Free‐volume variation in polyethylenes of different crystallinities: Positron lifetime,density, and X‐ray studies

High‐quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X_c = 3–82%). The specific volumes of the crystalline and amorphous phases (V_c and V_a, respectively) were estimated from density and wide‐angle X‐ray scattering (WAXS) experiments. Some samples (those with low values of X_c) were branched PEs, and those with high values of X_c were linear PEs for which X_c was varied with changes in the crystallization temperature. Both V_c and V_a increase with decreasing X_c in the range 0% ≤ X_c ≤ 56% (the branched PEs) but are constant for X_c ≥ 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer‐generated spectra. Four lifetime components appeared in all of the PEs; the two long‐lived ones are attributed to pick‐off annihilation of ortho‐positronium (o‐Ps) in crystalline regions (τ₃) and in holes of the amorphous phase (τ₄). With increasing X_c, τ₃ decreases from about 1.2 to 1 ns, τ₄ decreases from 3.0 to 2.5 ns, and the intensity I₄ decreases from 29 to 0%. An increase in I₃ from 6 to 12% was observed. A comparison with simulations shows that the true I₃ value approaches 0 for X_c → 0%. The decrease in I₄ is weaker than the increase in X_c; this leads to the conclusion that the apparent specific o‐Ps yield in the amorphous phase I₄^Xc increases with X_c. Possible reasons for this surprising results are discussed. The fractional free hole volume [h = (V_a ? V_occ)/V_a, where V_occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X_c = 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X_c = 56%. The mean size (v) of the local free volumes (holes) estimated from τ₄ decreases from 200 to 150 ų. The number density of holes (N_h) calculated from these values (N_h = h/v) also decreases from 0.8 to 0.6 nm^?3 in the range 0% ≤ X_c ≤ 56%. The values of V_a, V_c, h, and N_h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline–amorphous interfacial phase (three‐phase model) on the observed lifetime parameters is also discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 65–81, 2002     

Bond dissociation energies of ligands in square planar Pd(II) and Pt(II) complexes: An assessment using trans influence

DFT calculations using MPWB1K method with COSMO continuum solvation model have been carried out to quantify the trans influence of various X ligands (E_X) in [Pt^IICl₃X]ⁿ⁻ complexes as well as the mutual trans influence of two X and Y ligands (E_XY) in [Pt^IICl₂XY]ⁿ⁻ complexes. A quantitative structure energy relationship (QSER) is derived for predicting the E_XY using E_X and E_Y and this relationship showed a strong similarity to a QSER derived for predicting E_XY of [Pd^IICl₂XY]ⁿ⁻ complexes. Quantification of the contributions of E_X and E_XY to the bond dissociation energy of the ligand X (BDE_X) in complexes of the type [M^IIX(Y)X′(Y′)] (M = Pd, Pt) is also achieved. The BDE_X of any ligand X in these complexes can be predicted using the equations, viz. BDE_X(Pd) = 1.196E_X − 0.603E_XY − 0.118E_X’Y’ + 0.442D_X + 15.169 for Pd(II) complexes and BDE_X(Pt) = 1.420E_X − 0.741E_XY − 0.125E_X’Y’ + 0.498D_X + 13.852 for Pt(II) complexes, where D_X corresponds to the bond dissociation energy of X in [M^IICl₃X]ⁿ⁻ complexes. These expressions suggest that the mutual trans influence from X and Y is more dominant than the mutual trans influence from X′ and Y′ and both factors contribute significantly to the weakening of M-X bond. We also obtained a strong linear relationship between E_X and the electron density ρ(r) at the bond critical point of M-Cl bond trans to the X in [M^IICl₃X]ⁿ⁻ and this allows us to express the BDE_X(Pd) and BDE_X(Pt) in terms of only the ρ(r) and D_X. We have demonstrated that using a database comprising of D_X and the ρ(r), the bond dissociation energy of X in complexes of the type [M^IIX(Y)X′(Y′)] can be predicted.     

<Emphasis Type="Italic">Ab-initio</Emphasis> Calculations of T-shaped Phosphine-Platinum(II) Complexes

Summary.  The geometries and total energies of several T-shaped platinum(II) complexes of the type (H₃P)PtXY (X, Y=Cl, CH₃, SiH₃, Si(OH)₃) were calculated by ab-initio methods. In the most stable isomer, the ligand with the smallest trans influence is trans to the PH₃ ligand. The trans influence increases in the order Cl<CH₃<SiH₃<Si(OH)₃. Corresponding author. E-mail: uschuber@mail.2serv.tuwien.ac.at Received October 14, 2002; accepted October 14, 2002 Published online May 2, 2003     

Kinetics and mechanism of the reaction of para‐chlorophenyl aryl chlorophosphates with anilines in acetonitrile

The kinetics and mechanism of the nucleophilic substitution reactions of p‐chlorophenyl aryl chlorophosphates ( 2 ) with anilines are investigated in acetonitrile at 55°C. Relatively large magnitudes of ρ_X and β_X values are indicative of a large degree of bond making in the TS. Smaller magnitudes of ρ_X (0.20 for X = H) and ρ_XY (?0.30) than those for the corresponding reactions with phenyl aryl chlorophosphates ( 1 ) (ρ_X = 0.54 for X = H and ρ_XY = ?1.31) are interpreted to indicate partial electron loss, or shunt, towards the electron acceptor equatorial ligand (p‐ClC₆H₄O‐) in the bipyramidal pentacoordinated transition state. The inverse secondary kinetic isotope effects (k_H/k_D = 0.64–0.87) involving deuterated aniline (ND₂C₆H₄X) nucleophiles, and small ΔH^? and large negative ΔS^? are obtained. These results are consistent with a concerted nucleophilic substitution mechanism. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 632–637, 2002     

Darstellung von trans-[Pt(N3)4X2]2− (X = Br,I, SCN,SeCN) durch oxidative Addition an [Pt(N3)4]2− in organischen Lösungsmitteln

Preparation of trans-[Pt(N₃)₄X₂]^2? (X ? Br, I, SCN, SeCN) by Oxidative Addition to [Pt(N₃)₄]^2? in Organic Solvents By oxidative addition to (TBA)₂[Pt(N₃)₄], dissolved in dichlormethane, trans-(TBA)₂[Pt(N₃)₄X₂], X ? Br, I, SCN, SeCN; TBA = Tetrabutylammonium, are formed. The vibrational spectra of these salts are assigned according to point group D_4h. From the resonance Raman spectrum of trans-(TBA)₂[Pt(N₃)₄I₂] the harmonic vibrational frequency ω₁ of v(Pt? I), A_1g, is calculated to be 138.50 cm^?1 and the inharmonicity constant x₁₁ = 0.27 cm^?1. The characteristical feature in the UV/VIS spectra is caused by intensive π(N,X) → a_1g, b_1g(Pt) CT transitions.     

Phosphor-, arsen- und antimonylid-komplexe des wolframs

The benzylidene(pentacarbonyl)tungsten complexes (CO)₅W[C(H)C₆H₄R-p] (R = H (Ia), Me (Ib)) react with trimethylphosphite, triphenylarsane and triphenylstibane (XY₃), respectively, via addition of XY₃ to the benzylidene carbon to give the new phosphorus, arsenic and antimony ylide complexes (CO)₅W[C(H)(C₆H₄R-p)XY₃] (R = H, XY₃ = P(OMe)₃ (Va), AsPh₃ (VIa), SbPh₃ (VIIa); R = Me, XY₃ = AsPh₃ (VIb)). The formation of the adducts in reversible.     

Liquid crystalline guanidinium phenylalkoxybenzoates: towards room temperature liquid crystals via bending of the mesogenic core and the use of triflate counter ions

A series of guanidinium salts 1(C _n ) _m –4(C _n ) _m ?X bearing phenyl alkoxybenzoate cores have been synthesised and their mesomorphic properties have been investigated by polarising optical microscopy (POM), differential scanning calorimetry (DSC) and powder X-ray diffraction experiments (small-angle X-ray scattering and wide-angle X-ray scattering). While compounds 1(C₁₂)₁?X and 3(C₁₂)₁?X with one alkoxy chain showed smectic A (SmA) phases irrespective of the counter ion, compounds 1(C₁₂)₂?OTf and 3(C₁₂)₂?OTf with two alkoxy chains displayed SmA phases and the corresponding chlorides 1(C₁₂)₂?Cl and 3(C₁₂)₂?Cl displayed Col_h. Guanidinium salts 1(C _n )₃–4(C _n )₃?X with three alkoxy chains showed Col_h phases. Whereas the use of cyclic guanidinium head groups rather than acyclic ones had only a minor influence on the mesophase properties, melting points were significantly decreased by bent core units instead of linear core units. Replacement of chloride counterions by triflate lead to a further depression of the clearing points and shifted the mesophase towards room temperature.     

Homoleptic Organoderivatives of High‐Valent Nickel(III)

Homoleptic perhalophenyl derivatives of divalent nickel complexes with the general formula [NBu₄]₂[Ni^II (C₆X₅)₄] [X=F ( 1 ), Cl ( 2 )] have been prepared by low‐temperature treatment of the halo‐complex precursor [NBu₄]₂[NiBr₄] with the corresponding organolithium reagent LiC₆X₅. Compounds 1 and 2 are electrochemically related by reversible one‐electron exchange processes with the corresponding organometallate(III) compounds [NBu₄][Ni^III (C₆X₅)₄] [X=F ( 3 ), Cl ( 4 )]. The potentials of the [Ni^III (C₆X₅)₄]^?/[Ni^II (C₆X₅)₄]^2? couples are +0.07 and ?0.11 V for X=F or Cl, respectively. Compounds 3 and 4 have also been prepared and isolated in good yield by chemical oxidation of 1 or 2 with bromine or the amminium salt [N(C₆H₄Br‐4)₃][SbCl₆]. The [Ni^III (C₆X₅)₄]^? species have SP‐4 structures in the salts 3 and 4 , as established by single‐crystal X‐ray diffraction methods. The [Ni^II (C₆F₅)₄]^2? ion in the parent compound 1 has also been found to exhibit a rather similar SP‐4 structure. According to their SP‐4 geometry, the Ni^III compounds (d⁷) behave as S=1/2 systems both at microscopic (EPR) and macroscopic levels (ac and dc magnetization measurements). The spin Hamiltonian parameters obtained from the analysis of the magnetic behavior of 3 and 4 within the framework of ligand field theory show that the unpaired electron is centered mainly on the metal atom, with >97 % estimated d contribution. Thermal decomposition of 3 and 4 proceeds with formation of the corresponding C₆X₅? C₆X₅ coupling compounds.     

The low frequency IR and Raman spectra of some complexes of dithiooxamide with cadmium halides

summary The low frequency IR and Raman spectra of Cd(DH ₄)X ₂ (X=Cl, Br;DH=dithiooxamide) have been discussed. On the basis of the cadmium isotope and H-D shift as well as chlorine-bromine substitution a band assignment in the region 500–33 cm^–1 has been made. A polymeric structure of Cd(DH ₄)X ₂ involving both dithiooxamide and halogen bridges with D_4h symmetry of the cadmium environment is assumed.

---

Die niederfrequenten IR- und Raman-Spektren einiger Komplexe von Dithiooxamid mit Cadmiumhalogeniden

Zusammenfassung Die IR- und Raman-Spektren von Cd(DH ₄)X ₂ (X=Cl, Br;DH=Dithiooxamid) werden im Bereich niedriger Frequenzen diskutiert. Basierend auf Cadmiumisotopen- und H-D-Verschiebungen mit zusätzlicher Cl-Br-Substitution werden die Banden im Bereich von 500–33 cm^–1 zugeordnet. Es wird eine polymere Struktur von Cd(DH ₄)X ₂ unter Anteilnahme sowohl von Dithioxamid- als auch Halogenbrücken mit einer D_4h-Symmetrie im Bereich des Cadmiumzentralions angenommen.

     

Dimethylhydroxyoxosulfonium(VI) Hexafluoridometallates, [(CH3)2SO(OX)]+[MF6]–(X = H,D; M = As,Sb)

Dimethylsulfone reacts in the binary superacidic systems XF/MF₅ (X = H, D; M = As, Sb) under the formation of the corresponding salts of the type [(CH₃)₂SO(OX)]⁺[MF₆]^–. The salts are characterized by low temperature vibrational spectroscopy. In case of [(CH₃)₂SO(OH)]⁺[SbF₆]^– a single‐crystal X‐ray structure analysis is reported. The salt crystallizes in the orthorhombic space group Pbca with eight formula units per unit cell [a = 10.3281(3) Å, b = 12.2111(4) Å, c = 13.9593(4) Å]. The experimental results are discussed together with quantum chemical calculations on the PBE1PBE/6‐311G++(3pd,3df) level of theory.     

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.     

Symmetry properties of chemical graphs. V. Internal rotation in XY⋅3XY⋅2XY3

Structures XY?₃XY?₂XY₃ of symmetry C_2v (of which propane is an example) are examined and the rearrangement due to the internal rotation of the end groups XY₃ studied. The isomerization graph is constructed, various forms of which are displayed and the symmetry of which has been determined. The order of the group is 72. There are nine prime (irreducible) representations (4A + E + 4G) with the following partitioning of the elements into classes: 1, 4², 6², 9, 12², 18. When the mechanism for rearrangement is generalized to include enantiomers, a duplex graph is produced with the order of the group 144 which is isomorphic to the group S₂(S₃,S₂) (generalized wreath product of the symmetric group S₂ and S₃). The corresponding graph has been constructed and displayed in one of more symmetrical forms. Isomorphism of groups of order 144 is discussed and a procedure is outlined in which correspondence between distinctive combinatorial objects is established by inducing permutations of m elements from available permutations of n elements. The scheme is based on selection of suitable graph invariants in one system and their labeling as m objects which form the basis for representation of the symmetry for the other system.     

Die neuen gemischtvalenten Chalkogenoindate MIn7X9 (M = Rb,Cs; X = S,Se): Strukturchemie,Röntgenund HRTEM‐Untersuchungen

The New Mixed Valent Chalcogenoindates MIn₇X₉ (M = Rb, Cs; X = S, Se): Structural Chemistry, X‐Ray and HRTEM Investigations Systematic X‐ray and HRTEM investigations on the ternary systems alkali metal (or thallium)–indium–chalcogen proved the existence of mixed valent solids with the simultaneous occurrence of indium species in different states of oxidation. Additionally to the earlier described solids MIn₅S₇ (M: Na, K, Tl: isotypic to InIn₅S₇ = In₆S₇ and TlIn₅S₇) and KIn₅S₆ (isotyp to TlIn₅S₆) in the actual work we present with MIn₇X₉ (M: Rb, Cs; X: S, Se) a new structure type which also contains indium in the states of oxidation +3 and +2. The formal state of oxidation In²⁺ corresponds to (In₂)⁴⁺ ions. A reasonable ionic formulation of these structures is given by: MIn₅S₇ = M⁺ 3[In³⁺] [(In₂)⁴⁺] 7[S^2–] (M = Na, K, Tl), MIn₅S₆ = M⁺ [In³⁺] 2[(In₂)⁴⁺] 6[S^2–] (M = K, Tl), MIn₇X₉ = M⁺ 3[In³⁺] 2[(In₂)⁴⁺] 9[S^2–]. The three structure types show common two dimensional structure elements which contain ethane analogous In₂X₆ units and cis and trans edge sharing double octahedron chains. The main interest of this work is a crystalchemical discussion taking into account the new compounds MIn₇X₉ and the results of special HRTEM investigations on MIn₇X₉. The HRTEM investigations aim on the identification and subsequent preparation of new phases which initially might be visible as nano size crystals or inclusions in the HRTEM only.     

Theoretical Studies of Inorganic Compounds. 341) Energy Decomposition Analysis of E–E Bonding in Planar and Perpendicular X2E−EX2 (E = B,Al, Ga,In, Tl; X = H,F, Cl,Br, I)

The nature of E–E bonding in group 13 compounds X₂E–EX₂ (E = B, Al, Ga, In, Tl; X = H, F, Cl, Br, I) has been investigated by means of an energy decomposition analysis (EDA) at the BP86/TZ2P level of theory. The calculated equilibrium geometries of all molecules B₂X₄?Tl₂X₄ have a perpendicular (D_2d) geometry. The largest energy barriers for rotation about the E‐E bond are predicted for the hydrogen species B₂H₄?Tl₂H₄. The EDA shows that the rotational barriers of B₂X₄?Tl₂X₄ may not be used for an estimate of the hyperconjugative strength in the D_2d structures except for the tetrahydrides. The values for the planar (D_2h) transition states reveals that π conjugation of the halogen lone‐pair electrons stabilizes the transition states. The bonding analysis shows that hyperconjugation in B₂I₄ is stronger than in B₂H₄ although the latter compound has a higher rotational barrier than the former. In B₂F₄, hyperconjugative stabilization of the perpendicular structure and conjugative stabilization of the planar structure nearly cancel each other yielding a nearly vanishing rotational barrier. The heavier analogues Al₂X₄?Tl₂X₄ have low rotational barriers and rather weak hyperconjugative interactions. The larger rotational barriers of the hydrogen systems Al₂H₄?Tl₂H₄ compared with the tetrahalogen compounds is explained with the cooperation of the relatively large hyperconjugation in the perpendicular form and the relatively weak conjugation in the planar transition structures. The EDA also indicates that the electrostatic (ΔE_elstat) and molecular orbital (ΔE_orb) components of the E–E bonding are similar in magnitude.Thecalculated B‐B bond dissociation energies of B₂X₄ (D_e = 93.0–108.4 kcal/mol) show that the bonds are rather strong. The heavier analogues Al₂X₄?Tl₂X₄ have weaker bonds (D_e = 16.6–61.7 kcal/mol). In general, the X₂E‐EX₂ bond dissociation energies follow the trend for atoms E: B ? Al > Ga > In > Tl and for atoms X: H > F > Cl > I.     

Kraftkonstanten von Verbindungen des Typs (CH3)3ElCl+X− (El = N,P, As,Sb; X− = SbCl6−)

Force Constants of Compounds of the Type (CH₃)₃ElCl⁺X^?(El = N, P, As, Sb; X^? = SbCl₆^?) For the cations (CH₃)₃NCl⁺ ( 1 ), (CH₃)₃PCl⁺ ( 2 ), (CH₃)₃AsCl⁺ ( 3 ), and (CH₃)₃SbCl⁺ ( 4 ) a normal coordinate analysis using a general valence force field is performed by the method of Fadini. The force constants are discussed. Calculations of the potential energy distribution show, that the skeletal vibrations in 4 are all characteristic vibrations, but there is a strong coupling of vibrations in 1 .     

Dihalomethanes as Bent Bifunctional XB/XB‐Donating Building Blocks for Construction of Metal‐involving Halogen Bonded Hexagons

The dihalomethanes CH₂X₂ (X=Cl, Br, I) were co‐crystallized with the isocyanide complexes trans‐[MX^M₂(CNC₆H₄‐4‐X^C)₂] (M=Pd, Pt; X^M=Br, I; X^C=F, Cl, Br) to give an extended series comprising 15 X‐ray structures of isostructural adducts featuring 1D metal‐involving hexagon‐like arrays. In these structures, CH₂X₂ behave as bent bifunctional XB/XB‐donating building blocks, whereas trans‐[MX^M₂(CNC₆H₄‐4‐X^C)₂] act as a linear XB/XB acceptors. Results of DFT calculations indicate that all XCH₂–X???X^M–M contacts are typical noncovalent interactions with estimated strengths in the range of 1.3–3.2 kcal mol^?1. A CCDC search reveals that hexagon‐like arrays are rather common but previously overlooked structural motives for adducts of trans‐bis(halide) complexes and halomethanes.     

Thermal Behavior and Decomposition Kinetics of the Complexes of CuX2 （X=NO3, Br, CI and CIO4） with 3,3＇-Dimethyl-1 -（1 H-1,2,4-triazol-1-yl）-2-butanone

The thermal behaviors of the complexes of Cu(DMTZB)4X2 (DMTZB=3,3‘-dimethyl-1-(1H-1,2,4-triazol-1-yl)-2-butanone, X=NO3 or ClO4) and Cu(DMTZB)2 X2 (X=Br or Cl) in a nitrogen atmosphere were studied under the non-isothermal conditions by simultaneous TG-DTG-DSC, EDS and elemental analysis techniques. The resuits showed that their decomposition proceeded in three different ways mainly depending on the anions in the molecules. The heat effect associated with the decomposition step of DMTZB molecules was also different. The decomposition mechanisms and the kinetic parameters of DMTZB were determined and calculated by jointly using four methods, which showed that its pyrolysis was controlled by D3 mechanism but with different activation energies and pre-exponential factors for different complexes.     

(2‐Acetyl­pyridine‐κN 4‐phenyl­thio­semicarbazonato‐κ2N1,S)­halogeno‐trans‐di­methyl­tin(IV) (halogeno = chloro and bromo)

A thio­semicarbazone derivative, 2‐acetyl­pyridine 4‐phenyl­thio­semicarbazone, was prepared and complexed to Lewis acids, Sn(CH₃)₂X₂, X = Cl and Br. The products, [SnX(C₁₄H₁₃N₄S)(CH₃)₂], were characterized by single‐crystal X‐ray diffraction, and IR, NMR and Mössbauer spectroscopies. They are isomorphous and crystallize in the monoclinic space group P2₁/n. The structure determination revealed discrete neutral complexes with the Sn^IV atom in a distorted octahedral coordination geometry, with the halogeno ligand and the thio­semicarbazone derivative in the equatorial plane and the methyl groups in axial positions.     

Bulk cyclopolymerization of 1,2:5,6‐diepithio‐3,4‐di‐O‐methyl‐1,2:5,6‐tetradeoxy‐D‐mannitol with quaternary ammonium salts leading to gel‐free thiosugar polymer

The bulk cyclopolymerization of diepisulfide, 1,2:5,6‐diepithio‐3,4‐di‐O‐methyl‐1,2:5,6‐tetradeoxy‐D ‐mannitol ( 1 ), was studied using R₄N⁺Br^? (R = ? CH₃, C₂H₅, C₃H₇, C₄H₉, and C₇H₁₅) and (C₄H₉)₄N⁺X^? (X = Cl, I, NO₃, and ClO₄) as the initiators. All the bulk polymerizations of 1 using quaternary tetraalkylammonium salts at 90 °C proceeded without gelation even at high conversion to produce gel‐free polymers consisting of 2,5‐anhydro‐1,5‐dithio‐D ‐glucitol (I) as the major cyclic repeating unit along with 1,5‐anhydro‐2,5‐dithio‐D ‐mannitol (II) and the desulfurized acyclic unit (III) as the minor units. The polymerization rate and molar fraction of the I unit increased with the increasing alkyl chain length of the tetraalkylammonium cation and the increasing nucleophilicity of the counteranion. Tetrabutylammonium chloride exhibited the highest catalytic activity and the highest stereoselectivity, that is, the thiosugar polymer with I:II:III = 81:15:4 and a number‐average molecular weight of 31.9 × 10³ was obtained in 85% yield for a polymerization time of 0.5 h. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 965–970, 2002     

Theoretical study of the relative stabilities of H+(X)2 and H+(X)3 conformers and their clustering energies: X  CO and N2

Third-order Møller–Plesset perturbation theory (MP 3) with a 6-31G** basis set was applied to study the relative stabilities of H⁺(X)₂ conformations (X ? CO and N₂) and their clustering energies. The effect of both basis set extensions and electron correlation is not negligible on the relative stabilities of the H⁺(CO)₂ clusters. The most stable conformation of H⁺(CO)₂ is found to be a C_∞v structure in which a carbon atom of CO bonds to the proton of H⁺(CO), whereas that of H⁺(N₂)₂ is a symmetry D_∞h structure. The second lowest energy conformations of H⁺(CO)₂ and H⁺(N₂)₂ lie within 2 kcal/mol above the energies of the most stable structures. Clustering energies computed using MP 3 method with the 6-31G** basis set are in good agreement with the experimental findings of Hiraoka, Saluja, and Kebarle. The low-lying singlet conformations of H⁺(X)₃ (X ? CO and N₂) have been studied by the use of the Hartree–Fock MO method with the 6-31G** basis set and second-order Møller–Plesset perturbation theory with a 4-31G basis set. The most stable structure is a T-shaped structure in which a carbon atom of CO (or a nitrogen atom of N₂) attacks the proton of the most stable conformation of H⁺(X)₂ clusters.