Re‐examining the Mechanisms of Competing Pericyclic Reactions of 1,3,7‐Octatriene

DFT (both B3LYP and M06‐2X), CASSCF, and CASPT2 calculations were used to investigate competing [3, 3] and [3, 5] sigmatropic shifts and intramolecular [4+2] cycloaddition of 1,3,7‐octatriene. In accord with previous results on 1,5‐hexadiene, CASSCF calculations found both stepwise and concerted pathways for the [3, 3] rearrangement. For the competing [3, 5] sigmatropic rearrangement, CASSCF and CASPT2 calculations revealed three stepwise pathways with similar barriers. UB3LYP and UM06‐2X calculations predicted a different potential energy landscape: no stepwise [3, 3] pathway, only two competing [3, 5] sigmatropic shifts, and an intramolecular Diels–Alder cycloaddition/homolytic ring‐opening pathway. Significant lowering of barriers for all rearrangements was predicted for some 1,3,7‐octatrienes with substituents at the 4‐ and 7‐positions.     

Concerted and stepwise reaction mechanisms for the addition of ozone to acetylene: a computational study

The mechanism of the reaction between acetylene and ozone to form a primary ozonide (POZ) in the gas phase has been studied theoretically. The concerted pathway, HCCH + O3 --> POZ, proceeds via a biradicaloid transition state TS0. The stepwise pathway is a three-step reaction, HCCH + O3 --> M1 --> M2 --> POZ, involving two biradical TSs and two biradical intermediates M1 and M2. The segment of the global potential energy surface (PES) for the concerted pathway is characterized as a R-PES, which is obtained from the restricted (R) density functional theory and Hartree-Fock-based methods. The RDFT and RHF solutions of TS0 and O3 are unstable toward spin-symmetry breaking. The wave function instability for TS0 and O3 results in a discontinuity between the R-PES and the region of the global PES encompassing the biradical TSs and the intermediates of the stepwise pathway, which are characterized with unrestricted (U) methods. The global PES is characterized separately as an U(R)-PES using a combination of the R and U methods. Several different values of barriers for the concerted pathway and the energy of concert (Ec) can be estimated due to complications arising from the discontinuity between the R- and the U(R)-PES and the existence of two different RDFT and UDFT O3 equilibrium geometries. RCCSD(T)//RDFT predicts a barrier of 8.2 kcal/mol. U(R)CCSD(T)/U(R)DFT predicts a barrier of 13.8 kcal/mol for the concerted and 15.3 kcal/mol for the stepwise pathway. Comparison between the R-PES barrier to the concerted pathway and the U(R)-PES barrier to the stepwise pathway suggests the former to be the only significant mechanism. Consideration of the energy difference between TS1, the TS for the first step of the stepwise mechanism, and TS0 within the global PES leads to a significantly smaller Ec. Geometry optimization with CASSCF and energy point calculations with MRMP2 are employed to characterize TS0 and TS1. MRMP2//CASSCF predicts the energy level of TS1 to be higher than that of TS0 by 2 kcal/mol. Analysis of experimental and computational data based on the low estimate of Ec shows that the possibility of the stepwise pathway being a secondary channel at elevated temperatures cannot be ruled out.     

Re-examining the Mechanisms of Competing Pericyclic Reactions of 1,3,7-Octatriene

DFT (both B3LYP and M06-2X), CASSCF, and CASPT2 calculations were used to investigate competing [3,?3] and [3,?5] sigmatropic shifts and intramolecular [4+2] cycloaddition of 1,3,7-octatriene. In accord with previous results on 1,5-hexadiene, CASSCF calculations found both stepwise and concerted pathways for the [3,?3] rearrangement. For the competing [3,?5] sigmatropic rearrangement, CASSCF and CASPT2 calculations revealed three stepwise pathways with similar barriers. UB3LYP and UM06-2X calculations predicted a different potential energy landscape: no stepwise [3,?3] pathway, only two competing [3,?5] sigmatropic shifts, and an intramolecular Diels-Alder cycloaddition/homolytic ring-opening pathway. Significant lowering of barriers for all rearrangements was predicted for some 1,3,7-octatrienes with substituents at the 4- and 7-positions.     

乙醇醛光解离机理的理论研究

采用多参考态方法, 在CASPT2//CASSCF/6-311+G(2df, 2p) 水平上计算了乙醇醛(HOCH2CHO)分子在三个最低电子态(S0、S1和T1)上驻点的电子结构和解离势能面。结合势能面交叉点,探讨了HOCH2CHO与波长有关的光解离机理,分析了可能的光解离产物。结果表明, 在实验光解波长240 – 400 nm的激发下,HOCH2CHO分子主要发生S1态上的解离反应或通过S0和S1态之间的振动相互作用驰豫到基态,随之发生基态解离反应。C-C键断裂生成基态光解产物HOCH2 (2A′)+ HCO (2A′)是最主要的反应途径;而在一定波长下,生成CH3OH + CO的基态协同反应、脱醛基氢及脱羟基通道都是能量上可行的反应途径。本文的计算结果和实验观察一致。     

The 1deltag dioxygen ene reaction with propene: a density functional and multireference perturbation theory mechanistic study

This study aims to determine whether a balance between concerted and non-concerted pathways exists, and in particular to ascertain the possible role of diradical/zwitterion or peroxirane intermediates. Three non-concerted pathways, via 1) diradical or 2) peroxirane intermediates, and 3) by means of hydrogen-abstraction/radical recoupling, plus one concerted pathway (4), are explored. The intermediates and transition structures (TS) are optimized at the DFT(MPW1K), DFT(B3LYP) and CASSCF levels of theory. The latter optimizations are followed by multireference perturbative CASPT2 energy calculations. (1) The polar diradical forms from the separate reactants by surmounting a barrier (deltaE(++)(MPW1K)=12, deltaE++(B3LYP)=14, and deltaE(++)(CASPT2)=16 kcal mol(-1) and can back-dissociate through the same TS, with barriers of 11 (MPW1K) and 8 kcal mol(-1) (B3LYP and CASPT2). The diradical to hydroperoxide transformation is easy at all levels (deltaE(++)(MPW1K)<4, deltaE(++)(B3LYP)=1 and deltaE(++)(CASPT2)=1 kcal mol(-1)). (2) Peroxirane is attainable only by passing through the diradical intermediate, and not directly, due to the nature of the critical points involved. It is located higher in energy than the diradical by 12 kcal mol(-1), at all theory levels. The energy barrier for the diradical to cis-peroxirane transformation (deltaE(++)=14-16 kcal mol(-1)) is much higher than that for the diradical transformation to the hydroperoxide. In addition, peroxirane can very easily back-transform to the diradical (deltaE(++)<3 kcal mol(-1)). Not only the energetics, but also the qualitative features of the energy hypersurface, prevent a pathway connecting the peroxirane to the hydroperoxide at all levels of theory. (3) The last two-step pathway (hydrogen-abstraction by (1)O(2), followed by HOO-allyl radical coupling) is not competitive with the diradical mechanism. (4) A concerted pathway is carefully investigated, and deemed an artifact of restricted DFT calculations. Finally, the possible ene/[pi2+pi2] competition is discussed.     

Ab initio computational studies of conformationally restricted cope rearrangements. First examples of fully concerted allenyl cope rearrangements

Results of (8,8)CASPT2/6-31G//(8,8)CASSCF/6-31G level calculations on the potential surface for the conformationally restricted allenyl Cope rearrangements of syn-5-propadienylbicylco[2.1.0]pent-2-ene (14) and syn-6-propadienylbicyclo[2.1.1]hex-2-ene (15) are reported. Both are found to proceed through concerted pathways. Also included are the results of (6,6)CASPT2/6-31G//(6,6)CASSCF/6-31G level calculations on the Cope rearrangements of syn-5-ethenylbicyclo[2.1. 0]pent-2-ene (18), syn-6-ethenylbicyclo[2.1.1]hex-2-ene (19), and syn-7-vinylnorborene (20), which are found to involve diallylic diradical intermediates 26, 30, and 36, respectively. Previous studies have shown that the allenyl Cope rearrangement of 1,2, 6-heptatriene (1) to 3-methylene-1,5-hexadiene (2) involves a single transition structure that either proceeds to the monoallylic cyclohexane-1,4-diyl derivative 3 or bypasses 3 to form 2 directly. (4) More recently, the conformationally restricted allenyl Cope rearrangement of syn-7-allenylnorbornene (7) has also been found to involve tricyclic monoallylic cyclohexane-1,4-diyl intermediate 11. (7) The rearrangements of 14 and 15 appear to represent the first reported examples of fully concerted allenyl Cope rearrangements. Concertedness in these cases is ascribed to two parallel factors: (1) the relative instability of possible tricyclic diradical intermediates 16 and 17, compared to diradical intermediates 3 and 11 formed in the rearrangements of 1 and 7, respectively; and (2) the opportunity that exists to form sp-sp(2) sigma bonds in transition structures 21 and 23 that lead, respectively, to products 22 and 24. By contrast, only weaker sp(2)-sp(2) sigma bonds could form in unobserved concerted transition structures leading to products 28 and 32, formed in the nonconcerted rearrangements of 18 and 19.     

Theoretical study of structure, vibrational frequencies, and electronic spectra of dibenzofuran and its polychlorinated derivatives

Minimum structures and harmonic vibrational frequencies of dibenzofuran (DF), 2,3,7,8-tetrachlorodibenzofuran (TCDF), and octachlorodibenzofuran (OCDF) were calculated using the multiconfigurational complete active space self-consistent field (CASSCF) and density functional theory (DFT) methods. The electronic transitions in these compounds were studied via the single-state multireference second-order perturbation theory (CASPT2) based on the CASSCF(14,13) references, as well as the time-dependent DFT (TD-B3P86) employing the cc-pVDZ (CASSCF/CASPT2) and 6-31G(d,p) (TD-B3P86) basis sets. The B3P86 geometry and harmonic vibrational frequencies of ground state DF agree very well with the experimental data, and the CASSCF/CASPT2 excitation energies and oscillator strengths are accurate enough to provide a reliable assignment of the absorption bands in the 200-300 nm region. The close agreements with experiment for the parent DF give the present theoretical approaches a valuable credit in predicting the properties of the environmentally toxic polychlorinated congeners, which is all the more important considering the difficulties and hazards in obtaining the experimental data.     

X, A, B, C, and D states of the C6H5F+ ion studied using multiconfiguration wave functions

Electronic states of the C6H5F+ ion have been studied within C2v symmetry by using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with an atomic natural orbital basis. Vertical excitation energies (Tv) and relative energies (Tv') at the ground-state geometry of the C6H5F molecule were calculated for 12 states. For the five lowest-lying states, 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, geometries and vibrational frequencies were calculated at the CASSCF level, and adiabatic excitation energies (T0) and potential energy curves (PEC) for F-loss dissociations were calculated at the CASPT2//CASSCF level. On the basis of the CASPT2 T0 calculations, we assign the X, A, B, C, and D states of the ion to 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, respectively, which supports the suggested assignment of the B state to (2)(2)B1 by Anand et al. based on their experiments. Our CASPT2 Tv and Tv' calculations and our MRCI T0, Tv, and Tv' calculations all indicate that the 2(2)B1 state of C6H5F+ lies below 1(2)B2. By checking the relative energies of the asymptote products and checking the fragmental geometries and the charge and spin density populations in the asymptote products along the CASPT2//CASSCF PECs, we conclude that the 1(2)B1, 1(2)B2, and 1(2)A1 states of C6H5F+ correlate with C6H5+ (1(1)A1) + F (2P) (the first dissociation limit). The energy increases monotonically along the 1(2)B1 PEC, and there are barriers and minima along the 1(2)B2 and 1(2)A1 PECs. The predicted appearance potential value for C6H5+ (1(1)A1) is very close to the average of the experimental values. Our CASPT2//CASSCF PEC calculations have led to the conclusion that the 1(2)A2 state of C6H5F+ correlates with the third dissociation limit of C6H5+ (1(1)A2) + F (2P), and a preliminary discussion is presented.     

Can large active-space CASSCF calculation make sense to the reaction analysis of iron complex? A benchmark study of methane oxidation reaction by FeO+

A methane oxidation reaction by FeO⁺ cation was theoretically investigated based on the density functional theory (DFT) and the complete active-space self-consistent field (CASSCF) method as well as the coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) to explore the active-space dependency to computational analyses in such strongly correlated reaction systems. A small active-space CASSCF(5e in 5o) calculation, which only includes five 3d orbitals of the Fe atom in the active-space, showed remarkable difference both in energy and geometry compared to those computed by the DFT and CCSD(T) methods. Interestingly, a large active-space CASSCF(17e in 17o) calculation, which includes almost all the valence orbitals gives a qualitative agreement with either the DFT or the CCSD(T) results in the first half part of the reaction, although it varies from them in the latter half part. Therefore, it is indicated that the active-space dependency is serious in some part of the reaction and the small active-space CASSCF might lead a wrong discussion. We further investigated the optimized geometry of the intermediate complex with the small and the large active-space CASSCF methods as well as the CCSD(T) method, and found that the CASSCF(5e in 5o)-optimized geometry is considerably different from the others. In consequence, a small active-space CASSCF/CASPT2 calculation does not really work for such a strongly correlated reaction system even qualitatively, and a sophisticated assessment using the large active-space CASSCF/CASPT2 method will be indispensable. © 2018 Wiley Periodicals, Inc.     

Theoretical study on the potential energy surface of NC<Subscript>3</Subscript>P isomers

Density functional theory (DFT) calculations have been used to study the isomerization process in the NC₃P system. At the DFT/B3LYP/6-311G(d) level, 28 triplet and 28 singlet minima were obtained on their respective potential energy surfaces. The linear triplet ³NCCCP is the lowest-energy structure among the isomers. On the triplet PES, only linear isomers ³NCCCP, ³CNCCP, ³CCCNP, and ³CCNCP possess great kinetic and thermodynamic stabilities to exist under low-temperature conditions (such as in the dense interstellar clouds). At the same time, one chain-like and four three-membered-ring isomers on the singlet PES have been located with high kinetic and thermodynamic stabilities. Further CCSD(T)/6-311G(2df)//QCISD/6-311G(d), CCSD(T)/cc-pVTZ//DFT/B3LYP/cc-pVTZ, and CASPT2(14,12)/cc-pVQZ//CASSCF(14,12)/cc-p VQZ calculations are performed on the structures, frequencies, and energies of the relevant species. The bonding natures were analyzed and the results were compared with the analogous NC₃N and NC₂P molecules so as to aid their future experimental or astrophysical detection.     

多组态二级微扰理论计算CH3O2激发光谱以及CH3O2→CH3＋O2解离反应

在C_s对称性和aug-cc-pVTZ基组水平下, 采用全活化空间自洽场方法(CASSCF)研究了CH₃O₂自由基基态及其阴阳离子的12个低激发态. 为了进一步考虑动态电子相关效应, 采用二级多组态微扰理论(CASPT2)获得更加精确的能量值. 所有计算得到的电子态都是价电子态, 而且所得绝热激发能和电子亲和势与实验值非常接近.在CASPT2//CASSCF理论水平下计算了CH₃O₂从²A"和²A'电子态的CH₃O₂→CH₃＋O₂的解离反应的势能曲线(PECs). 优化得到的裂解产物的几何结构和能量与分别优化CH₃和O₂得到的结果进行比较, 从而确定裂解产物的电子态. 结果表明, 从²A"和²A'电子态的解离反应分别对应产物CH₃(²A")＋O₂(³A")和CH₃(²A")＋O₂(¹A").     

A cornucopia of cycloadducts: theoretical predictions of the mechanisms and products of the reactions of cyclopentadiene with cycloheptatriene

The potential cycloaddition reactions between cyclopentadiene and cycloheptatriene have been explored theoretically. B3LYP/6-31G was used to locate the transition states, intermediates, and products for concerted pathways and stepwise pathways passing through diradical intermediates. Interconversions of various cycloadducts through sigmatropic shifts were also explored. CASPT2/6-31G single point calculations were employed to obtain independent activation energy estimates. MM3 was also used to compute reaction energetics. Several bispericyclic cycloadditions in which two cycloadducts are linked by a sigmatropic shift have been identified. B3LYP predicts, in line with frontier molecular orbital predictions, that the [6+4] cycloaddition is the favored concerted pathway, but an alternative [4+2] pathway is very close in energy. By contrast, CASPT2 predicts that a [4+2] cycloaddition is the preferred pathway. B3LYP predicts that the lowest energy path to many of the cycloadducts will involve diradical intermediates, whereas CASPT2 predicts that each of the products of orbital symmetry allowed reactions will be reached most readily by closed shell processes-concerted cycloadditions and sigmatropic shift rearrangements of cycloadducts.     

A comparative electron correlation treatment in H(2)S-benzene dimer with DFT and wavefunction-based ab initio methods

The S₀ (X¹A′), T₁ (a³A″), S₁ (A¹A″), T₂ (b³A′), and S₂ (B¹A′) states of the (trans-)HONO molecule were studied by using the CASSCF and CASPT2 methods. The CASPT2(//CASPT2) adiabatic and vertical excitation energy values are in good agreement with available experimental data. The CASPT2//CASSCF potential energy curves (PECs) calculations indicate that: (i) all the five states correlate with the products of OH (X²Π) + NO (X²Π); (ii) along each of the T₁, S₁, and T₂ PECs there is a minimum followed by a transition state (barrier); and (iii) the repulsive S₂ PEC crosses the T₂, S₁, and T₁ PECs. The geometries and relative energies for the stationary points along these PECs were calculated at the CASPT2(//CASPT2) level, and the calculations predict that the barrier height value for S₁ is negligibly small (0.0018 eV).     

Unusual magnetic properties of mixed-valence system: multiconfigurational method theoretical study on Mn2+ cation

The geometry structure, dissociation energy, vibrational frequencies, and low-lying spin-state energy spectrum of Mn2+ are investigated by using ab initio CASSCF/ECP10MDF, complete active space self-consistent field/atomic natural orbital basis sets (CASSCF/ANO-s), CASPT2/ECP10MDF, and second-order perturbation theory with CASSCF reference function/atomic natural orbital basis sets (CASPT2/ANO-s) levels of theory. For the ground state the dissociation energy of 1.397 eV calculated at the CASPT2/ANO-s level supports Jarrlod's experimental value of 1.39 eV. The equilibrium bond length and vibrational frequency are 2.940 A calculated at the CASPT2/ANO-s level of theory and 214.4 cm-1 calculated at the CASSCF/ANO-s level of theory, respectively. On the basis of the mixed-valence model, the Heisenberg exchange constant J(-71.2 cm-1) and the double-exchange constant B(647.7 cm-1) are extracted explicitly from the low-lying energy spectrum calculated at the higher levels of theory. The magnetic competition between the weaker Heisenberg exchange interactions and the stronger double-exchange interactions makes the ground state a 12Sigmag+ state, consistent with electron paramagnetic resonance experimental observation, which explains unusual magnetic properties of Mn2+, quite different from the antiferromagnetic ground state of Mn2 and Cr2. On the other hand, the results calculated at the higher levels of theory show the consistent antiferromagnetic Heisenberg exchange interactions between 3d-3d for Cr2, Mn2+, and Mn2.     

Experimental and theoretical study of 2,6-difluorophenylnitrene, its radical cation, and their rearrangement products in argon matrices.

2,6-Difluorophenylnitrene was reinvestigated both experimentally, in Ar matrices at 10 K, and computationally, by DFT and CASSCF/CASPT2 calculations. Almost-pure samples of both neutral rearrangement products (the bicyclic azirine and the cyclic ketenimine) of a phenylnitrene were prepared and characterized for the first time. These samples were then subjected to X-irradiation in the presence of CH2Cl2 as an electron scavenger, which led to ionization of the neutral intermediates. Thereby, it was shown that only the phenylnitrene and the cyclic ketenimine yield stable radical cations, whereas the bicyclic azirine decays to both of these compounds on ionization. The cyclic ketenimine yields a novel aromatic azatropylium-type radical cation. The electronic structure of the title compound is discussed in detail, and its relation to those of the iso-pi-electronic benzyl radical and phenylcarbene is traced.     

Thermal [1,3] sigmatropic rearrangements of bicyclic and tricyclic vinylcyclobutanes: a gray zone between the concerted and stepwise extremes

Four typical thermal [1,3] sigmatropic rearrangements of bicyclic and tricyclic vinylcyclobutanes and one fancied analogous reaction (R2 in Scheme 1) were examined using CASSCF, CASPT2 and CAS+1+2 methods to discern the reaction mechanisms. Computed results indicate that it is difficult to simply designate these reactions as traditional single-step concerted or stepwise mechanisms, but a situation locating between these two extremes seems to be reasonable. The extent the reaction exhibits as a single-step concerted or stepwise path is much dependent on the geometrical constraints of reactant. For example, the system with three-member ring will tend to behave like a single-step concerted process, where only one rotation movement around C–C bond could be found when the bridged C–C is broken. However, the species with four-member ring will be much closer to the stepwise mechanism involving diradical varieties, because there are two different rotation movements exist when the bridged C–C is broken. Our calculation will also rationalize that only suprafacial retention product could be yielded for the thermal [1,3] sigmatropic rearrangement of tricyclic vinylcyclobutane.