Distance dependence analysis of the electron transfer reactivity for the metastable FeOH2/FeOH2 system: an ab initio investigation

A novel theoretical scheme and ab initio application in discussing the electron transfer (ET) reactivity are presented in this paper, and are also calibrated in terms of the mono-hydrated iron ion system, Fe²⁺–OH₂/Fe³⁺–OH₂. The detailed geometry optimizations have been made at UMP2(full)/6-311+G^* level, and the activation geometrical configuration and the energy have been obtained at this level of theory using the activation model and the ab initio potential energy surface fitted from MP2(full)/6-311+G^* single point energies. The corresponding energy quantities (such as the activation energy, and dissociation energy) have also been obtained at different levels of theory (HF, MP2, MP3, MP4, QCISD and PUHF, PMP2 and PMP3 with the spin-projection) and a same basis set (6-311+G^*). The electron correlation calculations include the all electron correlation and the valence electron correlation. The electronic transmission coefficient is calculated using the ab initio potential energy surface slopes and the coupling matrix element determined from the two-state model and the Slater-type d-electron wave functions. The pair distribution function is calculated using two different schemes. Taking the pair distribution function and the local ET rate into account, a statistically averaged overall observed ET rate scheme and a spherically averaged local ET rate scheme are proposed. The relevant kinetic parameters are obtained in terms of these new schemes at different ab initio calculational levels. The contact distance dependence of these parameters and the applicability of the presented models and ab initio calculational method are also discussed.     

Ab initio study of some peroxides. HOOH, CH3OOH and, CH3OOCH3

The geometries of HOOH, CH₃OOH, and CH₃OOCH₃, were optimized with different basis sets (3-21G, 6-31G^*(*) and D95^**) at different levels of theory (HF, MP2, MP4, and CI). HF/3-21G optimizations result in planar trans conformations for all three peroxides. HF/6-31G^** calculations predict skew conformations for HOOH and CH₃OOH, but a planar trans struture for CH₃OOCH₃. For the larger basis set the calculated bond lengths, especially the O-O bonds, are too short. Optimizations for HOOH including electron correlation at the MP2, MP3, MP4, CI, and CCD level improve the agreement for bond lengths and the OOH angle, but result in dihedral angles Which are too large by 3– 8°. In the case of CH₃OOCH₃, similar calculations at the MP2 and CI level predict planar trans structures instead of the experimentally observed skew conformation. On the other hand, MP4 single point calculations at MP2 optimized parameters result in a correct skew structure. For all three peroxides a computationally “economic” method, i.e., single point calculations at MP2 or MP4 level with HF/3-21G optimized parameters, result in close agreement between calculated and experimental structures.     

Ab initio studies on the electronic structures of certain 10π-electron six-membered ring compounds

By using ab initio methods of all-electron or effective core potential calculations, the electronic structures and the possible aromaticity of some 10π-electron systems, C₆H₆⁴⁻ (1), N₆⁴⁻ (2), P₆⁴⁻ (3), S₆²⁻ (4), Te₆²⁻ (5) and S₃N₃⁻ (6), have been studied at the SCF levels using 4-31G//4-31G and 6-31G^*//6-31G^* basis sets. The bonding characteristics of these systems are analysed in terms of the canonical molecular orbital and the Foster-Boys localized molecular orbital results. The application of the second-order Jahn-Teller theorem to the stability of these diamagnetical planar species is presented.     

Ab initio prediction of MnOH2/MnOH2 electron transfer reactivity at electron correlation level

An ab initio calculation of electron transfer reactivity of Mn²⁺OH₂/Mn³⁺OH₂ redox system, in gas and in solution, has been made in this paper. The detailed geometry optimization and the scanning of the potential energy surfaces have been carried out at UMP2 (full)/6-311+G^* level. The relevant energy quantities (such as the activation energy and the binding energy) are calculated at different levels of theory (HF, MP2, MP3, MP4 and QCISD and corresponding spin-projection PUHF, PMP2 and PMP3) with the same basis set (6-311+G^*). Both all-electrons and valence electrons have been correlated in energy calculations. The electronic transmission coefficient is calculated using the ab initio potential energy surface slopes and the coupling matrix element determined from the two-state model and the Slater-type d-electron wave functions. The pair distribution function is obtained using both a classical sphere approximation scheme and a novel scheme. The relevant kinetic parameters are obtained at different ab initio levels in terms of the new model. The contact-distance dependence of these parameters and the applicability of the presented models are also discussed.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

Structure and conformational stability of CH2CHCH2X (X=F, Cl and Br) molecules—post Hartree–Fock and density functional theory methods

The molecular structure and conformational stability of CH₂CHCH₂X (X=F, Cl and Br) molecules were studied using ab initio and density functional theory (DFT) methods. The molecular geometries of 3-fluoropropene were optimized employing BLYP and B3LYP levels of theory of DFT method implementing 6-311+G(d,p) basis set. The MP2/6-31G^*, BLYP and B3LYP levels of theory of ab initio and DFT methods were used to optimize the 3-chloropropene and 3-bromopropene molecules. The structural and physical parameters of the molecules are discussed with the available experimental values. The rotational potential energy surface of the above molecules were obtained at MP2/6-31G^* and B3LYP/6-311+G(d,p) levels of theory. The Fourier decomposition of the rotational potentials were analyzed. The HF/6-31G^* and MP2/6-31G^* levels of theory have predicted the cis conformer as the minimum energy structure for 3-fluoropropene, which is in agreement with the experimental values, whereas the BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory reverses the order of conformation. The ΔE values calculated for 3-chloropropene at MP2/6-31G^*, BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory show that the gauche form is more stable than the cis form, which is in agreement with the experimental value. The same levels of theory have also predicted that the gauche form is stable than cis for 3-bromopropene molecule. The maximum hardness principle has been able to predict the stable conformer of 3-fluoropropene at HF/6-31G^* level of theory, but the same level of theory reverses the conformational stability of 3-chloropropene and 3-bromopropene molecules and MP2/6-31G^* level of theory predicted the stable conformer correctly.     

A theoretical investigation on the potential energy surface of CN2H rotation of the encapsulated 1-bicyclo[2.2.1]heptyldiazirine

The potential energy surface (PES) of CN₂H rotation of the encapsulated 1-bicyclo[2.2.1]heptyldiazirine (BHD) inside a molecular container: Cram’s hemicarcerand (CH) was explored using two different DFT involved ONIOM methods: B3LYP/6-31G^**//ONIOM(B3LYP/6-31G^*: AM1) and B971/6-31G^**//ONIOM(B971/6-31G^*: AM1). The free-state PES of CN₂H rotation was also calculated, respectively by B3LYP/6-31G^**//B3LYP/6-31G^* and B971/6-31G^**//B971/6-31G^* methods for comparison. The findings in this study have shown that the PES profiles differ from each other notably in the two states. In the encapsulated state the rotation barrier corresponding to the free-state conversion with the largest rotation barrier increases by about 2 kcal/mol, which has exceeded the largest rotation barrier in the free-state. The conformational preference behavior towards certain BHD isomers, which might be in better conformational compatibility with the container, has been demonstrated.     

Molecular structure and conformational stability of allylisocyanate—post-Hartree–Fock and density functional theory studies

The molecular structure and conformational stability of allylisocyanate (CH₂CHCH₂NCO) molecule was studied using the ab initio and DFT methods. The geometries of possible conformers, C-gauche (δ=120°, θ=0°) (δ=C=C–C–N and θ=C–C–N=C) and C-cis N-trans (δ=0° and θ=180°) were optimized employing HF/6-31G^*, MP2/6-31G^* levels of theory of ab initio and BLYP, B3LYP, BPW91 and B3PW91 methods of DFT implementing the atomic basis set 6-311+G(d,p). The structural and physical parameters of the above conformers were discussed with the experimental and theoretical values of the related molecules, methylisocyanate and 3-fluoropropene. It has been found that the N=C=O bond angle is not linear as the experimental result for both the conformers and the theoretical bond angle is 173°. The rotational potential energy surfaces have been performed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The Fourier decomposition potentials were analysed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The HF/6-31G^* level of theory predicted that the C-gauche conformer is more stable than the C-cis N-trans conformer by 0.41 kJ/mol, but the MP2 and DFT methods predicted the C-cis N-trans conformer is found to be more stable than the C-gauche conformer. The calculated chemical hardness value at the HF/6-31G^* level of theory predicted the C-cis N-trans form is more stable than C-gauche form, whereas the chemical hardness value at the MP2/6-31G^* level of theory favours the slight preference towards the C-gauge conformer.     

Ab initio molecular orbital study on three feasible mechanisms for substitution of the vinylic carbon in F2C=C(OMs)BMe3−

A substitution on 2,2-difluorovinylic carbon was investigated by using ab initio molecular orbital calculations. Three feasible mechanisms, which are the S_N1-like, the S_N2-type and the addition-elimination mechanisms, were ex- amined for a model borate, 2,2-difluoro-1-mesyloxyvinyl(trimethyl)borate. Four TSs were obtained depending on the position of Li⁺ around the vinylborate although activation energies in the gas phase are rather high (ca. 30–40 kcal mol⁻¹) in comparison with that expected from the experimental conditions. It was confirmed at the SCRF-IPCM calculations that the solvent effect reduces the acti- vation energy of one S_N2-type mechanism very much (4. l kcal mol⁻¹ at the B3LYP/6-31+G^*//RHF/6-31+G^/s* level of theory) while those for the other mechanisms do not change very much. Therefore, the S_N2-type mechanism is applicable to the substitution reaction observed for the vinylborate.     

Structural characterisation of [Pt(NH3)4]2[W(CN)8][NO3]·2H2O donor–acceptor complex

The bimetallic [Pt(NH₃)₄]₂[W(CN)₈][NO₃]·2H₂O is characterised by single-crystal X-ray diffraction [S.G.P2₁/m(11), a=8.0418(7), b=19.122(2), c=9.0812(6) Å, Z=2]. All platinum centres have the square-plane D_4h geometry with average dimensions Pt(1)–N 2.042(2) and Pt(2)–N 2.037(10) Å. The octacyanotungstate anion has the square-antiprismatic D_4d configuration with average dimensions W(1)–C 2.164(13), C–N 1.140(12), W(1)–N 3.303(5) Å. The structure exhibits two different mutual orientations of Pt versus W units resulting in Pt(2)–W(1), W(1)^* separations of 4.77(2), 4.55(2)^* and Pt(1)–W(1) of 6.331(8) Å. A centrosymmetric structure reveals groups of two distinct columns: the first is formed by intercalated NO₃⁻ between parallel [Pt(1)(NH₃)₄]²⁺ planes and the second consists of [W(CN)₈]³⁻ interlayered by, parallel to square faces of W-antiprisms, [Pt(2)(NH₃)₄]²⁺. The structure is stabilised through a three-dimensional hydrogen bond network via nitrogen atoms of cyanide ligands, hydrogen atoms of NH₃ ligands, water molecules and oxygen atoms of NO₃⁻ counteranions. The vibrational pattern and the range of ν(CN) frequencies attributable to the electronic environment of W(V) and W(IV) are consistent with the ground state Pt(II)↔W(V) charge transfer.     

Reactions of Cp Ru(η-C6H5CHO) OSO2CF3 (Cp = C5Me5) with substituted anilines forming ruthenium Schiff base complexes

Cp^* Ru(η⁶-C₆H₅CHO)⁺OSO₂CF₃⁻ (1) (Cp^* = C₅Me₅) reacts with substituted anilines forming ruthenium Schiff base complexes containing an η⁶-coordinated Cp^* Ru⁺ group. The 2:1 reaction of 1 with 1,4-phenylenediamine yielded only the monocondensation product, whereas the 2:1 reaction of 1 with 1,4-xylylenediamine yielded the dicondensation product.     

Ab initio calculations of minimum-energy pathways of the nucleophilic addition of the H anion, LiH molecule and Li/H ion pair to acetylene and methylacetylene

Ab initio calculations were performed for special points of the minimal energy pathways (MEP) of the nucleophilic addition reactions of the isolated H⁻ anion, LiH molecule and Li⁺/H⁻ ion pair to acetylene (A) and methylacetylene (MA) molecules, proceeding in accordance (M) and against (aM) the Markovnikov's rule. All structural parameters were optimized using the restricted Hartree–Fock (RHF) method. For the addition of H⁻, the 6-31++G^* basis set was used and for the reactions of LiH and Li⁺/H⁻ the 6-31G^* basis set with the subsequent recalculation of single point energies, taking into account of electron correlation energy by means of the second-order Möller–Plesset perturbation theory at the MP2/6-31++G^** level. The results of calculations demonstrate, that the energy characteristics of both M- and aM-additions with H⁻ do not differ sufficiently (0.1–1.2 kcal/mol for the activation energies (ΔE_a) and the reaction heats (ΔQ)). The substitution of the H atom by the CH₃ group in A molecule results in practically the same values of ΔQ and ΔE_a. On the contrary, for the LiH molecule and Li⁺/H⁻ ionic pair, the M-addition is favorable (charge control). It is found that the presence of electrophile decreases the activation energy by 3–5 kcal/mol as compared with the addition of the isolated hydride ion H⁻.     

S2 → S0 fluorescence in an aromatic thioketone, xanthione

In addition to the red phosphorescence (T₁(³ A₂n, π^*) → S₀) xanthione exhibits in solution an emission with a maximum at ≈ 23 000 cm⁻¹ and φ_f(298°) = 5 × 10⁻³. It is shown that this emission is fluorescence from the second excited singlet state (S₂ (¹A₁ π, π^*) → S₀).     

Benzooxirene. Ab initio calculations

Ab initio calculations have been performed on benzooxirene, the corresponding oxo carbene (“ketocarbene”), and the transition state linking the two. At the highest level used, QCISD(T)/6-31G^*//MP2(FULL)/6-1G^* with MP2(FULL)/ 6-31G^* zero point energy corrections, the relative energies of the oxirene, the transition state and the carbene are 0, 24.6, and −17.8 kJ mol⁻¹. Correlation energy effects are very important in this system: at the QCISD(T) level the oxirene lies above the carbene, as at the MP4 and HF levels, but at the MP2 level the ordering is reversed. Benzooxirene is probably slightly nonplanar: the HF/6-31G^* geometry is C_2v but the MP2(Fermi contact)/6-31G^* geometry is C_s with a 6-/3-ring coplanarity deviation of about 6.9 °, although in the MP2(FULL)/6-31G^* geometry this is reduced to about 3.1 °.     

Vibrational spectra and density functional study of propylgermane

Raman and infrared spectra of propylgermane, CH₃CH₂CH₂GeH₃, and its Ge-deuterated analog, CH₃CH₂CH₂GeD₃, were investigated in their gaseous, liquid and solid states. The normal coordinate treatment was carried out by density functional theory (DFT) calculation, using B3LYP/6-31G^* and 6-311++G^** basis sets, and the corresponding fundamental vibrations were assigned. The trans (T) and gauche (G) forms around the central C–C bond coexisted in the gaseous and liquid states and only the T form existed in the solid state. From the temperature dependent measurements of the Raman spectra in the liquid state, the enthalpy difference was found to be ΔH(T−G)=−0.36±0.02 kcalmol⁻¹ with the T form being more stable. The energy differences between the isomers obtained by DFT calculations were ΔE(T−G)=−0.46 kcalmol⁻¹ and ΔE(T−G)=−0.87 kcalmol⁻¹ by the 6-31G^* basis set and 6-311++G^** basis set, respectively.     

1.54 and 1.75 μm infrared luminescence of Y2O3:Er

A new 1.75 μm infrared emission transition of Y₂O₃:Er³⁺ is assigned to the ⁴S_3/2 → ⁴I_9/2 transition of Er³⁺ ions situated at the C₂ sites of cubic RE₂O₃ (RE = Y, Gd, Lu). The intensities of features in the 1.54 μm ⁴I_15/2–⁴I_13/2 absorption transition due to Er³⁺ at S₆ and C₂ sites are consistent with the site occupation ratio and the relative magnetic dipole–electric dipole intensity contributions of Er³⁺ at the different sites. The 1.54 μm emission lines are predominantly from Er³⁺ ions at C₂ sites. The different behaviours of the emission intensities 1.75 and 1.54 μm groups with change in Er³⁺ dopant ion concentration, preparation technique, Yb³⁺ co-doping, temperature change and different excitation line are rationalized.     

Dimers, trimers and oligomers of sulfur oxides: an ab initio and density functional study

Ab initio (HF/3-21G^*), DFT (B3LYP with basis sets 6-31G^*, 6-311+G^* and 6-311+G(2d)) and, in some cases, MP2/6-31G^* calculations, were done on cyclic dimers, trimers, etc. and on acyclic oligomers (with OH and H on the ends) of sulfur monoxide and sulfur dioxide. The four cyclic (SO)_n molecules were (S–O)₂ (1,3,2,4-dioxadithietane, 1a), (S–O)₃ (1,3,5,2,4,6-trioxatrithiane, 2a), (S(=O))₄ (tetrathietane 1,2,3,4-tetraoxide, 1b), and (S(=O))₆ (hexathiane 1,2,3,4,5,6-hexaoxide, 2b). The four cyclic (SO₂)_n molecules were the dioxide of 1a (1,3,2,4-dioxadithietane 2,4-dioxide, 1c), the trioxide of 2a (1,3,5,2,4,6-trioxatrithiane 2,4,6-trioxide, 2c), the tetraoxide of 1b (tetrathietane 1,1,2,2,3,3,4,4-octaoxide, 1d) and the hexaoxide of 2b (hexathiane 1,1,2,2,3,3,4,4,5,5,6,6-dodecaoxide, 2d). The 16 acyclic molecules (oxides of disulfane, trisulfane, etc. and oxides of oxadisulfane, dioxatrisulfane, etc.) were (–S–O–)_n, (–S(=O)–)_n, (–S(=O)O–)_n, and (–S(=O)₂–)_n, with n from 2 to 5 and HO, H at the ends. Most of these species are relative minima on the B3LYP/6-31G^* potential energy surface. In energy content, the SO dimer, etc. lie below, and the SO₂ dimer, etc. above, their SO_x components, at all the electron-correlated levels.     

A study of the B2 excited state geometries of the metal-metal quadruply bonded compounds Mo2X4(PMe3)4 (X = Cl, Br or I)

The excited state geometries of the metal-metal quadruply bonded compounds Mo₂X₄(PMe₃)₄ (X = Cl, Br or I) have been studied by means of resonance Raman and absorption spectroscopy. A fit of the parameters of a simple theoretical model to the experimental data indicates that the metal-metal bond increases some 10 pm on excitation to the ¹B₂ (δδ^*) state, whereas other geometric changes are small. Furthermore, the phenomenological lifetime factor of the excited state, Γ, is found to be dependent on the vibrational quantum number, ν, of this state.     

A localized molecular orbital study on the bonding of> Mo3S4]2Mo> and> Mo3S4]CuI> versus (C6H6)2Cr and C6H6Cr(CO)3

The energy-localized CNDO/2 molecular orbitais have been calculated for the clusters containing molybdenum, > {Mo₃S₄₂Mo}⁸⁺ and> Mo₃S₄]CuI> ⁴⁺, versus the prototype arene-metal sandwich (C₆H₆)₂Cr and half-sandwich complexes C₆H₆Cr(CO)₃. The bonding characteristics of these compounds are described from a localization bonding viewpoint. There are two typical M-arene and M-[Mo₃S₄] bondings. One is formed by electron donation from the three-center two-electron π-bonds in the arene or [Mo₃S₄]⁴⁺ ligands into the vacant hybrid orbitais of the “stranger” metal atom. In the other M-arene or M-[Mo₃S₄] bond there is very little donation by the lone electron pair occupying the d AOs of the “stranger” metal atom to the arene or [Mo₃S₄]⁴⁺ ligands. The analogy of the ligand [Mo₃S₄]⁴⁺ in the clusters studied with the ligand benzene is also briefly discussed.