Algorithm for variational calculations of molecular symmetry in solving anharmonic vibrational problems

A universal program for variational calculations of molecular symmetry in solving anharmonic vibrational problems, realized by the author, is described. The program uses the group-theoretical method. Symmetrized basis wave functions are constructed with the aid of the generalized KJebsch-Gordan series suggested by the author. The method of constructing symmetrized basis wave functions and the program for adequate calculations of molecular symmetry were verified for many molecules of different symmetry groups: O_h, O, T_d, T_h, T, D_∞h, C_t8v, D_nd, D_nh, D_n, C_nv, C_nh, S_2n, C_n, C_i, C_s, and C₁ where 2 ≤n ≤6. It was confirmed that the program provides correct results and high-speed operation. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1146–1153, November–December, 1997.     

The infrared spectra of polycyclic aromatic hydrocarbons containing a five-membered ring: symmetry breaking and the B3LYP functional

The infrared spectra of six molecules, each of which contains a five-membered ring, and their cations are determined using density functional theory; both the B3LYP and BP86 functionals are used. The computed results are compared with the experimental spectra. For the neutral molecules, both methods are in good agreement with experiment. Even the Hartree–Fock (HF) approach is qualitatively correct for the neutral species. For the cations, the HF approach fails, as found for other organic ring systems. The B3LYP and BP86 approaches are in good mutual agreement for five of the six cation spectra, and are in good agreement with experiment for four of the five cations where the experimental spectra are available. It is only for the fluoranthene cation where the BP86 and B3LYP functionals yield different results; the BP86 approach yields the expected C _{2 v} symmetry, while the B3LYP approach breaks symmetry. The experimental spectra support the BP86 spectra over the B3LYP spectra, but the quality of the experimental spectra does not allow a critical evaluation of the accuracy of the BP86 approach for this difficult system. Received: 9 February 1999 / Accepted: 31 March 1999 / Published online: 14 July 1999     

Molecular and electronic structure of some binary polyhedral clusters

The molecular and electronic structures of some polyhedral alternate molecules X_nY_n, where n=12, 16; X=B, Al, Si; Y=N,P,C, and of homoatomic clusters C₂₄, Si₂₄, C₃₂, and Si₃₂ are calculated in a valence approximation by the MNDO method. It is suggested that the σ-frameworks of these molecules are formed of four- and six-membered rings, with each X atom having only Y atoms as neighbors. The singlet states of all these systems have local minima on the corresponding potential energy surfaces with T_h symmetry for n=12 and T_d symmetry for n=16. The main structural parameters, heats of formation, ionization potentials, and effective charge distributions are given. It is concluded that the X_nY_n heteroatomic clusters can exist when X and Y are atoms of Group III and V elements, respectively, or both are atoms of Group IV elements. A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 6, pp.976–982, November–December, 1995. Translated by L. Smolina     

Hydration of platinum(II) complexes: a molecular mechanics study using atom-based force-field parameters

 This work is related to the interaction of water with two platinum(II) complexes, [Pt(NH₃)₄]²⁺ (denoted 1) and trans-[Pt(OH)₂(NH₃)₂] (denoted 2). We have considered two approaches of a water molecule to complexes 1 and 2 along the z-axis normal to the platinum(II) coordination plane: approach I, with the water oxygen oriented towards Pt, and approach II, with one water hydrogen directed towards Pt. Calculations have been performed within a molecular mechanics method based upon the interaction potentials proposed earlier by Claverie et al. and subsequently adjusted to results obtained with symmetry – adapted perturbational theory as well as with supermolecule (up to second-order M?ller–Plesset, MP2) methods. We discuss some possible simplifications of the potentials mentioned. The results relative to the hydration of Pt complexes 1 and 2 following approach I or II are discussed and compared to recent (MP2) ab initio energy–distance curves that we have recently determined. The MP2 calculations have shown that besides exchange–repulsion contributions, which are very similar in all hydrated complexes, approach I is mainly governed by electrostatics, whereas for approach II both electrostatic and dispersion contributions are important. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

Fuzzy symmetries of two classes of linear polyacene molecules

The fuzzy symmetries of two kinds of linear polyacene molecules are probed into in the paper. In these molecules, any one of the benzene rings abreast connects at most other two rings in two ways: either its two opposite C–C bonds combine with two other rings, respectively, or its two meta-position C–C bonds connect two rings in cis- and trans-form, respectively. The former is called p-polyacenes (or straight polyacenes), and the latter is m-polyacenes (or kinked ones). It can be thought as the planar molecule with approximate one-dimensional space periodic transformation (parallel translation) symmetry, namely, group G₁²{{\rm G}_{1}^{2}} symmetry, when the number of its benzene ring is very large; on the other hand, it can be considered as the fuzzy group G₁²{{\rm G}_{1}^{2}} symmetry, if the benzene ring number is not large enough. The p-polyacene and m-polyacene with 20 benzene rings are analyzed as typical examples, and the energies of the π-molecular orbital (MO) and the fuzzy symmetry characters related to the space symmetry transformations are carefully examined. Moreover, the π-MOs of the p-polyacenes and m-polyacenes with different numbers of benzene ring are investigated to obtain the related rules.     

Effect of ligand coordination type on the relative stability of linear mercury clusters

The problem of stabilization of linear mercury clusters with acceptor ligands coordinated along the symmetry axis of the cluster is discussed in terms of the MNDO method. It is shown that stable four-membered rings Hg₂Cl₂ may be formed. It is proposed that the structure of linear mercury clusters with side coordination of ligands be described as the result of “polymerization” of short stable linear molecules XHg_nX (n=1, 2) and HgX ₂ ¹⁻ , HgX ₃ ¹⁻ ions with accepting terminal groups. Mordovia State University. Institute of Organoelement Compounds, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 1, pp. 26–34, January–February, 1998. This work was performed in the framework if the interindustry scientific and technical program “Fullerenes and Atomic Clusters.”     

A quantum-chemical and gas phase electron diffraction study of the structure of formylphosphine and acetyldimethylphosphine

The equilibrium geometry and energy and structural changes accompanying inversion motion in the phosphorus fragment and acyl group internal rotation in the H₂PCHO and Me₂PCMeO molecules were calculated by the MP2(full) method using basis sets from 6–31G(d, p) to 6–311G(3df, 2p). The structure of Me₂PCMeO was determined by electron diffraction using the dynamic model of acyl group internal rotation based on the quantum-chemical potential function of torsional motion. Acylphosphines have amide-type equilibrium conformations with acyl groups rotated through ∼100° from their orientation in the C=O/PX₂ anti- form, where X = H, Me (C ₁ symmetry). Considerable pyramidality of the phosphorus fragment distinguishes the equilibrium structures of acylphosphines from amides with a planar molecular frame (C _s symmetry). The r _h1 geometric parameters of the Me₂PCMeO molecule determined by electron diffraction closely agree with quantum-chemical estimates for the equilibrium configuration.     

Influence of the out-of-plane distortions of nuclear configurations of molecules with then-AO of the heteroatom directed along theC 2 symmetry axis on spin-orbit coupling between thenπ*- and ππ*-states

This paper studies changes in the matrix elements (U_mp) of spin-orbit coupling between the nπ^*- and ππ^*-states, which are induced by the (“chair,” “bath”) distortions of the nuclear configurations of molecules. The analysis is performed for acridine molecules in which the n-p_z atomic orbital (AO) of the heteroatom is directed along the C₂ symmetry axis. Earlier, for molecules with a planar nuclear configuration of C_2v symmetry and with the heteroatom lying on the C₂ axis, we established the dependence of U_mp on the symmetry of ππ^*-states [Γ(ππ^*)=A₁ or B₂]. The values of U_mp differ by more than one order of magnitude; this is in line with the difference between the interconversion rate constants (K_isc; two or three orders). In this work we have found that this contrast in U_mp (and, accordingly, in K_isc) is retained when the nuclear configuration of the acridine molecule is distorted to the “chair” (AC-A) configuration, although the individuality of both molecular orbital types (nσ-MO and π-MO) and states nπ^* and ππ^* is annihilated to a certain extent. For the “bath” (AC-B) conformation the difference in U_mp considerably diminishes. Reasons for the changes in the matrix elements of spin-orbit coupling and rate constants of the S-T conversion are analyzed. The available energy level diagram is critically analyzed, and a slightly different diagam as well as a scheme of nonradiating deactivation of acridine are suggested. L. Ya. Karpov Physicochemical Scientific Research Institute. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 292–297, March–April, 1995. Translated by L. Smolina     

Solid solutions of normal paraffins

The results of the X-ray diffraction and thermal X-ray diffraction studies of the paraffins C_nH_2n+2 are revised based on new principles asserting the existence of several types of rotator states of paraffins. Along with the known isomorphism factors, such as the parity (symmetry) of the starting components and the difference between the chain lengths of their molecules (Δn), there is a factor that is specific to paraffins: differences in the energy state of molecules entering solid solutions. St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 929–938. September–October, 1996. Translated by L. Smolina     

Structures and aromaticity of the planar Al<Subscript>2</Subscript>P<Subscript>2</Subscript><Superscript><Emphasis Type="Italic">n</Emphasis>−</Superscript> (<Emphasis Type="Italic">n</Emphasis>=1–4) clusters

Clusters Al₂P₂ ⁿ⁻ (n = 1–4) were theoretically investigated using density functional theory (DFT) methods at the B3LYP/6-311+G* and B3PW91/6-311+G* levels of theory. The calculated results showed that the planar structure (D _2h symmetry) of Al₂P₂ ⁿ⁻ (n = 1–4) species was the global minimum. And the negative nucleus-independent chemical shift (NICS) value of Al₂P₂ ⁿ⁻ (n = 1–4) species indicated the existence of a ring current in the planar structure (D _2h symmetry). A detailed molecular orbital (MO) analysis revealed that the planar structures (D _2h symmetry) had π aromaticity, which further exhibited the strongly aromatic character for Al₂P₂ ⁿ⁻ (n = 1–4) species.     

Structures of Rydberg transitions in the absorption spectra of methyl-substituted derivatives of bis(η6-benzene)chromium

The effect of methylation of ligands in bis(η⁶-benzene)chromium (1) on the structure of Rydberg transitions in absorption spectra has been studied. A detailed analysis and interpretation of all Rydberg elements of the vapor-phase spectra of bis(η⁶-benzene)chromium (2), bis(η⁶-o-xylene)chromium (3), bis(η⁶-m-xylene)chromium (4), and bis(η⁶-mesitylene)chromium (5) was carried out. The vapor-phase electronic absorption spectrum of bis(η⁶-p-xylene)chromium (6) was measured, and the assignment of the Rydberg bands was made for the first time. The first ionization potentials of complexes 2–5 were refined. The energy of detachment of the 3d_z ² electron and the parameters of the Rydberg excitations for molecule 6 were determined. The vibronic components of the 3d_z ²→R4p _x,y transition in the spectra of complexes 2 and 6 were assigned. The differences in the Rydberg structure of the spectra of compounds 2–6 were analyzed in terms of the selection rules for optical transitions in the corresponding symmetry groups. The vapor-phase spectra correspond to conformers with the symmetry groupsC _2v andC ₂ for complexes 2–4, with the symmetry groupsD _3h andD ₃ for compound 5, and with the symmetry groupD _2d for complex 6. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 897–903, May, 1998.     

Ab initio calculations of atomic interaction in the ClCH2OCH3 molecule

Ab initio calculations of both ClCH₂OCH₃ and ClCH₂CH₃ molecules and various ClCH₂OCH₃ structures with fixed angles of rotation of the methoxy group about the C−O bond were performed by the restricted Hartree-Fock method in the valence-split 6–31 G^* basis set with full optimization of the geometry. The populations of the valent p-orbitals of the chlorine atoms in these molecules have been analyzed. The³⁵Cl NQR frequencies and the asymmetry parameters of the electric field gradient (EFG) at the³⁵Cl nuclei have been calculated. Good agreement with experimental NQR frequencies was obtained for the calculations where only the populations of the less diffuse 3p-components of these orbitals were used. The³⁵Cl NQR frequency in ClCH₂OCH₃ is lower than that in ClCH₂CH₃ due to the higher population of the less diffuse component of the p_σ-orbital of the Cl atom in the former molecule. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 431–434, March, 1997.     

Molecular structure and conformation of triphenylsilane from gas-phase electron diffraction and theoretical calculations, and structural variations in H4?nSiPhn molecules (n?=?1–4)

The molecular structure of triphenylsilane has been investigated by gas-phase electron diffraction and theoretical calculations. The electron diffraction intensities from a previous study (Rozsondai B, Hargittai I, J Organomet Chem 334:269, 1987) have been reanalyzed using geometrical constraints and initial values of vibrational amplitudes from calculations. The free molecule has a chiral, propeller-like equilibrium conformation of C ₃ symmetry, with a twist angle of the phenyl groups τ = 39° ± 3°; the two enantiomeric conformers easily interconvert via three possible pathways. The low-frequency vibrational modes indicate that the three phenyl groups undergo large-amplitude torsional and out-of-plane bending vibrations about their respective Si–C bonds. Least-squares refinement of a model accounting for the bending vibrations gives the following bond distances and angles with estimated total errors: r _g(Si–C) = 1.874 ± 0.004 ?, 〈r _g(C–C)〉 = 1.402 ± 0.003 ?, 〈r _g(C–H)〉 = 1.102 ± 0.003 ?, and ∠_aC–Si–H = 108.6° ± 0.4°. Electron diffraction studies and MO calculations show that the lengths of the Si–C bonds in H_4−n SiPh _n molecules (n = 1–4) increase gradually with n, due to π → σ*(Si–C) delocalization. They also show that the mean lengths of the ring C–C bonds are about 0.003 ? larger than in unsubstituted benzene, due to a one hundredth angstrom lengthening of the C_ipso–C_ortho bonds caused by silicon substitution. A small increase of r(Si–H) and decrease of the ipso angle with increasing number of phenyl groups is also revealed by the calculations.     

Crystal structure of (5-methylcyclopentadienyl)-(1,5-cyclooctadiene) iridium(I)

XRD is used to determine the structure of Cp′Ir(cod) at a temperature of 150(2) K. Crystallographic data for C₁₄H₁₉Ir are: a = 10.8272(5) ?, b = 9.7746(4) ?, c = 10.9180(5) ?, β = 97.3310(10)°, monoclinic symmetry, space group P2₁/n, V = 1146.02(9) ?³, Z = 4, d _calc= 2.199 g/cm³, R = 0.0246. The structure is molecular, built of neutral molecules. The metal atom coordinates carbon atoms of two cyclic ligands: 5-methylcyclopentadienyl-ion (Cp′) and 1,5-cyclooctadiene (cod). Five Ir-C_Cp′ distances lie in the range of 2.21–2.28 ?; four Ir-C_cod distances differ insignificantly, and their average value is 2.114(13) ?. The C₁₁C₁₂C₁₃C₁₄C₁₅ and C₁C₂C₅C₆ planes of ligand fragments are almost parallel, and the angle between normals is 1.9°. In the crystal, molecules are bonded only by van der Waals interactions; in the structure, the eight shortest Ir...Ir distances are in the range of 5.608–7.257 ?. Original Russian Text Copyright ? 2009 by K. V. Zherikova, N. B. Morozova, and I. A. Baidina __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 3, pp. 591–594, May–June, 2009.     

Thermal decomposition of ammonium dinitramide and mechanism of anomalous decay of dinitramide salts

Thermal decomposition of ammonium dinitramide proceedsvia homolytic rupture of the N−NO₂ bond and partially by the proton transfer reaction. The monomolecular decay of the anion to N₂O and NO₃ ⁻ in the solid state at 60 °C occurs with higher rates than those in the melt. This is related to a change in the reactivity of the anion due to the violation of its symmetry on going to the solid state. The absence of hydrogen bonds between the anion and cations or water molecules is an additional condition for the fast decay. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 50–54, January, 1999.     

Composition and structure refinement of superconducting crystals Y1? x Tb x Ba2Cu3O6+δ ( x = 0.10; δ = 0.75)

Crystals of Y_0.90Tb_0.10Ba₂Cu₃O_6.75 have been prepared by spontaneous crystallization from slowly cooled non-stoichiometric melt of the system Y-Tb-Ba-Cu-O. Average size of platelet crystals having mirror surface is 2×2, the largest — 8×9 mm with thickness 0.1–0.2 mm. The crystals have been characterized by powder X-ray diffraction and electron microprobe analysis. Tetragonal symmetry of the crystals has been determined by X-ray diffraction. Magnetic susceptibility measurements have revealed that the crystals manifest transition to superconducting state without additional annealing (T _c = 60 K). Structures and compositions — Y/Tb ratio (σ = 0.01) and oxygen content (σ = 0.04) — have been refined for two single crystals. Possibility of rhombic distortion of the tetragonal symmetry is discussed. __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 49, No. 6, pp. 1101–1107, November–December, 2008. Original Russian Text Copyright ? 2008 by L. P. Kozeeva, N. V. Podberezskaya, N. V. Kuratieva, M. Yu. Kamaneva, and A. G. Blinov     

A novel coprecipitation method towards the synthesis of Ni<Subscript>x</Subscript>Mn<Subscript>x</Subscript>Co<Subscript>(1–2x)</Subscript>(OH)<Subscript>2</Subscript> for the preparation of lithium metal oxides

A series of mixed metal hydroxide (Ni _x Mn _x Co_(1–2x)(OH)₂) precursors for the preparation of lithiated mixed metal oxides (LiNi _x Mn _x Co_(1–2x)O₂) were prepared using a novel coprecipitation approach based on the thermal decomposition of urea. Three different methods were used to achieve the temperature required to decompose urea and subsequently precipitate the hydroxides. The first two methods consisted of either a hydrothermal or microwave-assisted hydrothermal synthesis at 180 °C and elevated pressures. The final method was an aqueous reflux at 100 °C. A complete series (x = 0.00–0.50) was prepared for each method and fully characterized before and after converting the materials to lithiated metal oxides (LiNi _x Mn _x Co_(1–2x)O₂). We observed the formation of a complex structure after the coprecipitation of the hydroxides. Scanning electron micrographs images demonstrate that the morphology and particle size of the hydroxide particles varied significantly from x = 0.00–0.50 under hydrothermal synthesis conditions. There is also a significant change in particle morphology as the urea decomposition method is varied. The X-ray diffraction profiles of the oxides synthesized from these hydroxide precursors all demonstrated phase pure oxides that provided good electrochemical performance.     

On the origin of Baeyer strain in molecules – an ab initio and DFT analysis

It is shown that destabilization energy of organic molecules containing small rings can be estimated by quasi–homodesmotic reactions involving acyclic “strain–free” counterparts. These destabilization energies E_s can be well reproduced at the HF level employing cc-pVTZ basis set, because the contributions of the electron correlation and ZPV energy practically cancel each other in most cases. A predominating factor leading to a decreased stability of molecules involving small ring fragments is given by the Ω bond bending or Baeyer strain. It leads to a dramatic decrease in the electron–nuclei attraction, which is a hallmark of the angular strain. Similar results are obtained by the DFT–B3LYP method. It is strongly pointed out that Baeyer strain cannot be singled out from the total destabilization energy in a precise quantitative way, since it is interlocked with other types of intramolecular interactions like the nonbonded repulsions, a significant increase in the stability of the CH bonds emanating from the small cyclic structures and by the σ–aromaticity or σ–antiaromaticity in three– and four–membered rings, respectively. Nevertheless, it is fair to say that Baeyer strain is the essential factor in determining decreased stability of small ring compounds and that the diminished electron–nuclear attraction is its characteristic signature at the global level. Dedicated to Professor Karl Jug on the occasion of his 65th birthday.     

Dibenzo-18-crown-6 diaqua(dibenzo-18-crown-6)potassium triiodide: Synthesis and crystal structure

A new compound, dibenzo-18-crown-6 diaqua(dibenzo-18-crown-6)potassium triiodide [K(Db18C6)(H₂O)₂)⁺ · I₃⁻ · Db18C6 (I), is synthesized and studied by X-ray crystallography. The crystals of compound I are orthorhombic: a = 22.065 ?, b = 22.140 ?, c = 9.433 ?, Z = 4, space group Pccn. Structure I is solved by a direct method and refined by the full-matrix least-squares method in the anisotropic approximation to R = 0.098 for all 5974 unique reflections. Structure I contains the following asymmetric units: a half of the I₃⁻ centrosymmetric anion and two halves of the mixed equally average [K(Db18C6)(H₂O)₂]⁺ host—guest complex cation (a) and a free Db18C6 molecule, each stacked on the axes 2 of the perpendicularly averaged plane of the eighteen-membered macroheterocycle. In complex I, both Db18C6 molecules (a and b) have a “butterfly” conformation with approximate symmetry C _2v . Original Russian Text ? A.N. Chekhlov, 2009, published in Zhurnal Neorganicheskoi Khimii, 2009, Vol. 54, No. 3, pp. 516–520.     

Synthesis and structure of the polymeric complex [Ag<Subscript>2</Subscript>(Ph<Subscript>3</Subscript>P)<Subscript>2</Subscript>B<Subscript>10</Subscript>H<Subscript>10</Subscript>]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

A method for the synthesis of the silver(I) complex with the closo-decaborate anion and triphenylphosphine [Ag₂(Ph₃P)₂B₁₀H₁₀] _n was developed and the structure of this complex was studied. The polymeric chain of the complex is formed with participation of Ag(I) atoms, which coordinate the B₁₀H₁₀²⁻ anions through the apical (B(1)–B(2), B(9)–B(10)) and equatorial (B(3)–B(6), B(5)–B(8)) edges, the metalligand bonding occurring through three-center two-electron bonds (MHB). The P atoms of two triphenylphosphine molecules are also incorporated in the inner coordination sphere of the metal: the CN of the silver atom is 4 + 1.