Multi‐state multi‐reference Møller–Plesset second‐order perturbation theory for molecular calculations

This work presents multi‐state multi‐reference Møller–Plesset second‐order perturbation theory as a variant of multi‐reference perturbation theory to treat electron correlation in molecules. An effective Hamiltonian is constructed from the first‐order wave operator to treat several strongly interacting electronic states simultaneously. The wave operator is obtained by solving the generalized Bloch equation within the first‐order interaction space using a multi‐partitioning of the Hamiltonian based on multi‐reference Møller–Plesset second‐order perturbation theory. The corresponding zeroth‐order Hamiltonians are nondiagonal. To reduce the computational effort that arises from the nondiagonal generalized Fock operator, a selection procedure is used that divides the configurations of the first‐order interaction space into two sets based on the strength of the interaction with the reference space. In the weaker interacting set, only the projected diagonal part of the zeroth‐order Hamiltonian is taken into account. The justification of the approach is demonstrated in two examples: the mixing of valence Rydberg states in ethylene, and the avoided crossing of neutral and ionic potential curves in LiF. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Analytic derivatives for the XYG3 type of doubly hybrid density functionals: Theory,implementation, and assessment

We present a theoretical development of the equations required to perform an analytic geometry optimization of a molecular system using the XYG3 type of doubly hybrid (xDH) functionals. In contrast to the well‐established B2PLYP type of DH functionals, the energy expressions in the xDH functionals are constructed by using density and orbital information from another standard Kohn–Sham (KS) functional (e.g., B3LYP) for doing the self‐consistent field calculations. Thus, the xDH functionals are nonvariational in both the hybrid density functional part and the second‐order perturbation part, each of which requires formally to solve a coupled‐perturbed KS equation. An implementation is reported here which combines the two parts by defining a total Lagrangian such that only a single set of the Z‐vector equations need to be solved. The computational cost with our implementation is of the same order as those for the conventional Møller–Plesset theory to the second order (MP2) and B2PLYP. Systematic test calculations are provided for covalently bonded molecules as well as compounds involving the intramolecular nonbonded interactions for the main group elements. Satisfactory performance of the xDH functionals demonstrates that the extra computer time on top of the conventional KS procedure is well‐invested, in particular, when the standard KS functionals and MP2 as well, are problematic. © 2013 Wiley Periodicals, Inc.     

Parallel pseudospectral electronic structure: II. Localized Møller–Plesset calculations

We have developed a parallel version of our pseudospectral localized Møller–Plesset electronic structure code. We present timings for molecules up to 1010 basis functions and parallel speedup for molecules in the range of 260–658 basis functions. We demonstrate that the code is scalable; that is, a larger number of nodes can be efficiently utilized as the size of the molecule increases. By taking advantage of the available distributed memory and disk space of a scalable parallel computer, the parallel code can calculate LMP2 energies of molecules too large to be done on workstations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1030–1038, 1998     

Natural bond orbital‐based energy density analysis for correlated methods: Second‐order Møller–Plesset perturbation and coupled‐cluster singles and doubles

Natural bond orbital‐based energy density analysis (NBO‐EDA), which split energies into atomic and bonding contributions, is proposed for correlated methods such as coupled‐cluster singles and doubles (CCSD) and second‐order Møller–Plesset (MP2) perturbation. Applying NBO‐EDA for CCSD and MP2 to ethylene and the Diels–Alder reaction, we are successful in obtaining useful knowledge regarding electron correlation of π‐ and σ‐type orbitals, and clarifying the difference of the reaction barriers and heat of reaction calculated by CCSD and MP2. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

气相中环丁烯负离子与N2O反应机理的理论研究

采用B3LYP 和MP2两种计算方法,在6-31++G(d, p)的基组下,对气相中环丁烯负离子与N2O反应的微观机理进行了较为系统的计算研究。结果表明,该反应存在两条反应通道,每条反应通道又包含着三条反应路径,产物分别为乙烯基重氮甲基负离子与甲醛,同时也应能检测到少量的环丁烯酮负离子及N2等产物。其中,通道1是主反应通道,路径1为主反应路径,路径3是路径1、2的竞争反应。理论计算结果与实验预测基本一致。     

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.     

Dynamic hyperpolarizabilities in Møller–Plesset perturbation theory

As a formulation for calculating the dynamic polarizabilities and hyperpolarizabilities, two different types of the time‐dependent Møller–Plesset perturbation theory (MPPT) are presented: the MPPT in the quasienergy derivative method (QED–MPPT) and the MPPT in the energylike derivative method (ELD–MPPT). The explicit expressions for the response properties in each of these MPPT up to the quadratic response [μ, α(−ω₁, ω₁), β(−ω_σ, ω₁, ω₂)] at an arbitrary correlated order are given. Calculations of the dynamic polarizabilities and hyperpolarizabilities dependent on one frequency at the second‐order MPPT (MP2), in the QED method (QED–MP2) and in the ELD method (ELD–MP2), are examined for 10‐electron systems: hydrogen fluoride and neon. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 251–271, 1999     

Exact size consistency of multireference Møller–Plesset perturbation theory

Single‐reference closed‐shell Møller–Plesset perturbation theory is well known for its size consistency, a quality that is essential for consistent comparisons of calculations on molecules of different size. However, it is far from obvious whether this quality can be retained in the multireference case. In this work it is shown that an exactly size consistently generalization to multireference perturbation theory can be constructed. The central result is that the zeroth‐order Hamiltonian should be constructed using separate projection operators for each excitation level, i.e., it should contain no couplings between different excitation levels. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 549–558, 1999     

Mechanism of Gold(I)‐Catalyzed Conia‐ene Reaction of β‐Ketoesters with Alkynes: A DFT Study

Density functional calculations have been performed to comparatively investigate two possible pathways of Au(I)‐catalyzed Conia‐ene reaction of β‐ketoesters with alkynes. Our studies find that, under the assistance of trifluoromethanesulfonate (TfO), the β‐ketoester is the most likely to undergo Model II to isomerize into its enol form, in which TfO plays a proton transfer role through a 6‐membered ring transition state. The coordination of the Au(I) catalyst to the alkynes triple bond can enhance the eletrophilic capability and reaction activity of the alkynes moiety, which triggers the nucleophilic addition of the enol moiety on the alkynes moiety to give a vinyl‐Au intermediate. This cycloisomerizaion step is exothermal by 21.3 kJ/mol with an energy barrier of 56.0 kJ/mol. In the whole catalytic process, the protonation of vinyl‐Au is almost spontaneous, and the formation of enol is a rate‐limiting step. The generation of enol and the activation of Au(I) catalyst on the alkynes are the key reasons why the Conia‐ene reaction can occur in mild condition. These calculations support that Au(I)‐catalyzed Conia‐ene reactions of β‐ketoesters with alkynes go through the pathway 2 proposed by Toste.     

Iron‐Catalyzed C−H Activation with Propargyl Acetates: Mechanistic Insights into Iron(II) by Experiment,Kinetics, Mössbauer Spectroscopy,and Computation

An iron‐catalyzed C?H/N?H alkyne annulation was realized by using a customizable clickable triazole amide under exceedingly mild reaction conditions. A unifying mechanistic approach combining experiment, spectroscopy, kinetics, and computation provided strong support for facile C?H activation by a ligand‐to‐ligand hydrogen transfer (LLHT) mechanism. Combined Mössbauer spectroscopic analysis and DFT calculations were indicative of high‐spin iron(II) species as the key intermediates in the C?H activation manifold.     

A DFT study on a mutipathways,one product reaction: Initially divergent radical reactions reconverge to form a single product

The mechanism for initially divergent radical reactions reconverging to form a single product is studied using density functional theory calculations. The calculation results suggest that there are six possible pathways from reactants to products. The free energy barriers of the rate‐determining steps of each pathway are almost equal. Thus, different from usual reaction, the selectivity of this reaction is determined by the relative value of free energy barriers of the two competitive reactions, that is, cyclization and bimolecular trapping, rather than that of rate‐determining steps. In all reaction pathways, cyclization reaction is more competitive than bimolecular trapping reaction due to its low free energy barrier. In addition, the free energy barriers of bimolecular trapping reaction between Bu₃SnH and reactants are all lower than that of NC? C₆H₁₁. However, Bu₃SnH is not always suitable due to its large steric repulsion. © 2014 Wiley Periodicals, Inc.     

Viability of Möbius Topologies in [26]‐ and [28]Hexaphyrins

Recently, hexaphyrins have emerged as a promising class of π‐conjugated molecules that display a range of interesting electronic, optical, and conformational properties, including the formation of stable Möbius aromatic systems. Besides the Möbius topology, hexaphyrins can adopt a variety of conformations with Hückel and twisted Hückel topologies, which can be interconverted under certain conditions. To determine the optimum conditions for viable Möbius topologies, the conformational preferences of [26]‐ and [28]hexaphyrins and the dynamic interconversion between the Möbius and Hückel topologies were investigated by density functional calculations. In the absence of meso substituents, [26]hexaphyrin prefers a planar dumbbell conformation, strongly aromatic and relatively strain free. The Möbius topology is highly improbable: the most stable tautomer is 33 kcal mol^?1 higher in energy than the global minimum. On the other hand, the Möbius conformer of [28]hexaphyrin is only 6.5 kcal mol^?1 higher in energy than the most stable dumbbell conformation. This marked difference is due to aromatic stabilization in the Möbius 4n electron macrocycle as opposed to antiaromatic destabilization in the 4n+2 electron system, as revealed by several energetic, magnetic, structural, and reactivity indices of aromaticity. For [28]hexaphyrins, the computed activation barrier for interconversion between the Möbius aromatic and Hückel antiaromatic conformers ranges from 7.2 to 10.2 kcal mol^?1, in very good agreement with the available experimental data. The conformation of the hexaphyrin macrocycle is strongly dependent on oxidation state and solvent, and this feature creates a promising platform for the development of molecular switches.     

DielsAlder Cyclization of a Dihydropyridine: NMR Spectroscopy,X‐Ray Crystallography,and DFT Computations. Bent Aromatic Dimeric Clusters in the Solid Phase

Structural studies of the N‐(2,4‐dinitrophenyl) derivative of a Diels? Alder‐cyclized 1,2‐dihydropyridine both unequivocally established the polycyclic framework and revealed interesting distortions of aromatic structure and unique dimeric clustering of the aromatic entities in the solid state.     

Mechanistic Study on Rh‐Catalyzed Stereoselective CC/CH Activation of tert‐Cyclobutanols

A mechanistic study was performed on the Rh‐catalyzed stereoselective C?C/C?H activation of tert‐cyclobutanols. The present study corroborated the previous proposal that the reaction occurs by metalation, β‐C elimination, 1,4‐Rh transfer, C?O insertion, and a final catalyst‐regeneration step. The rate‐determining step was found to be the 1,4‐Rh transfer step, whereas the stereoselectivity‐determining step did not correspond to any of the aforementioned steps. It was found that both the thermodynamic stability of the product of the β‐C elimination and the kinetic feasibility of the 1,4‐Rh transfer and C?O insertion steps made important contributions. In other words, three steps (i.e., β‐C elimination, 1,4‐Rh transfer, and C?O insertion) were found to be important in determining the configurations of the two quaternary stereocenters.