Theoretical studies on the electrocyclic reactions of bis(allene) and vinylallene. Role of allene group

The reaction mechanisms of the electrocyclic ring closure of bis(allene) and vinylallene were studied by ab initio MO methods. The conrotatory and disrotatory pathways of the electrocyclic reactions from bis(allene) to bis(methylene)cyclobutene were determined by a CASSCF method. The transition state on the conrotatory pathway is 26.8 kcal/mol above bis(allene) and about 23 kcal/mol lower than that on the disrotatory pathway at a MRMP calculation level. The activation energy on the conrotatory pathway is lower by 23 kcal/mol than that of the electrocyclic reaction of butadiene. This lower energy barrier comes from the interactions of the "side pi orbitals" of the allene group. The interaction of the "vertical pi orbitals" of the allene group is predominant at the early stage of the reaction. The activation energy of the electrocyclic reaction of vinylallene is about 8.5 kcal/mol higher than that on the conrotatory pathway of bis(allene).     

A comparative assessment of the perturbative and renormalized coupled cluster theories with a noniterative treatment of triple excitations for thermochemical kinetics, including a study of basis set and core correlation effects

The CCSD, CCSD(T), and CR-CC(2,3) coupled cluster methods, combined with five triple-zeta basis sets, namely, MG3S, aug-cc-pVTZ, aug-cc-pV(T+d)Z, aug-cc-pCVTZ, and aug-cc-pCV(T+d)Z, are tested against the DBH24 database of diverse reaction barrier heights. The calculations confirm that the inclusion of connected triple excitations is essential to achieving high accuracy for thermochemical kinetics. They show that various noniterative ways of incorporating connected triple excitations in coupled cluster theory, including the CCSD(T) approach, the full CR-CC(2,3) method, and approximate variants of CR-CC(2,3) similar to the triples corrections of the CCSD(2) approaches, are all about equally accurate for describing the effects of connected triply excited clusters in studies of activation barriers. The effect of freezing core electrons on the results of the CCSD, CCSD(T), and CR-CC(2,3) calculations for barrier heights is also examined. It is demonstrated that to include core correlation most reliably, a basis set including functions that correlate the core and that can treat core-valence correlation is required. On the other hand, the frozen-core approximation using valence-optimized basis sets that lead to relatively small computational costs of CCSD(T) and CR-CC(2,3) calculations can achieve almost as high accuracy as the analogous fully correlated calculations.     

Application of renormalized coupled-cluster methods to potential function of water

The goal of this paper is to examine the performance of the conventional and renormalized single-reference coupled-cluster (CC) methods in calculations of the potential energy surface of the water molecule. A comparison with the results of the internally contracted multi-reference configuration interaction calculations including the quasi-degenerate Davidson correction (MRCI(Q)) and the spectroscopically accurate potential energy surface of water resulting from the use of the energy switching (ES) approach indicates that the relatively inexpensive completely renormalized (CR) CC methods with singles (S), doubles (D), and a non-iterative treatment of triples (T) or triples and quadruples (TQ), such as CR-CCSD(T), CR-CCSD(TQ), and the recently developed rigorously size extensive extension of CR-CCSD(T), termed CR-CC(2,3), provide substantial improvements in the results of conventional CCSD(T) and CCSD(TQ) calculations at larger internuclear separations. It is shown that the CR-CC(2,3) results corrected for the effect of quadruply excited clusters through the CR-CC(2,3)+Q approach can compete with the highly accurate MRCI(Q) data. The excellent agreement between the CR-CC(2,3)+Q and MRCI(Q) results suggests ways of improving the global potential energy surface of water resulting from the use of the ES approach in the regions of intermediate bond stretches and intermediate energies connecting the region of the global minimum with the asymptotic regions. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Potential energy curve for isomerization of N2H2 and C2H4 using the improved virtual orbital multireference Møller-Plesset perturbation theory

Multireference M?ller-Plesset (MRMP) perturbation theory [K. Hirao, Chem. Phys. Lett. 190, 374 (1992)] is modified to use improved virtual orbitals (IVOs) and is applied to study ground state potential energy curves for isomerization and dissociation of the N2H2 and C2H4 molecules. In contrast to traditional MRMP or multistate multiconfiguration quasidegenerate perturbation theory where the reference functions are obtained from (often difficult to converge) state averaged multiconfiguration self-consistent field methods, our reference functions are represented in terms of computationally efficient IVOs. For convenience in comparisons with other methods, a first order complete active space configuration interaction (CASCI) calculation with the IVOs is followed by the use of the IVOs in MRMP to incorporate residual electron correlation effects. The potential energy curves calculated from the IVO-MRMP method are compared with computations using state-of-the-art coupled cluster singles and doubles (CCSD) methods and variants thereof to assess the efficacy of the IVO-MRMP scheme. The present study clearly demonstrates that unlike the CCSD and its variants, the IVO-MRMP approach provides smooth and reliable ground state potential energy curves for isomerization of these systems. Although the rigorously size-extensive completely renormalized CC theory with noniterative triples corrections (CR-CC(2,3)) likewise provides relatively smooth curves, the CR-CC(2,3) calculations overestimate the cis-trans barrier height for N2H2. The ground state spectroscopic constants predicted by the IVO-CASCI method agree well with experiment and with other highly correlated ab initio methods.     

A theoretical study of cyclohexyne addition to carbonyl-Cα bonds: allowed and forbidden electrocyclic and nonpericyclic ring-openings of strained cyclobutenes

The mechanism of cyclohexyne insertion into a C(O)-C(α) bond of cyclic ketones, explored experimentally by the Carreira group, has been investigated using density functional theory. B3LYP and M06-2X calculations were performed in both gas phase and THF (CPCM, UAKS radii). The reaction proceeds through a stepwise [2 + 2] cycloaddition of cyclohexyne to the enolate, followed by three disparate ring-opening possibilities of the cyclobutene alkoxide to give the product: (1) thermally allowed conrotatory electrocyclic ring-opening, (2) thermally forbidden disrotatory electrocyclic ring-opening, or (3) nonpericyclic C-C bond cleavage. Our computational results for the model alkoxide and potassium alkoxide systems show that the thermally allowed electrocyclic ring-opening pathway is favored by less than 1 kcal/mol. In more complex systems containing a potassium alkoxide (e-f), the barrier of the allowed conrotatory ring-opening is disfavored by 4-8 kcal/mol. This suggests that the thermodynamically more stable disrotatory product can be formed directly through a "forbidden" pathway. Analysis of geometrical parameters and atomic charges throughout the ring-opening pathways provides evidence for a nonpericyclic C-C bond cleavage, rather than a thermally forbidden disrotatory ring-opening. A true forbidden disrotatory ring-opening transition structure was computed for the cyclobutene alcohol; however, it was 19 kcal/mol higher in energy than the allowed conrotatory transition structure. An alternate mechanism in which the disrotatory product forms via isomerization of the conrotatory product was also explored for the alkoxide and potassium alkoxide systems.     

Thermal isomerization of tricyclo[4.1.0.0(2,7)]heptane and bicyclo[3.2.0]hept-6-ene through the (E,Z)-1,3-cycloheptadiene intermediate

The thermal isomerization of tricyclo[4.1.0.0(2,7)]heptane and bicyclo[3.2.0]hept-6-ene was studied using ab initio methods at the multiconfiguration self-consistent field level. The lowest-energy pathway for thermolysis of both structures proceeds through the (E,Z)-1,3-cycloheptadiene intermediate. Ten transition states were located, which connect these three structures to the final product, (Z,Z)-1,3-cycloheptadiene. Three reaction channels were investigated, which included the conrotatory and disrotatory ring opening of tricyclo[4.1.0.0(2,7)]heptane and bicyclo[3.2.0]hept-6-ene and trans double bond rotation of (E,Z)-1,3-cycloheptadiene. The activation barrier for the conrotatory ring opening of tricyclo[4.1.0.0(2,7)]heptane to (E,Z)-1,3-cycloheptadiene was found to be 40 kcal mol(-1), while the disrotatory pathway to (Z,Z)-1,3-cyclohetpadiene was calculated to be 55 kcal mol(-1). The thermolysis of bicyclo[3.2.0]hept-6-ene via a conrotatory pathway to (E,Z)-1,3-cycloheptadiene had a 35 kcal mol(-1) barrier, while the disrotatory pathway to (Z,Z)-1,3-cyclohetpadiene had a barrier of 48 kcal mol(-1). The barrier for the isomerization of (E,Z)-1,3-cycloheptadiene to bicyclo[3.2.0]hept-6-ene was found to be 12 kcal mol(-1), while that directly to (Z,Z)-1,3-cycloheptadiene was 20 kcal mol(-1).     

Computational and Experimental Evidence of Two Competing Thermal Electrocyclization Pathways for Vinylheptafulvene

The thermal electrocyclic ring‐closure reaction of vinylheptafulvene (VHF) to form dihydroazulene (DHA) is elucidated herein by using DFT and ¹H NMR spectroscopy. Two different transition states were found computationally; one corresponds to a disrotatory pathway, which is allowed according to the Woodward–Hoffmann selection rules, whereas the other corresponds to a conrotatory pathway. The conrotatory pathway is found to be zwitterionic in the transition state, whereas the disrotatory transition state varies in zwitterionic character depending on solvent and substituents in the molecular framework. The conrotatory and disrotatory transition states are found to have similar energy and their relative stability varies with solvent polarity and functionalization at the C1 position. To support these findings, we chemically ring‐opened diastereomerically pure 1‐(benzothiazol‐2‐yl)‐DHA to give the VHF form, then subsequently thermally reconverted the VHF to DHA in a range of solvents with various polarities. We found that, depending on solvent polarity, different ratios of anti‐ and syn‐diastereoisomers of DHA were formed in a systematic manner, which supports the existence of two distinct thermal ring‐closure pathways for VHF.     

Performance of the correlation consistent composite approach for transition states: a comparison to G3B theory

The correlation consistent composite approach (ccCA) was applied to the prediction of reaction barrier heights (i.e., transition state energy relative to reactants and products) for a standard benchmark set of reactions comprised of both hydrogen transfer reactions and nonhydrogen transfer reactions (i.e., heavy-atom transfer, SN2, and unimolecular reactions). The ccCA method was compared against G3B for the same set of reactions. Error metrics indicate that ccCA achieves "chemical accuracy" with a mean unsigned error (MUE) of 0.89 kcal/mol with respect to the benchmark data for barrier heights; G3B has a mean unsigned error of 1.94 kcal/mol. Further, the greater accuracy of ccCA for predicted reaction barriers is compared to other benchmarked literature methods, including density functional (BB1K, MUE=1.16 kcal/mol) and wavefunction-based [QCISD(T), MUE=1.10 kcal/mol] methods.     

Electrocyclic ring opening of cis-bicyclo[m.n.0]alkenes: the anti-Woodward-Hoffmann quest

The dubbed anti-Woodward-Hoffmann ring-opening reaction of cis-bicyclo[4.2.0]oct-7-ene to yield cis,cis-cycloocta-1,3-diene has been intensively studied with robust, high-level computational methods. This reaction has been found to proceed through a conrotatory allowed pathway to afford cis,trans-cycloocta-1,3-diene followed by E to Z isomerization, instead of a disrotatory forbidden pathway, as suggested. Computational calculations of kinetic isotope effects are consistent with this interpretation and the experimental values. The study of lower bicyclic homologues with [3.2.0], [2.2.0] and [2.1.0] skeletons indicates the feasibility of a mechanistic change towards the anti-Woodward-Hoffmann disrotatory path. This is clearly favored for the ring opening of the highly strained cis-bicyclo[2.1.0]pent-2-ene and is highly competitive with the conrotatory path for cis-bicyclo[2.2.0]hex-2-ene. Therefore, the rearrangement of the smallest bicyclic cyclobutene is predicted computationally to be an anti-Woodward-Hoffmann disrotatory electrocyclic ring-opening reaction.     

Extension of the renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed hamiltonian to open-shell systems: a benchmark study

The recently formulated completely renormalized coupled-cluster method with singles, doubles, and noniterative triples, exploiting the biorthogonal form of the method of moments of coupled-cluster equations (Piecuch, P.; W?och, M. J. Chem. Phys. 2005, 123, 224105; Piecuch, P.; W?och, M.; Gour, J. R.; Kinal, A. Chem. Phys. Lett. 2006, 418, 467), termed CR-CC(2,3), is extended to open-shell systems. Test calculations for bond breaking in the OH radical and the F2+ ion and singlet-triplet gaps in the CH2, HHeH, and (HFH)- biradical systems indicate that the CR-CC(2,3) approach employing the restricted open-shell Hartree--Fock (ROHF) reference is significantly more accurate than the widely used CCSD(T) method and other noniterative triples coupled-cluster approximations without making the calculations substantially more expensive. A few molecular examples, including the activation energies of the C2H4 + H --> C2H5 forward and reverse reactions and the triplet states of the CH2 and H2Si2O2 biradicals, are used to show that the dependence of the ROHF-based CR-CC(2,3) energies on the method of canonicalization of the ROHF orbitals is, for all practical purposes, negligible.     

Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian

Completely renormalized (CR) coupled-cluster (CC) approaches, such as CR-CCSD(T), in which one corrects the standard CC singles and doubles (CCSD) energy for the effects of triply (T) and other higher-than-doubly excited clusters [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], are reformulated in terms of the left eigenstates Phimid R:L of the similarity-transformed Hamiltonian of CC theory. The resulting CR-CCSD(T)(L) or CR-CC(2,3) and other CR-CC(L) methods are derived from the new biorthogonal form of the method of moments of CC equations (MMCC) in which, in analogy to the original MMCC theory, one focuses on the noniterative corrections to standard CC energies that recover the exact, full configuration-interaction energies. One of the advantages of the biorthogonal MMCC theory, which will be further analyzed and extended to excited states in a separate paper, is a rigorous size extensivity of the basic ground-state CR-CC(L) approximations that result from it, which was slightly violated by the original CR-CCSD(T) and CR-CCSD(TQ) approaches. This includes the CR-CCSD(T)(L) or CR-CC(2,3) method discussed in this paper, in which one corrects the CCSD energy by the relatively inexpensive noniterative correction due to triples. Test calculations for bond breaking in HF, F(2), and H(2)O indicate that the noniterative CR-CCSD(T)(L) or CR-CC(2,3) approximation is very competitive with the standard CCSD(T) theory for nondegenerate closed-shell states, while being practically as accurate as the full CC approach with singles, doubles, and triples in the bond-breaking region. Calculations of the activation enthalpy for the thermal isomerizations of cyclopropane involving the trimethylene biradical as a transition state show that the noniterative CR-CCSD(T)(L) approximation is capable of providing activation enthalpies which perfectly agree with experiment.     

Ab initio study of the pathways and barriers of tricyclo[4.1.0.0(2,7)]heptene isomerization

The thermal isomerization of tricyclo[4.1.0.0(2,7)]heptene has been studied using computational chemistry with structures determined at the MCSCF level and energies at the MRMP2 level. Both the allowed conrotatory and forbidden disrotatory pathways have been elucidated resulting in cycloheptatriene isomers. Four reaction channels are available for the conrotatory pathway depending on which bond breaks first in the bicyclobutane moiety leading to enantiomeric pairs of (E,Z,Z)-1,3,5-cycloheptatriene and (Z,E,Z)-1,3,5-cycloheptatriene intermediates. The activation barrier is calculated to be 31.3 kcal·mol?1 for two channels and 37.5 kcal·mol?1 for the other two. The lower activation barrier leading to the (E,Z,Z)-1,3,5-cycloheptatriene enantiomeric pair is proposed to be due to resonance within the transition state. The same behavior was observed for the disrotatory pathway with activation barriers of 42.0 kcal·mol?1 and 55.1 kcal·mol?1 for the two channels, again with one transition state resonance stabilized. The barriers for trans double bond rotation of the intermediate cycloheptatrienes are determined to be 17.1 and 17.4 kcal·mol?1, about 5 kcal·mol?1 more than that for the seven carbon diene (E,Z)-1,3-cycloheptadiene. The electrocyclic ring closure of the trans cycloheptatrienes have been modeled and barriers determined to be 11.1 and 11.9 kcal·mol?1 for the formation of bicyclo[3.2.0]hepta-2,6-diene. This structure was previously reported as the end product for thermolysis of the parent tricyclo[4.1.0.0(2,7)]heptene. The thermodynamically more stable cycloheptatriene can be formed from bicyclo[3.2.0]hepta-2,6-diene through a two step process with a calculated pseudo first-order barrier of 36.4 kcal·mol?1. The trans-cycloheptatrienes reported herein are the first characterization of a small seven-membered ring triene with a trans double bond.     

Perturbing π-clouds with Substituents to Study the Effects on Reaction Dynamics of gauche-1,3-Butadiene to Bicyclobutane Electrocyclization

The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (−F) and donating (−CH₃) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the −CH₃ substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to −F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with −F or −CH₃, the conversion proceeds via the conrotatory pathway.     

Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

The recently developed [P. Piecuch and M. Wloch, J. Chem. Phys. 123, 224105 (2005)] size-extensive left eigenstate completely renormalized (CR) coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bond-breaking reactions between C, H, Si, and Cl (except H2) and the H2Si[Double Bond]SiH2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R=1-3Re for all of the studied single bond-breaking reactions, where R and Re are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1 mhartree in the region R=1-3Re of the H-SiH3, H-Cl, H3Si-SiH3, Cl-CH3, H-CH3, and H3C-SiH3 bonds. The maximum errors are -2.1, 1.6, and 1.6 mhartree in the R=1-3Re region of the H3C-CH3, Cl-Cl, and H3Si-Cl bonds, respectively, while the discrepancy for the H2Si[Double Bond]SiH2 double bond-breaking reaction is 6.6 (8.5) mhartree at R=2(3)Re. CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CR-CC(2,3) termed CR-CCSD(T).     

Reversal of Orbital Symmetry Control in Electrocyclic Ring Closures through Craig‐Möbius Aromaticity

Experimentalists are challenged to find the organometallic thermal electrocyclizations that are computationally predicted to proceed with opposite stereoselectivity compared to their metal‐free parent 4n and 4n+2 π‐electron systems. While ring closure of, for example, s‐cis‐butadiene proceeds conrotatory, an iron alkyl complex formed by replacement of a (CH) unit by an [FeH] metal fragment results in a disrotatory electrocyclization.     

Development of a 3-body:many-body integrated fragmentation method for weakly bound clusters and application to water clusters (H2O)(n = 3-10, 16, 17)

A 3-body:many-body integrated quantum mechanical (QM) fragmentation method for non-covalent clusters is introduced within the ONIOM formalism. The technique captures all 1-, 2-, and 3-body interactions with a high-level electronic structure method, while a less demanding low-level method is employed to recover 4-body and higher-order interactions. When systematically applied to 40 low-lying (H(2)O)(n) isomers ranging in size from n = 3 to 10, the CCSD(T):MP2 3-body:many-body fragmentation scheme deviates from the full CCSD(T) interaction energy by no more than 0.07 kcal mol(-1) (or <0.01 kcal mol(-1) per water). The errors for this QM:QM method increase only slightly for various low-lying isomers of (H(2)O)(16) and (H(2)O)(17) (always within 0.13 kcal mol(-1) of the recently reported canonical CCSD(T)/aug-cc-pVTZ energies). The 3-body:many-body CCSD(T):MP2 procedure is also very efficient because the CCSD(T) computations only need to be performed on subsets of the cluster containing 1, 2, or 3 monomers, which in the current context means the largest CCSD(T) calculations are for 3 water molecules, regardless of the cluster size.     

A pseudopotential-based composite method: the relativistic pseudopotential correlation consistent composite approach for molecules containing 4d transition metals (Y-Cd)

The correlation consistent composite approach (ccCA) has proven to be an effective first-principles-based composite approach for main group and first-row transition metal species. By combining relativistic pseudopotentials and ccCA, accurate energetic and thermodynamic data for heavier elements, including transition metals, is obtainable. Relativistic pseudopotential ccCA (rp-ccCA) was formulated and tested on 25 molecules from the G3∕05 set that contain 4p elements (Ga-Kr). A 32.5% time savings was obtained using rp-ccCA, relative to ccCA employing all-electron basis sets. When implementing rp-ccCA to compute dissociation energies and enthalpies of formation for molecules from the 4p block, rp-ccCA results in a mean absolute deviation of 0.89 kcal?mol(-1) from experimental data. rp-ccCA was also applied to a set of 30 4d transition metal-containing molecules, ranging from diatomics to Mo(CO)(6), and enthalpies of formation for these species were obtained with a mean absolute deviation of 2.89 kcal mol(-1) in comparison to experimental data. Based on quality of the experimentally available enthalpies of formation, where the average value of reported experimental error bars is 3.43 kcal mol(-1), rp-ccCA is within transition metal chemical accuracy for the 4d molecule set. rp-ccCA is a pseudopotential-based composite method for transition metals and is shown to yield accurate thermodynamic results for molecules containing heavy elements Ga-Kr and Y-Cd.     

Conformational studies by dynamic NMR. 78. Stereomutation of the helical enantiomers of trigonal carbon diaryl-substituted compounds: dimesitylketone, dimesitylthioketone, and dimesitylethylene.

The free energies of activation for the enantiomerization of the title compounds (Mes2C = X, Mes = 2,4,6-trimethylphenyl) were determined by dynamic NMR to be 4.6, 6.5, and 9.2 kcal mol-1 for X = O, S, and CH2, respectively. Single-crystal X-ray diffraction showed that the structure of dimesitylketone is that of a propeller (C2 symmetry) with the mesityl rings twisted by 50 degrees with respect to the plane of carbonyl. The same structure was predicted by molecular mechanics calculations, which also produced good agreement between computed and experimental barriers for a dynamic process where a disrotatory one-ring flip pathway reverses the helicity of the conformational enantiomers. Solid-state NMR spectra indicated that the enantiomerization barrier in the crystal must be much higher (at least 19 kcal mol-1) than that in solution. Contrary to the case of dimesitylketone, the calculated barrier of dimesitylethylene agrees better with the experimental value if the enantiomerization process is assumed to be a conrotatory two-ring flip pathway.