the graph with the largest spread in U(n,k).      

On construction of diatomic potential energy functions

The Clinton function α_n( R ) corresponding to the model potential energy function U_n( R ), is proposed as a test of applicability of U_n( R ). Such an analysis is given for some model potential energy functions.     

Ab initio study of bonding trends for f0 actinide oxyfluoride species

 Fully relativistic, four-component Dirac–Fock calculations and quasirelativistic pseudopotential calculations at different ab initio levels are used to study the bonding trends among the naked, triatomic [OAnO] ^q+ groups or the oxyfluorides [AnO _n F _m ] ^q with f ⁰ configurations. The triatomic f ⁰ series is suggested to range from the bent ThO₂ via the linear OPaO⁺ to at least NpO₂ ³⁺, a possible new gas-phase species. The neutral oxyfluoride molecules include the experimentally unknown NpO₂F₃ and PuO₂F₄. The latter is a candidate for the so far unknown oxidation state Pu(VIII), which is found to lie considerably above Pu(VI), but to be locally stable. Their all-oxygen isoelectronic analogues are NpO₅ ³⁻, known in the solid state, and the unknown PuO₆ ⁴⁻. Further possible candidates for Pu(VIII) are PuO₄(D _4h ) and the cube-shaped PuF₈(O _h ). Isoelectronic UF₈ ²⁻ is calculated to be D _4d , in agreement with experiment. Received: 18 May 2001 / Accepted: 21 June 2001 / Published online: 11 October 2001