Paul Geerlings

Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene

Abstract The first all-electron ab initio study of Youngs modulus and Poisson ratio for a number of closed single-walled nanotubes is presented. At the Hartree–Fock 6-31G ∗ level, the results obtained compare well with experimental as well as previous theoretical studies, predicting a Youngs modulus higher than 1 TPa. The calculated Youngs modulus for a graphene layer is found to be smaller than for its (5,5)-nanotube counterpart.

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.

Influence of the π–π interaction on the hydrogen bonding capacity of stacked DNA/RNA bases

The interplay between aromatic stacking and hydrogen bonding in nucleobases has been investigated via high-level quantum chemical calculations. The experimentally observed stacking arrangement between consecutive bases in DNA and RNA/DNA double helices is shown to enhance their hydrogen bonding ability as opposed to gas phase optimized complexes. This phenomenon results from more repulsive electrostatic interactions as is demonstrated in a model system of cytosine stacked offset-parallel with substituted benzenes. Therefore, the H-bonding capacity of the N3 and O2 atoms of cytosine increases linearly with the electrostatic repulsion between the stacked rings. The local hardness, a density functional theory-based reactivity descriptor, appears to be a key index associated with the molecular electrostatic potential (MEP) minima around H-bond accepting atoms, and is inversely proportional to the electrostatic interaction between stacked molecules. Finally, the MEP minima on surfaces around the bases in experimental structures of DNA and RNA–DNA double helices show that their hydrogen bonding capacity increases when taking more neighboring (intra-strand) stacking partners into account.

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.

On the performance of density functional methods for describing atomic populations, dipole moments and infrared intensities

Abstract Atomic populations according to the Mulliken, electrostatic, natural population, and atomic polar tensor (APT) definitions were evaluated for first- and second-row compounds using different correlated ab initio techniques, DFT methods, and basis sets. All definitions except Mulliken exhibit modest basis set sensitivity. B3LYP predicts partial charges in agreement with high-level ab initio results. Exact-exchange corrections are more important than gradient corrections for this property. B3LYP with at least sdpf basis sets usually predicts dipole moments and infrared intensities in agreement with more accurate calculations, while semiquantitative IR intensities are obtained even with the modest cc-pVDZ basis set.

Intrinsic framework electronegativity: A novel concept in solid state chemistry

The charge‐dependent ‘‘effective’’ electronegativity χα of an atom α in a molecule or crystal, i.e., χα=(χ0α+Δχα)+2(η0α +Δηα)qα +∑β≠α qβ/Rαβ differs from the expression for the isolated atom (χ0α+2η0αqα) because of corrections to the electronegativity (Δχα) and hardness (Δηα), respectively, and due to the external potential generated by the surrounding charges qβ at distances Rαβ (new quantum‐mechanical proof given). After calibration of Δχα and Δηα for all atom types, ab initio charges can be reproduced to within a few hundredths of an electron by the electronegativity equilization method (using χav=χα=χβ⋅⋅⋅ and ∑β qβ=constant). Application of this algorithm to the solid state (i.e., charges and external potential being generated in a self‐consistent way and using Ewald’s method for determining the Madelung potential) leads to a novel method for determining ‘‘ab initio quality’’ charges and the value of the average electronegativity. If applied to SiO2 polymorphs, a relation between the refractive index ...

Calculation of ionization energies, electron affinities, electronegativities, and hardnesses using density functional methods

The performance of two exact exchange methods is tested in the calculation of ionization energies, electron affinities, electronegativities, and hardnesses using Dunning’s correlation consistent basis sets. Comparison is made to experiment and other density functional methods, including the local density approximation and two gradient corrected functionals. The obtained electronegativities and hardnesses are also compared with high level coupled cluster results. Both the exact exchange methods show an excellent performance in the calculation of all four properties, yielding mean absolute deviations from experiment below 0.20 eV for all basis sets.

Calculation of molecular electrostatic potentials and Fukui functions using density functional methods

Abstract The performance of different density functional methods in the calculation of molecular electrostatic potentials and Fukui functions, i.e. two reactivity indices based on the electron density, is investigated. It turns out, as a whole, that the exact exchange functionals B3LYP and B3PW91 yield results close to accurate electron correlation methods if basis sets of sufficient quality are used.

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.

Quantum-chemical study of the Fukui function as a reactivity index1: Part 2. Electrophilic substitution on mono-substituted benzenes

Abstract The Fukui function f−, and the condensed form fc−, are studied as reactivity indices for electrophilic substitution reactions on substituted benzenes. The systems studied are PhX with X = O−, NH2, OH, F, CN, NO2, CHO, NH3+, and CHCH2. The results were obtained from SCF and density calculations using the 3-21G basis. A comparison between the Fukui function and experimental data, the molecular electrostatic potential (MEP), the HOMO-density and the Laplacian of the electronic charge distribution was made. The comparison between the Fukui function and the MEP indicated that these two properties might be complementary to each other. The Fukui function seems to describe the soft-soft interactions, whereas the MEP describes the hard-hard interactions. The HOMO-density was found to be a poor approximation to the Fukui function f−, even when taking the (HOMO-1)-density into account. A comparison of the Laplacian of the electronic charge distribution and the Fukui function showed that the relation between these two properties is not as obvious as expected.