Ligand Exchange Processes on Solvated Zinc Cations – DFT Analysis of Hydrogen Cyanide Exchange on [Zn(HCN)6]2+

The mechanisms for hydrogen cyanide exchange on [Zn(HCN)₆]²⁺ were studied using density functional theory (B3LYP/6‐311+G**), and showed that the limiting dissociative (D) pathway is more favorable than the associative interchange (I_a) mechanism. The activation barrier for the dissociative mechanism (7 kcal · mol^–1) is clearly lower than for the interchange mechanism (15.9 kcal · mol^–1).     

Hydrogen Cyanide Exchange on [Al(HCN)6]3+ – A DFT Study

The hydrogen cyanide exchange mechanism of [Al(HCN)₆]³⁺ has been investigated by DFT calculations (B3LYP/6‐311+G**). The calculations provide theoretical evidence that the hydrogen cyanide exchange proceeds via a limiting dissociative (D) mechanism involving a stable five‐coordinate intermediate [Al(HCN)₅ · (HCN)₂]³⁺. The activation energy for the D‐mechanism is 23.4 kcal · mol^–1, which is 2.8 kcal · mol^–1 lower than for the seven‐coordinate transition state [Al(HCN)₇]^3+? for the alternative associative (A) pathway. The difference in stability between the two intermediates [Al(HCN)₅ · (HCN)₂]³⁺ (12.1 kcal · mol^–1) and [Al(HCN)₇]³⁺ (25.7 kcal · mol^–1) in comparison to [Al(HCN)₆ · (HCN)]³⁺ is much more pronounced and further supports a limiting dissociative mechanism.     

Computational study on the mechanism and thermodynamic of atmospheric oxidation of HCN with ozone

Oxidation of hydrogen cyanide with ozone on the singlet potential energy surface is carried out using the MP2 and CCSD(T)//MP2 theoretical approaches in connection with the 6-311++G(d,p) basis set. In this reaction, energy barrier of transition states are low, so the reaction of HCN with ozone can occur easily at atmospheric condition. With variety of pre-reactive complex, five types of products are obtained at the MP2 method which four types of them have enough thermodynamic stability at the standard condition. CO₂ + HNO are final adducts in a process that is computed to be exothermic by ?132.605 kcal/mol in standard enthalpy and spontaneous by ?144.166 kcal/mol in Gibbs free energy of reaction. In kinetic viewpoint, the production of OCN + HO₂ adducts path with one low level transition state is the most favored path.     

Density functional theory and post-Hartree-Fock studies on molecular structure and harmonic vibrational spectrum of formaldehyde

Density functional theory (DFT) with the Becke's three-parameter exchange correlation functional and the functional of Lee, Yang and Parr, gradient-corrected functionals of Perdew, and Perdew and Wang [the DFT(B3LYP), DFT(B3P86) and DFT(B3PW91) methods, respectively], and several levels of conventional ab initio post-Hartree-Fock theory (second- and fourth-order perturbation theory M?ller-Plesset MP2 and MP4(SDTQ), coupled cluster with the single and double excitations (CCSD), and CCSD with perturbative triple excitation [CCSD(T)], configuration interaction with the single and double excitations [CISD], and quadratic configuration interaction method [QCISD(T)], using several basis sets [ranging from a simple 6-31G(d,p) basis set to a 6-311+ +G(3df, 2pd) one], were applied to study of the molecular structure (geometrical parameters, rotational constants, dipole moment) and harmonized infrared (IR) spectrum of formaldehyde (CH₂O). High-level ab initio methods CCSD(T) and QCISD(T) with the 6-311+ +G(3df, 2pd) predict correctly molecular parameters, vibrational harmonic wavenumbers and the shifts of the harmonic IR spectrum of ¹²CH₂ ¹⁶O upon isotopic substitution. Received: 30 January 1997 / Accepted: 7 May 1997     

Generation and characterization of ionic and neutral methylene isothiocyanate by a combined tandem mass spectrometry and computational study

The heterocumulene, methyleneisothiocyanate ion, CH₂?N?C?S⁺ (1a⁺), is generated by the dissociative electron ionization of 2‐mercaptoimidazole. This conclusion follows from tandem mass spectrometry experiments and theoretical calculations at the B3LYP/6‐311G** and G2/G2(MP2) levels. The calculations predict that 1a⁺ is separated by high energy barriers from its isomers CHNCHS (1b⁺), CHNCSH (1d⁺), CNCHSH (1e⁺) and CHNHCS (1f⁺). The low energy metastable ions 1a⁺ dissociate by loss of HCN via the pathway 1a⁺ → 1b⁺ → HCS⁺ + HCN. Neutralization‐reionization experiments confirm the theoretical prediction that the hitherto unknown heterocumulene CH₂?N?C?S ^. is a stable species in the rarefied gas phase. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Ab Initio Study on the Potential Energy Surfaces of B4 Cluster

The singlet and triplet potential energy surfaces (PES) for the isomerization and dissociation reactions of B₄ isomers have been investigated using ab initio methods. Ten B4 isomers have been identified and of these 10 species, 4 have not been reported previously. The singlet rhombic structure ¹1 is found to be the most stable on the B₄ surface, in agreement with the results of previous reports. Several isomerization and dissociation pathways have been found. On the singlet PES, the linear ¹3b can rearrange to rhombus ¹1 directly, while ¹3c rearranges to ¹1 through two‐step reactions involving a cyclic intermediate. On the triplet PES, the capped triangle structure ³2 undergoes ring opening to the linear isomer ³3b with a barrier of 34.8 kcal/mol and 44.9 kcal/mol, and the latter undergoes ring closure to the square structure ³1 with a barrier of 30.4 kcal/mol and 33.0 kcal/mol at the MP4/6–311+G(3df)//MP2/6–311G(d) and CCSD/aug‐cc‐pVTZ//MP2/6–311G(d) levels of theory, respectively. The direct decomposition of singlet B₄ yielding to B₃+B is shown to have a large endothermicity of 87.3 kcal/mol (CCSD), and that producing 2B₂ to have activation energy of 133.4 kcal/mol (CCSD).     

A quantum mechanical approach to the kinetics of the hydrogen abstraction reaction H2O2 + •OH → HO2 + H2O

The kinetics of the hydrogen abstraction from H₂O₂ by ^?OH has been modeled with MP2/6‐31G*//MP2/6‐31G*, MP2‐SAC//MP2/6‐31G*, MP2/6‐31+G**//MP2/6‐31+G**, MP2‐SAC// MP2/6‐31+G**, MP4(SDTQ)/6‐311G**//MP2/6‐31G*, CCSD(T)/6‐31G*//CCSD(T)/6‐31G*, CCSD(T)/6‐31G**//CCSD(T)/6‐31G**, CCSD(T)/6‐311++G**//MP2/6‐31G* in the gas phase. MD simulations have been used to generate initial geometries for the stationary points along the potential energy surface for hydrogen abstraction from H₂O₂. The effective fragment potential (EFP) has been used to optimize the relevant structures in solution. Furthermore, the IEFPCM model has been used for the supermolecules generated via MD calculations. IEFPCM/MP2/6‐31G* and IEFPCM/CCSD(T)/6‐31G* calculations have also been performed for structures without explicit water molecules. Experimentally, the rate constant for hydrogen abstraction by ^?OH drops from 1.75 × 10^?12 cm³ molecule^?1 s^?1 in the gas phase to 4.48 × 10^?14 cm³ molecule^?1 s^?1 in solution. The same trend has been reproduced best with MP4 (SDTQ)/6‐311G**//MP2/6‐31G* in the gas phase (0.415 × 10^?12 cm³ molecule^?1 s^?1) and with EFP (UHF/6‐31G*) in solution (3.23 × 10^?14 cm³ molecule^?1 s^?1). © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 502–514, 2005     

Theoretical study on the gas phase reaction mechanism of acetylene with nitrous oxide

The reaction mechanism of C₂H₂ and N₂O on the singlet potential energy surface is investigated in this study, at the B3LYP/6-311++G(3df,3pd), MP2/6-311++G(d,p), and CCSD(T) levels of theory. We have obtained three kinds of products in both methods, B3LYP and MP2, which have enough thermodynamic stability. The results reveal that the product P1, CH₂CO + N₂, is spontaneous and exothermic with ?86.176 and ?83.149 kcal/mol in Gibbs free energy and enthalpy of reaction at the MP2 level, respectively. Hence, the product P1 is thermodynamically the most favored adduct of the C₂H₂ + N₂O gas phase reaction at atmospheric pressure and 298.15 K temperature.     

An investigation on the reaction mechanism of the F2+Cl2→2ClF using the B3LYP method

The reaction mechanism of F₂+Cl₂→2ClF has been investigated with the density functional theory at the B3LYP/6‐311G* level. Six transition states have been found for the three possible reaction paths and verified by the normal mode vibrational and IRC analyses. Ab initio MP2/6‐311G* geometry optimizations and CCSD(T)/6‐311G(2df)//MP2/6‐311G* single‐point energy calculations have been performed for comparison. It is found that when the F₂ (or Cl₂) molecule decomposes into atoms first and then the F (or Cl) atom reacts with the molecule Cl₂ (or F₂) nearly along the molecular axis, the energy barrier is very low. The calculated energy barrier of F attacking Cl₂ is zero and that of Cl attacking F₂ is only 15.57 kJ?mol^?1 at the B3LYP level. However, the calculated dissociation energies of F₂ and Cl₂ are as high as 145.40 and 192.48 kJ?mol^?1, respectively. When the reaction proceeds through a bimolecular reaction mechanism, two four‐center transition states are obtained and the lower energy barrier is 218.69 kJ?mol^?1. Therefore, the title reaction F₂+Cl₂→2ClF is most probably initiated from the atomization of the F₂ molecule and terminated by the reaction of F attacking Cl₂ nearly along the Cl? Cl bond. MP2 calculations lead to the same conclusion, but the geometry of TS and the energy barrier are somewhat different. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

AB initio study of thermodynamic stability and structure of cage molecules B4N4H8 and Be4O4H8

Stable molecular structures of heterocubane systems B₄N₄H₈ 2 and Be₄O₄H₈, isoelectronic to the cubane molecule, are investigated by ab initio (RHF/6-31G**, MP2(full)/6-31C**, and MP2(full)/6-311+ + G**) methods and are shown to be highly thetmodynamically stable. Decomposition of structure 2 into two 1,3,2,4-diazadiboroethidine molecules 6 or four iminobomne NBNH molecules 11 is an endothermal process taking 10.1 (RHF/6-31G**), 39.6 (MP2(full)/6-31G**) kcaUmole and 140.6 (RHF/6-31G**), 161.4 (MP2(full)/6-31G**) kcal/mole, respectively. Decomposition of structure 3 into two 1,3,2,4-dioxydi-beryllothidine molecules 12 or four molecules 13 is also an endothermal reaction taking 22.1 (RHF/6-31G**), 39.8 (MP2(full)/6-31G**) kcal/mole and 127.1 (RHF/6-31G**), 155.2 (MP2(full)/631G**) kcal/mole, respectively. The geometrical characteristics of simple molecules BeH₂ 15, Be₂ 16 and 17, Be₂H₂ 18, Be₂H₄ 19, BeO 20, and Be₂O₂ 21 are calculated. Translated from Zhumal Struktumoi Khim ii, Vol. 41, No. 1, pp. 3-13, January–February, 2000     

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.     

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.     

Conformational study of the structure of free 12-thiacrown-4 and some of its cation metal complexes

Conformational search of 12-thiacrown-4, 12t4, was performed using the CONFLEX method and the MMFF94S force field whereby 156 conformations were predicted. Optimized geometries of the 156 predicted conformations were calculated at the HF, B3LYP, CAM-B3LYP, M06, M06L, M062x and M06HF levels using the 6-311G** basis set. The correlation energy was recovered at the MP2 level using the same 6-311G** basis set. Optimized geometries at the MP2/6-311G** level and G3MP2 energies were calculated for some of the low energy conformations. The D ₄ conformation was predicted to be the ground state conformation at all levels of theory considered in this work. Comparison between the dihedral angles of the predicted conformations indicated that for the stability of 12t4, a SCCS dihedral angle of 180° requirement is more important than a gauche CSCC dihedral angle requirement. Conformational search was performed also for the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes using the CONFLEX method and the CAChe-augmented MM3 and MMFF94S force fields. Conformations with relative energies less than 10?kcal/mol at the MP2/6-31+G*//HF/6-31+G* level, with double zeta quality basis set on the metal cations, were considered for computations at the same levels as those used for free 12t4, using also the 6-311G** basis set. The cc-pVTZ-pp basis set was used for the metal cations. The predicted ground state conformations of the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes are the C ₄, C ₄, C ₄, C _2v and C ₄ conformations, respectively. This is in agreement with the experimental X-ray data for the 12t4?CAg⁺ and Cd²⁺ cation metal complexes, but experimentally by X-ray, the 12t4?CBi³⁺ and Cu⁺ cation metal complexes have C _s and C ₄ structures, respectively.     

The C7-C10 cycloalkanes revisited

The conformers of cycloheptane through cyclodecane have been examined at the B3LYP/6-311+G* and MP2/6-311+G* theoretical levels, with some additional calculations at the CCD/6-311+G* and CCSD(T)/6-311++G** levels. With cyclooctane, B3LYP predicts that the boat-chair and crown conformers have similar energies, whereas MP2 and CCSD(T) predict that the crown conformer is 2 kcal/mol higher in energy. The latter is in agreement with the electron diffraction data. With cyclononane, B3LYP predicts that two of the higher-energy conformers found in molecular mechanics calculations should convert to one of the lower-energy conformers. However, MP2/6-311+G* optimizations find them to be true minima on the potential energy surface. B3LYP systematically predicts larger C-C-C bond angles for these compounds than either MP2 or CCD. The results of molecular mechanics MM4 calculations are generally in good agreement with those obtained using MP2.     

Protonated acetylene revisited

The potential energy surface for protonated acetylene has been re-examined with large basis sets and highly correlated methods. The energy difference of 3.6–3.8 kcal/mol between the classical structure and non-classical (bridged) structure computed with CCSD (T)/cc-pVQZ, CCSD(T)/6-311+G(3df,2pd), BD(T)/cc- pVQZ, BD(T)/6-311+G(3df,2pd) and CBS-APNO methods is in very good agreement with the best previous calculations, 3.7–4.0 kcal/mol. In contrast, BLYP, B3LYP, PW91, PBE and TPSS density functional methods do rather poorly, yielding −0.52. 0.29, 1.81, 2.16 and 0.62 kcal/mol, respectively, with the 6-311+G(3df,2pd) basis. MP2 calculations predict the classical structure to be a transition state; however, frequency calculations at the CCSD/6-311+G(3df,2pd) level of theory show that the classical structure is a local minimum. CCSD(T), BD(T) and CBS-APNO energy calculations along the MP2/6-311+G(3df,2pd) reaction path indicate that the classical structure is a shallow local minimum separated from the non-classical structure by a very small barrier of 0.11–0.13 kcal/mol. Because the barrier for proton exchange between the non-classical isomers via the classical structure is broad and nearly flat at the top, the tunneling splitting should be reduced, possibly accounting for the 15% difference between the calculated and experimental barrier heights. Contribution to the Fernando Bernardi Memorial Issue.     

Enthalpy of formation and bond energies on unsaturated oxygenated hydrocarbons using G3MP2B3 calculation methods

Enthalpies of unsaturated oxygenated hydrocarbons and radicals corresponding to the loss of hydrogen atoms from the parent molecules are intermediates and decomposition products in the oxidation and combustion of aromatic and polyaromatic species. Enthalpies (Δ_fH⁰₂₉₈) are calculated for a set of 27 oxygenated and nonoxygenated, unsaturated hydrocarbons and 12 radicals at the G3MP2B3 level of theory and with the commonly used B3LYP/6‐311g(d,p) density functional theory (DFT) method. Standard enthalpies of formation (Δ_fH⁰₂₉₈) are determined from the calculated enthalpy of reaction (ΔH⁰_rxn,298) using isodesmic work reactions with reference species that have accurately known Δ_fH⁰₂₉₈ values. The deviation between G3MP2B3 and B3LYP methods is under ±0.5 kcal mol^?1 for 9 species, 18 other species differs by less than ±1 kcal mol^?1 , and 11 species differ by about 1.5 kcal mol^?1. Under them are 11 radicals derived from the above‐oxygenated hydrocarbons that show good agreement between G3MP2B3 and B3LYP methods. G3 calculations have been performed to further validate enthalpy values, where a discrepancy of more than 2.5 kcal mol^?1 exists between the G3MP3B3 and density functional results. Surprisingly the G3 calculations support the density functional calculations in these several nonagreement cases. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 633–648, 2005     

Ab initio study on the reaction mechanism of ozone with bromine atom

Ab initio calculations of the potential energy surface (PES) for the Br+O₃ reaction have been performed using the MP2, CCSD(T), and QCISD(T) methods with 6‐31G(d), 6‐311G(d), and 6‐311+G(3df). The reaction begins with a transition state (TS) when the Br atom attacks a terminal oxygen of ozone, producing an intermediate, the bromine trioxide (M), which immediately dissociates to BrO+O₂. The geometry optimizations of the reactants, products, and intermediate and transition states are carried out at the MP2/6‐31G(d) level. The reaction potential barrier is 3.09 kcal/mol at the CCSD(T)/6‐311+G(3df)//MP2 level, which shows that the bromine atom trends intensively to react with the ozone. The comparison of the Br+O₃ reaction with the F+O₃ and Cl+O₃ reactions indicates that the reactions of ozone with the halogen atoms have the similar reaction mechanism. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Theoretical study on reactions of cyclic-N3 with NO, NO2 and Cl2

In this article, we report our detailed mechanistic study on the reactions of cyclic-N₃ with NO, NO₂ at the G3B3//B3LYP/6-311+G(d) and CCSD(T)/aug-cc-pVTZ//QCISD/6-311+G(d)+ZPVE levels; the reactions of cyclic-N₃ with Cl₂ was studied at the G3B3//B3LYP/6-311+G(d) and CCSD(T)/aug-cc-pVTZ//QCISD/6-31+G(d)+ZPVE levels. Both of the singlet and triplet potential-energy surfaces (PESs) of cyclic-N₃ + NO, cyclic-N₃ + NO₂ and the PES of cyclic-N₃ + Cl₂ have been depicted. The results indicate that on singlet PESs cyclic-N₃ can undergo the barrierless addition–elimination mechanism with NO and NO₂ forming the respective dominant products N₂ + ¹cyclic-NON and ¹NNO(O) + N₂. Yet the two reactions on triplet PESs are much less likely to take place under room temperature due to the high barriers. For the cyclic-N₃ + Cl₂ reaction, a Cl-abstraction mechanism was revealed that results in the product cyclic-N₃Cl + Cl with an overall barrier as high as 14.7 kcal/mol at CCSD(T)/aug-cc-pVTZ//QCISD/6-31+G(d)+ZPVE level. So the cyclic-N₃ radical could be stable against Cl₂ at low temperatures in gas phase. The present results can be useful for future experimental investigation on the title reactions.     

Formic acid catalyzed gas-phase reaction of H2O with SO3 and the reverse reaction: a theoretical study

The formic acid catalyzed gas‐phase reaction between H₂O and SO₃ and its reverse reaction are respectively investigated by means of quantum chemical calculations at the CCSD(T)//B3LYP/cc‐pv(T+d)z and CCSD(T)//MP2/aug‐cc‐pv(T+d)z levels of theory. Remarkably, the activation energy relative to the reactants for the reaction of H₂O with SO₃ is lowered through formic acid catalysis from 15.97 kcal mol^?1 to ?15.12 and ?14.83 kcal mol^?1 for the formed H₂O ??? SO₃ complex plus HCOOH and the formed H₂O ??? HCOOH complex plus SO₃, respectively, at the CCSD(T)//MP2/aug‐cc‐pv(T+d)z level. For the reverse reaction, the energy barrier for decomposition of sulfuric acid is reduced to ?3.07 kcal mol^?1 from 35.82 kcal mol^?1 with the aid of formic acid. The results show that formic acid plays a strong catalytic role in facilitating the formation and decomposition of sulfuric acid. The rate constant of the SO₃+H₂O reaction with formic acid is 10⁵ times greater than that of the corresponding reaction with water dimer. The calculated rate constant for the HCOOH+H₂SO₄ reaction is about 10^?13 cm³ molecule^?1 s^?1 in the temperature range 200–280 K. The results of the present investigation show that formic acid plays a crucial role in the cycle between SO₃ and H₂SO₄ in atmospheric chemistry.