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.     

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.     

Structure and stabilities of the isomers of SiB2H4

Ab initio quantum-mechanical methods at the HF/6–31G*, MP2/6–31G* and MP2/6–31G* levels are used to study the relative stabilities of the isomers of SiB₂H₄. Isomers obtained using the analogy between trivalent boron and divalent silicon are calculated to be more stable compared to isomers where carbon is replaced by the isovalent silicon. 2π aromaticity and the preference of silicon for lower valency control the relative stabilities of SiB₂H₄ isomers.     

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.     

A comparative molecular field analysis (CoMFA) study using semiempirical, density functional, ab initio methods and pharmacophore derivation using DISCOtech on sigma 1 ligands

The Comparative Molecular Field Analysis (CoMFA) was developed to investigate a three-dimensional quantitative structure activity relationship (3D-QSAR) model of ligands for the sigma 1 receptor. The starting geometry of sigma-1 receptor ligands was obtained from the Tripos force field minimizations and conformations were decided from DISCOtech using the SYBYL 6.8. program. The structures of 48 molecules were fully optimized at the ab initio HF/3-21G* and semiempirical AM1 calculations using GAUSSIAN 98. The electrostatic charges were calculated using several methods such as semiempirical AM1, density functional B3LYP/3-21G*, and ab initio HF/3-21G*, MP2/3-21G* calculations within GAUSSIAN 98. Using the optimized geometries, the CoMFA results derived from the HF/3-21G method were better than those from AM1. The best CoMFA was obtained from HF/3-21G* optimized geometry and charges (R2 = 0.977). Using the optimized geometries, the CoMFA results derived from the HF/3-21G methods were better than those from AM1 calculations. The training set of 43 molecules gave higher R2 (0.989-0.977) from HF/3-21G* optimized geometries than R2 (0.966-0.911) values from AM1 optimized geometries. The test set of five molecules also suggested that HF/3-21G* optimized geometries produced good CoMFA models to predict bioactivity of sigma 1 receptor ligands but AM1 optimized geometries failed to predict reasonable bioactivity of sigma 1 receptor ligands using different calculations for atomic charges.     

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 °.     

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.     

Pyramidane 2. Further computational studies: potential energy surface, basicity and acidity, electron-withdrawing and electron-donating power, ionization energy and electron affinity, heat of formation and strain energy, and NMR chemical shifts

The novel cycloalkane pyramidane (tetracyclo[2.1.0.0^1,30^2,5]pentane, [3.3.3.3]fenestrane), C₅H₄, with a pyramidal carbon atom, was investigated further. Calculations at the B3LYP/6-31G^* and G2(MP2) levels supported earlier conclusions from QCISD(T)/6-31G^*//MP2(FC)/6-31G^* energies that pyramidane lies in a deep well (ca. 100 kJ mol⁻¹) on the potential energy surface. The pyramidal carbon is predicted to have a lone electron pair, and calculations (CBS-4) indicate that pyramidane is remarkably basic for a saturated hydrocarbon (proton affinity 976, cf. 922 and 915 kJ mol⁻¹ for pyridine and aniline, respectively). The calculated (CBS-4) acidity is similar to that of tetrahedrane and toluene; the pyramidyl group (C₅H₃) attached to an atom bearing a lone electron pair appears to be much more strongly electron-withdrawing than the phenyl group. The infrared CO stretching frequency and C–CHO rotational barriers of pyramCHO, PhCHO and cyclopropylCHO indicate that the pyramidyl group is comparable to phenyl and cyclopropyl in its ability to donate electrons to an electron-deficient carbon. The adiabatic ionization energy of pyramidane is ca. 9.0 eV (MP2/6-31G^*, energy differences and Koopmans’ theorem), similar to that of typical cycloalkanes. The heat of formation of pyramidane was calculated by the G2(MP2) method and isodesmic reactions to be to be 585 kJ mol⁻¹ and the strain energy was estimated to be 622 kJ mol⁻¹; pyramidane is 122 kJ mol⁻¹ more strained than its isomer spiropentadiene. Application of the NMR NICS method, varying the position of the probe nucleus, gave no evidence for benzenoid-type aromaticity in the potentially cyclobutadiene cation-like base of pyramidane.     

Ab initio study on the mechanism of forming a silapolycyclic compound between silylidene and formaldehyde

The mechanism of the cycloaddition reaction of forming a silapolycyclic compound between singlet silylidene and formaldehyde has been investigated with MP2/6-31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD(T)//MP2/6-31G* method. From the potential energy profile, it can be predicted that the cycloaddition reaction process of forming the silapolycyclic compound (P₂) for this reaction consists of four steps: (I) the two reactants first form a semi-cyclic intermediate INT1a through a barrier-free exothermic reaction of 32.5 kJ mol⁻¹; (II) this intermediate then isomerizes to an active four-membered ring intermediate INT1 via a transition state TS1a with an energy barrier of 30.8 kJ mol⁻¹; (III) INT1 further reacts with formaldehyde to form an intermediate INT2, which is also a barrier-free exothermic reaction of 30.1 kJ mol⁻¹; (IV) INT2 isomerizes to a silapolycyclic compound P₂ via a transition state TS2 with a barrier of 50.6 kJ mol⁻¹. Comparing this reaction path with other competitive reaction paths, we can see that this cycloaddition reaction has an excellent selectivity.     

Conformational effects in UV absorption spectra of tetrasilanes

UV absorption of cyclic carbosilanes (SiMe₂)₄(CH₂)_n, N = 1–4 (1–4), and Si₄Me₁₀ (5) provides an experimental counterpart to the singlet transition energy and intensity correlation diagrams for the syn-anti conformational transformation in tetrasilane. A new third transition is found between the two previously known singlet transitions. Transition energies are nearly independent of the dihedral angle, while intensities vary widely. All trends agree with CIS/3–21G^*//HF/3–21G^* calculations. The Sandorfy C and ladder C models of σ conjugation fail to describe electronically excited states of tetrasilane, since they do not consider the lateral bonds to substituents.     

Structure and conformational properties of carbonylbisimidosulfuryl fluoride, O=C(N=S(O)F2)2

The molecular structure and conformational properties of O=C(N=S(O)F₂)₂ (carbonylbisimidosulfuryl fluoride) were determined by gas electron diffraction (GED) and quantumchemical calculations (HF/3-21G* and B3LYP/6-31G*). The analysis of the GED intensities resulted in a mixture of 76(12)% syn–syn and 24(12)% syn–anti conformer (ΔH⁰=H⁰(syn–anti)−H⁰(syn–syn)=1.11(32) kcal mol⁻¹) which is in agreement with the interpretation of the IR spectra (68(5)% syn–syn and 32(5)% syn–anti, ΔH⁰=0.87(11) kcal mol⁻¹). syn and anti describe the orientation of the S=N bonds relative to the C=O bond. In both conformers the S=O bonds of the two N=S(O)F₂ groups are trans to the C–N bonds. According to the theoretical calculations, structures with cis orientation of an S=O bond with respect to a C–N bond do not correspond to minima on the energy hyperface. The HF/3-21G* approximation predicts preference of the syn–anti structure (ΔE=−0.11 kcal mol⁻¹) and the B3LYP/6-31G* method results in an energy difference (ΔE=1.85 kcal mol⁻¹) which is slightly larger than the experimental values. The following geometric parameters for the O=C(N=S)₂ skeleton were derived (r_a values with 3σ uncertainties): C=O 1.193 (9) Å, C–N 1.365 (9) Å, S=N 1.466 (5) Å, O=C–N 125.1 (6)° and C–N=S 125.3 (10)°. The geometric parameters are reproduced satisfactorily by the HF/3-21G* approximation, except for the C–N=S angle which is too large by ca. 6°. The B3LYP method predicts all bonds to be too long by 0.02–0.05 Å and the C–N=S angle to be too small by ca. 4°.     

A comparative study on the nature and strength of O–O, S–S, and Se–Se bond

A computational study on dichalcogenide molecules (R₂X₂; X = O, S, Se; R = H, CH₃, NH₂) has been carried out employing B3LYP and MP2 levels using 6-31+G*, 6-311+G*, 6-311++G**, and PVDZ basis sets. The relative energies have been evaluated at G2MP2 also. The rotational barriers and bond dissociation energies indicate that S–S bond is stronger than Se–Se and O–O bond. NBO analysis at MP2/6-31+G* suggest the presence of partial π character between X–X bond that decreases in the order S–S > Se–Se > O–O. Fuki functions for nucleophilic and electrophilic attack fail to distinguish the reactivity of S and Se. The proton affinities of the O₂H₂, S₂H₂, Se₂H₂ decrease in the order Se > S > O.     

Ab initio method study on the isomerization of 3-amino-2-pyridone

Ab initio caculations with RHF/6-31G and MP2/6-31G have been used to study the isomerization of 3-amino-2-pyridone in gas-phase and in water. The results obtained show that 3-amino-2-pyridone is isomerized into 3-amino-2-hydroxy pyridine via a four-center cyclic transition state in the gas-phase, and via a six-center cyclic transition state in water. The activation energies of this reaction are 226.3336(RHF/6-31G) and 171.2269(MP2/6-31G) in gas-phase, and 81.6398(RHF/6-31G) and 59.8668(MP2/6-31G) kJ mol⁻¹ under the condition of a single water molecule as the catalyst, respectively.     

A computational study of adducts between atomic chlorine and carbon dioxide, carbonyl sulfide and carbon disulfide

The geometries and vibrational frequencies of the adducts ClCO₂, ClCOS and ClCS₂ were derived at the Hartree-Fock (HF) 3-21G (^*) level. The C_a, structure of ClCO₂ corresponds to one C-O bond and one C=O bond. Similarly, C_a, ClCS₂ has one C-S and one C=S bond, and ClCOS has one C-S and one C-O bond. Single-point spin-projected fourth-order Møller-Plesset (MP4) 3-21G (^*) calculations at these geometries were used in bond-separation reactions to derive ΔH^o₀ for adduct formation, which is calculated to be about 39 kJ mol⁻¹ exothermic for ClCOS and ClCS₂, but about 39 kJ mol⁻¹ endothermic for ClCO₂. The C_2v structures for ClCO₂ and ClCS₂ were also characterized. The geometry of ClCS₂ has not been determined experimentally; comparison with an available measured entropy for ClCS₂ suggests that the C_2v structure is the one formed by addition of Cl to CS₂, although the energy relative to the C_a form is not reliably calculated because of instability in the HF wavefunction.     

Theoretical studies on the gas-phase pyrolysis of 2-phenoxycarboxylic acids: an ONIOM approach

Various ONIOM combinations-ONIOM(HF/6-31G*: PM3), ONIOM(B3LYP/6-31G*: PM3), ONIOM(MP2/6-31G*: PM3), and ONIOM(MP2/6-31G*: HF/3-21G)--were applied to investigate thermal decomposition mechanisms of four 2-phenoxycarboxylic acids (2-phenoxyacetic acid, 2-phenoxypropionic acid, 2-phenoxybutyric acid, and 2-phenoxyisobutyric acid) in the gas phase. All the transition states and intermediates of the reaction paths were optimized. The reaction pathway of four reactants yielding the phenol, CO, and the corresponding carbonyl compound was characterized on the potential energy surface and found to proceed stepwise. The first step corresponds to the elimination of phenol and the formation of alpha-lactone intermediate through a five-membered ring transition state, and the second step is the cycloreversion process of alpha-lactone intermediate to form CO and the corresponding carbonyl compound. The reaction pathway of latter three compounds to produce the carboxylic acid and phenol via a four-membered cyclic transition structure was also examined theoretically. Comparison with experiment indicates that the activation parameters for the fist reaction channel are accurately predicted at the ONIOM(MP2/6-31G*: HF/3-21G) level of theory.     

Calculated structures and relative stabilities of furoxan,some 1,2-dinitrosoethylenes and other isomers

The structures and relative stabilities of furoxan and some of its isomers, e.g., the 1,2-dinitrosoethylenes, have been determined by means of ab initio Hartee–Fock and Møller–Plesset calculations. Geometries were optimized at the HF/3-21G, HF/6-31G* and MP2/6-31G* levels, and subsequently used for computing MP2/6-31G*, MP3/6-31G*, and MP4/6-31G* energies. The results are markedly affected by the inclusion of electronic correlation, which renders three of the isomers unstable. It also emphasizes the importance of a zwitterionic contribution to the structure of furoxan, which promotes ring-opening through a cis 1,2-dinitrosoethylene intermediate/transition state that has an MP4/6-31G*//MP2/6-31G* energy that is 31.6 kcal/mol above furoxan.     

Computational studies of the structure and vibrational spectra of hexafluorodisilane

Ab initio calculations predict that D_3d symmetry of Si₂F₆ is more stable than D_3h symmetry. The calculated potential barrier to internal rotation was 0.77, 0.73 and 0.78 kcal/mol using HF/6-31G*, B3LYP/6-31G* and MP2/6-31G* methods respectively, which was in good agreement with the experimental value between 0.51±0.10 and 0.73±0.14 kcal/mol. The optimized geometries, harmonic force fields, infrared intensities, Raman activities, and vibrational frequencies are reported for D_3d symmetry of Si₂F₆ from HF/6-31G* and B3LYP/6-31G*. A normal coordinate analysis was carried out. The average error between the scaled DFT frequencies obtained from the B3LYP/6-31G* calculation and observed frequencies was 4.2 cm⁻¹ and the average error between the scaled HF and observed frequencies was 2.2 cm⁻¹.     

Prediction of geometries and interaction energies of complexes formed by small molecules using semiempirical and ab initio methods

The accuracy of the semiempirical quantum mechanics methods (AM1 and PM3), and the ab initio methods (6-31G^** and MP2/6-31G^**) in predicting intermolecular geometries and interaction energies have been evaluated by detailed studies of 17 bimolecular complexes formed by small molecules. Comparisons between calculated and experimental geometries for 12 complexes are presented. It was found that AM1 gave reasonably good predictions of the geometries of complexes such as CH₄ · CH₄, which have very weak interactions, but it is not as good as other methods in predicting intermolecular geometry for complexes where hydrogen bonding interactions play an important role. This is consistent with its inability to reproduce the charge transfer in the formation of hydrogen bonds in these complexes.

PM3 is able to predict intermolecular geometries for most complexes, including those with hydrogen bonding; its major flaw is its tendency to overestimate the strength of the interactions between hydrogen atoms. Care should be taken therefore in using PM3 to study complicated molecular systems with multiple hydrogen atom interactions and the method's weakness in handling complexes in which electrostatic forces are important should also be noted.

Among ab initio methods, both the 6-31G^** and the MP2/6-31G^** were found to outperform AM1 and PM3 in prediction of intermolecular geometry. Both of these ab initio methods showed excellent consistency in geometry prediction for most of the complexes studied, although MP2/6-31G^** is better than 6-31G^**. It is noted that the MP2/6-31G^** did not produce the correct geometry for the CO₂· HF complex.

For 12 complexes for which experimental geometry data are available, AM1, PM3, 6-31G^**, and MP2/6-31G^** successfully predicted the geometry in 10, 12, 12, and 11 cases, respectively. The average errors given by AM1 in the predicted intermolecular distances were 0.264, 0.272, 0.091, and 0.061 Å, respectively. In comparison to the ab initio methods, AM1 and PM3 commonly underestimated the molecular interaction energy in such complexes by ˜ 1–2 kcal mol⁻¹.     

Conformation and reactivity of α-oxo-ketenes: Ab initio and semiempirical (AM1, PM3) calculations

Ab initio MP2/6-31G*//MP2/6-31G* and semiempirical AM1 and PM3 calculations on a series of differently substituted α-oxo-ketenes are used to investigate E/Z-isomerism and rotational barriers in these molecules. Sterically crowded derivatives are found to exist solely as s-E conformers. The unusual stability of these derivatives thus can be attributed to their inability to adopt the s-Z conformation required for the normal α-oxo-ketene reactions. With respect to structures and energies, the PM3 method (especially in the case of highly crowded molecules) is found to be less reliable than AM1. Ab initio HF/3-21G and PM3 vibrational frequencies appear to be of sufficient accuracy for a distinction between s-Z and s-E conformers. In this respect, the AM1 method appears less reliable. © 1994 by John Wiley & Sons, Inc.     

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.