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The atom-atom polarizability and the transmission probability at the Fermi level, as obtained through the source-and-sink-potential method for every possible configuration of contacts simultaneously, are compared for polycyclic aromatic compounds. This comparison leads to the conjecture that a positive atom-atom polarizability is a necessary condition for transmission to take place in alternant hydrocarbons without non-bonding orbitals and that the relative transmission probability for different configurations of the contacts can be predicted by analyzing the corresponding atom-atom polarizability. A theoretical link between the two considered properties is derived, leading to a mathematical explanation for the observed trends for transmission based on the atom-atom polarizability. [ABSTRACT FROM AUTHOR]

A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet (ST) excitation energies of benzene (n=1) and n-acenes (C4n+2H2n+4) ranging from naphthalene (n=2) to heptacene (n=7) is presented, on the ground of single- and multireference calculations based on restricted or unrestricted zero-order wave functions. High-level and large scale treatments of electronic correlation in the ground state are found to be necessary for compensating giant but unphysical symmetry-breaking effects in unrestricted single-reference treatments. The composition of multiconfigurational wave functions, the topologies of natural orbitals in symmetry-unrestricted CASSCF calculations, the T1 diagnostics of coupled cluster theory, and further energy-based criteria demonstrate that all investigated systems exhibit a 1Ag singlet closed-shell electronic ground state. Singlet-triplet (S0-T1) energy gaps can therefore be very accurately determined by applying the principles of a focal point analysis onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets (X=D, T, Q, 5) and single-reference methods [HF, MP2, MP3, MP4SDQ, CCSD, CCSD(T)] of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations [CCSD(T)] in the limit of an asymptotically complete basis set (cc-pV∞Z), the S0-T1 vertical excitation energies of benzene (n=1) and n-acenes (n=2–7) amount to 100.79, 76.28, 56.97, 40.69, 31.51, 22.96, and 18.16 kcal/mol, respectively. Values of 87.02, 62.87, 46.22, 32.23, 24.19, 16.79, and 12.56 kcal/mol are correspondingly obtained at the CCSD(T)/cc-pV∞Z level for the S0-T1 adiabatic excitation energies, upon including B3LYP/cc-PVTZ corrections for zero-point vibrational energies. In line with the absence of Peierls distortions, extrapolations of results indicate a vanishingly small S0-T1 energy gap of 0 to ∼4 kcal/mol (∼0.17 eV) in the limit of an infinitely large polyacene. [ABSTRACT FROM AUTHOR]

The effect of the recently uncovered nonuniqueness of the external magnetic field B(r[accent:_right_hook_over]) corresponding to a given pair of density n(r[accent:_right_hook_over]) and spin density ns(r[accent:_right_hook_over]) on the derivative of the energy functional of spin-polarized density functional theory, and its implications for the definition of chemical reactivity descriptors, is examined. For ground states, the nonuniqueness of B(r[accent:_right_hook_over]) implies the nondifferentiability of the energy functional Ev,B[n,ns] with respect to ns(r[accent:_right_hook_over]). It is shown, on the other hand, that this nonuniqueness allows the existence of the one-sided derivatives of Ev,B[n,ns] with respect to ns(r[accent:_right_hook_over]). Although the N-electron ground state can always be obtained from the minimization of Ev,B[n,ns] without any constraint on the spin number Ns=∫ns(r[accent:_right_hook_over])dr[accent:_right_hook_over], the Lagrange multiplier μs associated with the fixation of Ns does not vanish even for ground states. μs is identified as the left- or right-side derivative of the total energy with respect to Ns, which justifies the interpretation of μs as a (spin) chemical potential. This is relevant not only for the spin-polarized generalization of conceptual density functional theory, the spin chemical potential being one of the elementary reactivity descriptors, but also for the extension of the thermodynamical analogy of density functional theory for the spin-polarized case. For higher-order reactivity indices, B(r[accent:_right_hook_over])’s nonuniqueness has similar implications as for μs, leading to a split of the indices with respect to Ns into one-sided reactivity descriptors. [ABSTRACT FROM AUTHOR]

A benchmark theoretical determination of the electron affinities of benzene and linear oligoacenes ranging from naphthalene to hexacene is presented, using the principles of a focal point analysis. These energy differences have been obtained from a series of single-point calculations at the Hartree–Fock, second-, third-, and partial fourth-order Mo\ller–Plesset (MP2, MP3, and MP4SDQ) levels and from coupled cluster calculations including single and double excitations (CCSD) as well as perturbative estimates of connected triple excitations [CCSD(T)], using basis sets of improving quality, containing up to 1386, 1350, 1824, 1992, 1630, and 1910 basis functions in the computations, respectively. Studies of the convergence properties of these energy differences as a function of the size of the basis set and order attained in electronic correlation enable a determination of the vertical electron affinities of the four larger terms of the oligoacene (C2+4nH2+2n) series within chemical accuracy (0.04 eV). According to our best estimates, these amount to +0.28, +0.82, +1.21, and +1.47 eV when n=3, 4, 5, and 6. Adiabatic electron affinities have been further calculated by incorporating corrections for zero-point vibrational energies and for geometrical relaxations. The same procedure was applied to determine the vertical electron affinities of benzene and naphthalene, which are found to be markedly negative (∼-1.53 and ∼-0.48 eV, respectively). Highly quantitative insights into experiments employing electron transmission spectroscopy on these compounds were also amenable from such an approach, provided diffuse atomic functions are deliberately removed from the basis set, in order to enforce confinement in the molecular region and enable a determination of pseudoadiabatic electron affinities (with respect to the timescale of nuclear motions). Comparison was made with calculations employing density functional theory and especially designed models that exploit the integer discontinuity in the potential or incorporate a potential wall in the unrestricted Kohn–Sham orbital equation for the anion. [ABSTRACT FROM AUTHOR]

The performance of several density-functional theory (DFT) methods for the calculation of current densities induced by a uniform magnetic field is examined. Calculations are performed using the BLYP and KT3 generalized-gradient approximations, together with the B3LYP hybrid functional. For the latter, both conventional and optimized effective potential (OEP) approaches are used. Results are also determined from coupled-cluster singles-and-doubles (CCSD) electron densities by a DFT constrained search procedure using the approach of Wu and Yang (WY). The current densities are calculated within the CTOCD-DZ2 distributed origin approach. Comparisons are made with results from Hartree-Fock (HF) theory. Several small molecules for which correlation is known to be especially important in the calculation of magnetic response properties are considered—namely, O3, CO, PN, and H2CO. As examples of aromatic and antiaromatic systems, benzene and planarized cyclooctatetraene molecules are considered, with specific attention paid to the ring current phenomenon and its Kohn-Sham orbital origin. Finally, the o-benzyne molecule is considered as a computationally challenging case. The HF and DFT induced current maps show qualitative differences, while among the DFT methods the maps show a similar qualitative structure. To assess quantitative differences in the calculated current densities with different methods, the maximal moduli of the induced current densities are compared and integration of the current densities to yield shielding constants is performed. In general, the maximal modulus is reduced in moving from HF to B3LYP and BLYP, and further reduced in moving to KT3, OEP(B3LYP), and WY(CCSD). The latter three methods offer the most accurate shielding constants in comparison with both experimental and ab initio data and hence the more reliable route to DFT calculation of induced current density in molecules. [ABSTRACT FROM AUTHOR]

Spin-polarized density functional theory (SP-DFT) allows both the analysis of charge-transfer (e.g., electrophilic and nucleophilic reactivity) and of spin-polarization processes (e.g., photophysical changes arising from electron transitions). In analogy with the dual descriptor introduced by Morell et al. [J. Phys. Chem. A 109, 205 (2005)], we introduce new dual descriptors intended to simultaneously give information of the molecular regions where the spin-polarization process linking states of different multiplicity will drive electron density and spin density changes. The electronic charge and spin rearrangement in the spin forbidden radiative transitions S0→T(n,π*) and S0→T(π,π*) in formaldehyde and ethylene, respectively, have been used as benchmark examples illustrating the usefulness of the new spin-polarization dual descriptors. These quantities indicate those regions where spin-orbit coupling effects are at work in such processes. Additionally, the qualitative relationship between the topology of the spin-polarization dual descriptors and the vertical singlet triplet energy gap in simple substituted carbene series has been also discussed. It is shown that the electron density and spin density rearrangements arise in agreement with spectroscopic experimental evidence and other theoretical results on the selected target systems. [ABSTRACT FROM AUTHOR]

A hardness based similarity index for studying the quantum similarity for atoms is analyzed. The investigation of hardness and Fukui functions of atoms leads to the construction of a quantum similarity measure, which can be interpreted as a quantified comparison of chemical reactivity of atoms. Evaluation of the new measure reveals periodic tendencies throughout Mendeleev’s table. Moreover on the diagonal the global hardness was recovered. Considering a corresponding quantum similarity index reveals that renormalization of the measure can mask periodic patterns. The hardness was calculated for atoms with nuclear charge 3≤=Z≤=103, using the best single configuration electron density functions available. Different hardness kernels were used and the importance of the different contributions to the kernel was investigated. The atomic self-similarities constructed in this way show a fair correlation with experimental atomic polarizability [ABSTRACT FROM AUTHOR]

A novel quantum similarity measure (QSM) is constructed based on concepts from information theory. In an application of QSM to atoms, the new QSM and its corresponding quantum similarity index (QSI) are evaluated throughout the periodic table, using the atomic electron densities and shape functions calculated in the Hartree-Fock approximation. The periodicity of Mendeleev’s table is regained for the first time through the evaluation of a QSM. Evaluation of the information theory based QSI demonstrates, however, that the patterns of periodicity are lost due to the renormalization of the QSM, yielding chemically less appealing results for the QSI. A comparison of the information content of a given atom on top of a group with the information content of the elements in the subsequent rows reveals another periodicity pattern. Relativistic effects on the electronic density functions of atoms are investigated. Their importance is quantified in a QSI study by comparing for each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock approximations. The smooth decreasing of the relevant QSI along the periodic table illustrates in a quantitative way the increase of relativistic corrections with the nuclear charge. [ABSTRACT FROM AUTHOR]

The electrophilicity index is analyzed within the framework of spin-polarized density-functional theory. In this context, constrained philicities, ωN≡(μN)2/(2ηNN), are introduced in order to define the capability of a system to acquire or donate electrons in a process at constant spin number. The spin-philicity/spin-donicity indices, ωS±≡(μS±)2/(2ηSS), are examined and rationalized here as the philicity of a given system to change its spin-polarization state, as being defined through the spin potential μS and spin hardness ηSS for a process at constant number of electrons. The local extension of these indices has been also outlined and numerical results have been discussed on the analysis of the electrophilic nature of some simple carbene systems both in the singlet and triplet states. [ABSTRACT FROM AUTHOR]

An extension of Cohen’s nuclear Fukui function is presented in the spin-polarized framework of density-functional theory (SP-DFT). The resulting new nuclear Fukui function indices [uppercase_phi_synonym]Nα and [uppercase_phi_synonym]Sα are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H2O, H2CO, and some simple nitrenes (NX) and phosphinidenes (PX), with X=H, Li, F, Cl, OH, SH, NH2, and PH2. Results have been interpreted in terms of chemical bonding in the context of Berlin’s theorem, which provides a separation of the molecular space into binding and antibinding regions. [ABSTRACT FROM AUTHOR]

The central role of the shape function σ(r_) from the density functional theory (DFT), the ratio of the electron density ρ(r_) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical hardness can be obtained from the long range behavior of the shape function and its derivative with respect to the number of electrons at a fixed external potential. Next, the energy of the system is minimized with the constraint that the shape function should integrate to unity; the associated Lagrange multiplier is shown to be related to the electronic chemical potential μ of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The structure and morphology of three polymer/graphene nanocomposites have been studied using classical molecular dynamics (MD) simulations. The simulations use 10-monomer oligomeric chains of three polymers: polyethylene (PE), polystyrene (PS) and polyvinylidene fluoride (PVDF). The structure of the polymer chains at the graphene surface has been investigated and characterized by pair correlation functions (PCF), g(r), g(ϑ) and g(r,ϑ). In addition, the influence of the temperature on the graphene/polymer interactions has been analysed for each of the three polymer/graphene nanocomposite systems. The results indicate that graphene induces order in both the PE and PVDF systems by providing a nucleation site for crystallisation, steering the growth of oligomer crystals according to the orientation of the graphene sheet, whereas the PS system remains disordered in the presence of graphene. The overall results are in line with the findings in a recent quantumchemical study by some of the present authors. [ABSTRACT FROM AUTHOR]

In recent years, expanded porphyrins have emerged as a promising class of π-conjugated molecules that display unique electronic, optical and conformational properties. Several expanded porphyrins can switch between planar and twisted conformations, which have different photophysical properties. Such a change of topology involves a Hückel–Möbius aromaticity switch in a single molecule and it can be induced by solvent, pH and metallation. These features make expanded porphyrins suitable for the development of a novel type of molecular switches for molecular electronic devices. Octaphyrins consisting of eight pyrrole rings, exhibit twisted-Hückel, Möbius and Hückel π-conjugation topologies depending on the oxidation and protonation state, with distinct electronic structures and aromaticity. Our working hypothesis is that a significant change in the conductance of expanded porphyrins will be observed after the topology switching. Despite the potential of Hückel–Möbius systems as conductance switches, the relationship between the conductance and the molecular topology is not yet understood. We have explored the performance of local descriptors of conductivity in simple molecules, as well as the relationship with conductance. Since these indexes provide a qualitative measure of delocalization and conductance in the probe molecules, we have carried out a local analysis of electrical conductance changes as a function of the π-conjugation in two examples. In one of them, the locality of the electronic changes ensures the ability of these indexes to describe the conductance as local. Moreover, it enables to identify which conformational switch would be more efficient from an electronic device perspective. However, we also show that it is not always possible to reduce conductance changes to one bond, and in those molecules where a deep rearrangement occurs far from the structural perturbation, local measures show a limited efficiency. This is a first step for the description of the connection between the molecular structure and conductance in molecular switches. [ABSTRACT FROM AUTHOR]

Two ethylene-bridged methylaluminium amidinates and one aluminium amidinate containing three terminal trimethylstannyl-ethynyl groups interconnected by π-coordinated potassium ions were prepared in situ. The re-oxidation of the ethylene-bridged compound by iodine followed by further reduction using the same activation procedure demonstrated the versatility of the approach. The reactivity of an ethylene-bridged methylaluminum amidinate towards HCl was examined to demonstrate the building block concept. DFT calculations were performed to gain insight into the mechanism of the in situ activation of diphenylacetylene. [ABSTRACT FROM AUTHOR]

N-fused pentaphyrins (NFP) are the stable forms of fully meso-aryl pentaphyrins(1.1.1.1.1). In order to determine the optimum conditions for viable Möbius topologies of these porphyrinoids, the conformational preferences, Hückel–Möbius interconversion pathways and aromaticity of [22] and [24]NFP have been investigated using density functional theory calculations. The conformation of the macrocycle is shown to be strongly dependent on the oxidation state and the macrocyclic aromaticity. [22]NFP prefers a highly aromatic and relatively strain-free Hückel conformation. However, antiaromatic Hückel and weakly aromatic Möbius conformers coexist in dynamic equilibrium in [24]NFP. The Hückel–Möbius aromaticity switch requires very low activation energy barriers (Ea = 3–4 kcal mol−1). Interestingly, the balance between Möbius and Hückel conformations in [24]NFP can be controlled by meso-substituents. The structure–property relationship between the molecular conformation, number of π electrons and aromaticity has been established in our study using energetic, magnetic, structural, and reactivity descriptors of aromaticity. Although the Möbius topology is indeed accessible for [24]NFP, it does not exhibit a distinct macrocyclic aromaticity mainly due to the large dihedral angles around the molecular twist. Regarding the computational methodology, B3LYP and M06 show the best overall performance for describing the experimental geometries of NFP and, importantly, our computational results support the experimental evidence available for N-fused pentaphyrins. [ABSTRACT FROM AUTHOR]

The essential aspects of zero-temperature grand-canonical ensemble density-functional theory are reviewed in the context of spin-density-functional theory and are used to highlight the assumption of symmetry between electron addition and subtraction that underlies the corrected Koopmans approach of Tozer and De Proft (TDP) for computing electron affinities. The issue of symmetry is then investigated in a systematic study of atomic electron affinities, comparing TDP affinities with those from a conventional Koopmans evaluation and electronic energy differences. Although it cannot compete with affinities determined from energy differences, the TDP expression yields results that are a significant improvement over those from the conventional Koopmans expression. Key insight into the results from both expressions is provided by an analysis of plots of the electronic energy as a function of the number of electrons, which highlight the extent of symmetry between addition and subtraction. The accuracy of the TDP affinities is closely related to the nature of the orbitals involved in the electron addition and subtraction, being particularly poor in cases where there is a change in principal quantum number, but relatively accurate within a single manifold of orbitals. The analysis is then extended to a consideration of the ground state Mulliken electronegativity and chemical hardness. The findings further emphasize the key role of symmetry in determining the quality of the results. [ABSTRACT FROM AUTHOR]

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness—in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results. [ABSTRACT FROM AUTHOR]

Global hardness and softness and the associated hard/soft acid/base (HSAB) principle have been used to explain many experimental observed reactivity patterns and these concepts can be found in textbooks of general, inorganic, and organic chemistry. In addition, local versions of these reactivity indices and principles have been defined to describe the regioselectivity of systems. In a very recent article (Chem.–Eur. J.2008, 14, 8652), the present authors have shown that the picture of these well-known descriptors is incomplete and that the understanding of these reactivity indices must be “reinterpreted”. In fact, the local softness and hardness contain the same “potential information” and they should be interpreted as the “local abundance” or “concentration” of their corresponding global properties. In this contribution, we analyze the implications of this new point of view for the applicability of these well-known descriptors when comparing two sites in three situations: two sites within one molecule, two sites in two different, but noninteracting molecules, and two sites in two different, but interacting, molecules. The implications on the HSAB principle are highlighted, leading to the discussion of the role of the electrostatic interaction. [ABSTRACT FROM AUTHOR]

Quantum molecular similarity (QMS), for which the first measures were introduced by Carbó in the early 1980s, has been shown to be an important concept when comparing properties and reactivity of different, albeit mostly related, molecules. In this article we investigate how various subfields of Density Functional Theory (DFT) contribute in their own way to the evaluation and the understanding of QMS, reflecting the combined interest of our group in both domains in recent years. The contribution of computational DFT is easy to pinpoint, as DFT can now be used in the evaluation of electron densities of ever-increasing quality. When establishing a link between the fundamental(s) of DFT and QMS the role of the shape function turns out to be predominant and an extension of Mezey's Holographic Electron Density Theorem for p(r) to the shape function σ(r) is presented. On this basis, similarity in shape is the fundamental issue to be looked at, both globally and locally. As an application, global and local similarity measures were evaluated using the Hirshfeld partitioning technique for the two enantiomers of CHFClBr, giving numerical evidence for the Holographic Electron Density Theorem. As an application of conceptual DFT, similarity indices constructed via DFT based local reactivity descriptors (e.g., local softness) are used to probe the ‘similarity of reactivity’ of a series of peptide isosteres. The use of the autocorrelation function for condensed indices turns out to be a valuable technique to circumvent the orientation-translation dependence of similarity indices. [ABSTRACT FROM AUTHOR]