Conformational analysis of 2-methyl-5-nitro-1,3,2-dioxaborinane

Quantum-chemical methods HF/6-31G(d), HF/6-31+G(d), MP2/6-31G(d)//HF/6-31G(d), and MP2/6-31+G(d)//HF/6-31+G(d) were used to investigate the conformational isomerization of 2-methyl-5-nitro-1,3,2-dioxaborinane. It has been shown that a potential energy surface of this compound includes two minima: an axial form of semi-chair and equatorial sofa together with a transition state belonging to the conformation of 2,5-twist-form. A comparison between experimental NMR ¹H and theoretical vicinal coupling constants was used to determine the quantitative conformational composition of cyclic boric acid ester and a value of ΔG ⁰ for nitro group at the ring carbon atom C⁵ in CCl₄ and C₆D₅NO₂ solutions.     

Ab initio HF-SCF study of naphthazarin: Geometries,isomerism, hydrogen bonding,and vibrational spectrum

The structural properties and intramolecular hydrogen bonding of a series of structures of naphthazarin molecule were investigated by ab initio HF-SCF methods. The geometries of theC _2v ,C _2h ,D _2h , andC _s symmetry structures were optimized using split-valence basis sets. MP2/6-31G^*// HF/6-31G single-point energy calculations indicate that theC _2v isomer (5,8-dihydroxy-1,4-naphthoquinone) is the lowest energy structure of the molecule and that theC _2h symmetry one (4,8-dihydroxy-1,5-naphthoquinone), lying 37 kJ/mol above theC _2v form, is the other stable isomer of naphthazarin. At the HF/6-31G level, the intramolecular proton exchange between two equivalentC _2v structures is a two-step process where each proton can be independently transferred through an unsymmetrical potential having a 1,5-quinone intermediate, theC _2h symmetry structure, and two equivalent transition states ofC _s symmetry, with a barrier height equal to 38 kJ/ mol (MP2/6-31G^*//HF/6-31G). The study of naphthazarin molecule is flanked by a theoretical investigation on theC _2v andC _2h isomers of the parent naphthoquinone and dihydroxynaphthalene molecules. The SCF vibrational spectrum of the ground state of naphthazarin, harmonic frequencies, and infrared and Raman band intensities were computed at the HF/6-31G level. The results of the calculations are compared with the matrix isolation FT-IR spectroscopy measurements and with the infrared and Raman spectra of the crystal molecule.     

On the additivity of basis set effects in some simple fluorine containing systems

The reactions F + H₂ → HF + H, HF → H + F, F → F⁺ + e^? and F + e^? → F^? were used as simple test cases to assess the additivity of basis set effects on reaction energetics computed at the MP4 level. The 6-31G and 6-311G basis sets were augmented with 1, 2, and 3 sets of polarization functions, higher angular momentum polarization functions, and diffuse functions (27 basis sets from 6-31Gd, p) to 6-31 ++ G(3df, 3pd) and likewise for the 6-311G series). For both series substantial nonadditivity was found between diffuse functions on the heavy atom and multiple polarization functions (e.g., 6-31 + G(3d, 3p) vs. 6-31 + G(d, p) and 6-31G(3d, 3p)). For the 6-311G series there is an extra nonadditivity between d functions on hydrogen and multiple polarization functions. Provided that these interactions are taken into account, the remaining basis set effects are additive to within ±0.5 kcal/mol for the reactions considered. Large basis set MP4 calculations can also be estimated to within ±0.5 kcal/mol using MP2 calculations, est. E_MP4(6-31 ++ G(3df, 3pd)) ≈ E_MP4(6-31G(d, p)) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31G(d, p)) or E_MP4(6-31 + G(d, p) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31 + G(d, p)) and likewise for the 6-311G series.     

Rotational barriers of disilane,hexafluorodisilane, and hexamethyldisilane: Ab initio,density functional,and molecular mechanics (MM3) studies

We investigated structures, vibrational frequencies, and rotational barriers of disilane (Si₂H₆), hexafluorodisilane (Si₂F₆), and hexamethyldisilane (Si₂Me₆) by using ab initio molecular orbital and density functional theories. We employed four different levels of theories (i.e., HF/6–31G*, MP2/6–31G*, BLYP/6–31G*, and B3LYP/6–31G*) to optimize the structures and to calculate the vibrational frequencies (except for Si₂Me₆ at MP2/6–31G*). MP2/6–31G* calculations reproduce experimental bond lengths well, while BLYP/6–31G* calculations largely overestimate some bond lengths. Vibrational frequencies from density functional theories (BLYP/6–31G* and B3LYP/6–31G*) were in reasonably good agreement with experimental values without employing additional correction factors. We calculated the ΔG^‡(298 K) values of the internal rotation by correcting zero-point vibration energies, thermal vibration energies, and entropies. We performed CISD/6–31G*//MP2/6–31G* calculations and found the ΔG^‡(298 K) values for the internal rotation of Si₂H₆, Si₂F₆, and Si₂Me₆ to be 1.36, 2.06, and 2.69 kcal/mol, respectively. The performance of this level was verified by using G2 and G2(MP2) methods in Si₂H₆. According to our theoretical results, the ΔG^‡(298 K) values were marginally greater than the ΔE^‡(0 K) values in Si₂F₆ and Si₂Me₆ due to the contribution of the entropy. In Si₂H₆ the ΔE^‡(0 K) and ΔG^‡(298 K) values were coincidently similar due to a cancellation of two opposing contributions between zero-point and thermal vibrational energies, and entropies. Our calculated ΔG^‡(298 K) values were in good agreement with experimental values published recently. In addition, we also performed MM3 calculations on Si₂H₆ and Si₂Me₆. MM3 calculated rotational barriers and thermodynamic properties were compared with high level ab initio results. Based on this comparison, MM3 calculations reproduced high level ab initio results in rotational barriers and thermodynamic properties of Si₂H₆ derivatives including vibrational energies and entropies, although large errors exist in some vibrational frequencies. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1523–1533, 1997     

A molecular orbital study of nitrogen inversion in aniline with extensive geometry optimization

The geometry and energy of aniline have been calculated using the 6-31G and 6-31G^*(5D) basis sets for the planar structure and various pyramidal structures, assuming that the ring and the N-atom bonded to it lie in the same plane, but otherwise with full geometry optimization. With the 6-31G basis set the planar structure is predicated to be the most stable, whereas the inclusion of polarization functions in the 6-31G^*(5D) basis set finds a pyramidal structure with the out-of-plane angle =42.3° to be most stable and the energy barrier to inversion via the planar transition state to be 1.59±0.02 kcal mol^–1, in close agreement with experiment. Completing the optimization, allowing the N-atom and the C- and H-atoms of the ring to take up equilibrium out-of-plane positions increases the calculated energy carrier to inversion by less than 0.1 kcal mol^–1 to 1.66 kcal mol^–1. The ring adopts a very shallow inverted boat-type conformation with N₇-C₁C₄ = 2.0°.     

C36 fullerenes and quasi-fullerenes: computational search through 598 cages

C₃₆ is computed at the SAM1 level and partially also at the HF/4-31G and B3LYP/6-31G^* levels. Altogether 598 cages are generated by a topological Stone–Wales treatment. Three cages contribute by more than 10% to the high-temperature equilibrium isomeric mixture – two conventional fullerenes with D_2d and C_2v symmetries and a C_s quasi-fullerene containing one four-membered ring.     

Steric and Electronic Structure of C6H5XCF3 Molecules (X = O or S): A Quantum-Chemical Study

The potential functions of internal rotation around the Csp ²-X bond in C₆H₅XCF₃ molecules (X = O or S) were obtained by quantum-chemical calculations in the HF/6-31G(d), MP2(f)/6-31G(d), and B3LYP/6-31G(d) approximations. The calculations were performed in the range of torsion angles (angle between the planes of the benzene ring and Csp ²-X-Csp ³ bonds) from 0° to 90° with a 15° step. The barriers to rotation around the Csp ²-X bonds (kJ mol^{- 1}) were evaluated: for C₆H₅XCF₃, 7.60 (HF), 3.04 (MP2), and 1.04 (B3LYP); for C₆H₅XCF₃, 16.57 (HF), 14.67 (MP2), and 8.73 (B3LYP). The geometries (bond angles and bond lengths), Koopmans ionization potentials, and dipole moments of the molecules were calculated. The hybridization, energy, and population of the lone electron pairs of the heteroatoms, and also the energy of their resonance interaction with antibonding orbitals and the natural atomic charges were evaluated using the NBO approach.     

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.     

The N4 molecule has an open-chain triplet C2h structure

The lowest-energy N₄ is computed ab initio to be the planar C_2h(³B_u) open-chain structure 13 . The open-chain N₄ singlet-state structures dissociate on geometry optimization. The tetraazatetrahedrane T_d structure 1 and the tetrazete D_2h structure 2 are minima at MP 2/6-31G *. However, both are higher in energy than 13 (24.1 and 21.2 Kcal/mol [UQCISD ) (T )(full)/6-311+G *//MP 2/6-31G * + ZPE (MP 2/6-31G )*, respectively]. The energy of 13 is 157.5 kcal/mol higher than that of two N₂(¹∑ molecules [UQCISD (T )(Full)/6-311+G *//MP 2/6-31G *] © 1993 John Wiley & Sons, Inc.     

Intramolecular Hypervalent X←X Interaction in Mono- and Bicyclic Heteroelement Compounds Containing Se and Te Atoms

Chalcogen-containing heterapentalene and quasimonocyclic compounds having SeÄSeÄSe and TeÄTeÄTe triads or SeÄSe and TeÄTe diads were studied by the ab initio [MP2(full)/6-31G**, MP2(fc)/6-31+G**, and MP2(fc)/LANL2DZ] and DFT methods (B3LYP/6-31G^**, B3LYP/6-31+G^**, and B3LYP/LANL2DZ). Heterapentalene compounds were found to be stable as planar bicyclic structures having a C _2v symmetry. The stability of quasimonocycic -chalcogenovinyl aldehydes increases with increase in the electron-acceptor power of the substituent at the X atom.     

Structures and stability of N9, N9 − and N9 + clusters

 Ab initio molecular orbital calculations for N₉, N⁻ ₉ and N⁺ ₉ isomers were carried out at the HF/ 6-31G*, B3PW91/6-31G*, B3LYP/6-31G* and MP2/ 6-31G* levels of theory. Stable equilibrium geometric structures were determined by harmonic vibrational frequency analyses at the HF/6-31G*, B3PW91/6-31G* and B3LYP/6-31G* levels of theory. The most stable free-radical N₉ cluster is structure 1 with C _{2 v} symmetry and that of anion N⁻ ₉ is structure 3 with C _s symmetry. Only one stable structure of the N⁺ ₉ cation with C _{2 v} symmetry was predicted. Their potential application as high-energy-density materials has been examined. Received: 15 June 1999 / Accepted: 11 October 1999 / Published online: 14 March 2000     

Synthesis and Spectroscopic Characterization of Two Different Types of Heterobimetallic Glycolate Complexes of Niobium(V)

An entirely new class of heterobimetallic homoleptic glycolate complexes of the type Nb(OGO)₃{Ta(OGO)₂} [where G=CMe₂CH₂CH₂CMe₂ (G¹) (3); CMe₂CH₂ CHMe(G²) (4); CHMeCHMe (G³) (5); CH₂CMe₂CH₂ (G⁴) (6); CMe₂CMe₂(G⁵) (7); CH₂CHMeCH₂ (G⁶) (8); CH₂CEt₂CH₂ (G⁷) (9); CH₂CMe(Prⁿ)CH₂ (G⁸) (10)] have been prepared by the reactions of Nb(OGO)₂(OGOH) [G=G¹ (1a); G² (1b); G³ (1c); G⁴ (1d); G⁵ (1e); G⁶ (1f); G⁷ (1g); G⁸ (1h)] with Ta(OGO)₂ (OPrⁱ) (G=G¹ (2a); G² (2b); G³ (2c); G⁴ (2d); G⁵ (2e) G⁶ (2f); G⁷ (2g); G⁸ (2h). In addition to the novel derivatives (2)–(10), our earlier investigations on heterobimetallic glycolate-alkoxide derivatives have been extended to derivatives of the type Nb(OGO) [where M=A1 n=3, G=G³ (11);G⁴ (12); G⁶ (13) G⁷ (14); G^s (15); G⁹=CH₂CH₂CH₂ (16) and M=Ti (n=4, G=G⁴) (17), Zr(n=4,G=G⁴) (18)], which are conveniently prepared by the reactions of metalloligands Nb(OGO)₂(OGOH) [G=G³ (1c); G⁴ (1d); G⁶ (1f); G⁷ (1g); G⁸ (1h); G⁹ (1i)] with different metal alkoxides. All of these new complexes have been characterized by elemental analyses, molecular weight determinations, and spectroscopic (I.r. and ¹H, ²⁷Al-n.m.r.) studies. Structural features of the new derivatives have been elucidated on the basis of molecular weight and spectroscopic data.     

Theoretical Investigations on Fluorine-Substituted Ethylene Dications C2HnF4-n 2+(n = 0–4)

The optimized geometries and energies of fluorine-substituted ethylene dications C₂H_nF_4-n ²⁺ (n = 0–4) have been investigated by means of ab initio methods. At the MP3/6-31G**//6-31G* + zero-point energy level of theory, the results predict that C₂F₄²⁺ and C₂HF₃²⁺ are planar, while C₂H₄²⁺, C₂H₃F²⁺ and 1,1—C₂H₂F₂²⁺ prefer a perpendicular geometry. For 1,2—C₂H₂F₂²⁺ an energy difference of only 0.3 kcal/mol is found between the (trans) planar and perpendicular structure. The stabilizations attributed to hyperconjugation, fluorine lone-pair donation, and (C? F) double-bond conjugation are discussed. A comparison is made for the C? C and C? F stretching frequencies determined at 6-31G*//6-31G* between the neutral and dicationic species. The theoretically determined ionization energies for the vertical process N⁺ → N²⁺ at the MP3/6-31G*//3-21G level are compared with experimental Q_min values.     

Cooperative atomic migrations in the associates of formic acid molecule with H2O...X systems (X=CH3OH,NH2OH,H2O2, HOF,and H2O)

The pathways and activation barriers of cooperative biproton migrations in the associates of the formic acid molecule with H₂O and X molecules (X=CH₃OH, NH₂OH, H₂O₂, FOH, and H₂O) are calculated by an ab initio method (3-21G and 6-31G^** basis sets). A cooperative triproton transfer occurs in the system with X=H₂O. The activation barriers of this transfer calculated in the 3-21G and 6-31G^** basis sets are 6.94 and 27.29 (through the structure of C₂ symmetry) or 7.99 and 26.08 kcal/mole (through the structure of C_s symmetry), respectively. In the systems with X=H₃COH, HOOH, and FOH, the biproton transfer is accompanied by synchronous shifts of two hydroxyl groups and overcomes high activation barriers (>40 kcal/mole), which is accounted for by poor stereochemical similarity for the low-barrier cooperative processes in the given molecular associates. Scientific Research Institute of Physical and Organic Chemistry, Rostov State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 845–858, September–October, 1996. Translated by I. Izvekova     

The aromatic diboracyclopropenyl (diboriranyl) anion; CB2H3 −: An ab initio study

The most stable structure of CB₂H₃ ^–, as established computationally, is the aromatic diboracyclopropenyl (diboriranyl) anion (5), while open-chainC _2v, isomer H₂BCBH (7) is only 3 kcal/mol higher in energy at the QCISD(T)/6-311 +G^**//MP2/6-31+G^*+ZPE (HF/6-31 +G^*). The 47-kcal/mol barrier between cyclic,5, and open-chain,7, structures suggests that both of them may be observed. The aromatic stabilization energy of the diboriranyl anion (18 kcal/mol) is half the value in the isoelectronic cyclopropenium ion, C₃H₃ ⁺. The computed, by IGLO method (5a), and experimental (6a) chemical shifts,(¹³C) and(¹¹B), agree within 4 ppm range. The theoretical vibrational frequencies of the most stable isomers,5 and7, are presented for experimental verification of these species.     

Ab initio molecular orbital calculations for 3,6-dihydro-1,2-dithiin and 3,6-dihydro-1,2-dioxin

Optimized geometries and total energies for the conformers of 3,6-dihydro-1,2-dithiin ( 2 ) and 3,6-dihydro-1,2-dioxin ( 3 ) were calculated at several ab initio MO levels: RHF/3-21G(*), RHF/6-31G*, MP2/6-31G*, and MP2/6-31G*/ /RHF/3-21G(*). For the dioxin, in addition to the above levels the corresponding nonextended basis sets ab initio methods were also carried out. The dithiin results are compared with those of simple disulfanes, HSSH and (CH₃)₂S₂, whose optimized geometries agree closely with the observed structures, which is the gauche (C₂ symmetry). For the disulfanes, the gauche geometries from RHF/3-21G(*) are in good agreement with the observed structure while the RHF/3-21G results best fit the dioxin. Pertinent structural data at the RHF/3-21G(*) for the half-chair (C₂) dithiin are: bond lengths, ? SS? , ? CS? , ? CC?, and ? C?C? , 2.050, 1.817, 1.515, and 1.317 Å, respectively; bond angles, CSS, ?CCS, and C?CS, 98.0, 114.2, and 127.8°, respectively; CSSC dihedral angle of 63.2°; and twist angle of 36.5°. The total energy for half-chair dithiin at MP2/6-31G*//RHF/3-21G(*) is less than the planar (C_2v) and the half-boat (C_s) structures by 69.67 and 29.05 kJ/mol, respectively. The calculated structural data (vs. observed) at RHF/3-21G for the half-chair dioxin are: bond lengths, ? OO? , ? CO? , ? CC?, and C?C, 1.464 (1.463), 1.454, 1.509, and 1.313 Å (1.338 Å), respectively; bond angles, COO, ?CCO, and C?CO, 105.0, 109.8 (110.3), and 120.7° (119.9°), respectively; COOC dihedral angle of 79.7° (80 ± 2°); and twist angle of 39.0 (38.3°). The total energy for half-chair dioxin at MP2/6-31G//RHF/3-21G is less than the planar and the half-boat structures by 70.35 and 42.85 kJ/mol, respectively. The total energies calculated at the extended basis sets (*) ab initio levels for the C₂ symmetry dioxin are much lower than those of the nonextended basis sets. © John Wiley & Sons, Inc.     

On the gas-phase reaction of C3O2+. with C3O2

The gas-phase, ion molecule reaction between C₃O₂^+. and C₃O₂ has been studied by both double-focusing and ion trap mass spectrometry, rationalized by the formation of a dimeric, odd electron cation [C₆O₄]^+. which decomposes extensively through sequential CO losses giving rise to [C₅O₃]^+. and [C₄O₂]^+. ions. The thermodynamics of this process have been investigated by means of ab initio calculation performed on the above species using different basis sets (STO-3G, 3-21G and 6-31G^*).     

Is tetrahedral H42+ a minimum? Anomalous behavior of popular basis sets with the standard p exponents on hydrogen

The nature of the tetrahedral H₄²⁺ stationary point (minimum or triply degenerate saddle) depends remarkably upon the theoretical level employed. Harmonic vibrational analyses with, e.g., the 6-31G** (and 6-31 + +G**) and Dunning's [4s2p1d;2s1p] [D95(d,p)] basis sets using the standard p exponent suggest (erroneously) that the T_d geometry is a minimum at both the HF and MP2 levels. This is not the case at definitive higher levels. The C₃H₄²⁺ structure with an apical H is another example of the failure of the calculations with the 6-31G**, 6-311G**, and D95(d,p) basis sets. Even at MP2/6-31G** and MP2/ cc-pVDZ levels, the C_3v structure has no negative eigenvalues of the Hessian. Actually, this form is a second-order saddle point as shown by the MP2/6-31G** calculation with the optimized exponent. The D_4h methane dication structure is also an example of the misleading performance of the 6-31G** basis set. In all these cases, energy-optimized hydrogen p exponents give the correct results, i.e., those found with more extended treatments. Optimized values of the hydrogen polarization function exponents eliminate these defects in 6-31G** calculations. Species with higher coordinate hydrogens may also be calculated reliably by using more than one set of p functions on hydrogen [e.g., the 6-31G(d,2p) basis set]. Not all cases are critical. A survey of examples, also including some boron compounds, provides calibration. © 1993 John Wiley & Sons, Inc.     

Quantum chemical study of the coordination of glycolic acid conformers and their conjugate bases to [Ca(OH2)n] (n=0–4) ions

A detailed exploration of the configurational and conformational space of glycolic acid and their conjugate bases has been carried out with the aid of first principles quantum chemical techniques at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory. The most stable configuration among the eight possible glycolic acid conformers corresponds to the E-s-cis, s-trans configuration, while the highest energy E-s-trans, s-cis conformer was found at 10.88 and 12.17 kcal mol⁻¹ higher in energy at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. Upon dissociation of glycolic acid the s-cis(syn), and s-trans(anti) configurations of the glycolate anion can be formed. The anti conformer was found to be less stable than the syn one by 14.20 and 16.87 kcal mol⁻¹ at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p)) levels of theory, respectively. The computed B3LYP/6-311+G(d,p) proton affinity of the syn conformer for the protonation process affording the more stable E-s-cis, s-trans conformer, in vacuum was found to be 325.35 kcal mol⁻¹ (ΔG⁰ value). From a methodological point of view, our results confirm the reliability of the integrated computational tool formed by the B3LYP density functional model. This model has subsequently been used to investigate the interaction of Ca²⁺ ions with the glycolic acid conformers and their conjugate bases in vacuum and in the presence of extra water ligands. For the complexes of glycolic acid conformers the η²–O,O–(COOH) coordination, that is the structure that arises from the coordination of the Ca²⁺ to the carboxylic group, is the global minimum of the PES, while the η²–O(OH),O–(COOH) coordination is a local minimum found at only 1.0 and 1.3 kcal mol⁻¹ higher in energy at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. Moreover, the two isomers exhibit nearly the same binding affinities, which are predicted to be 89 and 85 kcal mol⁻¹ at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. The same holds also true for the complexes of the glycolate anion. The η²–O,O–(COO⁻) coordination involving the syn conformer of the glycolato ligand, is the global minimum, while the η²–O(OH),O–(COO⁻) one lies at 1.5 and 5.6 kcal mol⁻¹ higher in energy at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. The other conformer with an η²–O,O–(COO⁻) coordination involving the anti conformer of the glycolato ligand, is less stable by only 0.2 kcal mol⁻¹ at both levels of theory. Noteworthy is the trend seen for the incremental binding energy due to the successive addition of water molecules to [HOCH₂C(O)O]Ca²⁺ species; the computed values are 30.4, 26.8, 22.9 and 16.2 kcal mol⁻¹ at the B3LYP/6-311+G(d,p) level of theory for the mono-, di-, tri- and tetraaqua complexes, respectively. This trend arising from the repulsion of the dipoles between the water ligands and from unfavorable many body interactions is in accordance with those anticipated from electrostatic considerations. The Ca(II)-water interaction weakens with increasing coordination of the metal. Obviously, it is the electrostatic nature of the Ca(II)-water interactions that accounts well for the computed coordination geometries of the cationic (aqua)(glycolato)calcium complexes. Calculated structures, relative stability and bonding properties of the conformers and their complexes with [Ca(OH₂)_n]²⁺ (n=0–4) ions are discussed with respect to computed electronic and spectroscopic properties, such as charge density distribution, harmonic vibrational frequencies and NMR chemical shifts.     

Molecular structures and electronic properties of helical thiophene carbon–sulfur oligomers, H2(C2S)nC2H2 (n?=?1–20)

Structure optimizations of the thiophene carbon–sulfur H₂(C₂S) _n C₂H₂ (n = 1–20) were carried out using density functional theory calculations at the B3LYP/6-31G(d) level. The B3LYP/6-31G(d) geometrical data for heptamer H₂(C₂S)₇C₂H₂ and undecamer H₂(C₂S)₁₁C₂H₂ are in good agreement with the X-ray crystallographic data for the helical (C₂S)_n β-heptathiophene and β-undecathiophene, respectively. Structural and electronic properties of helical oligothiophenes obtained at the B3LYP/6-311++G(d,p)//B3LYP/6-31G(d) level are reported. The strain energy formula of n oligothiophenes as a linear function of their molecular length was obtained.