F. De Proft

A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes.

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 (C(4n+2)H(2n+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 (1)A(g) singlet closed-shell electronic ground state. Singlet-triplet (S(0)-T(1)) 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-pVinfinityZ), the S(0)-T(1) 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-pVinfinityZ level for the S(0)-T(1) 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 S(0)-T(1) energy gap of 0 to approximately 4 kcal/mol (approximately 0.17 eV) in the limit of an infinitely large polyacene.

Atomic charges, dipole moments, and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms‐in‐molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.

HSAB principle: Applications of its global and local forms in organic chemistry

The hard and soft acids and bases (HSAB) principle, both in its local and global versions, is applied, to a series of chemical reactions, including eleminations and substitutions, Diels–Alder cycloadditions, enolate–ion alkylation, and 1,3-dipolar additions. It will be shown that this principle, in the different resolutions, provides a powerful tool in the study of regioselectivity problems in organic chemistry.

On the importance of the "density per particle" (shape function) in the density functional theory

The central role of the shape function sigma(r) from the density functional theory (DFT), the ratio of the electron density rho(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 micro of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined.

A benchmark theoretical study of the electron affinities of benzene and linear acenes.

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 Moller-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 (C(2+4n)H(2+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 ( approximately -1.53 and approximately -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.

The electronegativity equalization method II: Applicability of different atomic charge schemes

The amenability of different schemes for the calculation of atomic charges in the electronegativity equalization method (EEM) is investigated. To that end, a large training set of molecules was composed, comprising H, C, N, O, and F, covering a wide range of medicinal chemistry. Geometries are calculated at the B3LYP/6-31G* level. Atomic charges are calculated using five different methods, belonging to different types of population analysis. Effective electronegativities and hardness values are calibrated from the different quantum chemically calculated atomic charges. The resulting quality of EEM charges is investigated for the different types of atomic charge calculation methods. EEM-derived Mulliken and NPA charges are in good agreement with the ab initio values, electrostatic potential derived, and Hirshfeld charges show no good agreement.

Acidity of alkyl substituted alcohols: Are alkyl groups electron-donating or electron-withdrawing?

Abstract Two important functional group properties, the group electronegativity and hardness, are calculated for a number of alkyl groups. The results indicate that alkyl groups become less electronegative and hard with increasing group size. The calculated properties are used in a study of the inversion of the alkyl alcohol acidity scale when going from aqueous solution to the gas phase. Finally, the Sanderson electronegativity equalization principle using functional group properties is shown to be a valuable tool in describing the charge distribution of these molecular systems.

Quantum similarity study of atomic density functions: Insights from information theory and the role of relativistic effects

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 Mendeleevs 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.

Hirshfeld partitioning of the electron density: Atomic dipoles and their relation with functional group properties

Atomic dipole moments, derived within the Hirshfeld partitioning of the molecular electron density, have been studied for compounds of the type HX and ClX, for a series of functional groups X frequently encountered in organic molecules. In the case of the HX compounds, the component of the atomic dipole moment on H along the axis connecting H with the central atom in X is found to be linearly correlated with the electronegativity of X, the hardness of X playing no significant role. In the case of the ClX compounds, the situation is less clear. However, evidence seems to point to the conclusion that for these compounds, also the group hardness plays an important role.

Magnetic properties and aromaticity of o-, m-, and p-benzyne

The relative aromaticities of the three singlet benzyne isomers, 1,2-, 1,3-, and 1,4-didehydrobenzenes have been evaluated with a series of aromaticity indicators, including magnetic susceptibility anisotropies and exaltations, nucleus-independent chemical shifts (NICS), and aromatic stabilization energies (all evaluated at the DFT level), as well as valence-bond Pauling resonance energies. Most of the criteria point to the o-benzyne<m-benzyne<p-benzyne aromaticity order, whereas the relative aromaticity of each isomer with respect to benzene depends on the aromaticity criterion. An additional aromaticity evaluation involved the transition state of the Bergman cyclization of (Z)-hexa-1,5-diyn-3-ene which yields p-benzyne. Dissected NICS calculations reveal an aromatic transition state with a larger total NICS but a smaller NICS(pi) component and thus lower aromaticity than benzene.