Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Electronic excitation energies are determined using the CAM-B3LYP Coulomb-attenuated functional ͓T. Yanai et al. Chem. Phys. Lett. 393, 51 ͑2004͔͒, together with a standard generalized gradient approximation ͑GGA͒ and hybrid functional. The degree of spatial overlap between the occupied and virtual orbitals involved in an excitation is measured using a quantity ⌳, and the extent to which excitation energy errors correlate with ⌳ 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 ⌳, 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 ⌳ 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.

We recently presented a new method for developing generalized gradient approximation (GGA) exchange-correlation energy functionals, using a least-squares procedure involving numerical exchange-correlation potentials and experimental energetics and nuclear gradients. In this paper we use the same method to develop a new GGA functional, denoted HCTH, based on an expansion recently suggested by Becke [J. Chem. Phys. 107, 8554 (1997)]. For our extensive training set, the new functional yields improved energetics compared to both the BLYP and B3LYP functionals [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 37, 785 (1988); J. Chem. Phys. 98, 5648 (1993); J. Phys. Chem. 98, 11623 (1994)]. The geometries of these systems, together with those of a set of transition metal compounds, are shown to be an improvement over the BLYP functional, while the reaction barriers for six hydrogen abstraction reactions are comparable to those of B3LYP. These improvements are achieved without introducing any fraction of exact orbital exchange into the new functional. We have also re-optimized the functional of Becke—which does involve exact exchange—for use in self-consistent calculations.

Conventional continuum exchange-correlation functionals (e.g., local density approximation, generalized gradient approximation) offer a poor description of many response properties, such as static polarizabilities and single photon vertical excitation energies to Rydberg states. These deficiencies are related to errors in the virtual Kohn–Sham orbitals and eigenvalues, which arise due to a fundamental deficiency in the potentials of conventional continuum functionals. Namely, although these potentials approximately average over the exact integer discontinuity in energetically important regions, they fail to do so asymptotically, because they vanish. Our recent functional HCTH [J. Chem. Phys. 109, 6264 (1998)] was designed with this deficiency in mind, although its potential still fails to exhibit the appropriate asymptotic form. In this paper, we present a new procedure that explicitly corrects this asymptotic deficiency for any continuum functional. Self-consistent Kohn–Sham calculations are performed using a corrected potential, which equals the conventional potential δEXC[ρα,ρβ]/δρσ(r) in energetically important regions, but which asymptotically behaves in the required average manner −(1/r)+Iσ+εHOMO,σ. The quantity −(1/r) is determined using a nonlocal expression; Iσ is an approximate σ spin ionization potential; and εHOMO,σ is the highest occupied σ spin eigenvalue. By applying this correction to the HCTH potential, we accurately reproduce the hydrogen atom eigenvalue spectrum, without significantly changing the total energy. We determine corrected orbitals and eigenvalues for a variety of molecules, and use them to compute excitation energies and static polarizabilities. We compare the results with those from a variety of other exchange-correlation functionals. Excitations to Rydberg states are determined as accurately as those to valence states; for CO, N2, H2CO, and C2H4, mean absolute errors are less than 0.35 eV. The static isotropic polarizabilities of 14 small molecules are of MP2 quality.

No abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Pyrene derivatives substituted at the 2- and 2,7-positions are shown to display a set of photophysical properties different from those of derivatives substituted at the 1-position. It was found that, in the 2- and 2,7-derivatives, there was little influence on the S(2) ← S(0) excitation, which is described as "pyrene-like", and a strong influence on the S(1) ← S(0) excitation, which is described as "substituent-influenced". In contrast, the 1-substituted derivatives display a strong influence on both the S(1) ← S(0) and the S(2) ← S(0) excitations. These observations are rationalized by considering the nature of the orbitals involved in the transitions. The existence of a nodal plane passing through the 2- and 7-positions, perpendicular to the molecular plane in the HOMO and LUMO of pyrene, largely accounts for the different behavior of derivatives substituted at the 2- and 2,7-positions. Herein, we report the photophysical properties of a series of 2-R-pyrenes {R = C(3)H(6)CO(2)H (1), Bpin (2; pin = OCMe(2)CMe(2)O), OC(3)H(6)CO(2)H (3), O(CH(2))(12)Br (4), C≡CPh (5), C(6)H(4)-4-CO(2)Me (6), C(6)H(4)-4-B(Mes)(2) (7), B(Mes)(2) (8)} and 2,7-R(2)-pyrenes {R = Bpin (9), OH (10), C≡C(TMS) (11), C≡CPh (12), C≡C-C(6)H(4)-4-B(Mes)(2) (13), C≡C-C(6)H(4)-4-NMe(2) (14), C(6)H(4)-4-CO(2)C(8)H(17) (15), N(Ph)-C(6)H(4)-4-OMe (16)} whose syntheses are reported elsewhere. Furthermore, we compare their properties to those of several related 1-R-pyrene derivatives {R = C(3)H(6)CO(2)H (17), Bpin (18), C≡CPh (19), C(6)H(4)-4-B(Mes)(2) (20), B(Mes)(2) (21)}. For all derivatives, modest (0.19) to high (0.93) fluorescence quantum yields were observed. For the 2- and 2,7-derivatives, fluorescence lifetimes exceeding 16 ns were measured, with most being ca. 50-80 ns. The 4-(pyren-2-yl)butyric acid derivative (1) has a long fluorescence lifetime of 622 ns, significantly longer than that of the commercially available 4-(pyren-1-yl)butyric acid (17). In addition to measurements of absorption and emission spectra and fluorescence quantum yields and lifetimes, time-dependent density functional theory calculations using the B3LYP and CAM-B3LYP functionals were also performed. A comparison of experimental and theoretically calculated wavelengths shows that both functionals were able to reproduce the trend in wavelengths observed experimentally.

The recently proposed CAM-B3LYP exchange-correlation energy functional, based on a partitioning of the r À1 12 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.

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.