Theoretical Study and NBO Analysis of the Decomposition Kinetics of Oxetane, 2-Methyloxetane and 2,2-Dimethyloxetane

A theoretical study of the thermal decomposition kinetics of oxetane (1), 2-methyloxetane (2), and 2,2-dimethyloxetane (3) has been carried out at the B3LYP/6-311+G**, B3PW91/6-311+G**, and MPW1PW91/6-311+G** levels of theory. The MPW1PW91/6-311+G** method was found to give a reasonable good agreement with the experimental kinetics and thermodynamic parameters. The decomposition reaction of compounds 1～3 yields formaldehyde and the corresponding substituted olefin. Based on the optimized ground state geometries using MPW1PW91/6-311+G** method, the natural bond orbital (NBO) analysis of donor-acceptor (bond-antibond) interactions revealed that the stabilization energies associated with the electronic delocalization from σC3-C4 bonding to σ*O1-C2 antibonding orbitals decrease from compounds 1 to 3. The σC3-C4→σO1-C2 resonance energies for compounds 1～3 are 2.63, 2.59 and 2.45 kcal mol-1, respectively. Further, the results showed that the energy gaps between σC3-C4 bonding and σ*O1-C2 antibonding orbitals decrease from compounds 1 to 3. Also, the decomposition process in these compounds are controlled by σ→σ* resonance energies. Moreover, the obtained order of energy barriers could be explained by the number of electron-releasing methyl groups substituted to the Csp3 atom (which is attached to oxygen atom). NBO analysis shows that the occupancies of σCsp3-O bonds decrease for compounds 1～3 as 3<2<1, and those of σCsp3-O bonds increase in the opposite order (3 > 2 > 1). This fact illustrates a comparatively easier thermal decomposition of the sCsp3-O bond in compound 3 compared to compound 2, and in compound 2 compared to compound 1. NBO results indicate that these reactions are occurring through a concerted and asynchronous four-membered cyclic transition state type of mechanism.     

Kinetic Study and NBO Analysis of the Dehydrogenation Mechanism of Five‐membered Ring Heterocyclic 2,5‐Dihydro‐[furan,thiophene, selenophene

The theoretical study of the dehydrogenation of 2,5‐dihydro‐[furan ( 1 ), thiophene ( 2 ), and selenophene ( 3 )] was carried out using ab initio molecular orbital (MO) and density functional theory (DFT) methods at the B3LYP/6‐311G**//B3LYP/6‐311G** and MP2/6‐311G**//B3LYP/6‐311G** levels of theory. Among the used methods in this study, the obtained results show that B3LYP/6‐311G** method is in good agreement with the available experimental values. Based on the optimized ground state geometries using B3LYP/6‐311G** method, the natural bond orbital (NBO) analysis of donor‐acceptor (bond‐antibond) interactions revealed that the stabilization energies associated with the electronic delocalization from non‐bonding lone‐pair orbitals [LP(e)_X3] to δ*_{C(1)  H(2)} antibonding orbital, decrease from compounds 1 to 3 . The LP(e)_X3→δ*_{C(1)  H(2)} resonance energies for compounds 1 – 3 are 23.37, 16.05 and 12.46 kJ/mol, respectively. Also, the LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the decrease of occupancies of LP(e)_X3 non‐bonding orbitals in ring of compounds 1 – 3 ( 3 > 2 > 1 ). The electronic delocalization from LP(e)_X3 non‐bonding orbitals to δ*_{C(1)  H(2)} antibonding orbital increases the ground state structure stability, Therefore, the decrease of LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the kinetic of the dehydrogenation reactions of compounds 1 – 3 (k ₁ >k ₂ >k ₃ ). Also, the donor‐acceptor interactions, as obtained from NBO analysis, revealed that the (_C(4)C(7)→δ*_{C(1)  H(2)} resonance energies decrease from compounds 1 to 3 . Further, the results showed that the energy gaps between (_C(4)C(7) bonding and δ*_{C(1)  H(2)} antibonding orbitals decrease from compounds 1 to 3 . The results suggest also that in compounds 1 – 3 , the hydrogen eliminations are controlled by LP(e)→δ* resonance energies. Analysis of bond order, natural bond orbital charges, bond indexes, synchronicity parameters, and IRC calculations indicate that these reactions are occurring through a concerted and synchronous six‐membered cyclic transition state type of mechanism.     

NBO and NICS analysis of the allylic rearrangements (the Cope and 3-aza-Cope rearrangements) of hexa-1,5-diene and N-vinylprop-2-en-1-amine: A DFT study

In this work, ab initio density functional theory (DFT) calculations have been performed on the 3,3-sigmatropic rearrangements of hexa-1,5-diene (Cope) and N-vinylprop-2-en-1-amine (3-aza-Cope) in the gas phase. The barrier heights and heats of reactions calculated at the B3LYP/6-311G** level of theory were in good agreement with experimental data. Transition states optimized with B3LYP/6-311G** theory were used for calculating the nucleus independent chemical shift (NICS) and, a natural bond orbital (NBO) analysis was also performed at the same level of theory. Our results indicate that the aromaticities of the transition states are controlled by the out-of-plane component and that the chair-like transition state of the Cope rearrangement exhibits the strongest aromatic character. Analysis of donor-acceptor (bonding and anti-bonding) interactions of σ_3–4 → π*_1–2 suggests that the TS structure in the hexa-1,5-diene reaction (the Cope rearrangement) has more aromatic character than the N-vinylprop-2-en-1-amine reaction (the 3-aza-Cope rearrangement). The NBO results show that in the hexa-1,5-diene and N-vinylprop-2-en-1-amine rearrangements, activation energies are controlled by σ_3–4 → π*_1–2 and σ_3–4 → π*_1–2 resonance energies.      

PO → Si intramolecular coordination in the derivatives of 1,4‐phosphasilacyclohexane 1‐oxides

The chair and boat conformers for a series of derivatives of 1,4‐phosphasilacyclohexane 1‐oxides have been calculated at the B3LYP/6‐311+G** level of theory in the gas phase and taking into account the effect of solvent polarity using the IEF‐PCM model. The stability of the boat conformers containing pentacoordinate silicon due to formation of the P?O→Si intramolecular coordination bond depends on the environment of the phosphorus atom and polarity of the solvent, and the strength of the transannular bond depends also on the nature of the substituents at the silicon atom. The highly polar boat conformers are strongly stabilized in the DMSO solution. NBO analysis showed the importance of the σ(C? Si) → σ*(H₃C? N) hyperconjugative interaction in the two H₃C? N? C? Si fragments of the ring favoring the formation of the pentacoordinate silicon atom. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Hybrid-DFT Study and NBO Analysis of the Stereoelectronic Interaction Effects (Associated with the Anomeric Effects) on the Conformational Properties of 2,3,5,6-Tetrahalo-1,4-dioxanes and Their Analogs Containing S and Se Atoms

NBO analysis and hybrid density functional theory–based method (B3LYP/6-311+G**) was used to study the anomeric effects (AE), dipole–dipole interactions, and steric repulsion effects on the conformational properties of 2,3,5,6-tetrahalo-1,4-dioxane [halo = F (1), Cl (2), Br (3)], 2,3,5,6-tetrahalo-1,4-dithiane [halo = F (4), Cl (5), Br (6)], and 2,3,5,6-etrahalo-1,4-diselenane [halo = F (7), Cl (8), Br (9)]. B3LYP/6-311+G** results revealed a strong axial preference in compounds 1–3. Gibbs free energy difference (G _eq–G _ax) values (e.g., ΔG _eq-ax) between the axial and equatorial conformations of compound 1 to compound 3 are 8.19, 3.86, and 3.13 kcal mol^?1, respectively, as calculated by the B3LYP/6-311+G** level of theory. On the other hand, the NBO analysis of donor–acceptor (bond–antibond) interactions revealed that the AE for compounds 1–3 are ?12.26, ?16.46, and ?18.11 kcal mol^?1, respectively. Contrary to the increase of the AE values from compound 1 to compound 3, the increase of the steric repulsions (e.g., 1,3-syn-axial repulsions) could fairly explain the decrease of the axial conformation stability in compounds 1–3 compared to their equatorial conformations. Further, the correlations between the AE, structural parameters, and conformational behavior of compounds 4–9 have been investigated.     

An Ab Initio Study and NBO Analysis of the Stability and Conformational Properties of Hexakis(trimethylelementhyl)benzene (Element = C,Si, Ge,and Sn)

Ab initio molecular orbital and density functional theory were used to investigate energetic and structural properties of the various conformations of hexa-tertbutylbenzene (1), hexakis(trimethylsilyl)benzene (2), hexakis (trimethylgermyl)benzene (3), and hexakis(trimethylstannyl)benzene (4). HF/3-21G//HF/3-21G and B3LYP/3-21G//HF/3-21G results revealed that the Twist-Boat (TB) conformer of compound 1 is more stable than the 1-Chair (C), 1-Boat (B), and 1-Planar (P) conformers. B3LYP/3-21G//HF/3-21G results show that the 1- TB conformer is more stable than 1- C, 1- B, and 1- P conformers of about 1.13, 4.34, and 99.94 kcal mol^?1 , respectively. Contrary to the stability order of compound 1 conformers, the C conformer of compounds 2–4 is more stable than TB, B, and P conformations, as calculated by B3LYP/3-21G//HF/3-21G and HF/3-21G//HF/3-21G levels of theory. The energy gap between the C and P conformers in compounds 1–4 is decreased in the following order: ΔE(4: C, P) < ΔE (3: C, P) < ΔE(2: C, P) < ΔE (1: C, P). This fact can be explained in terms of the increase of C _aromatic -M (M═C, Si, Ge, and Sn) bond lengths and the decrease of steric (van der Waals) repulsions in the previously discussed compounds. For compounds 1–3, the calculations were also performed at the B3LYP/ 6-31G*//HF/3-21G level of theory. However, the comparison showed that the results at B3LYP/3-21G//HF/3-21G methods correlated well with those obtained at the B3LYP/6-31G*// HF/6-31G method. Further, NBO analysis revealed that in compounds 1–4, the resonance energy associated with the σ_M-C1 to σ*_C2-C3 delocalization is 5.20, 9.68, 11.15, and 12.27 kcal mol^?1, respectively. These resonance energy values could explain the easiness of the ring flipping processes of C, B, and TB conformers of compounds 4 to 1. Also, the NBO results showed that by an increase of the σ_M-C1 → σ *_C2-C3 resonance energies in compounds 1–4, the σ_M-C1 bonding orbital occupancies decrease. This fact could fairly explain the increase of the C_aryl-M bond length from compound 1 to 4. The NBO results are also in good agreement with the calculated energy barriers for the ring flipping of the chair conformations in compounds 1–4, as calculated by B3LYP and HF methods.     

Theoretical Studies on Intermolecular Hydrogen-bond Interactions between Hexamethylenetetramine and Nitric Acid

The structures of the complexes generated by hexamethylenetetramine and nitric acid have been fully optimized by B3LYP method at the 6-311++G** and aug-cc-pVTZ levels. The intermolecular hydrogen-bonding interactions have been calculated by the B3LYP/6-311++G**, B3LYP/aug-cc-pVTZ, MP2(full)/6-311++G** and CCSD(T)/6-311++G** methods, respectively. The NBO (nature bond orbital), AIM (atom in molecule), temperature effect and solvation effect have been analyzed to reveal the origin of the interactions. The results indicate that the stable hydrogen-bonded complexes could be generated by hexamethylenetetramine and nitric acid. The interactions follow the order of (a)>>(e)>(b)>(c)>(d)>(f)>(g). The C-N bonds which are adjacent to the methylene involving the hydrogen bonds tend to break in the chemical reaction. Due to the exothermic process, low temperature is conducive to the formation of the composition, which tallies with the experimental result.     

Halogen switching of azacarbenes C2NH ground states at ab initio and DFT levels

Relative stabilities and singlet–triplet energy differences are calculated for 24 C₂NX azacarbenes (where X is H, F, Cl, and Br). Three skeletal arrangements are employed including azacyclopropenylidene, [(imino)methylene]carbene, and cyanocarbene. Halogens appear to alternate the electronic ground states of C₂NH azacarbenes, from triplet to singlet states, at MP3/6‐311++G**, B1LYP/6‐311++G**, B3LYP/6‐311++G**, MP2/6‐311++G**, MP4(SDTQ)/6‐311++G**, QCISD(T)/6‐311++G**, CCSD(T)/6‐311++G**, CCSD(T)/cc‐pVTZ, G1, and G2 levels of theory. The aromatic characters of singlet cyclic azacyclopropenylidenes are measured using GIAO–NICS calculations. Linear correlations are found between the B3LYP/6‐311++G** calculated LUMO–HOMO energy gaps (ΔE_{HOMO ‐ LUMO}) of the singlet carbenes versus their corresponding singlet–triplet energy separations (ΔE). Electrophilic characters are found for all singlet azacarbenes in their addition reactions to alkenes with the highest electrophilicity being exhibited for X = F. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:377–388, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20442     

The nature of resonance and hyperconjugation for cyclic β-silyl substituted carbocations: NBO, NRT, EDA, and NMR studies

The stabilities of various cyclic β-silyl carbocations and their desilylated analogues, relative to tert-butyl cation, were calculated in the gas phase at B3LYP/6-311++G** level of theory. Natural bond orbital (NBO) theory was used for the calculation of charges and bond orders. The contribution of carbenium ion [R¹R²C⁺–CR³R⁴Si(Me)₃] and silylium ion [R¹R²C=CR³R⁴ Si(Me) ₃ ⁺ ] to the resonance structures was investigated by natural resonance theory (NRT). The localized molecular orbitals energy decomposition analysis (LMO-EDA) was employed to estimate the bond dissociation energy of β-silyl carbocations to R¹R²C=CR³R⁴ and Si(Me) ₃ ⁺ fragments via the MP2/6-311++G** method. The silylium ion is the most important resonance structure of β-silyl cycloalkyl (cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl) and cyclopentadienyl cations. In the case of β-silyl phenylcyclopropyl, benzocyclobutyl, cyclopropenyl, and tropylium ions, the carbenium ion is the major contributor (due to the delocalization of positive charge). The calculated ²⁹Si and ¹³C nuclear magnetic resonance (NMR) chemical shifts complement these results.     

Ab initio study of dehalohydrogenation reaction of 2-halo-2,3-dihydrophosphinine

Decomposition of 2-fluoro-2,3-dihydrophosphinine (1), 2-chloro-2,3-dihydrophosphinine (3), 2-bromo-2,3-dihydrophosphinine (5) to phosphinine was investigated using Molecular orbital and density functional theory. Study on the B3LYP/6-311+G** level of theory revealed that the required energy for the decomposition of compounds 1, 3, and 5 to phosphinine is 30.56 kcal·mol^?1, 28.23 kcal·mol^?1, and 24.03 kcal·mol^?1, respectively. HF/6-311+G**//B3LYP/6-311+G** calculated barrier height for the decomposition of compound 1, 3, and 5 to phosphinine is 57.56 kcal·mol^?1, 37.26 kcal·mol^?1, and 30.77 kcal·mol^?1, respectively. Also, MP2/6-311+G**//B3LYP/6-311+G** results indicated that the barrier height for the decomposition of compound 1, 3, and 5 to phosphinine is 46.59 kcal·mol^?1, 47.28 kcal·mol^?1, and 42.57 kcal·mol^?1, respectively. Natural bond orbital (NBO) population analysis and nuclear independent chemical shift (NICS) results showed that, reactants are non-aromatic but products of elimination reaction are aromatic, C-H and C-X bonds are broken and H-X bond is appear.     

Ab initio Molecular Orbital Study of Dithiopyrrolopyrrole and Its Structural Isomers

Abstract

Ab initio molecular orbital calculations at HF/6-31G*, HF/6-311+G**, and B3LYP/6-311+G** levels of theory for geometry optimization are reported for 1,4-dithiopyrrolo[3,4-c]pyrrole (DtPP, 1) and its twelve structural isomers (2–13). Compounds 1–3 include 2 C─CH and 2 NH─CS structural units. Structural isomers 4–7 include 2 C–CH units, together with 2 NH and 2 C–S groups. Isomers 8–13 possess 2 CH, 2 C, 2 NH, and 2 C─S fragments. According to these calculations, isomers 2, 4, and 8, are more stable than 1.     

The structure, Raman spectra, and force fields of methylbromosilanes CH3SiClnBr3−n (n = 0, 1, 2)

The laser-excited Raman spectra of liquid CH₃SiCl_nBr_3?n (n = 0, 1, 2) were studied. Quantumchemical calculations of these substances with geometry optimization were performed to determine their harmonic force fields and vibrational frequencies. The calculations were made using the HF/6-31G* and HF/6-311++G** approximations and density functional theory at the B3LYP/6-31G* and B3LYP/6-311++G** levels. An interpretation of the spectra was suggested and the calculated force fields were discussed in comparison with the data on related compounds.     

Structure of bis(trifluoromethanesulfonyl)imide in inert and protophilic media

According to the data of IR spectroscopy, dielectrometry, and HF/6-31G**, B3LYP/6-311G** quantum chemical calculations bis(trifluoromethanesulfonyl)imide (CF₃SO₂)₂NH in nonpolar medium (CCl₄) exists as an H-complex formed by its molecules in two tautomeric (NH and OH) forms. In a polar medium (CH₂C1₂) linear chain polyassociates with a bifurcate hydrogen bond are formed similar to those existing in the crystal. In the presence of protophilic solvents ion pairs consisting of the protonated molecule of the base and dimeric anion of bis(trifluoromethanesulfonyl)imide are formed.     

Substituent effect on intramolecular hydrogen bonding in 2‐hydroxybenzaldehyde

The effect of some substituents on intramolecular hydrogen bonding of 5‐X‐2‐hydroxybenzaldehyde (5‐X‐2‐HBA) has been studied by B3LYP and MP2 methods using 6‐311++G** and AUG‐cc‐PVTZ basis sets. The relationship between hydrogen bond energy E_HB and electron donation (or withdrawal) of substituents has been investigated. An approximately good linear relationship has been detected between Hammett coefficients and hydrogen bond formation energy (R² = 0.98). Herein, population analysis has been performed by atoms in molecules (AIM) and natural bond orbital (NBO) methods. The results of AIM and NBO analyses are in a good agreement with calculated energy values. Furthermore, correlation between ring aromaticity and hydrogen bonding has been investigated by nucleus‐independent chemical shift (NICS) at GIAO/B3LYP/6‐311++G** level of theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical study of light-metal tetrahydroborates

Ab initio calculations of the structural, energetic, vibrational, and magnetic characteristics of the lowest-lying structures for isolated molecules and ions of light-metal tetrahydroborates (Li, Na, Be, Mg, and Al) have been performed by the perturbation theory (MP2), quadratic configuration interaction (QCISD(T)), coupled cluster (CCSD(T)), and density functional theory (B3LYP) methods using the 6-31G*, 6-31G**, 6-311+G**, and 6-311++G** basis sets. The trends in the behavior of the structural parameters, the energies of different decomposition pathways, barriers to internal rotation of BH₄ groups, normal mode frequencies, magnetic shielding constants, and spin density distribution (in radicals) have been analyzed in various related series of these compounds. The results obtained by ab initio methods and at the DFT level are compared. The economical approximation B3LYP/6-311++G**//B3LYP/6-311+G** adequately reproduces the results obtained at the higher level of theory CCSD(T)/6-311++G*s*//MP2/6-31G* even though it requires considerably shorter CPU times and smaller amounts of memory.     

Theoretical Study on Hydrogen Interaction between 5-Fluorouracil and Glycine

The geometries,electronic structure,IR spectrum and other properties of hydrogen interaction between 5-fluorouracil and glycine were studied at the B3LYP/6-31+G* level.Single point energy calculations were executed at the B3LYP/6-311++G** and B3LYP/aug-cc-pvdz levels,and natural bond orbital (NBO) analysis was carried out at the B3LYP/6-31+G* level.Finally,the hydrogen bonds were discussed via AIM electronic density topology analysis.     

Theoretical Studies on Energetic Property and Stability of Pyrazine and Pyridine Derivatives

Density functional calculations at the B3LYP level with 6‐311G** and aug‐cc‐pVDZ basis sets were performed to predict the heats of formation (HOFs) for two pyrazine derivatives and eight pyridine derivatives. In the isodesmic reactions designed for the computation of heats of formation (HOFs), pyrazine and pyridine were chosen as reference compounds. The N‐oxidations for the ring nitrogen of pyrazine and pyridine derivatives decrease the HOF values when N‐oxide oxygen is neighboring with amino groups, but increase when it neighbors with nitro groups. Thermal stability was evaluated via bond dissociation energies (BDE) at the UB3LYP/6‐311G** level. As a whole, the homolysis of C–NO₂ bonds is the main step for bond dissociation of the title compounds. The BDE values of title compounds are influenced by intramolecular hydrogen bonds. The hydrogen bond effects associated with the length of the H···O bonds were analyzed by the electron density at the critical points and natural bond orbital.     

Theoretical study of the electronic structure of CnS (n=1-6) thiocumulenes

Linear sulfur-carbon chains C(n)S (n=1-6) of astronomical interest were examined by means of several theoretical methods. The three smallest compounds of the series were chosen to evaluate the performance of several computational models, including Hartree-Fock theory, density functional theory with the Becke's three parameter exchange functional and the correlation functional of Lee, Yang, and Parr (B3LYP), and electron-correlated methods (second-order Moller-Plesset perturbation method (MP2), configuration interaction method including single and double excitations (CISD), and quadratic configuration interaction method including single and double excitations (QCISD) in combination with a large variety of basis sets. The systematic comparison between the experiment and theory indicates that the B3LYP/6-311G** method can be considered suitable for the study of the electronic structures of the C(n)S compounds. The electronic ground states of the C(n)S molecules alternate between 1Sigma and 3Sigma for odd and even values of n, respectively. The B3LYP/6-311G** wave functions for these electronic ground states were analyzed by means of the atoms in molecules (AIM) and natural bond orbital (NBO) methods. Both approaches suggest that the electronic structures for the singlet and triplet compounds must be considered separately. According to the NBO method, singlet compounds can be properly represented by acetylenic structures with alternating single and triple bonds (S[triple bond]C-C[triple bond]C...). However, triplet compounds are better described by means of double bond-double bond cumulenic structures (S=C=C=C=C...) as a consequence of the average between different alpha and beta electronic densities. AIM delocalization indexes and NBO interactions between localized orbitals also indicate that these structures are strongly pi delocalized. Finally, the different singlet and triplet structures proposed provide a consistent explanation for the geometries, dipole moments, and spin-density values of the C(n)S compounds studied.     

A study of internal rotations and vibrational spectra of oxiranemethanol (glycidol)

The conformational stability and the C–O and O–H internal rotations in oxiranemethanol were investigated at the DFT-B3LYP/6-311G**, MP2/6-311G** and MP4(SDQ)/6-311G** levels of theory. Three minima were predicted in the CCOH potential energy scans of the molecule to have relative energies of about 2 kcal/mol or less and all were calculated to have real frequencies upon full optimization of structural parameters at the DFT and the MP2 levels of calculations. The Cg1 (H bond inner) conformation was predicted to be the lowest energy conformation for oxiranemethanol in excellent agreement with an earlier microwave study. The equilibrium mixture was calculated from Gibb's free-energy changes to be about 79% Cg1, 17% G1g and 3% Gg1 at the B3LYP/6-311G** level and about 87% Cg1, 11% G1g and 2% Gg1 at the MP2/6-311G** level for oxiranemethanol at 298.15 K. No conclusive evidence was obtained for the presence of high-energy form in the liquid phase of oxiranemethanol. The vibrational frequencies of oxiranemethanol in its three stable forms were computed at the B3LYP level and complete vibrational assignments were made for the lowest energy Cg1 form on basis of calculated and experimental data of the molecule.     

Tautomerism and the maximum hardness principle

Through the application of the atom–bond electronegativity equalization method (ABEEM) to the calculation of the hardnesses of more than 300 tautomers, it can be seen that the maximum hardness principle is nearly useless to account for their relative stabilities. Moreover, by calculating the energies of these tautomers with the HF, B3LYP, B3PW91, and MP2 methods at the 6‐31G, 6‐31G*, 6‐31G**, 6‐31+G**, 6‐311G**, or 6‐311++G** level, it is found that all these methods may not be always reliable in predicting their relative stabilities. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006