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.     

Ab initio molecular-orbital study of structures and energetics of Si3H3 neutral and anion

The geometric structures and isomeric stabilities of various stationary points in Si(3)H(3) neutral and its anion are investigated at the coupled-cluster singles, doubles (triples) [CCSD(T)] level of theory. For geometrical surveys, the basis sets used are of the Dunning's correlation consistent basis sets of triple-zeta quality for the neutral. To the anions, the Dunning's correlation consistent basis sets of double-zeta quality with diffuse functions are applied. For the three lower-lying anion isomers, the Dunning's correlation consistent basis sets of triple-zeta quality with diffuse functions (aug-cc-pVTZ) are also used. The final energies for the optimized stationary points are calculated at the CCSD(T) level of theory with the aug-cc-pVTZ basis sets. The basis sets of 6-311++G(3df,2pd) were also used for the lower-lying anion isomers. The Gaussian-2 method was performed only for the lower-lying anion isomers to clarify the relative stabilities. The global minimum neutral 1 (C(1):(2)A) has an unsymmetrical hydrogen-bridged bond; the conformer 2 in C(s) symmetry is a saddle point connecting the two equivalent isomers 1. Two lower-lying isomers (3 and 4) are also predicted within the energy range of 20 kJmol. In the anion, however, the conformer 4 (C(s):(1)A(')) with five formal valence electrons is a global minimum. Two more isomers (2 and 3) lie within 20 kJmol as in the neutral; the conformer 1 converts to the isomer 2. The quartets for the neutrals and diradical triplets for the anions were further studied; lower-lying quartets and triplets, competing with the corresponding doublet and singlet, respectively, were not found in the present systems. The vertical and adiabatic electron affinities of the global minimum neutral 1, producing the second lowest-lying anion isomer 2, amount to 2.18 and 2.35 eV, respectively, at the CCSD(T)/aug-cc-pVTZ level of theory. The electron addition to the third lowest-lying neutral isomer 4 produces the largest vertical electron affinities of 2.48 eV. The D(3h) structure, being the global minimum in the corresponding Si(3)H(3) (+) cation (trisilacyclopropenyl cation), converts to the isomer 8 (C(s)) or 11 (C(2)) due to the Jahn-Teller effect in the Si(3)H(3) neutral.     

Ab initio molecular orbital study of structures and energetics of Si(3)H(2), Si(3)H(2) (+), and Si(3)H(2) (-)

The geometric structures, isomeric stabilities, and potential energy profiles of various isomers and transition states in Si(3)H(2) neutral, cation and anion are investigated at the coupled-cluster singles, doubles (triples) level of theory. For the geometrical survey, the basis sets used are of the Dunning's correlation consistent basis sets of triple-zeta quality (cc-pVTZ) for the neutral and cation and the Dunning's correlation consistent basis sets of double-zeta quality with diffuse functions (aug-cc-pVDZ) for the anion. For the final energy calculations, the aug-cc-pVTZ: Dunning's correlation consistent basis sets of triple-zeta quality with diffuse functions and cc-pVQZ: Dunning's correlation consistent basis sets of quadruple-zeta quality basis sets are used for the neutral and the aug-cc-pVTZ ones for the cation and anion. The global minimum neutral (I-1: (1)A(1)) has the same framework as that (cyclopropenylidene) of the C(3)H(2) molecule. Other low-lying three isomers (I-2, I-3, and I-4) are also predicted to be within 20 kJ/mol. Five transition states are optimized and their energy relationships with the isomers are clarified. The geometric structure of the global minimum cation (C-1: (2)A(1)) has the same framework as that of the neutral, but that of the anion (A-1: (2)A(')) differs very much from those of the neutral and cation. The calculated vertical and adiabatic ionization potentials from the global minimum neutral (I-1) are 7.85 and 7.77 eV, respectively. The adiabatic electron affinity of the neutral I-1 and the electron detachment energy of the global minimum anion (A-1) are predicted to be 1.21 and 1.92 eV, respectively. The two-electron three-centered bond is widely observed in the present Si(3)H(2) neutral, cation, and anion. The contour plots of their localized molecular orbitals clearly show the existence of such nonclassical chemical bonds.     

Ab initio MO calculation of hydration energies of ammonium ions and their solvation effect

The hydration energies for the NH⁺₄ and CH₃NH⁺₃ ions were calculated by an ab initio MO method. The aqueous solvation energy difference between these two ions was found to be accounted for by the interactions of the ions with a few solvent molecules.     

Ab initio MO study on the global minimum structure of C3H3 anion: propynl-1-yl versus allenyl anions

The geometrical structures of the C₃H⁻₃ anion are surveyed at the coupled-cluster doubles (CCD) level of theory with the aug-cc-pVDZ basis set. To clarify the CCD geometries, the stable two isomers -- propynl-l-yl 1 and allenyl 2 anions -- are further optimized at the coupled-cluster singles, doubles (triples) (CCSD(T)) level of theory both with the aug-cc-pVDZ and aug-cc-pVTZ basis sets. The final energies are calculated at the CCSD(T) and the complete active space self-consistent field (CASSCF) multi-reference internally contracted CI (MRCI) levels of theory with the aug-cc-pVTZ basis set. At the MRCI level of theory including both the corrections due to the cluster energies (MRCI+Q) and the zero-point vibrational energies, the allenyl anion 2 is about 1.3 kcal mol⁻¹ lower in energy than the propynl-l-yl anion 1. These results contrast with the previous theoretical estimates, where the propynl-l-yl anion 1 is 2-3 kcal mol⁻¹ lower in energy than the allenyl anion 2. The activation energies of the intramolecular hydrogen transfer in the 1 → 2 conversion reactions are 63.5 kcal mol⁻¹ at the MRCI+Q level of theory with the aug-cc-pVTZ basis set including the zero-point energy corrections. The adiabatic electron affinity of the planer propargyl (H₂CCCH) radical, which is the global minimum of the C₃H₃ radical, is calculated to be 0.976 eV (after correction for the zero-point energy changes) at the CCSD(T) level of theory with the aug-cc-pVTZ basis set. The present electron affinity is in fairly good agreement with the experimental one (0.893 eV) observed by Oakes and Ellison.     

Appearance of anterior cruciate ligament autografts in their tibial bone tunnels on oblique axial MRI.

The objective of this study was to observe the changing appearance of human anterior cruciate ligament (ACL) grafts in their tibial bone tunnels by MRI using oblique axial images. One-hundred and eight knees in 75 patients were studied by MRI at 1-33 months after arthroscopic ACL reconstructions using double-looped, autogenous semitendinosus and/or gracilis tendons. Knees with poor stability were excluded from this study. The examinations were performed at 0.2T with spin echo proton density and T2-weighted oblique axial images. Appearances of grafts were mainly described on spin echo proton density images based upon time after surgery. The grafts appeared as homogeneous, low signal intensity areas in the bone tunnels at 1 month after the surgery. Ring-shaped low signal intensity areas were observed along the wall of the bone tunnels in the 2- to 3-month group. In many grafts from this group, each tendinous bundle appeared as a low signal area separated by a high signal intensity area. In all cases in the 4- to 6-month group, the thickness of the ring-shaped low signal intensity area had increased, whereas the thickness of the high signal intensity area had decreased. In almost all of the cases, the interior of the bone tunnel gradually became a homologous low signal intensity region by 7 to 12 months after the surgery. According to these results, it is suggested that the maturation of the tendon-bone interface was completed from 6 to 12 months after the ACL reconstruction.     

Calibration of the isomer shift of121Sb and119Sn by means of Mössbauer spectroscopy and molecular orbital calculation

The relationship between the isomer shifts in Mössbauer spectroscopy and the electron contact densities has been investigated for several antimony and tin compounds. Mössbauer spectra for¹²¹Sb in rapidly frozen solutions of antimony compounds were measured. The isomer shifts are compared with the valence electron densities at the antimony nucleus calculated with theab initio molecular orbital method. The relative difference of the nuclear charge radius ΔR/R could be obtained as ΔR/R =?(10.2±1.0)×10^?4 for the 37.15 keV M1 transition of¹²¹Sb. Further, some computations of the electron density at the tin nucleus for several tin compounds were performed. By comparing the valence electron contact densities with isomer shifts, which had been reported for several tin compounds in rare-gas matrix states, the value of ΔR/R for 23.87 keV M1 transition in¹¹⁹Sn was estimated to be (1.57±0.03)×10^?4.     

Theoretical study on the β−-decay effect in mono-tritiated two hydrogen bonded systems: proton transfer along the hydrogen bond direction

The effect of tritium β^?-decay on the “two” hydrogen bonds in mono-tritiated formamide dimer (A), formic acid dimer (B), and acetic acid-formic acid (C) was studied with ab initio MO calculations. The tritium β^?-decay in (A) and (B) is expected to result in spontaneous transfer of one proton along the hydrogen bond direction: no proton transfer takes place in (C).