Fluorine is the most electronegative element in the periodic table. When bound to carbon it forms the strongest bonds in organic chemistry and this makes fluorine substitution attractive for the development of pharmaceuticals and a wide range of speciality materials. Although highly polarised, the C–F bond gains stability from the resultant electrostatic attraction between the polarised Cδ+ and Fδ– atoms. This polarity suppresses lone pair donation from fluorine and in general fluorine is a weak coordinator. However, the C–F bond has interesting properties which can be understood either in terms of electrostatic/dipole interactions or by considering stereoelectronic interactions with neighbouring bonds or lone pairs. In this tutorial review these fundamental aspects of the C–F bond are explored to rationalise the geometry, conformation and reactivity of individual organofluorine compounds.

Understanding organofluorine chemistry. An introduction to the C–F bond

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Moller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr_2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

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Advances in molecular quantum chemistry contained in the Q-Chem 4 program package

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

RESEARCH ARTICLE Advances in molecular quantum chemistry contained in the Q-Chem 4 program package

Challenges for density functional theory.

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Electronic excitation energies are determined using the CAM-B3LYP Coulomb-attenuated functional [T. Yanai et al. Chem. Phys. Lett. 393, 51 (2004)], together with a standard generalized gradient approximation (GGA) and hybrid functional. The degree of spatial overlap between the occupied and virtual orbitals involved in an excitation is measured using a quantity Lambda, and the extent to which excitation energy errors correlate with Lambda is quantified. For a set of 59 excitations of local, Rydberg, and intramolecular charge-transfer character in 18 theoretically challenging main-group molecules, CAM-B3LYP provides by far the best overall performance; no correlation is observed between excitation energy errors and Lambda, reflecting the good quality, balanced description of all three categories of excitation. By contrast, a clear correlation is observed for the GGA and, to a lesser extent, the hybrid functional, allowing a simple diagnostic test to be proposed for judging the reliability of a general excitation from these functionals--when Lambda falls below a prescribed threshold, excitations are likely to be in very significant error. The study highlights the ambiguous nature of the term "charge transfer," providing insight into the observation that while many charge-transfer excitations are poorly described by GGA and hybrid functionals, others are accurately reproduced.

/pdf/excitation-energies-in-density-functional-theory-an-ep38p1jml8.pdf

Excitation energies in density functional theory : an evaluation and a diagnostic test.

The recently proposed CAM-B3LYP exchange–correlation energy functional, based on a partitioning of the r−112 operator in the exchange interaction into long- and short-range components, is assessed for the determination of molecular thermochemistry, structures, and second order response properties. Rydberg and charge transfer excitation energies and static electronic polarisabilities are notably improved over the standard B3LYP functional; classical reaction barriers also improve. Ionisation potentials, bond lengths, NMR shielding constants and indirect spin–spin coupling constants are comparable with the two functionals. CAM-B3LYP atomisation energies and diatomic harmonic vibrational wavenumbers are less accurate than those of B3LYP. Future research directions are outlined.

Assessment of a Coulomb-attenuated exchange-correlation energy functional.

Singlet and triplet vertical excitation energies from time-dependent density functional theory (TDDFT) can be affected in different ways by the inclusion of exact exchange in hybrid or Coulomb-attenuated/range-separated exchange-correlation functionals; in particular, triplet excitation energies can become significantly too low. To investigate these issues, the explicit dependence of excitation energies on exact exchange is quantified for four representative molecules, paying attention to the effect of constant, short-range, and long-range contributions. A stability analysis is used to verify that the problematic TDDFT triplet excitations can be understood in terms of the ground state triplet instability problem, and it is proposed that a Hartree-Fock stability analysis should be used to identify triplet excitations for which the presence of exact exchange in the TDDFT functional is undesirable. The use of the Tamm-Dancoff approximation (TDA) significantly improves the problematic triplet excitation energies, recovering the correct state ordering in benzoquinone; it also affects the corresponding singlet states, recovering the correct state ordering in naphthalene. The impressive performance of the TDA is maintained for a wide range of molecules across representative functionals.

Influence of Triplet Instabilities in TDDFT.

Low orbital overlap and triplet instability problems in time-dependent density functional theory (TDDFT) are investigated for a new benchmark set, encompassing challenging singlet and triplet excitation energies of local, charge-transfer, and Rydberg character. The low orbital overlap problem is largely overcome for both singlet and triplet states by the use of a Coulomb-attenuated functional. For all the categories of functional considered, however, errors associated with triplet instability problems plague high overlap excitations, as exemplified by the excited states of acenes and polyacetylene oligomers. Application of the Tamm–Dancoff approximation reduces these errors for both singlet and triplet states, while leaving low-overlap excitations unaffected. The study illustrates the synergy between overlap and stability and highlights the success of a combined, Coulomb-attenuated Tamm–Dancoff approach.

Overcoming Low Orbital Overlap and Triplet Instability Problems in TDDFT

We report calculations of core excitation energies and near-edge X-ray absorption fine structure (NEXAFS) spectra computed with time-dependent density functional theory (TDDFT). TDDFT with generalized gradient approximation and standard hybrid exchange-correlation functionals is known to underestimate core excitation energies. This failure is shown to be associated with the self-interaction error at short interelectronic distances. Short-range corrected hybrid functionals are shown to reduce the error in the computed core excitation energies for first and second row nuclei in a range of molecules to a level approaching that observed in more traditional excited states calculations in the ultraviolet region. NEXAFS spectra computed with the new functionals agree well with experiment and the pre-edge features in the NEXAFS spectra of plastocyanin are correctly predicted.

http://besley.chem.nottingham.ac.uk/publications/pdf/pap44.pdf

Michael J. G. Peach

Papers

Excitation energies in density functional theory : an evaluation and a diagnostic test.

Assessment of a Coulomb-attenuated exchange-correlation energy functional.

Influence of Triplet Instabilities in TDDFT.

Overcoming Low Orbital Overlap and Triplet Instability Problems in TDDFT

Time-dependent density functional theory calculations of near-edge X-ray absorption fine structure with short-range corrected functionals