Hetero‐π‐systems from 2 + 2 cycloreversion,part 2.1Ab initio thermochemical study of heterocyclobutanes 2 + 2 cycloreversion to form heteroethenes H2C=X (X=NH,O, SiH2, PH,S)

Ab initio and DFT thermochemical study of diradical mechanism of 2 + 2 cycloreversion of parent heterocyclobutanes and 1,3‐diheterocyclobutanes, cyclo‐(CH₂CH₂CH₂X), and cyclo‐(CH₂XCH₂X), where X = NH, O, SiH₂, PH, S, was undertaken by calculating closed‐shell singlet molecules at three levels of theory: MP4/6‐311G(d)//MP2/6‐31G(d)+ZPE, MP4/6‐311G(d,p)//MP2/6‐31G (d,p)+ZPE, and B3LYP/6‐311+G(d,p)+ZPE. The enthalpies of 2 + 2 cycloreversion decrease on going from group 14 to group 16 elements, being substantially higher for the second row elements. Normally endothermic 2 + 2 cycloreversion is predicted to be exothermic for 1,3‐diazetidine and 1,3‐dioxtane. Strain energies of the four‐membered rings were calculated via the appropriate homodesmic reactions. The enthalpies of ring opening via the every possible one‐bond homolysis that results in the formation of the corresponding 1,4‐diradical were found by subtracting the strain energies from the central bond dissociation energies of the heterobutanes CH₃CH₂—CH₂XH, CH₃CH₂—XCH₃, and HXCH₂—XCH₃. The latter energies were determined via the enthalpies of the appropriate dehydrocondensation reactions, using C—H and X—H bond energies in CH₃XH calculated at G2 level of theory. Except 1,3‐disiletane, in which ring‐opening enthalpy attains 69.7 kcal/mol, the enthalpies of the most economical ring openings do not exceed 60.7 kcal/mol. The 1,4‐diradical decomposition enthalpies found as differences between 2 + 2 cycloreversion and ring‐opening enthalpies were negative, the least exothermicity was calculated for ⋅ CH₂SiH₂CH₂CH₂. The only exception was 1,3‐disiletane, which being diradical, CH₂SiH₂CH₂SiH₂, decomposed endothermically. Since decomposition of the diradical containing two silicon atoms required extra energy, raising the enthalpy of the overall reaction to 78.9 kcal/mol, 1,3‐disiletane was predicted to be highly resisting to 2 + 2 cycloreversion. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:704–720, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20377     

Tautomerism of monochalcogenosilanoic acids CH3Si(O)XH (X = S,Se, Te) in the gas phase and in the polar and aprotic solution: An ab initio computational investigation

Computational investigations by an ab initio molecular orbital method (HF and MP2) with the 6‐311+G(d,p) and 6‐311++G(2df, 2pd) basis sets on the tautomerism of three monochalcogenosilanoic acids CH₃Si(?O)XH (X = S, Se, and Te) in the gas phase and a polar and aprotic solution tetrahydrofuran (THF) was undertaken. Calculated results show that the silanol forms CH₃Si(?X)OH are much more stable than the silanone forms CH₃Si(?O)XH in the gas‐phase, which is different from the monochalcogenocarboxylic acids, where the keto forms CH₃C(?O)XH are dominant. This situation may be attributed to the fact that the Si? O and O? H single bonds in the silanol forms are stronger than the Si? X and X? H single bonds in the silanone forms, respectively, even though the Si?X (X = S, Se, and Te) double bonds are much weaker than the Si?O double bond. These results indicate that the stability of the monochalcogenosilanoic acid tautomers is not determined by the double bond energies, contrary to the earlier explanation based on the incorrect assumption that the Si?S double bond is stronger than the S?O double bond for the tautomeric equilibrium of RSi(?O)SH (R?H, F, Cl, CH₃, OH, NH₂) to shift towards the thione forms [RSi(?S)OH]. The binding with CH₃OCH₃ enhances the preference of the silanol form in the tautomeric equilibrium, and meanwhile significantly lowers the tautomeric barriers by more than 34 kJ/mol in THF solution. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Conformational energies for 2-substituted butanes

The conformational free energies for some 2-substituted butanes where X = F, Cl, CN, and CCH were calculated using G3-B3, CBS-QB3, and CCSD(T)/6-311++G(2d,p) as well as other theoretical levels. The above methods gave consistent results with free energies relative to the trans conformers as follows: X = CCH, g+ = 0.77 +/- 0.05 kcal/mol. g- = 0.88 +/- 0.05 kcal/mol; X = CN, g+ = 0.85 +/- 0.05 kcal/mol, g- = 0.75 +/- 0.05 kcal/mol; X = Cl, g+ = 0.70 +/- 0.05 kcal/ml, g- = 0.80 +/- 0.05 kcal/mol; and X = F, g+ = 0.53 +/- 0.05 kcal/mol, g- = 0.83 +/- 0.05 kcal/mol. The conformational free energies also were estimated using the observed liquid phase IR spectra and intensities calculated using B3LYP/6-311++G** and MP2/6-311++G**. The rotational free energy profiles for all of the compounds were estimated at the G3-B3 level.     

OXO (X=Cl,Br)与X (2P3/2)反应机理的理论研究

用密度泛函B3LYP/6-311+G**和高级电子相关的组态相互作用QCISD(T)/6-311+G**方法研究了OXO与X (2P3/2)双自由基反应的微观机理.研究结果表明该反应存在两个反应通道,产物分别为XO和X2+O2.由于形成产物XO的活化势垒较低,因而是主要反应通道,这与实验观察到的结果是一致的.而形成X2+O2的通道从动力学上看是不利的.     

Rotational barriers in monomeric CH2=CX-COOH and CH2=CX-CONH2 (X is H or CH3) and vibrational analysis of methacrylic acid and methacrylamide

The internal rotations in acrylic and methacrylic acids CH2=CX-COOH and their amides CH2=CX-CONH2 (X is H or CH3) were investigated by DFT-B3LYP calculations with 6-311+G** basis set. The potential energy curves were consistent with two minima that correspond to planar cis and trans conformation in the case of the acids (or cis and near-trans forms in the case of the amides). Acrylic acid and acrylamide were predicted to have the cis form as the low and predominant conformation of the molecules. In the case of the methacrylic acid and methacrylamide, the conformational relative stability was predicted to reverse as going from the acrylic to the metha compounds. The trans conformer in methacrylic acid or the near-trans in methacrylamide were predicted to be thermodynamically low energy structures of the molecules. The CCCO rotational barrier was calculated to vary from 4 to 6kcal/mol in the four molecules. The OCOH and OCNH torsional barriers were calculated to be about 13 and 22kcal/mol in the acids and the amides, respectively. The vibrational frequencies of methacrylic acid and methacrylamide were computed at the DFT-B3LYP/6-311+G** level and reliable vibrational assignments were made on the basis of normal coordinate analyses and comparison with experimental data of both molecules in their low energy conformations.     

Potential Functions of Internal Rotation around the Csp2-X Bonds and Intermolecular Interactions in the Compounds CH2 = CHXCH3 (X = O,S, Se)

The potential functions of internal rotation around the Csp ²-X bonds in the CH₂ = CHXCH₃ molecules (X = O, S, Se) were determined by MP2/6-31G* and MP2/6-31G** calculations. The stationary points were identified by solution of vibrational problems. The rotation barriers were evaluated taking into account the zero-point vibration energy. The intramolecular interactions were considered in terms of the method of natural bond orbitals. The degrees of hybridization, energies, and populations of the orbitals of the lone electron pairs of the O, S, and Se atoms, the energies of their donor-acceptor interaction with the antibonding * and * orbitals of the double bond, and the natural atomic charges in various conformations were determined.     

Theoretical study on structures and stability of triplet SiC<Subscript>3</Subscript>O isomers

Various levels of calculations are carried out~for exploring the potential energy surface (PES) of triplet SiC₃O, a molecule of potential interest in interstellar chemistry. A total of 38 isomers are located on the PES including chain-like, cyclic and cage-like structures, which are connected by 87 interconversion transition states at the DFT/B3LYP/6-311G(d) level. The structures of the most relevant isomers and transition states are further optimized at the QCISD/6-311G(d) level followed by CCSD(T)/6-311+G(2df) single-point energy calculations. At the QCISD level, the lowest lying isomer is a linear SiCCCO 1 (0.0 kcal/mol) with the ³ ∑ electronic state, which possesses great kinetic stability of 59.5 kcal/mol and predominant resonant structure . In addition, the bent isomers CSiCCO 2 (68.3 kcal/mol) and OSiCCC 5 (60.1 kcal/mol) with considerable kinetic stability are also predicted to be candidates for future experimental and astrophysical detection. The bond natures and possible formation pathways in interstellar space of the three stable isomers are discussed. The predicted structures and spectroscopic properties for the relevant isomers are expected to be informative for the identification of SiC₃O and even larger SiC _n O species in laboratory and interstellar medium. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Electronic states of XC<Subscript>3</Subscript>H<Subscript>3</Subscript>Si five-membered rings (X = CH,N, P,and As)

Stable configurations of XC₃H₃Si five-membered rings, 1 _X and 2 _X (X = CH, N, P, and As) in the singlet and triplet states are found at B3LYP/6-311++G** level of theory. All the singlet states of 1 _X and 2 _X have lower potential energy than the triplet state. The ΔG _s−t differences between the singlet and triplet states of 1 _X and 2 _X changes at the B3LYP/6-311++G** level in the order (in kcal/mol): 1 _N (−17.56) > 1 _CH (−15.26) > 1 _P (−4.96) > 1 _As (−3.45) and 2 _CH (−15.26) > 2 _N (−9.21) > 2 _P (−7.39) > 2 _As (−6.15), respectively.     

Potential energy scans and vibrational assignments of cyclopropanecarboxylic acid and cyclopropanecarboxamide

The structural stability and internal rotations in cyclopropanecarboxylic acid and cyclopropanecarboxamide were investigated by the DFT-B3LYP and the ab initio MP2 calculations using 6-311G** and 6-311+G** basis sets. The computations were extended to the MP4//MP2/6-311G** and CCSD(T)//MP2/6-311G** single-point calculations. From the calculations the molecules were predicted to exist predominantly in the cis (C=O group eclipses the cyclopropane ring) with a cis-trans barrier of about 4-6kcal/mol. The OCOH torsional barrier in the acid was estimated to be about 12-13kcal/mol while the corresponding OCNH torsional barrier in the amide was calculated to be about 20kcal/mol. The equilibrium constant k for the cis<-->trans interconversion in cyclopropanecarboxylic acid was calculated to be 0.1729 at 298.15K that corresponds to an equilibrium mixture of about 85% cis and 15% trans. The vibrational frequencies were computed at the DFT-B3LYP level. Normal coordinate calculations were carried out and potential energy distributions were calculated for the low energy cis conformer of the molecules. Complete vibrational assignments were made on the basis of normal coordinate calculations and comparison with experimental data of the molecules.     

Transition state structure and energetics of the N(2)O + X (X = Cl,Br) reactions

The structural and vibrational properties of the transition state of the N(2)O + X (X = Cl,Br) reactions have been characterized by ab initio methods using density functional theory. We have employed Becke's hybrid functional (B3LYP), and transition state optimizations were performed with 6-31G(d), 6-311G(2d,2p), 6-311+G(3d,2p), and 6-311+G(3df,2p) basis sets. For the chlorine atom reaction the coupled-cluster method (CCSD(T)) with 6-31G(d) basis set was also used. All calculations resulted in transition state structures with a planar cis arrangement of atoms for both reactions. The geometrical parameters of transition states at B3LYP are very similar, and the reaction coordinates involve mainly the breaking of the N-O bond. At CCSD(T)/6-31G(d) level a contribution of the O-Cl forming bond is also observed in the reaction coordinate. In addition, several highly accurate ab initio composite methods of Gaussian-n (G1, G2, G3), their variations (G2(MP2), G3//B3LYP), and complete basis set (CBS-Q, CBS-Q//B3LYP) series of models were applied to compute reaction energetics. All model chemistries predict exothermic reactions. The G3 and G2 methods result in the smallest deviations from experiment, 1.8 and 0 kcal mol(-1), for the enthalpies of reaction for N(2)O reaction with chlorine and bromine, respectively. The G3//B3LYP and G1 methods perform best among the composite methods in predicting energies of the transition state, with a deviation of 1.9 and 3.0 kcal mol(-1), respectively, in the activation energies for the above processes. However, the B3LYP/6-311+G(3df,2p) method gives smaller deviations of 0.4 and -1.0 kcal mol(-1), respectively. The performance of the methodologies applied in predicting transition state energies was analyzed.     

Theoretical study on structures and stabilities of N4X (X = O,S, Se,Te) series

The stable and transition structures of N₄X (X = O, S, Se, Te) series with singlet state are optimized with the ab initio (MP2) and density functional theory (B3LYP) methods using the 6‐311+G(d) basis set. The ring isomers are found to be the global minima for N₄O, N₄S, N₄Se, and the chain isomer is the minimum for N₄Te. The stabilities are studied by evaluating the dissociation barriers with respect to dissociation. The reactants and products connected by transition structures are determined by applying the intrinsic reaction coordinate (IRC) calculations. The C_2v, C_3v and ring isomers decompose into linear NNX and N₂ molecules, however, the chain isomers decompose into cyclic N₂X and N₂ firstly. A new possible isomerization mechanism between the cyclic and linear structures of N₂X series is studied. The cyclic structures of N₂X convert into linear structures easily with the very low barriers. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Ligand‐Exchange Processes on Solvated Beryllium Cations. Part III

On the basis of DFT calculations (B3LYP/6‐311+G**), the possibility to include solvent effects is considered in the investigation of the H₂O‐exchange mechanism on [Be(H₂O)₄]²⁺ within the widely used cluster approach. The smallest system in the gas phase, [Be(H₂O)₄(H₂O)]²⁺, shows the highest activation barrier of +15.6 kcal/mol, whereas the explicit addition of five H‐bonded H₂O molecules in [{Be(H₂O)₄(H₂O)}(H₂O)₅]²⁺ reduces the barrier to +13.5 kcal/mol. Single‐point calculations applying CPCM (B3LYP(CPCM:H₂O)/6‐311+G**//B3LYP/6‐311+G**) on [Be(H₂O)₄(H₂O)]²⁺ lower the barrier to +9.6 kcal/mol. Optimization of the precursor and transition state of [Be(H₂O)₄(H₂O)]²⁺ within an implicit model (B3LYP(CPCM:H₂O)/6‐311+G** or B3LYP(PCM:H₂O)/6‐311+G**) reduces the activation energy further to +8.3 kcal/mol but does not lead to any local minimum for the precursor and is, therefore, unfavorable.     

Structure of the boronic acid dimer and the relative stabilities of its conformers

Despite the widespread use of boronic acids in materials science and as pharmaceutical agents, many aspects of their structure and reactivity are not well understood. In this research the boronic acid dimer, [HB(OH)(2)](2), was studied by second-order M?ller-Plesset (MP2) perturbation theory and coupled cluster methodology with single and double excitations (CCSD). Pople split-valence 6-31+G*, 6-311G**, and 6-311++G** and Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the calculations. A doubly hydrogen-bonded conformer (1) of the dimer was consistently found to be lowest in energy; the structure of 1 was planar (C(2h)) at most computational levels employed but was significantly nonplanar (C(2)) at the MP2/6-311++G** and CCSD/6-311++G** levels, the result of an intrinsic problem with Pople-type sp-diffuse basis functions on heavy atoms. The dimerization energy, enthalpy, and free energy for the formation of (1) from the exo-endo conformer of the monomer were -10.8, -9.2, and +1.2 kcal/mol, respectively, at the MP2/aug-cc-pVTZ level. Several other hydrogen-bonded conformers of the dimer were local minima on the potential energy surface (PES) and ranged from 2 to 5 kcal/mol higher in energy than 1. Nine doubly OH-bridged conformers, in which the boron atoms were tetracoordinated, were also local minima on the PES, but they were all greater than 13 kcal/mol higher in energy than 1; doubly H-bridged structures proved to be transition states. MP2 and CCSD results were compared to those from the BLYP, B3LYP, OLYP, O3LYP, PBE1PBE, and TPSS functionals with the 6-311++G** and aug-cc-pVTZ basis sets; the PBE1PBE functional performed best relative to the MP2 and CCSD results. Self-consistent reaction field (SCRF) calculations predict that boronic acid dimerization is less favorable in solution than in vacuo.     

Theoretical predictions of the structure, gas-phase acidity and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid

Results of ab initio self-consistent-field (SCF) and density functional theory (DFT) calculations of the gas-phase structure, acidity (free energy of deprotonation, ΔG^o), and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid (3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone, H₂C₄Se₂S₂) are reported. The global minimum found on the potential energy surface of 1,2-diseleno-3,4-dithiosquaric acid presents a planar conformation. The ZZ isomer was found to have the lowest energy among the three planar conformers and the ZZ and ZE isomers are very close in energy. The optimized geometric parameters exhibit a bond length equalization relative to reference compounds, cyclobutanediselenone, and cyclobutenedithiol. The computed aromatic stabilization energy (ASE) by homodesmotic reaction (Eq 1) is −20.1 kcal/mol (MP2(fu)/6-311+G** //RHF/6-311+G**) and −14.9 kcal/mol (B3LYP//6-311+G**//B3LYP/6-311+G**). The aromaticity of 1,2-diseleno-3,4-dithiosquaric acid is indicated by the calculated diamagnetic susceptibility exaltation (Λ) −17.91 (CSGT(IGAIM)-RHF/6-311+G**//RHF/6-311+G**) and −31.01 (CSGT(IGAIM)-B3LYP/6-311+G**//B3LYP/6-311+G**). Thus, 1,2-diseleno-3,4-dithiosquaric acid fulfils the geometric, energetic and magnetic criteria of aromaticity. The calculated theoretical gas-phase acidity is ΔG^o _1(298K)=302.7 kcal/mol and ΔG^o _2(298K)=388.4 kcal/mol. Hence, 1,2-diseleno-3,4-dithiosquaric acid is a stronger acid than squaric acid(3,4-dihydroxy-3-cyclobutene-1,2-dione, H₂C₄O₄). Received: 11 April 2000 / Accepted: 7 July 2000 / Published online: 27 September 2000     

On the aromatic character of the heterocyclic bases of DNA and RNA

Studies based on ab initio optimized geometries (at B3LYP/6-311+G** and MP2/6-311+G** levels) and on experimental structures retrieved from the Cambridge Structural Database (CSD) reveal that the nucleobases constituting DNA and RNA differ significantly in their aromatic character, as shown by the geometry-based index of aromaticity HOMA that ranges from 0.466 for thymine to 0.917 for adenine, based on B3LYP/6-311+G** calculations, and 0.495-0.926, respectively, if based on the MP2/6-311+G** level. Aromaticity of the bases decreases markedly with an increase of the number of double-bond C=X (X = N, O) substituents at the rings. H-bonds involving C=O groups in Watson-Crick pairs cause an increase of the aromatic character of the rings.     

Keto<==>enol, imine<==>enamine, and nitro<==>aci-nitro tautomerism and their interrelationship in substituted nitroethylenes. Keto, imine, nitro, and vinyl substituent effects and the importance of H-bonding

Tautomeric isomers and conformers of 2-nitrovinyl alcohol (1), 2-nitrovinylamine (2), and 1-nitro-propene (3) are reported at the MP2 and B3LYP levels of theory, using the 6-31G* basis set, with energy evaluation at B3LYP/6-311+G** and G2MP2. The nitroalkenes are the global minima on their respective potential energy surfaces. The barriers for the concerted 1,5-H transfer to the corresponding nitronic acids amount to only 5.0 kcal/mol for 1, 13.2 kcal/mol for 2, and a sizable 37.8 kcal/mol for 3. Whereas the aci-nitro tautomer of 2-nitrovinyl alcohol is easily accessible, beta-iminonitronic acid has little kinetic stability. H-bonding is a strong stabilizing factor in these nitroalkenes, estimated at 7.0 and 3.7 kcal/mol for the OH and NH2 derivatives, respectively, while its stabilization in their nitronic acids amounts to as much as 13 kcal/mol. The H-bonds are evident from the very short O...H and N...H distances and are characterized by bond critical points. The NO2 substituent effect of about 11.4 kcal/mol at G2MP2 on both the classical keto <==> enol and imine <==> enamine tautomeric processes stabilizes the nitroethylene derivatives. The keto, imine, and vinyl substituent effects at G2MP2 on the nitro <==> aci-nitro tautomeric process are also determined as are their pi-resonance components. The substituents have a large influence on the ionization energies of the nitroethylene derivatives.     

Does CH prefer a C2v rather than a Cs structure?

The closely related C_s ( 1 ) and C_2v ( 3 ) structures of CH have been reinvestigated at many ab initio levels using MP2/6-31G** and MP2/6-311 + + G(2df, 2pd) geometries. The largest basis sets employed were 6-311G(3df, 2p), 6-311 + + G(3df, 3pd), and the Dunning “correlation consistent” polarized triple-split valence basis set (cc-pVTZ). Electron correlation was probed at the MP4 level, but the QCISD method was also used with the largest basis sets. While electron correlation favors 3 over 1 by about 2 kcal/mol, the correlated relative energies with all basis sets employed range from 0.36–1.03 kcal/mol in favor of 1 . The best estimate of this difference, 0.86 kcal/mol, is essentially identical with the (scaled) zero-point energy difference, 0.84 kcal/mol, favoring 3 over 1 . These results indicate that 1 and 3 have almost exactly the same energy at 0 K. Our best value for the dissociation energy of CH is 42.0 kcal/mol [QCISD(T)/6-311 + + G(3df, 3pd)//MP2(fu)/6-311 + + G(2df, 2pd), corrected to 298 K], which agrees very well with the experimental value. © 1992 by John Wiley & Sons, Inc.     

13C NMR, infrared, solvation and theoretical investigation of the conformational isomerism in 1-haloacetones (X = Cl, Br and I)

The solvent dependence of the 13C NMR spectra of chloroacetone (CA), bromoacetone (BA) and iodoacetone (IA) are reported and the 3J(CH) couplings analysed using ab initio calculations and solvation theory. In CA the energy difference (E(cis) - E(gauche)) between the cis (Cl-C-C=O 0 degrees) and gauche (Cl-C-C=O 155 degrees) conformers is 1.7 kcal mol(-1) in the vapour, decreasing to 0.8 kcal mol(-1) in CCl4 solution and to -1.0 kcal mol(-1) in the pure liquid. The conformational equilibrium, in BA, is between the more polar cis (Br-C-C=O 0 degrees) and gauche (Br-C-C=O 132 degrees) conformations. The energy difference (E(cis) - E(gauche)) is 1.8 kcal mol(-1) in the vapour, decreasing to 0.9 kcal mol(-1) in CCl4 solution and to -0.4 kcal mol(-1) in the pure liquid. The energy difference (E(cis) - E(gauche)), in IA, between the cis (I-C-C=O 0 degrees) and gauche (I-C-C=O 104 degrees) conformers is 1.1 kcal mol(-1) in the vapour phase, decreasing to 0.5 kcal mol(-1) in CCl4 solution and to -0.5 kcal mol(-1) in the pure liquid. The vapour state energy difference for BA [1.4 kcal mol(-1) at B3LYP/6-311++G(d,p)] and for IA [1.6 kcal mol(-1) at B3LYP/6-311++G(d,p)/LANL2DZ)] are in very good agreement with the above values. For CA the agreement is also satisfactory [1.4 kcal mol(-1) at B3LYP/6-311++G(d,p)].     

Structures and Aromaticity of Three-membered BeXP （X = C,Si, Ge） and CYP （Y = O,S, Se） Rings

Three-membered BeXP （X = C, Si, Ge） and CYP （Y = O, S, Se） rings are theoretically investigated using density functional theory （DFT） methods at the B3LYP/6-311＋G^＊ and B3PW91/6-311＋G^＊ levels of theory. The research results show that the size of atoms has a great influence on the structural stability of these species. The wiberg bond indexs （WBIs） suggest the existence of delocalization in these structures. Negative nucleus-independent chemical shift （NICS） values for these species indicate that a strong ring current exists in these three-membered structures （Cs symmetry）. A detailed molecular orbital （MO） analysis further reveals that a delocalized π MO strengthens the structural stability and makes these species show strong aromatic characters.     

Vibrational analyses of sulfamoyl halides NH2SO2X (X is F, Cl and Br)

The structural stability of sulfamoyl halides NH(2)-SO(2)X (X is F, Cl and Br) were investigated by DFT-B3LYP/6-311+G** and ab initio MP2/6-311+G** calculations. From the calculations the molecules were predicted to exist only in the anti (XS bond is anti with respect to nitrogen lone pair) conformation with the possibility of very low abundance of the syn (SO(2) and NH(2) groups eclipse each other) form of only the fluoride. The equilibrium constant for the syn<-->anti conformational conversion of sulfamoyl fluoride was calculated to be 0.0172 that corresponds to an equilibrium mixture of about 2% syn and 98% anti at 298.15K. The vibrational frequencies were computed at DFT-B3LYP level for the stable anti conformer of the d(0) and d(2) (ND(2)-SO(2)X) deuterated species of the three molecules. Normal coordinate calculations were then carried out and the potential energy distributions were calculated for the molecules.