Communication: variational many-body expansion: accounting for exchange repulsion, charge delocalization, and dispersion in the fragment-based explicit polarization method

A fragment-based variational many-body (VMB) expansion method is described to directly account for exchange repulsion, charge delocalization (charge transfer) and dispersion interactions in the explicit polarization (X-Pol) method. The present VMB/X-Pol approach differs from other fragment molecular orbital (FMO) techniques in two major aspects. First, the wave function for the monomeric system is variationally optimized using standard X-Pol method, as opposed to the iterative update procedure adopted in FMO. Second, the mutual polarizations in the dimeric terms are also variationally determined, whereas single-point energy calculations of the individual dimers embedded in a static monomer field are used in FMO. The second-order (two-body) VMB (VMB2) expansion method is illustrated on a series of water hexamer complexes and one decamer cluster, making use of Hartree-Fock theory, MP2, and the PBE1 and M06 density functionals to represent the monomer and dimer fragments. The computed binding energies are within 2 kcal/mol of the corresponding results from fully delocalized calculations. Energy decomposition analyses reveal specific dimeric contributions to exchange repulsion, charge delocalization, and dispersion. Since the wave functions for one-body and all two-body terms are variationally optimized in VMB2 and X-Pol, it is straightforward to obtain analytic gradient without the additional coupled-perturbed Hartree-Fock step. Thus, the method can be useful for molecular dynamics simulations.     

Application of natural bond orbital analysis to delocalization and aromaticity in C-substituted tetrazoles.

Energies of two tautomeric forms of 10 tetrazole derivatives substituted at C5 were established by DFT/B3LYP calculations carried out at the 6-311++G level. In each case the calculated energy of the 2H-tautomer was lower than that of the 1H. Furthermore, three geometric aromaticity indices of both forms were calculated, as were the values of nuclear independent nuclear shift and aromatic stabilization energy. The electronic properties were evaluated with the help of the natural bonding orbital theory. Following this a new pi-delocalization parameter, the root-mean square of pi-electron density localized on the atoms of the five-membered tetrazole ring, SDn, was introduced. It was concluded that the electronic delocalization can be described equally well by three different parameters: SDn, the extent of the transfer of electron density from the p(z) orbital of one nitrogen to the rest of the pi electron system, and population of two antibonding pi orbitals. Arguably, the information provided by the electronic parameters is similar to that contained in the geometric (structural) aromaticity indices except for tetrazole substituted by -BH(2).     

The reactive intermediate in acetylene polymerization: Results of quantum chemical calculations on charge delocalization and its consequences

The charge delocalization in the conjugated vinyl intermediates, which are assumed to be the reactive intermediates in acetylene polymerization, is calculated, taking into account σ as well as π electrons. Delocalization is shown to exist, but it is of a different kind for cations and anions. In the anion, the σ charge is localized at the reactive center and the π change is displaced into the system. In the cations, the σ charge flows towards the reactive center and the π charge is more or less unaffected. π-overlap charges between the carbon atoms are much less affected than in the case of the corresponding allyl type anion and cation. The calculated charge delocalizations are compared with the little experimental evidence there is, and possible implications of σ and π delocalizations on reactivity and specificity of reaction are discussed.     

Persistent oxidation dications from twisted fluoranthenes, benzo[k]fluoranthene and dimethyldibenzo[j.l]fluoranthene: charge delocalization mode, tropicity, and formation of novel 8,8'-bifluoranthenyls. An NMR and theoretical study.

First examples of persistent oxidation dications from fluoranthene-PAHs namely 1,3,4,6,7,10-hexamethyl- 2 and 3,4-dichloro-1,6,7,10-tetramethylfluoranthene 3, benzo[k]fluoranthene 6, and 3,6-dimethyldibenzo[j,l]fluoranthene 9 are reported. Charge delocalization mode and tropicity in the resulting nonalternant dications are examined. Quenching of the superacid solutions of the dications resulted in the formation of novel 8,8'-bifluoranthenyls 2a-4a. AM1 was used as an initial guide for dication generation (DeltaDeltaH(f) degrees and ionization potentials) and for probing the structures of the crowded fluoranthene substrates and their bifluoranthenyls. In selected cases, the dications and their neutral precursors were calculated at the B3LYP/6-31G(d,p) level. Charge delocalization mode (difference in NPA charges) and DFT/GIAO-derived NMR chemical shifts were obtained for comparison with experiment; aromaticity was assessed via nucleus independent chemical shift (NICS) calculations.     

Relationship of charge to antiaromaticity in bis-fluorenyl dications and fluorenyl monocations: experimental support for theoretical calculations

The antiaromaticity of fluorenyl cations is dependent on the magnitude of the charge of the system. Theoretical assessments of antiaromaticity and charge were supported by experimental NMR chemical shifts. Delocalization was related to antiaromaticity, and evaluated through the standard deviation of the charges on carbons of the fluorenyl systems.     

Spectra and structure of small ring compounds: Part XXXVIII. Cyclobutanol

The Raman spectrum of gaseous cyclobutanol has been recorded and the far infrared spectrum of the gas has been obtained at a resolution of 0.5 cm^?1. At least six Q-branches arising from the low frequency ring-puckering motion have been observed and assigned on the basis of a potential of the form V(X) = (6.32 ± 0.21) × 10⁵X⁴?(4.18 ± 0.04) × 10⁴X²+ (8.81 ± 1.20) × 10³X³ with a reduced mass of 170 amu. An energy difference between the equatorial and axial forms was found to be 50–150 cm^?1 with the equatorial being more stable and a barrier of 700–900 cm^?1 was found for the interconversion. Three O-H stretching modes were observed in the Raman spectrum. It is concluded that the O-H moiety has both the gauche and trans conformations present in the equatorial form but only the gauche conformer is present in the axial form of the ring. Three O-H torsional modes were observed at 244 (trans conformer), 226.5 and 181.5 cm^?1 (gauche conformer) for the equatorial form and one O-H torsion at 237.5 cm^?1 (gauche conformer) for the axial form. The potential function governing the O-H torsional motion for the equatorial form was found to be V₁ = 280 ± 7 cm^?1 (800 cal mole^?1) and V₃ = 425 ± 3 cm^? (121.5 cal mole^?1) with the trans conformer being more stable than the gauche by approximately 206 cm^?1 (589 cal mole^?). The barriers to trans-gauche and gauche-gauche interconversion have essentially the same values, 500 cm^?1 (1430 cal mole^?1).     

The role of triplet repulsion in elementary steps of cyclic chain termination of oxidizing polymers and other substances

Parabolic model of the transition state was used for analysis of activation energies of reduction of benzoquinone (Q), aminyl (Am^*), and nitroxyl (AmO^*) radicals by peroxyl radicals of different structure. It was proved that radicals HO₂^* and R₂C(OH)O₂^* reduce Am^*, and AmO^* with zero activation energy due to low triplet repulsion in the transition state. On the contrary alkylperoxyl radicals reduce Am^* and AmO^* slowly due to high triplet repulsion and sufficiently high activation energy. That is why AmH and AmOH perform cyclic chain termination in oxidizing substances where peroxyls with OH-group are generated.     

Phosphine-phosphite ligands: chelate ring size vs. activity and enantioselectivity relationships in asymmetric hydrogenation

A series of new phosphine-phosphite ligands P(C)(n)OP (n = 1-4) have been synthesized and used for rhodium-catalyzed asymmetric hydrogenation of prochiral olefins in order to study the effect of the chelate ring size. Excellent ees (up to 97.5%) were obtained in the hydrogenation of dimethyl itaconate and an increase of activity and enantioselectivity was observed in the hydrogenation of (Z)-α-acetamidocinnamic acid methyl ester with the increasing length of the backbone of the ligands.     

Use of semiempirical models for calculation of B terms in MCD spectra—III : Pariser-Parr-Pople (PPP) predictions for dications and dianions of pentalene and heptalene

The PPP model is used to predict the MCD spectra of the doubly-charged ions of pentalene and heptalene. The excited states of the 10 π-electron ions are both related to those of naphthalene and exhibit interesting configuration pairing similar to that found in alternant hydrocarbons. Certain aspects of the results are very sensitive to the choice of parameters and to inclusion of doubly excited configurations in the PPP model. Comparison with the so far non-existent experimental data would probably be useful for testing the various proposed versions of the model.     

The origin of aromaticity: important role of the sigma framework in benzene.

The physical nature of aromaticity is addressed at a high ab initio level. It is conclusively shown that the extrinsic aromatic stabilization energy of benzene E(ease)B, estimated relative to its linear polyene counterpart(s), is very well-reproduced at the Hartree-Fock (HF) level. This is a consequence of the fact that the contributions arising from the zero-point vibrational energy (ZPVE) and electron correlation are rather small. More specifically, they yield together 2.0 kcalmol(-1) to the destabilization of benzene. A careful scrutiny of the HF energies by virial theorem shows further that the kinetic energies of the sigma and pi electrons E(T)HF(sigma) and E(T)HF(pi) are strictly additive in the gauge linear zig-zag polyenes, which also holds for their sum Et(T)HF This finding has the important corollary that E(ease)B is little dependent on the choice of the homodesmic reactions involving zig-zag polyenes. A detailed physical analysis of the sigma- and pi-electron contributions to extrinsic aromaticity requires explicit introduction of the potential energy terms Vne, Vee, and Vnn, which signify Coulomb interactions between the electrons and the nuclei. The Vee term involves repulsive interaction Vee(sigmapi) between the sigma and pi electrons, which cannot be unequivocally resolved into sigma and pi contributions. The same holds for the Vnn energy, which implicitly depends on the electron density distribution via the Born-Oppenheimer (BO) potential energy surface. Several possibilities for partitioning Vee(sigmapi) and Vnn terms into sigma and pi components are examined. It is argued that the stockholder principle is the most realistic, which strongly indicates that E(ease)B is a result of favorable sigma-framework interactions. In contrast, the pi-electron framework prefers the open-chain linear polyenes.     

Electron delocalization and electrostatic repulsion at the origin of the strong spin coupling in mixed-valence keggin polyoxometalates: ab initio calculations of the one- and two-electron processes

We present here a general theoretical procedure to treat the problem of electron delocalization and magnetic interactions in high-nuclearity mixed valence clusters based on polyoxometalates. The main interactions between the delocalized electrons of mixed-valence polyoxometalate anions are extracted from valence spectroscopy ab initio calculations on embedded fragments. Electron transfer, magnetic coupling and exchange transfer parameters between nearest and next-nearest-neighbor metal ions, as well as the value of the electrostatic repulsion between pairs of metal ions are determined. These parameters are introduced in a model Hamiltonian that considers the whole anion. It thus provides macroscopic properties that should be compared with the experimental data. This method is applied to a two-electron-reduced polyoxowolframate Keggin anion. The results demonstrate that the electron transfer processes, combined with the Coulombic repulsion between the "extra" electrons, induce a strong antiferromagnetic coupling between the two delocalized spins providing a definite explanation of the diamagnetic properties of these high nuclearity mixed-valence clusters.     

Presentation of a new index for estimation of aromaticity in halo‐ and cyanobenzenes: The role of potential energy in aromaticity

A linear correlation has been obtained between average values of Hamiltonian kinetic energy ( ) and potential energy ( ) calculated at the bond critical points using atoms in molecules method. This relation was used to introduce a new index ( ) for estimation of aromaticity in halo‐ and cyanobenzenes. Potential energy has different terms such as attraction between nuclei and electrons, also repulsion of electrons which affect the inertia and mobility of electrons, respectively. Therefore, contribution of potential energy in this relation must be controlled. Contribution of potential energy in aromaticity has been managed using a fitting parameter. This parameter was obtained by fitting the aromaticity stabilization energy data with values of aromaticity calculated by index for halo‐ and cyanobenzenes. The contribution of potential energy in index is complete when molecule is nonaromatic and is negligible when molecule is antiaromatic. Indeed, molecule is aromatic when contribution of potential energy in index lies between above limits. © 2013 Wiley Periodicals, Inc.     

The lead tetraacetate reaction of alcohols containing a small ring. Part II. Cyclobutane-methanols and cyclopropane-ethanols

The leadtetraacetate and lead tetraacetate/metal chloride oxidations of cyclobutane-methanol, cyclopropane-ethanol and the corresponding α, α-diniethyl alcohols have been investigated and compared with the oxidative reactions of cyclobutane-carboxylic acid, cyclopropane-acetic acid and 4-pentenoic acid, performed with the same reagents and under similar conditions. It was found that alcohol β-fragmentation and acid decarboxylation follow a remarkably similar mechanistic course, affording comparable results when the substrates are of the same structural type ( 1, 2 and 5; 3, 4 and 6 ) or are converted to the same intermediate alkyl radical fragments ( 3, 4, 6 and 7 ). In addition, cyclization products formed from cyclopropane-ethanol (dihydropyran derivative 31 ) and 4-penteuoic acid (γ-lactones 38 ) have been isolated and identified.     

Spectra and structure of small ring compounds: XXIX. Microwave spectrum of γ-butyrolactone

The microwave spectrum of γ-butyrolactone has been recorded from 12.4 to 40.0 GHz. Both A-type and B-type transitions were observed. The R-branch assignments have been made for the ground state and the first two excited states of the ring-puckering and the first excited state of the ring twisting modes. It is shown that the ring skeleton is non-planar from the magnitude of the μ_c component of the dipole moment as well as from the value of I_c?(I_a+I_b). From the relative intensity measurements of the ground and the excited state, the ring twisting mode appears to be governed by a double minimum potential. The dipole moment was determined to be 4.27±0.03 D with components of μ_a = 4.04±0.03 D, μ_b = 1.42±0.03 D, μ_c = 0.33±0.02 D. From an investigation of the Raman spectrum of the gas, the ring puckering vibration was found to have a frequency of 148 cm^?1, whereas the ring twisting mode was found at 225 cm^?1.     

Relative reactivities of cyclic ethers in cationic copolymerizations: Effects of ring strain and basicity

The relative reactivities of α-monosubstituted cyclic ethers having rings of three to six members toward a cation were estimated from their copolymerizations with 3,3-bis-(chloromethyl)oxetane (M₁) catalyzed by boron trifluoride etherate in methylene chloride at 0°C. It was found that the reactivity of these cyclic ethers was dominated by both the ring strain and the basicity. The following empirical equation was derived to represent the relative reactivity of cyclic ethers: log (1/r₁) = ?0.086ΔRS ? 0.31ΔB + 0.57, where ΔRS and ΔB are constants, characteristic of ring strain and basicity of the cyclic ethers and determined from the differences in free energy of polymerization of the corresponding cycloalkanes and in basicity between M₁ and M₂ monomers, respectively. A good linear correlation was observed between the reactivities calculated from this equation and those obtained from the experiments.     

UV spectra and excitation delocalization in DNA: influence of the spectral width.

The singlet excited states of the model DNA duplex (dA)10.(dT)10 are studied. Calculations are performed in the exciton theory framework. Molecular dynamics calculations provide the duplex geometry. The dipolar coupling is determined using atomic transition charges. The monomer transition energies are simulated by Gaussian functions resembling the absorption bands of nucleosides in aqueous solutions. Most of the excited states are found to be delocalized over at least two bases and result from the mixing of different monomer states. Their properties are only weakly affected by conformational changes of the double helix. On average, the highest oscillator strength is carried by the upper eigenstates. The duplex absorption spectra are shifted a few nanometers to higher energies with respect to the spectra of noninteracting monomers. The states with larger spatial extent are located close to the maximum of the absorption spectrum.     

Solvothermal vs. bench-top reactions: control over the formation of discrete complexes and coordination polymers

The formation of discrete complexes [M(mcoe)2S2] (M = Cu, Ni; S = MeOH, H2O) vs. a nitroso-bridged ferromagnetically-coupled Cu(II) coordination polymer [Cu(mcoe)2] is influenced by the use of solvothermal reaction conditions.