Fuzzy Symmetry Characteristics of Propadine Molecule

The fuzzy symmetry characteristics for the internal-rotation of propadine were analyzed using the fuzzy symmetry theory for molecule and molecular orbital (MO). In the process of rotation, three different symmetry point groups D_2h, D_2d, and D₂ were considered. Using the D_4h point group, which is the minimal point group including all symmetry elements of D_2h, D_2d, and D₂, we can analyze the fuzzy symmetry for this process. The elements included in D_4h point group can be classified to four subsets: (i) G0—it includes all the elements in D₂ point group, also belongs to all the above three point groups of D_2h, D_2d, and D₂; (ii) G1—it includes the elements in D_2h point group, but not in D_2d point group; (iii) G2—it includes the elements in D_2d point group, but not in D_2h point group; (iv) G3—it includes the elements in D_4h point group, but not in D_2h or D_2d point group. On the basis of the above four subsets, we analyzed the membership functions and the regularity of variation in MOs for the internal-rotation of propadine.     

Tetra-hydrides of the third-row transition elements: spin–orbit coupling effects on geometrical deformation in WH4 and OsH4

The dissociation energies of MH₄ (M =  La, Hf–Hg) were computed using full optimized reaction space (FORS) multi-configuration self-consistent field (MCSCF) and second-order multi-reference Møller–Plesset perturbation methods with the SBKJC basis sets augmented by a set of polarization functions (SBKJC(f,p)). It was shown that of the molecules examined, only four tetra-hydrides HfH₄, TaH₄, WH₄, and OsH₄ with T_d symmetry are lower in energy than the corresponding dissociation limits. For WH₄ and OsH₄, the potential energy surfaces from the D_4h to the T_d structure were explored from both theoretical calculations and symmetry arguments based on the pseudo-Jahn- Teller effect. As for WH₄, it is found that the ground state could be ³E_g, ³A_2g, or ³B_2g at the D_4h structure. The present calculations suggest that the ground state is ³E_g, and that this state is stabilized by the e_u deformation into a C_2v structure (³B₁) and then sequentially to the most stable T_d structure (³A₂). If the molecular system is promoted to the lowest ³B_2g state, the D_4h structure can directly deform into the most stable T_d structure along the b_2u vibrational mode. For OsH₄, the ground state (⁵B_1g) at the D_4h structure deforms into a D_2d structure and the resulting ⁵B₂ state strongly interacts with the lowest ³E and ¹A₁ states due to the spin-orbit couplings (SOCs). As a result, it was shown that the relativistic potential energy of the lowest spin-mixed state (ground state) monotonically decreases along the D_2d deformation path from the D_4h to the T_d structure.     

Organomagnesium clusters: Structure, stability, and bonding in archetypal models

We have studied the molecular structure and the nature of the chemical bond in the monomers and tetramers of the Grignard reagent CH₃MgCl as well as MgX₂ (X = H, Cl, and CH₃) at the BP86/TZ2P level of theory. For the tetramers, we discuss the stability of three possible molecular structures of C_2h, D_2h, and T_d symmetry. The most stable structure for (MgCl₂)₄ is D_2h, the one for (MgH₂)₄ is C_2h, and that of (CH₃MgCl)₄ is T_d. The latter is 38 kcal/mol more stable with chlorines in bridge positions and methyl groups coordinated to a Mg vertex than vice versa. We find through a quantitative energy decomposition analysis (EDA) that the tetramerization energy is predominantly composed of electrostatic attraction ΔV_elstat (60% of all bonding terms ΔV_elstat + ?E_oi) although the orbital interaction ?E_oi also provides an important contribution (40%).     

Theoretical identification of the lowest-energy structure of (SiC)12 heterocluster: Segregation of C and Si in planar and cage structures

The structures and relative stabilities of various plane and cage isomers of (SiC)₁₂ cluster have been systematically computed using density functional theory at the level of BLYP. A number of starting configurations were generated from the low-energy isomers of C₂₄ cluster via replacing 12 C atoms by Si atoms, which are D_6h planar structure, and the D_6d, D_2h, O_h, and D_4h symmetrical fullerene cages. The heterofullerene cage obeying six isolated squares rules are not the most preferred structural motif for (SiC)₁₂ cluster. The structural candidates with fully alternating Si–C arrangement are energetically unfavorable. Instead, the (SiC)₁₂ cluster tend to adopt plane, bowl, saddle, and highly distorted cage structures. In all cases, segregation of C atoms is a common feature.     

Group 14 structural variations: perhalo derivatives of the “dimetallenes”: dicarbenes, disilenes, digermenes, distannenes, and diplumbenes

Trends in the structural variations of all perhalo derivatives of dicarbenes and their Group 14 analogues have been studied. This included all M₂X₄ molecules, where M = C, Si, Ge, Sn, or Pb, and X = F, Cl, Br, or I. Mapping the potential energy surface of all molecules has uncovered several isomers. The stability of these isomers depends on both the Group 14 atoms and the halogen ligands. Several isomers were found stable; the ones that are global minima include (with their symmetries and an example in parenthesis): the typical ethene structure X₂M=MX₂ (D _2h, F₂C=CF₂), an X₃M–MX structure (C _S, F₃Si–SiF, a trifluorosilyl–silylene), another X₃M–MX structure (C ₁, Cl₃Si–SiCl), one more X₃M–MX structure with a single halogen bridge (C ₁, I₂Si–μI–SiI), a trans double halogen bridged structure (D _2h, FSn–μF₂–SnF), and another trans double-bridged structure with puckered ring (C _S, IPb–μI₂–PbI). Some of the other structures that are stable but are not the global minima include: a trans-bent structure X₂M–MX₂ (C _2h, all X₂Si–SiX₂), cis double-bridged structure (C _2v with planar ring, FPb–μF₂–PbF, or with puckered ring, C _2v, IGe–μI₂–GeI), and even a square bipyramidal structure (D _4h, Sn–μF₄–Sn). The energy differences between some of the structures are small and the application of another computational method and using a different basis set might alter their relative stabilities. Reasons for the difference in the stabilities of isomers have been discussed.     

Theoretical investigation of structure and stability of oligomers of LiH,NaH, LiF,and NaF

The molecules Li_nH_n, Na_nH_n, Li_nF_n, n=1,..., 4, and NaF and Na₂F₂ are investigated by means of extended basis set SCF and CEPA-PNO computations. In analogy to the D _2h structure of dimers, it is found that trimers have a planar cyclic D _3h equilibrium geometry. For the tetramer of LiH and NaH, the D _4h structure has about the same energy as the 3-dimensional T _d structure, whereas the latter is definitely favoured for Li₄F₄. Correlation effects are investigated for the oligomerization of LiH and the dimerization of LiF. The effect of electron correlation on corresponding E turns out to be small (<4 kJ/mol), except for the case that the T _d tetramer is involved which has a rather large correlation energy.     

Flattened fullerenes

Quantum-chemical calculations of giant flattened fullerenes C _n (lentil-shaped) have been carried out. The topology, molecular and electronic structure of these fullerenes have been studied. Such molecules consist of two identical coronenoid fragments of a graphite layer, which are arranged one above the other, and a system of polycondensed five- and six-membered cycles, which form a side surface of the cluster. Polyhedral structures with isolated pentagons of three symmetry types (D _6h ,D _6d , andD _3h ) have been considered. The topology of these structures is described in terms of planar molecular graphs. Electronic structures of eleven flattened lentil-shaped C _n clusters (n = 72–216) have been studied in the π approximation. Most of the considered systems have closed or quasi-closed electron shells (according to Hückel) and rather large energy gaps separating the highest occupied and lowest unoccupied MO, which is indicative of their kinetic stability. Fragments of the potential energy surfaces of the C₇₂ and C₉₆ fullerenes have been studied by the MNDO, AM1, and MNDO/PM3 methods. For the C₉₆ cluster, two local energy minima, which correspond to the lentil-shaped isomers withD _6h andD _6d symmetry, have been determined. As a result of optimization of geometric parameters, it was found that all three methods give close values of heights (H = 6.7 Å) and diameters (D = 9.8 Å) for both isomers. The clusters change to quasi-two-dimensional systems (H«D) with increasing sizes of coronenoid fragments.     

Angular parameters of the overlap integrals of f-orbitals

Angular parameters are calculated for these integrals for - and -types in the complexes MX₆ (O_h and D_3h symmetry), MX₈ (O_h, D_4d, D_2d, D_6h, C_2V, and D_3h), and MX₉ (D_3h). Examples are given of the use of the angular parameters in considering coordination compounds of the lanthanide elements: stabilization energy of the addend field and geometry of the compounds in the ground and excited states.     

Exploring the Potential Energy Surface of E2P4 Clusters (E=Group 13 Element): The Quest for Inverse Carbon‐Free Sandwiches

Inverse carbon‐free sandwich structures with formula E₂P₄ (E=Al, Ga, In, Tl) have been proposed as a promising new target in main‐group chemistry. Our computational exploration of their corresponding potential‐energy surfaces at the S12h/TZ2P level shows that indeed stable carbon‐free inverse‐sandwiches can be obtained if one chooses an appropriate Group 13 element for E. The boron analogue B₂P₄ does not form the D_4h‐symmetric inverse‐sandwich structure, but instead prefers a D_2d structure of two perpendicular BP₂ units with the formation of a double B?B bond. For the other elements of Group 13, Al–Tl, the most favorable isomer is the D_4h inverse‐sandwich structure. The preference for the D_2d isomer for B₂P₄ and D_4h for their heavier analogues has been rationalized in terms of an isomerization‐energy decomposition analysis, and further corroborated by determination of aromaticity of these species.     

Deuteration effects on the phosphorescence of aromatic hydrocarbons

Observations of the phosphorescence decay of isotopic mixtures of naphthalene-h_s and -d_s, phenanthrene-h₁₀ and -d₁₀, and chrysene-h₁₂ and -d₁₂, in ethanol solutions at 77 K are analysed to determine the ratio k_PT^H/k_PT^D of the triplet radiative rate parameters of the perprotonated and perdeuterated compounds. The ratio is 1.20 (±0.07) for naphthalene, 1.39 (±0.06) for phenanthrene, and 0.98 (±0.04) for chrysene.     

Some continuous geometry transitions and the consequences for a transition‐metal atom

By considering a transition‐metal ion in the field of some symmetrically placed ions, we illustrate the consequences of a continuous change of the structure of the ligands on the energies of the 3d electrons of the transition‐metal atom. Both a rigorous mathematical derivation and an analysis based on group theory are presented. For six ions surrounding the transition‐metal atom, a continuous D_∞h → D_3d → O_h→ D_3d→ D_6d transition is observed, whereas for four ions, a continuous D_{∞ h}→ D_2d→ T_d→ D_2d→ D_4d transition results. Although the two systems possess many similarities, interesting differences are found as well. Finally, we demonstrate that when including orbital interactions between the ligands and the transition‐metal atom, quantitative differences occur. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Raman spectra of lanthanide sesquioxide single crystals: Correlation between A and B-type structures

Structures and Raman spectra of lanthanide sesquioxide single crystals with A-type trigonal structure (La₂O₃, Pr₂O₃, Nd₂O₃, Sm₂O₃) and B-type monoclinic structure (Sm₂O₃, Eu₂O₃, Gd₂O₃) are compared. The B form (C³_2h or $\text{C2}\text{m}\text{, Z = 6}$) derives from the A form (D³_3d or $\text{P}\text{3}\text{m1, Z = 1}$) by a slight lattice deformation, implying a splitting of D_3d and C_3v atomic positions into less symmetrical C_2h and C_s sites. This close structural relationship allows one to relate the Raman active modes of the B-type crystals to vibrations of the A-type crystals and to deduce an interpretation of the complex B-type spectra from those of the simpler A-type spectra. Furthermore, it is shown that the frequency of the modes which mainly involve metal-oxygen stretching motion increases with the lanthanide atomic number in the A and B series. This evolution is interpreted in terms of increasing compactness of the structure.     

Triplet states in isotopically mixed anthracene crystals: High resolution optical spectroscopy

The triplet O,O transitions of guest and host in isotopically mixed anthracene crystals of various compositions (A-h₁₀, ¹³C-monosubstituted A-h₁₀, A-d₁h₉, A-d₂h_g in A-d₁₀ and A-d₁₀ in A-h₁₀) have been investigated using high resolution laser excitation spectroscopy. The guest aggregate spectra have been studied in polarized light as a function of guest concentration up to 15%. The analyses allow us to identify the monomer, dimer and trimer lines. From the dimer splittings the dominant resonance pair interactions are dedu The comparison of different mixed crystal systems with guest levels below and above the host exciton band reveals that quasiresonance and superexchange corrections are of minor importance. The experimental resonance pair interactions are used to calculate the triplet exciton band structure of anthracen and the observed guest polarization behaviour is interpreted quantitatively by the Rashba effect. Finally, the lower Davydov component of the host is s and broadened with increasing guest concentration. The shift is discussed using a theoretical model of Lifshitz.     

Structural stability and energetics of C,Si, and Ge microclusters: empirical many-body potential energy function calculation

The structural stability and energetics of carbon, silicon, and germanium microclusters containing 3?7 atoms have been investigated by using a recently developed empirical many-body potential energy function (PEF), which comprises two- and three-body atomic interactions. The PEF satisfies both bulk cohesive energy per atom and bulk stability exactly. It has been found that the most stable C_3?4 microclusters are linear withD _∞h symmetry but C_5?7 microclusters are planar withD _nh symmetry. Silicon and germanium microclusters show similar structural stability. TheX _n (X=Si, Ge;n=3?7) microclusters are found to be most stable in the following forms:X ₃ is triangular withD _3h symmetry,X ₄ is tetragonal withT _d symmetry,X ₅ is square pyramidal withD _4h symmetry,X ₆ is bipyramidal square withO _h symmetry, and finallyX ₇ is square pyramidal having two atoms underneath withD _2h symmetry.     

Hyperfine structure measurements of103Rh

Hyperfine structure has been measured in 28 states of¹⁰³Rh below 34,000 cm^?1. The magnetic dipole interactionA constants in the metastable states 4d ⁸ 5s ⁴ P _5/2,3/2,² P _3/2,1/2,² D _5/2,3/2,² G _9/2,7/2 and 4d ⁷ 5s ^{2 4} F _{9/2,7/2,5/2,3/2} have been determined using the laser radio-frequency double-resonance method and in the states 4d ⁸ 5p ⁴ D _{7/2,5/2,3/2,1/2},⁴ G _7/2,5/2,⁴ F _{9/2,7/2,5/2,3/2},² G _9/2,7/2,² F _7/2,5/2 and² D _5/2,3/2 by high-resolution laser spectroscopy.     

Molecular reorientation of liquid benzene. Anisotropic Raman scattering of the CH and CD stretching modes in the deuterated molecules

The anisotropic Raman spectra of the CH and CD stretching modes in seven deuterated benzenes of D_6h, D_3h, D_2h and C_2h symmetry are reported. The reorientational linewidths are interpreted within the model of anisotropic rotational diffusion. The data are consistent with NMR relaxation studies. The study covers the temperature range between T/T_c = 0.49 and T/T_c = 0.97.     

Crystal and molecular structure of bis[tetracarbonyldiphenylphosphidomanganese(0)]

The crystal structure of bis[tetracarbonyldiphenylphosphidomanganese(0)] has been determined by an X-ray diffraction study. The complex crystallizes in the monoclinic space group P2₁/n with four molecules in a unit cell of dimensions, a 15.714(4), b 16.446(5), c 12.016(4) Å, and β 101.25(2)°. The molecule has approximately centrosymmetric bi-octahedral D_2h structure. Each manganese atom is bonded to two phosphorus atoms of μ-diphenylphosphide groups and four carbonyl carbon atoms. The separation of the manganese atoms is 3.690(1) Å.     

Hyperfine structure measurements in Kr II

The fast ion beam laser technique has been utilized to study the hyperfine structure in the transitions 4d ⁴ D _7/2-5p ⁴ D ₇ ^2/0 at 6420 Å and 4d ⁴ D _7/2-5p ⁴ D ₅ ^2/0 at 6303 Å in singly-charged krypton. The magnetic dipole and electric quadrupole hyperfine constants have been extracted for the upper levels of the transitions.     

Force field for in-plane vibrations of pyrazine

A general quadratic force field has been calculated using the MINDO/3 approximation for the in-plane vibrations of pyrazine. Analytical first derivatives and numerical second derivatives of the energy have been computed. The force constants have been refined to fit experimental frequencies of pyrazine-h₄, pyrazine-d₄ and cis-pyrazine-d₂.     

A theoretical study on the strength of multiple metal-metal bonds in binuclear complexes and transition-metal dimers by a non-local density functional method

The strength of multiple metal-metal bonds in the metal dimers M₂ (M = Cr, Mo or W) and binuclear complexes M₂(OH)₆ (M = Cr, Mo or W), M₂Cl₄(PH₃)₄ M = V, Cr, Mn, Nb, Mo, Tc, Ta, W or Re) has been studied by a non-local density functional theory. The method employed here provides metal-metal bond energies [D(M-M)] in good accord with experiments for Cr₂ and Mo₂, and predicts that W₂ of the three dimers M₂ (M = Cr, Mo or W) has the strongest metal-metal bond with D(W-W) = 426 kJ mol⁻¹ and R(W-W) = 2.03 Å. Among the binuclear complexes studied here we find the 3d elements to form relatively weak metal-metal bonds (40–100 kJ mol⁻¹), compared to the 4d and 5d elements with bonding energies ranging from 250 to 450 kJ mol⁻¹. The metal-metal bond for a homologous series is calculated to be up to 100 kJ mol⁻¹ stronger for the 5d complex, than for the 4d complex. An energy decomposition of D(M-M) revealed that the σ-bond is somewhat stronger than each of the π-bonds, and one order of magnitude stronger than the δ-bond. For the same transition metal we find D(M-M) to be larger for M₂(PH₃)₄Cl₄ (M = Cr, Mo or W) than for M₂(OH)₆ (M = Cr, Mo or W), and attribute this to a stronger π-interaction in the former series. While many of the findings here are in agreement with previous HFS studies, the order of stability D(3d-3d) « D(4d-4d) < D(5d-5d) differs from the order D(3d-3d) « D(5d-5d) < D(4d-4d) obtained by the HFS method, and the present method provides in general more modest values for D(M-M) than the HFS scheme.