Woodward-Hoffmann rules in density functional theory: initial hardness response

The Woodward-Hoffmann rules for pericyclic reactions, a fundamental set of reactivity rules in organic chemistry, are formulated in the language of conceptual density functional theory (DFT). DFT provides an elegant framework to introduce chemical concepts and principles in a quantitative manner, partly because it is formulated without explicit reference to a wave function, on whose symmetry properties the Woodward-Hoffmann [J. Am. Chem. Soc. 87, 395 (1965)] rules are based. We have studied the initial chemical hardness response using a model reaction profile for two prototypical pericyclic reactions, the Diels-Alder cycloaddition of 1,3-butadiene to ethylene and the addition of ethylene to ethylene, both in the singlet ground state and in the first triplet excited state. For the reaction that is thermally allowed but photochemically forbidden, the initial hardness response is positive along the singlet reaction profile. (By contrast, for the triplet reaction profile, a negative hardness response is observed.) For the photochemically allowed, thermally forbidden reaction, the behavior of the chemical hardness along the initial stages of the singlet and triplet reaction profiles is reversed. This constitutes a first step in showing that chemical concepts from DFT can be invoked to explain results that would otherwise require invoking the phase of the wave function.     

Arylazide cycloaddition to methyl propiolate: DFT-based quantitative prediction of regioselectivity

Several 1(4-substituted)phenyl-4- or 5-methoxycarbonyl-1,2,3-triazoles have been synthesized by 1,3-dipolar cycloaddition of the corresponding arylazides to methyl propiolate in carbon tetrachloride. The regioselectivity of these reactions cannot be rationalized on the basis of the electronic demands of the reactants or frontier molecular-orbital theory. Therefore, we applied to this problem a quantitative formulation of the HSAB principle to this problem developed within density functional theory. Global and local reactivity indices were computed at B3LYP/6-311+G(d,p) level both in vacuo and in carbon tetrachloride (by the COSMO approach). The direction of charge transfer upon reactive encounter has been determined and the computed regioselectivity has been shown to be in good agreement with the experimental results. The relationship between computed and experimental data and how it is affected by the solvent have been discussed.     

H2S键合金属(II)咪唑卟啉配合物的结构、光谱和反应活性

选取8个典型的二价金属咪唑卟啉MP(M=Ca, Mg, Zn, Cu, Ni, Fe, Co, Mn; P代表咪唑卟啉)与H₂S(L)形成轴向金属配合物(L-MP; L-MP^*-L, P^*代表卟啉), 应用轨道和自旋概念密度泛函工具, 在优化构型的基础上, 通过自然键轨道(NBO)方法和前线轨道能级研究了它们的分子结构、光谱性质和反应活性. 模拟结果揭示L-MP和L-MP^*-L结构、光谱及其反应活性不同于其前体MP. MP排斥钙而选择镁; L对MP的结构影响较少, 与咪唑铁卟啉(FeP)能形成最稳定的单轴配合物(L-FeP), 其电子吸收光谱较前体FeP有显著的变化; 铁的亲核Fukui轨道指数值(f_Fe⁺)大于其他原子的Fukui指数, 且发生符号改变. 铁体系的自旋极化Fukui密度图也支持以上结论. 在这些典型的赤道键合配合物中, 金属M与N(S)原子之间的二级微扰相互作用能、自然电荷以及概念密度泛函指数等存在一系列线性关系. 以上结果可为理解内源性H₂S与血管性物质的相互作用机理提供启示.     

Investigation into the Regiochemistry of Some Pyrazoles Derived from 1,3‐Dipolar Cycloaddition of Methyl Methacrylate with Some Nitrilimines: A Combined Theoretical and Experimental Study

1,3‐Dipolar cycloaddition between methyl methacrylate as dipolarophile and some nitrilimines which were generated in situ afforded the new pyrazoles. The regiochemistry and reactivity of these reactions has been investigated on the basis of density functional theory (DFT)‐based reactivity indexes and activation energy calculations. The theoretical ¹³C NMR chemical shifts of the cycloadducts which were obtained by GIAO method were comparable with the observed values.     

Investigation into the Regiochemistry of 1,3‐Dipolar Cycloaddition of C,N‐Diphenyl Nitrone with Some Vinyl Sulfoximines as Dipolarophile: Theoretical Studies

The regiochemistry of 1,3‐dipolar cycloaddition reactions of C,N‐diphenyl nitrone with some vinyl sulfox‐ imines as dipolarophile was investigated using density functional theory (DFT)‐based reactivity indexes and activation energy calculations at B3LYP/6‐31G(d) level of theory. Analysis of the geometries and bond orders (BOs) at the TS structures associated with the different reaction pathways shows that these 1,3‐dipolar cycloaddition reactions occur via an asynchronous concerted mechanism. Analysis of the local electrophilicity and nucleophilicity indexes permits an interpretation about the regioselectivity of these 1,3‐dipolar cycloaddition reactions. The theoretical results obtained in the work clearly predict the regiochemistry of the isolated cycloadducts and agree to experimental outcomes.     

Excited‐State Proton Transfer and Intramolecular Charge Transfer in 1,3‐Diketone Molecules

The photophysical signature of the tautomeric species of the asymmetric (N,N‐dimethylanilino)‐1,3‐diketone molecule are investigated using approaches rooted in density functional theory (DFT) and time‐dependent DFT (TD‐DFT). In particular, since this molecule, in the excited state, can undergo proton transfer reactions coupled to intramolecular charge transfer events, the different radiative and nonradiative channels are investigated by making use of different density‐based indexes. The use of these tools, together with the analysis of both singlet and triplet potential energy surfaces, provide new insights into excited‐state reactivity allowing one to rationalize the experimental findings including different behavior of the molecule as a function of solvent polarity.     

Electronic Structure of N-Bridged High-Valent Diiron-Oxo

Density functional theory (DFT) and an advanced ab initio technique based on density matrix renormalization group (DMRG-CASPT2) were employed to investigate a reactive N-bridged high-valent diiron-oxo species involved in H-abstraction reactions. We studied in detail two important doublet states, the ground state with two iron(IV) centers and a mixed valence Fe^V-Fe^IV excited state. We found that the latter state is low-lying. Furthermore, its electronic structure and spin density imply that it has significantly higher H-abstraction reactivity than the ground state. This low-lying excited state might be the reason behind the high oxidation reactivity of this diiron-oxo species towards methane.     

Exploring the H-abstraction reactions of CHCl·-/CCl2·- with CX3H（X = F,Cl,Br and I） using the density functional theory method

Gas-phase hydrogen abstraction reactions have been compared using the popular density functional theory(DFT) functional BHandHLYP/aug-cc-pVTZ/RECP level of theory,on the basis of the model reaction CHCl·-/CCl2·-+ CX3H(X = F,Cl,Br and I).Our theoretical findings suggest the efficiency of the H-abstraction reactions induced by either CHCl·-or CCl2·-increases as the substrate is changed from CF3H to CI3H,and that CHCl·-has a higher activity in hydrogen abstraction than CCl2·-for a given substrate.The entropy effect at 298 K does not significantly change the trend in reactivity of the various reactions,which is in general controlled by the heights of activation energies △E≠.Therefore,we have explored the origin of the energy barriers △E≠ of the reactions using the activation strain model of chemical reactivity.     

Theoretical studies on phosphoraniminato derivatives of Keggin-type polyoxometalates [PW11O39{MVNPPh3}]3− (M = Fe,Ru): Electronic structures and bonding features

Transition metal phosphoraniminato derivatives of Keggin-type polyoxometalates(POMs) are important intermediates in N-transfer reactions.Density functional theory(DFT) has been employed to calculate the electronic structures,bonding features and redox properties of the iron and ruthenium phosphoraniminato derivatives of Keggin-type POMs,[PW11O39{MVNPPh3}] 3-(M = Fe,Ru).Our DFT calculations show that both anions have the same qualitative M-N single bond features.However,the calculations predict that the FeN system possesses a lower energy and more accessible metalnitrogen antibonding orbital than the RuN system.This results in a greater weakening of the Fe-N bond in the reduction process,and thus enhances its N-transfer reactivity.     

Universal mathematical identities in density functional theory: results from three different spin-resolved representations

This paper supersedes previous theoretical approaches to conceptual DFT because it provides a unified and systematic approach to all of the commonly considered formulations of conceptual DFT, and even provides the essential mathematical framework for new formulations. Global, local, and nonlocal chemical reactivity indicators associated with the "closed-system representation" ([N(alpha),N(beta),nu(alpha)(r),nu(beta)(r)]) of spin-polarized density functional theory (SP-DFT) are derived. The links between these indicators and the ones associated with the "open-system representation" ([mu(alpha),mu(beta),nu(alpha)(r),nu(beta)(r)]) are derived, including the spin-resolved Berkowitz-Parr identity. The Legendre transform to the "density representation" ([rho(alpha)(r),rho(beta)(r)]) is performed, and the spin-resolved Harbola-Chattaraj-Cedillo-Parr identities linking the density representation to the closed-system and open-system representations are derived. Taken together, these results provide the framework for understanding chemical reactions from both the electron-following perspective (using either the closed-system or the open-system representation) and electron-preceding perspective (density representation). A powerful matrix-vector notation is developed; with this notation, identities in conceptual DFT become universal. Specifically, this notation allows the fundamental identities in conventional (spin-free) conceptual DFT, the [N(alpha),N(beta)] representation, and the [N=N(alpha)+N(beta),N(S)=N(alpha)-N(beta)] representation to be written in exactly the same forms. In cases where spin transfer and electron transfer are coupled (e.g., radical+molecule reactions), we believe that the [N(alpha),N(beta)] representation may be more useful than the more common [N,N(S)] representation.     

Influence of Ligand Architecture on Oxidation Reactions by High‐Valent Nonheme Manganese Oxo Complexes Using Water as a Source of Oxygen

Mononuclear nonheme Mn^IV?O complexes with two isomers of a bispidine ligand have been synthesized and characterized by various spectroscopies and density functional theory (DFT). The Mn^IV?O complexes show reactivity in oxidation reactions (hydrogen‐atom abstraction and sulfoxidation). Interestingly, one of the isomers (L¹) is significantly more reactive than the other (L²), while in the corresponding Fe^IV?O based oxidation reactions the L²‐based system was previously found to be more reactive than the L¹‐based catalyst. This inversion of reactivities is discussed on the basis of DFT and molecular mechanics (MM) model calculations, which indicate that the order of reactivities are primarily due to a switch of reaction channels (σ versus π) and concomitant steric effects.     

DFT-HSAB prediction of regioselectivity in 1,3-dipolar cycloadditions: behavior of (4-substituted)benzonitrile oxides towards methyl propiolate

The regioselectivity of 1,3-dipolar cycloadditions between (4-substituted)benzonitrile oxides and methyl propiolate cannot be rationalized on the basis of the electron demand of the reactants or frontier molecular-orbital theory. To this problem, we have applied a quantitative formulation of the hard-soft acid-base principle developed within the density functional theory. Global and local reactivity indices were computed at B3LYP/6-311+G(d,p) level. The details of charge transfer upon the reactive encounter have been elucidated, and the computed regioselectivity has been shown to be in good agreement with experimental data.     

New Insights into the Reactivity of Cisplatin with Free and Restrained Nucleophiles: Microsolvation Effects and Base Selectivity in Cisplatin–DNA Interactions

The reactivity of cisplatin towards different nucleophiles has been studied by using density functional theory (DFT). Water was considered first to analyze the factors that govern the transformation of cisplatin into more electrophilic aquated species by using an activation‐strain model. It was found that the selectivity and reactivity of cisplatin is a delicate trade‐off between strain and interaction energies and that the second chloride is a worse leaving group than the first. When similar studies were carried out with imidazole, guanine (G), and adenine (A), it was found that in general the second nucleophilic substitution reactions have lower activation barriers than the first ones. Finally, simulations of the structural restrictions imposed by the DNA scaffold in intra‐ and interstrand processes showed that the geometries of the reaction products are nonoptimal with respect to the unrestrained A and G nucleophiles, although the energetic cost is not considerable under physiological conditions, which thus permits nucleophilic substitution reactions that lead to highly distorted DNA.     

Structure, spectroscopy, and reactivity properties of porphyrin pincers: a conceptual density functional theory and time-dependent density functional theory study

Porphyrin and pincer complexes are both important categories of compounds in biological and catalytic systems. The idea to combine them is computationally investigated in this work. By employment of density functional theory (DFT), conceptual DFT, and time-dependent DFT approaches, structure, spectroscopy, and reactivity properties of porphyrin pincers are systematically studied for a selection of divalent metal ions. We found that the porphyrin pincers are structurally and spectroscopically different from their precursors and are more reactive in electrophilic and nucleophilic reactions. A few quantitative linear/exponential relationships have been discovered between bonding interactions, charge distributions, and DFT chemical reactivity indices. These results are implicative in chemical modification of hemoproteins and understanding chemical reactivity in heme-containing and other biologically important complexes and cofactors.     

A density functional theory study on the electrocyclization of 1,2,4,6-heptatetraene analogues: converting a pericyclic to a pseudopericyclic reaction

A comprehensive B3LYP/6-31+G* study on the electrocyclization of 1,2,4,6-heptatetraene analogues was conducted. Starting from the cyclization of (2Z)-2,4,5-hexatrienal, a pericyclic disrotatory process favored by the assistance of a electron lone pair, we incorporated small modifications in its molecular structure to obtain a truly pseudopericyclic process. To this purpose electronegative atoms (fluorine and nitrogen) were added to give a more electrophilic character on the carbon atom which is attacked by the electron lone pair of the oxygen atom. The complete pathway for each reaction was determined, and changes in magnetic properties were monitored with a view to estimating the aromatization associated with each process. This information, together with the energetic and structural results, allowed us to classify the reactions as pseudopericyclic or pericyclic. Among all studied reactions only one was a truly pseudopericyclic process and another was a borderline case. The features of this unequivocally pseudopericyclic case were analyzed in depth.     

Type‐I Dyotropic Reactions: Understanding Trends in Barriers

To understand the factors that control the activation barrier of type‐I 1,2‐dyotropic reactions (X‐EH₂‐CH₂‐X*→X*‐EH₂‐CH₂‐X, with E=C and Si, X=H, CH₃, SiH₃, F to I) and trends therein as a function of the migrating groups X, we have explored ten archetypal model reactions of this class using relativistic density functional theory (DFT) at ZORA‐OLYP/TZ2P. The main trends in reactivity are rationalized using the activation strain model of chemical reactivity, which had to be extended from bimolecular to unimolecular reactions. Thus, the above type‐I dyotropic reactions can be conceived as a relative rotation of the CH₂CH₂ and [X???X] fragments in X‐CH₂‐CH₂‐X. The picture that emerges from these analyses is that reduced C? X bonding in the transition state is the origin of the reaction barrier. Also the trends in reactivity on variation of X can be understood in terms of how sensitive the C? X interaction is towards adopting the transition‐state geometry. A valence bond analysis complements the analyses and confirms the picture emerging from the activation strain model.