How do electron localization functions describe π-electron delocalization?

Scalar fields provide an intuitive picture of chemical bonding. In particular, the electron localization function (ELF) has proven to be highly valuable in interpreting a broad range of bonding patterns. The discrimination between enhanced or reduced electron (de)localization within cyclic π-conjugated systems remains, however, challenging for ELF. In order to clearly distinguish between the local properties of ten highly and weakly π-(de)localized prototype systems, we compare the ELFs of both the canonical wave functions and electron-localized states (diabatic) with those of two closely related scalar fields: the electron localizability indicator (ELI-D) and the localized orbital locator (LOL). The simplest LOL function distinguishes enhanced from weak π-(de)localization in an insightful and reliable manner. LOL offers the finest contrast between annulenes with 4n/4n + 2 π electrons and their inorganic analogues as well as between hyperconjugated cyclopentadiene derivatives. LOL(π) also gives an appealing and intuitive picture of the π-bond. In contrast, the most popular ELF fails to capture subtle contrasting local electronic properties and suffers from the arbitrariness of the σ/π dissection. The orbital separation of the most recent ELI-D is clear-cut but the interpretations sometime less straightforward in the present context.     

Can an eight π-electron bare ring be planar?

Here we explore in silico an alternative to make planar eight π-electron bare ring systems with substitutions of some cyclooctatetraene ring carbon atoms by heavier group 14 elements. We found that the most stable eight membered rings with formulae C(4)Si(4)H(8), C(4)Ge(4)H(8), and C(4)Sn(4)H(8) have a perfect planar structure, enhancing delocalization energy as compared to cot.     

Structure of α-NaCaAlF6 determined ab initio from conventional powder diffraction data

α-NaCaAlF₆ is prepared by solid state reaction as poor quality crystals. The structure is determined ab initio from conventional X-ray powder data. The cell is monoclinic, space group P2₁/c, Z = 8, with a = 8.7423(3) Å, b = 5.1927(2) Å, c = 20.3514(9) Å and β = 91.499(2)°. The final Rietveld refinement leads to R_P = 10.6% and R_B = 5.2 %. The structure is built up from isolated AlF₆ octahedra, interconnected by CaF₇ polyhedra sandwiched between layers of NaF₈ and NaF₇ polyhedra extending in the be plane.     

Isoprene Reactivity on Water Surfaces from ab initio QM/MM Molecular Dynamics Simulations

Isoprene is the most abundant volatile organic compound in the atmosphere after methane. While gas-phase processes have been widely studied, the chemistry of isoprene in aqueous environments is less well known. Nevertheless, some experiments have reported unexpected reactivity at the air-water interface. In this work, we have carried out combined quantum-classical molecular dynamics simulations of isoprene at the air-water interface, as well as ab initio and density functional theory calculations on isoprene-water complexes. We report the first calculation of the thermodynamics of adsorption of isoprene at the water surface, examine how hydration influences its electronic properties and reactivity indices, and estimate the OH-initiated oxidation rate. Our study indicates that isoprene interacts with the water surface mainly through H−π bonding. This primary interaction mode produces strong fluctuations of the π and π^* bond stabilities, and therefore of isoprene's chemical potential, nucleophilicity and ionization potential, anticipating significant dynamical effects on its reactivity at the air-water interface. Using data from the literature and free energies reported in our work, we have estimated the rate of the OH-initiated oxidation process at the air-water interface (5.0×10¹² molecule cm⁻³ s⁻¹) to be about 7 orders of magnitude larger than the corresponding rate in the gas phase (8.2×10⁵ molecule cm⁻³ s⁻¹). Atmospheric implications of this result are discussed.     

1,3- and 1,5-Sigmatropic Shifts: Insights into the Structure-Reactivity Relationship from ab initio Calculations

Thermal [ 1,n]-sigmatropic rearrangements of hydrogen shift have been of considerable theoretical and experimental interests during the past several decades.[1,2] In this paper, a group of intramolecular proton transfers in hydrocarbons and heteroatom substituted analogues, including twelve 1,3- and twelve corresponding 1,5-sigmatropic rearrangements (Scheme 1), have been investigated at the QCISD(T)/6-3 1 1G(d,p)∥B3LYP/6-311++G(d,p) level of theory.     

Proton-CO2(X1Σ) orientational anisotropy from an ab initio SCF potential energy surface

Ab initio calculations have been carried out, over an extended range of relative distances and geometries, to obtain the SCF potential energy surface that describes the ground-state interaction between H⁺ and the CO₂ molecular target treated as a rigid rotor. Various aspects of the forces are discussed with special attention to their general dependence on internal angle, affecting rotational excitation of CO₂ during colisional encounters. The corresponding multipolar coefficients are calculated and the asymptotic behaviour of their lowest terms compared with results from perturbation theory, thus providing some qualitative indication on the expected energy-transfer probability in molecular-beam experiments or in ion diffusion processes.     

Is HO3 minimum cis or trans? An analytic full-dimensional ab initio isomerization path

The minimum energy path for isomerization of HO(3) has been explored in detail using accurate high-level ab initio methods and techniques for extrapolation to the complete basis set limit. In agreement with other reports, the best estimates from both valence-only and all-electron single-reference methods here utilized predict the minimum of the cis-HO(3) isomer to be deeper than the trans-HO(3) one. They also show that the energy varies by less than 1 kcal mol(-1) or so over the full isomerization path. A similar result is found from valence-only multireference configuration interaction calculations with the size-extensive Davidson correction and a correlation consistent triple-zeta basis, which predict the energy difference between the two isomers to be of only Δ = -0.1 kcal mol(-1). However, single-point multireference calculations carried out at the optimum triple-zeta geometry with basis sets of the correlation consistent family but cardinal numbers up to X = 6 lead upon a dual-level extrapolation to the complete basis set limit of Δ = (0.12 ± 0.05) kcal mol(-1). In turn, extrapolations with the all-electron single-reference coupled-cluster method including the perturbative triples correction yield values of Δ = -0.19 and -0.03 kcal mol(-1) when done from triple-quadruple and quadruple-quintuple zeta pairs with two basis sets of increasing quality, namely cc-cpVXZ and aug-cc-pVXZ. Yet, if added a value of 0.25 kcal mol(-1) that accounts for the effect of triple and perturbative quadruple excitations with the VTZ basis set, one obtains a coupled cluster estimate of Δ = (0.14 ± 0.08) kcal mol(-1). It is then shown for the first time from systematic ab initio calculations that the trans-HO(3) isomer is more stable than the cis one, in agreement with the available experimental evidence. Inclusion of the best reported zero-point energy difference (0.382 kcal mol(-1)) from multireference configuration interaction calculations enhances further the relative stability to ΔE(ZPE) = (0.51 ± 0.08) kcal mol(-1). A scheme is also suggested to model the full-dimensional isomerization potential-energy surface using a quadratic expansion that is parametrically represented by a Fourier analysis in the torsion angle. The method illustrated at the raw and complete basis-set limit coupled-cluster levels can provide a valuable tool for a future analysis of the available (incomplete thus far) experimental rovibrational data.     

Role of the 3(ππ*) state in photolysis of lumisantonin: insight from ab initio studies

The CASSCF and CASPT2 methodologies have been used to explore the potential energy surfaces of lumisantonin in the ground and low-lying triplet states along the photoisomerization pathways. Calculations indicate that the (1)(nπ*) state is the accessible low-lying singlet state with a notable oscillator strength under an excitation wavelength of 320 nm and that it can effectively decay to the (3)(ππ*) state through intersystem crossing in the region of minimum surface crossings with a notable spin-orbital coupling constant. The (3)(ππ*) state, derived from the promotion of an electron from the π-type orbital mixed with the σ orbital localized on the C-C bond in the three-membered alkyl ring to the π* orbital of conjugation carbon atoms, plays a critical role in C-C bond cleavage. Based on the different C-C bond rupture patterns, the reaction pathways can be divided into paths A and B. Photolysis along path A arising from C1-C5 bond rupture is favorable because of the dynamic and thermodynamic preferences on the triplet excited-state PES. Path B is derived from the cleavage of the C5-C6 bond, leading first to a relatively stable species, compared to intermediate A-INT formed on the ground state PES. Accordingly, path B is relatively facile for the pyrolytic reaction. The present results provide a basis to interpret the experimental observations.     

Does the interconversion of polysulfur compounds proceed via hypervalent intermediates? An ab initio MO study

Ab initio MO calculations at the CCSD(T)/6-311++G(2df,p)//MP2/6-311++G** level have been carried out to determine the reaction energies and Gibbs energies of the homolytic dissociation of the S-S bonds in the chainlike sulfanes H2Sn (n = 2-4). Good agreement with the experimental data is observed. At the same level of theory, the formation of the hypothetical sulfuranes H2S(SH)2, H2S(SSH)2, and S(SH)4 from H2S and the mentioned sulfanes has been studied. Species of this type had been proposed as intermediates in the interconversion reactions of polysulfur compounds (e.g., formation of S7 from S8 and vice versa). The three sulfuranes serve here as model compounds. On the basis of the Gibbs energies and activation energies at 298 K, it is shown that the formation of the three sulfuranes from sulfanes requires too much energy and activation energy to successfully compete with homolytic dissociation reactions. In addition, the formation of the methylsubstituted sulfurane S(SMe)4 from the sulfanes Me2S2 and Me2S3 was studied to elucidate the mechanism of the formal exchange of sulfur atoms between polysulfane molecules. However, both the reaction energy of 199 kJ mol(-1) and the activation energy of 287 kJ mol(-1), calculated at the MP2/6-31G* level, are much higher than the homolytic dissociation energy of the S-S bonds in chain- and ringlike polysulfur compounds, such as Me2S4 (140 kJ mol(-1)) and sulfur homocycles (150 kJ mol(-1)). Therefore, it is concluded that the observed interconversion reactions of sulfur rings and of chainlike polysulfanes do not proceed via sulfurane-type intermediates. Instead, these reactions will take place by a radical chain mechanism at high temperatures, while at temperatures below 100 degrees C they are most probably initiated either by traces of nucleophiles that are present as impurities or by the polar surface groups usually present on the walls of the vessels used.     

Substituent Effects in π-Hole Regium Bonding Interactions Between Au(p-X-Py)2 Complexes and Lewis Bases: An ab initio Study

Long range substituent effects in regium bonding interactions involving Au(I) linear complexes are investigated for the first time. The Au(I) atom is coordinated to two para-substituted pyridine ligands. The interaction energy (RI-MP2/def2-TZVP level of theory) of the π-hole regium bonding assemblies is affected by the pyridine substitution. The Hammett's plot representations for several sets of Lewis bases have been carried out and, in all cases, good regression plots have been obtained (interaction energies vs. Hammett's σ parameter). The Bader's theory of “atoms-in-molecules” has been used to evidence that the electron density computed at the bond critical point that connects the Au-atom to the electron donor can be used as a measure of bond order in regium bonding. Several X-ray structures retrieved from the Cambridge Structural Database (CSD) provide experimental support to the existence of π-hole regium bonding in [Au(Py)₂]⁺ derivatives.     

Is large-scale ab initio Hartree-Fock calculation chemically accurate? Toward improved calculation of biological molecule properties

Numerical errors in total energy values in large-scale Hartree–Fock calculations are discussed. To obtain total energy values within chemical accuracy, 0.01 kcal/mol, stricter numerical accuracy is required as basis size increases. In molecules with 10,000 basis sizes, such as proteins, numerical accuracy for total energy values must be retained to at least 11 digits (i.e., to the order of 1.0D-10) to keep accumulation of numerical errors less than the chemical accuracy (0.01 kcal/mol). With this criterion, we examined the sensitivity analysis of numerical accuracy in Hartree–Fock calculation by uniformly replacing the last bit of the mantissa part of a double-precision real number by zero in the Fock matrix construction step, the total energy calculation step, and the Fock matrix diagonalization step. Using a partial summation technique in the Fock matrix generation step, the numerical error for total energy value of molecules with basis size greater than 10,000 was within chemical accuracy (0.01 kcal/mol), whereas with the conventional method the numerical error with several thousand basis sets was larger than chemical accuracy. Computation of one Fock matrix element with parallel machines can include the partial summation technique automatically, so that parallel calculation yields not only high-performance computing but also more precise numerical solutions than the conventional sequential algorithm. We also found that the numerical error of the Householder-QR diagonalization routine is equal to or less than chemical accuracy, even with a matrix size of 10,000. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 443–454, 1999     

Do aurophilic interactions compete against hydrogen bonds? Experimental evidence and rationalization based on ab initio calculations

[M(C6F5)(N(H)=CPh2)] (M = Ag (1) and Au (2)) complexes have been synthesized and characterized by X-ray diffraction analysis. Complex 1 shows a ladder-type structure in which two [Ag(C6F5)(N(H)=CPh2)] units are linked by a Ag(I)-Ag(I) interaction in an antiparallel disposition. The dimeric units are associated through hydrogen bonds of the type N-H...F(ortho). On the other hand, gold(I) complex 2 displays discrete dimers also in an antiparallel conformation in which both Au(I)-Au(I) interactions and N-H.F(ortho) hydrogen bonds appear within the dimeric units. The features of these coexisting interactions have been theoretically studied by ab initio calculations based on four different model systems in order to analyze them separately. The interactions have been analyzed at HF and MP2 levels of theory showing that, in this case, even at larger distances. The Au(I)-Au(I) interaction is stronger than Ag(I)-Ag(I) and that N-H.F hydrogen bonding and Au(I)-Au(I) contacts have a similar strength in the same molecule, which permits a competition between these two structural motifs giving rise to different structural arrangements.     

Do traditional, chlorine-shared, and ion-pair halogen bonds exist? An ab initio investigation of FCl:CNX complexes

Ab initio MP2/aug'-cc-pVTZ calculations have been carried out to determine the structures, binding energies, and bonding of complexes FCl:CNX, with X = CN, NC, NO(2), F, CF(3), Cl, Br, H, CCF, CCH, CH(3), SiH(3), Li, and Na. Equation-of-motion coupled cluster calculations have also been carried out to determine the coupling constants (1)J(F-Cl), (1X)J(Cl-C), and (2X)J(F-C) across these halogen bonds. As the strength of the base is systematically increased, the nature of the halogen bond changes from traditional, to chlorine-shared, to ion-pair. The type of halogen bond present in a complex can be readily determined from its structure, binding energy, AIM bonding analyses, and spin-spin coupling constants. Coupling constants across halogen bonds are compared with corresponding coupling constants across traditional, proton-shared, and ion-pair hydrogen bonds.     

Proton transfers in aromatic and antiaromatic systems. How aromatic or antiaromatic is the transition state? An ab initio study

An ab initio study of six carbon-to-carbon identity proton transfers is reported. They refer to the benzenium ion/benzene (C6H7(+)/C6H6), the 2,4-cyclopentadiene/cyclopentadienyl anion (C5H6/C5H5(-)), and the cyclobutenyl cation/cyclobutadiene (C4H5(+)/C4H4) systems and their respective noncyclic reference systems, that is, [structure: see text], [structure: see text] and [structure: see text]. For the aromatic C6H7(+)/C6H6 and C5H6/C5H5(-) systems, geometric parameters and aromaticity indices indicate that the transition states are highly aromatic. The proton-transfer barriers in these systems are quite low, which is consistent with a disproportionately high degree of transition-state aromaticity. For the antiaromatic C4H5(+)/C4H4 system, the geometric parameters and aromaticity indices indicate a rather small degree of antiaromaticity of the transition state. However, the proton-transfer barrier is higher than expected for a transition state with a low antiaromaticity. This implies that another factor contributes to the barrier; it is suggested that this factor is angle and torsional strain in the transition state. The question whether charge delocalization at the transition state might correlate with the development of aromaticity was also examined. No such correlation was found, that is, charge delocalization lags behind proton transfer as is commonly observed in nonaromatic systems involving pi-acceptor groups.     

Flexibility of a biotinylated ligand in artificial metalloenzymes based on streptavidin—an insight from molecular dynamics simulations with classical and ab initio force fields

In the field of enzymatic catalysis, creating activity from a non catalytic scaffold is a daunting task. Introduction of a catalytically active moiety within a protein scaffold offers an attractive means for the creation of artificial metalloenzymes. With this goal in mind, introduction of a biotinylated d⁶-piano-stool complex within streptavidin (SAV) affords enantioselective artificial transfer-hydrogenases for the reduction of prochiral ketones. Based on an X-ray crystal structure of a highly selective hybrid catalyst, displaying significant disorder around the biotinylated catalyst [η⁶-(p-cymene)Ru(Biot-p-L)Cl], we report on molecular dynamics simulations to shed light on the protein–cofactor interactions and contacts. The results of these simulations with classical force field indicate that the SAV-biotin and SAV-catalyst complexes are more stable than ligand-free SAV. The point mutations introduced did not affect significantly the overall behavior of SAV and, unexpectedly, the P64G substitution did not provide additional flexibility to the protein scaffold. The metal-cofactor proved to be conformationally flexible, and the S112K or P64G mutants proved to enhance this effect in the most pronounced way. The network of intermolecular hydrogen bonds is efficient at stabilizing the position of biotin, but much less at fixing the conformation of an extended biotinylated ligand. This leads to a relative conformational freedom of the metal-cofactor, and a poorly localized catalytic metal moiety. MD calculations with ab initio potential function suggest that the hydrogen bonds alone are not sufficient factors for full stabilization of the biotin. The hydrophobic biotin-binding pocket (and generally protein scaffold) maintains the hydrogen bonds between biotin and protein.