Maximum radius of convergence perturbation theory: test calculations on Be,Ne, H<Subscript>2</Subscript> and HF

Maximum radius of convergence (MAXR _c) perturbation theory [(2000) Journal of Chemical Physics 112:6997] is tested on the beryllium and neon atoms using calculations that are truncated in high orders. Calculations are also performed on the ground-state potential-energy curves of H₂ and HF. The neon atom calculations use the 3-21G basis set with added diffuse s and p functions. All other calculations use the STO-3G minimum basis set. MAXR _c perturbation theory consistently performs well. The Epstein–Nesbet and Møller–Plesset perturbative expansions frequently diverge or exhibit slow convergence compared to the expansions obtained from MAXR _c. AcknowledgementsJ.P. Fi. acknowledges support for a grant from the Japanese Society for the Promotion of Science.Contribution to the Björn Roos Honorary Issue     

Vibrational linestrengths for the ground and first excited electronic states of HeH<Subscript>2</Subscript><Superscript>+</Superscript>

Together with recent improved potential-energy surface calculations for the ground (X) and first excited (Ã) electronic states of HeH₂ ⁺, the electric dipole moment surfaces for each state and the transition dipole moments connecting the two states were evaluated for the entire range of the energy calculations. Using these functions the linestrengths of all dipole-allowed transitions between the bound vibrational levels within each of the two states (XX) and (ÃÃ) as well as between them (ÃX) are evaluated here. These data are believed to be useful both in the experimental search for the yet unobserved molecular spectra of HeH₂ ⁺ and in evaluating theoretical rates for the radiative association or photodissociation processes involving the two lowest electronic states of the ion.Contribution to the Björn Roos Honorary Issue     

<Emphasis Type="Italic">Ab initio</Emphasis> structural study of M(mda)<Subscript>2</Subscript> complexes (M = Be,Mg, Ca; mda = C<Subscript>3</Subscript>O<Subscript>2</Subscript>H<Subscript>3</Subscript>)

The structure of M(mda)₂ (M = Be, Mg, Ca; mda = C₃O₂H₃) bis-complexes was investigated by the ab initio Hartree-Fock method and by including electron correlation in terms of second order Möller-Plesset perturbation theory; for calculations we used triple-zeta valence basis sets complemented with polarization functions. Two most probable geometrical nuclear configurations (D _2h and D _2d ) are considered for each molecule. The structure with two mutually orthogonal chelate ligands (D _2d symmetry) corresponds to the potential energy surface (PES) minimum. The planar D _2h configuration corresponds to the first order saddle point on PES; consequently, its relative energy determines the height of the barrier to the D _2d D _2h D _2d intramolecular rearrangement. Correlation equations that relate the calculated values of equilibrium internuclear distances, force constants, and rearrangement barrier heights to the value of the ionic radius of the metal atom have been obtained. These correlations were employed to evaluate the molecular constants for Sr(mda)₂ and Ba(mda)₂. The theoretical data are compared with the available experimental literature data.Original Russian Text Copyright © 2004 by V. V. Sliznev, S. B. Lapshina, and G. V. GirichevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 611–623, July–August, 2004This revised version was published online in April 2005 with a corrected cover date.     

Structure of palladium(I) carbonylcarboxylate clusters [Pd<Subscript>2</Subscript>(CO)<Subscript>2</Subscript>(RCOO)<Subscript>2</Subscript>]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in solution: NMR and IR study

The structures of palladium carbonylcarboxylate clusters [Pd₂(CO)₂(RCOO)₂] _n (n = 2, R = CH₃, CH₂Cl, CF₃, n = 3, R = CMe₃, CHMe₂, n-C₅H₁₁) are studied in benzene and tetrahydrofuran solutions by IR and ¹H and ¹³C NMR spectroscopy. The clusters in the solid state have a planar cyclic metal framework with pairs of the carbonyl and carboxylate ligands alternately coordinated on its sides. In solutions, compounds under consideration contain one-type carbonyl ligands and one-type carboxylate ligands; their structures are similar to thaso in the solid state.     

Theoretical study of metal tetrahydroborates and alanates L(MH<Subscript>4</Subscript>)<Subscript>3</Subscript>, HL(MH<Subscript>4</Subscript>)<Subscript>2</Subscript>, and H<Subscript>2</Subscript>L(MH<Subscript>4</Subscript>)(L = Be,Mg, Al,Sc, Ti,V, Zn; M = B,Al)

The structural and energetic characteristics of the lowest-lying structures for isolated molecules and ions of light-metal boro-and aluminohydrides L (MH₄)₃, HL(MH₄)₂, and H₂L(MH₄)(L = Be, Mg, Al, Sc, Ti, V, Zn; M = B, Al) with different coordination modes of and groups were calculated by the perturbation theory (MP2), coupled cluster (CCSD(T)), and density functional theory (B3LYP) methods using the 6-31G*, 6-311+G**, and 6-311++G** basis sets. The preferable coordination modes of the ligands in these complexes, as well as the differences and trends in the behavior of the structural parameters and dissociation energies for the loss of BH₃ (AlH₃) molecules and BH ₄ ^? (AlH ₄ ^? ) ions were analyzed in various related series of hydroborates and hydroaluminates.     

Quantum-chemical study of C<Subscript>n</Subscript>F2<Subscript><Emphasis Type="Italic">n</Emphasis>+2</Subscript> conformers. Structure and IR spectra

Quantum-chemical calculations of the geometrical structure and vibrational spectra of C_nF_2n+2 oligomers (n = 5–8) in the chain and branched conformations are reported. The lengthening of the chain of C_nF_2n+2 does not substantially affect the geometrical parameters of the oligomers. In all cases under study, the most optimal structure of the molecule is a zigzag chain with bond lengths R(C-C) = 1.53 –1.54 and R(C-F) = 1.36 –1.34 ; the chain is rolled into a helix, which makes an angle of 17° with the plane. The IR spectra are sensitive to the structural deficiency of oligomers C_nF_2n+2 associated with the lateral trifluoromethyl groups formed in the chain; the spectra can be used for revealing defects of this type in the structure of polytetrafluoroethylene (PTFE). The possibility of defects associated with the lateral CF₃ groups in the structure of PTFE and its low-temperature modifications is explained based on the calculated total energies of C_nF2 _n+2.Original Russian Text Copyright © 2004 by L. N. Ignatieva, A. Yu. Beloliptsev, S. G. Kozlova, and V. M. BuznikTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 632–643, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

A Systematic Search for Structures and Stabilities of Asymmetric Clusters (HfInN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1-6)

In order to find single source precursors (SSP), the structures, relative stabilities, and IR spectra of small asymmetric clusters (HFInN₃) _n (n = 1–6) are systematically investigated by means of the density functional theory at the B3LYP level. The obtained geometries show that the frameworks of clusters (HFInN₃) _n (n = 2–6) prefer to be 2n-membered ring with alternating indium and α-nitrogen atoms. The averaged binding energies reveal that all of asymmetric clusters (HFInN₃) _n (n = 1–6) can continue to gain energy as the cluster size n increasing. The second-order difference of energy (Δ₂E) and the HOMO-LUMO energy gap (E_gap) as a function of the cluster size n both exhibit a pronounced even-odd alternation phenomenon. The influences of cluster size n and temperature T on the thermodynamic properties of clusters are discussed. Judged by enthalpies and Gibbs free energies, the formations of the most stable clusters (HFInN₃) _n (n = 2–6) from the monomer are thermodynamically favorable in the range of 200–800 K.     

Perturbation energy expansions based on two-component relativistic Hamiltonians

The approximate elimination of the small-component approach provides ansätze for the relativistic wave function. The assumed form of the small component of the wave function in combination with the Dirac equation define transformed but exact Dirac equations. The present derivation yields a family of two-component relativistic Hamiltonians which can be used as zeroth-order approximation to the Dirac equation. The operator difference between the Dirac and the two-component relativistic Hamiltonians can be used as a perturbation operator. The first-order perturbation energy corrections have been obtained from a direct perturbation theory scheme based on these two-component relativistic Hamiltonians. At the two-component relativistic level, the errors of the relativistic correction to the energies are proportional to ⁴ Z ⁴, whereas for the relativistic energy corrections including the first-order perturbation theory contributions, the errors are of the order of ⁶ Z ⁶–⁸ Z ⁸ depending on the zeroth-order Hamiltonian.Contribution to the Björn Roos Honorary Issue     

Studies on the copolymerization of norbornene with CO catalyzed by a new catalytic system PdCl<Subscript>2</Subscript>/phen/M(CF<Subscript>3</Subscript>SO<Subscript>3</Subscript>)<Subscript>n</Subscript>

A new three-component catalytic system, PdCl₂/phen/M(CF₃SO₃)_n where M = La, Y, Yb, Zn, and Cu, was studied for the copolymerization of norbornene (NBE) with CO to prepare polyketone (PK). It was found that the CF₃SO₃H catalytic system gave a low catalytic activity for the copolymerization of norbornene with CO, but when M(CF₃SO₃)_n was introduced instead of CF₃SO₃H, the PdCl₂/phen/M(CF₃SO₃)_n catalytic system exhibited much higher activity. The effects of ligands, M(CF₃SO₃)_n, solvents, and temperatures on the copolymerization have been discussed in detail. The results showed that with 1,10-phenanthroline (phen) and Cu(CF₃SO₃)₂ used as cocatalysts, the corresponding reaction rate reached 82 000 g PK (mol Pd)⁻¹h⁻¹ when the reaction was carried out in methanol at 90°C and 3.0 MPa of CO, and the weight average molecular weight (M _w) of the resultant copolymer is 1090 g/mol. The copolymer was characterized with various techniques such as FT-IR, ¹HNMR, ¹³CNMR, TGA, and DSC. The infrared spectrum of the product includes two features at 1697 and 1732 cm⁻¹ for the NBE/CO copolymer in CH₃OH that are attributed to carbonyl groups in ketones (repeating unit) and esters (end group), respectively. Due to the tension of the ring of norbornene, the degree of copolymerization is not high. Published in Russian in Kinetika i Kataliz, 2007, Vol. 48, No. 1, pp. 51–58. This article was submitted by the authors in English.     

Photochemical reactions of <Emphasis Type="Italic">cis</Emphasis>-[(η<Superscript>4</Superscript>-NBD)M(CO)<Subscript>4</Subscript>] (NBD = norbornadiene; M = Cr,Mo) olefin complex with ligand,containing S and N donor atoms

New complexes cis-[M(CO)₄-DABRd] (M = Cr(I), Mo(II) and fac-[M(CO)₃-SAT] (M = Cr(III), Mo(IV)) have been synthesized by the photochemical reactions of cis-[(η⁴-NBD)M(CO)₄] (NBD is norbornadiene; M=Cr, Mo) with 5-(4-dimethylaminobenzylidene) rhodanine (DABRd) and salicylidene-3-amino-1,2,4-triazole (SAT) ligands and characterized by elemental analysis, FT-IR and ¹H NMR spectroscopy, and mass spectrometry. The spectroscopic studies show that the DABRd ligand acts as a bidentate ligand coordinating via both NH-(S)C=S sulfur donor atoms in I and II and SAT ligand behaves as a tridentate ligand coordinating via its all imine nitrogen-C=N-donor atoms in III and IV to the metal center. The article was submitted by the authors in English.     

Density functional theory study of UO<Stack> <Subscript>2</Subscript> <Superscript>2+</Superscript> </Stack> solvation in 1-butyl-3-methylimidazolium chloride

Structural characteristics and energies of [UO₂Cl₄(BMIm)_n]^(n–2)+ (n = 1-4) solvation complexes have been studied by the density functional theory (DFT) method in the SVWN5 local functional approximation.     

Reaction of the novel Ru<Subscript>3</Subscript>(CO)<Subscript>10</Subscript>[Ph<Subscript>2</Subscript>P(CH<Subscript>2</Subscript>)<Subscript>2</Subscript>Si(OEt<Subscript>3</Subscript>)]<Subscript>2</Subscript> complex on SBA-15 and MCM-41 mesoporous silicas

The reaction of Ru₃(CO)₁₂ with 2(diphenylphosphino)ethyl-triethoxysilane (DPTS) in hydrocarbons, leads to the functionalized Ru₃(CO)_12−n [Ph₂P(CH₂)₂Si(OEt₃)] _n (n = 1,2) complexes. The complex with two phosphine substituents was chemically anchored on mesoporous silicas, SBA-15 and MCM-41, in order to obtain two hybrid materials characterized by a different localization of the metal centre on the surface of the porous supports. A detailed investigation of the cluster, before and after chemical anchoring on the mesoporous silicas, was pursued. Particular attention was also devoted to the study of the morphological, structural and textural properties of the metal-functionalised silicas (Ru/SBA-15 and Ru/MCM-41) by infrared spectroscopy (FT-IR), scanning electron microscopy, X-ray diffraction and N₂ physisorption analysis.     

Synthesis and crystal structure of [Cr(NH<Subscript>3</Subscript>)<Subscript>5</Subscript>Cl][PdBr<Subscript>4</Subscript>]

A new binary complex salt — chloropentaamminechromium(III) tetrabromopalladate(II) [Cr(NH₃)₅Cl][PdBr₄] — has been synthesized. The compound was characterized by elemental, X-ray diffraction, and X-ray phase analysis. The salt is isostructural with the previously investigated compounds [M(NH₃)₅Cl][PtCl₄] (M = Ir, Rh, Ru, Co, Cr) and [CM(NH₃)₅Cl][PdBr₄] (M = Ir, Rh, Co). Crystallographic data: space group Pnma, a = 17.068(2) Å, b = 8.315(12) Å, c = 9.653(14) Å; V = 1370.0(3) ų, Z = 4, d _calc = 2.903 g/cm³.     

Density Functional Theory and Low-Temperature Matrix Investigations of CO-Loss Photochemistry from [(C<Subscript>5</Subscript>R<Subscript>5</Subscript>)Ru(CO)<Subscript>2</Subscript>]<Subscript>2</Subscript> (R = H,Me) Complexes

The photochemical CO-loss products of the diruthenium complexes [CpRu(CO) ₂]₂ (5; Cp = ⁵-C₅H₅), [Cp*Ru(CO)₂]₂ (5*; Cp* = ⁵-C₅(CH₃)₅) and CpCp*[Ru(CO)₂]₂ (5) have been studied experimentally in low-temperature (96 K) matrices in 3-methylpentane by using IR spectroscopy. It is proposed that all three complexes undergo single-CO-loss chemistry but that the products have different structures. The single-CO-loss product from 5 is proposed to have one bridging and two terminal carbonyl ligands, whereas 5* and 5 generate triply bridged CO-loss products similar to that observed from [CpFe(CO)₂]₂ and [Cp*Fe(CO)₂]₂. Double-CO-loss from 5* and 5* 9 is also apparently observed. Relativistic DFT calculations have been carried out on various isomers of the starting materials and on potential CO-loss products from 5. The calculations suggest that the triply bridged product Cp₂Ru₂(-CO)₃ (6) might have a singlet ground state in contrast to the corresponding diiron complex Cp₂Fe₂(-CO)₃ (3), which has a triplet ground state.     

Dissymmetrization of crystal structures of grossular-andradite garnets Ca<Subscript>3</Subscript>(Al,Fe)<Subscript>2</Subscript>(SiO<Subscript>4</Subscript>)<Subscript>3</Subscript>

The crystal structures of three birefringent grossular-andradite natural garnets Ca₃(Al,Fe)₂(SiO₄)₃ were investigated using single-crystal X-ray diffraction data (MoK_α, number of reflections measured 8065, 10619, 9213; R = 2.81, 2.74, 3.26%). According to the values of unit cell constants, inconsistent intensities of reflections and appearance of additional (forbidden) reflections explored garnets have different symmetry: cubic, sp. gr. (Fe/(Fe + Al) = 0.078, Δn = 0.0002); orthorhombic, sp. gr. Fddd (Fe/(Fe + Al) = 0.58, Δn = 0.0089); triclinic, sp. gr. or I1 and pseudo-orthorhombic (Fe/(Fe + Al) = 0.23, Δn = 0.0066). Careful refinement of all crystal structures in space groups , Fddd and has confirmed the symmetry reduction detected on the diffraction patterns and shown that dissymmetrization of cubic garnets connects with partial ordering of trivalent cations over Y-sites. Direct linear relationship between Fe-occupancy, an average Y–O bond lengths and octahedral O–O edges has been revealed. Cluster models of dissymmetrization have been regarded. Evidence for the “growth dissymmetrization” phenomena (kinetic phase transformations) as the reasons of the symmetry reduction of cubic garnets has been discussed. The reasonable assumption that the garnets crystal structures described as orthorhombic are triclinic, but the deviations from the orthorhombic symmetry so small, that cannot be manifested by of X-ray diffraction study has been taken.     

Formation of 1-D polymer in recrystallization of the adduct Mn[(OOCC<Subscript>5</Subscript>H<Subscript>4</Subscript>)Mn(CO)<Subscript>3</Subscript>]<Subscript>2</Subscript>[O(H)Me]<Subscript>4</Subscript> from acetonitrile

It was found that the recrystallization of the adduct Mn[(OOCC₅H₄)Mn(CO)₃]₂[O(H)Me]₄ from hot acetonitrile in the presence of benzene produces polymer [μ-(OOCC₅H₄)Mn(CO)₃]₄[μ-η²-(OOCC₅H₄)Mn(CO)₃]₂(NCMe)₂(OH₂)₂([μ-η²-(OOCC₅H₄)Mn(CO)₃]₂)[μ-(OOCC₅H₄)Mn(CO)₃]₄[μ-η²-(OOCC₅H₄)Mn(CO)₃]₂(OH₂)_2n. The obtained polymer was characterized by X-ray diffraction analysis.     

An <Emphasis Type="Italic">ab initio </Emphasis> Quantum-Chemical Study of C<Subscript>6</Subscript>H<Subscript>5</Subscript>S(O)CH<Subscript>3</Subscript> and C<Subscript>6</Subscript>H<Subscript>5</Subscript>S(O)CF<Subscript>3</Subscript>

The potential functions of internal rotation around the C -S bond in the C₆H₅S(O)CH₃ and C₆H₅S(O)CF₃ molecules were obtained by ab initio MP2(full)/6-31+G* calculations. The stationary points were identified by solving the vibrational problems. The structures in which the plane of the C -S-C bonds is approximately perpendicular to the benzene ring plane correspond to the energy minimum. The barriers to rotation around the C -S bond, corrected for the zero-point vibration energy, are 21.29 [C₆H₅S(O)CH₃] and 28.98 [C₆H₅S(O)CF₃] kJ mol⁻¹. The bond angles (deg) are as follows: 95.7 (CSC), 107.1 (C SO), 106.3 (C SO) in C₆H₅S(O)CH₃; 93.5 (CSC), 108.2 (C SO), 105.2 (C SO) in C₆H₅S(O)CF₃. The bond lengths are as follows (Å): 1.520 (S=O), 1.804 (C -S), 1.810 (C -S) in C₆H₅S(O)CH₃; 1.507 (S=O), 1.799 (C -S), 1.870 (C -S) in C₆H₅S(O)CF₃. According to the results of NBO calculations, the formally double S=O bond consists of a strongly polarized covalent σ bond (S→O) and an almost ionic bond. An increase in the S=O bond multiplicity relative to a single bond is mainly due to hyperconjugation by the mechanism n(O)→σ*(C -S) and n(O)→σ*(C -S) and, to a lesser extent, by interaction of the oxygen lone electron pairs with the Rydberg orbitals of the S atoms, characterized by a large contribution of the d component.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 1, 2005, pp. 96–104.Original Russian Text Copyright © 2005 by Bzhezovskii, Il’chenko, Chura, Gorb, Yagupol’skii.     

Theoretical study of V<Subscript>20</Subscript>O<Subscript>50</Subscript> oxovanadate cluster compounds with alkali metal atoms

The energies and structural and spectroscopic characteristics of model М _n V₂₀O₅₀ systems corresponding to compounds of the V₂₀O₅₀ oxovanadate cluster with alkali metal atoms (M = Li, K; n = 1–20) have been calculated by the density functional theory method (B3LYP). It has been demonstrated that, in the K _n V₂₀O₅₀ compounds, all the metal atoms are coordinated in the outer sphere to the edges of the hollow dodecahedral V₂₀O₅₀ cage to form three-center O_t?K?O_t bridges with terminal oxygen atoms. In the Li _n V₂₀O₅₀ compounds, the metal atoms can be coordinated both outside and inside the V₂₀O₅₀ cage. At n = 4, the most favorable isomer is endohedral Li₄O₄@V₂₀O₄₆ in the quintet state (S = 5), in which the four Li atoms are located in the inner cavity of the inverted O₄@V₂₀O₄₆ isomer of the oxovanadate cluster with four O atoms oriented to the cage center and form with them a corrugated eight-membered ring Li₄O₄. The decrease in energy caused by the formation of the endohedral isomer (4Li + V₂₀O₄₅₀ → Li₄O₄@V₂₀O₄₆) is estimated at ~377 kcal/mol. The exohedral isomer 4Li ? V₂₀O₅₀ (S = 5), in which the Li atoms are coordinated to the outside of the V₂₀O₅₀ cage, is ~23 kcal/mol less favorable. For the other members of the Li series with n from 4 to 20, the endohedral isomers with the inner Li₄O₄ ring remain preferable. At n > 4, the extra Li atoms fill the outer sphere of the cage, being coordinated to its edges to form three-center O_t?Li?O_t bridges with terminal oxygen atoms. The specific energy of formation of Li _n V₂₀O₅₀ (by the scheme nLi + V₂₀O₄₅₀ → Li₄O₄@V₂₀O₄₆Li_n-4) per Li atom monotonically decrease from ~98 (n = 2) to ~80 kcal/mol (n = 20). For K _n V₂₀O₅₀, these energies are ~20?25 kcal/mol lower than for the lithium analogues and decrease from ~80 (n = 2) to ~64 kcal/mol (n = 12). The atoms of both alkali metals in the M _n V₂₀O₅₀ systems have large positive effective charges (0.85e?0.92e for K and 0.65e?0.78e for Li), which also monotonically decrease with increasing n. The addition of each alkali metal atom is accompanied by its ionization (М → М⁺) along with the reduction of one of the neighboring pentavalent vanadium atoms to the tetravalent state (V^V → V^IV) and localization of the unpaired electron in its 3d shell. For all Li _n V₂₀O₅₀ complexes, the states with maximal multiplicity and parallel spins are the most preferable.     

Comparative study of the lanthanide (Ln) and actinide (An) triflate complexes M(OTf)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

Theoretical studies on the lanthanide and actinide triflate complexes M(OTf) _n where M = La, Ce, Gd, Yb, Lu, Th, U, Np, Pu, Am, Cm, Bk, and No; n = 3 and 4, are carried out using functional density theory (DFT). The study of An(OTf)₃ complexes showed that the three OTf groups are bidentate, generating a trigonal prism (TP). Two limiting structures of TP are observed; the most distorted is the thorium triflate Th(OTf)₃ and the ideal one is U(OTf)₃. The highest population contribution of 5d orbital compared to 5f orbital in Th–O bond of Th(OTf)₃ explains the distortion. The intramolecular rearrangement of the OTf ligands in Ln(OTf)₃ generates two conformers. In Yb(OTf)₃, the pseudo-eclipsed and the staggered conformations are stable and can be isolated.     

Thermolytic Transformation of Organometallic Polymers Containing the Cr(CO)<Subscript>5</Subscript> Precursor into Nanostructured Chromium Oxide

Thermal treatment in air of the organometallic polymer (1) results in the formation of nanometer-size metal oxide particles. Cr particles in the 35–85 nm range, mostly 54 nm, immersed in an phosphorus oxides matrix were found. ATG studies in air suggest that the formation of the nanostructures occurs in four steps, the first involving loss of the carbonyl groups of the Cr(CO)₅ fragment. The following steps involve the oxidation of the organic matter and finally the oxidation of the chromium to give the pyrolytic product. The use of these kinds of organometallic polymers as precursors for a general and potential new route to materials having metal/metal oxide nanostructures is discussed.