A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

Semiempirical GGA-type density functional constructed with a long-range dispersion correction.

Molecular structure does not easily identify the intricate noncovalent interactions that govern many areas of biology and chemistry, including design of new materials and drugs. We develop an approach to detect noncovalent interactions in real space, based on the electron density and its derivatives. Our approach reveals the underlying chemistry that compliments the covalent structure. It provides a rich representation of van der Waals interactions, hydrogen bonds, and steric repulsion in small molecules, molecular complexes, and solids. Most importantly, the method, requiring only knowledge of the atomic coordinates, is efficient and applicable to large systems, such as proteins or DNA. Across these applications, a view of nonbonded interactions emerges as continuous surfaces rather than close contacts between atom pairs, offering rich insight into the design of new and improved ligands.

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Revealing noncovalent interactions.

An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R−6. The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The “double counting” of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene · H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1463–1473, 2004

Accurate description of van der Waals complexes by density functional theory including empirical corrections

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

The role of fluorine in drug design and development is expanding rapidly as we learn more about the unique properties associated with this unusual element and how to deploy it with greater sophistication. The judicious introduction of fluorine into a molecule can productively influence conformation, pKa, intrinsic potency, membrane permeability, metabolic pathways, and pharmacokinetic properties. In addition, 18F has been established as a useful positron emitting isotope for use with in vivo imaging technology that potentially has extensive application in drug discovery and development, often limited only by convenient synthetic accessibility to labeled compounds. The wide ranging applications of fluorine in drug design are providing a strong stimulus for the development of new synthetic methodologies that allow more facile access to a wide range of fluorinated compounds. In this review, we provide an update on the effects of the strategic incorporation of fluorine in drug molecules and applications in po...

Applications of Fluorine in Medicinal Chemistry

The dispersion interaction in the helium dimer is considered from the viewpoint of the force on a nucleus. At large internuclear separations, Brueckner coupled cluster BD(T) forces agree well with near-exact dispersion forces. The atomic density distortion associated with the dispersion force is quantified by comparing the BD(T) dimer density with a superposition of atomic densities. For density functional theory calculations in the Hartree-Fock-Kohn-Sham (HFKS) formalism, the accuracy of the dispersion force is governed by the correlation potential. Calculations using the conventional Lee-Yang-Parr [Phys. Rev. B 37, 785 (1988)] potential only generate a small density distortion, giving forces significantly smaller than BD(T). The BD(T) electron densities are therefore used to determine improved correlation potentials using a modified Zhao-Morrison-Parr (ZMP) approach [Phys. Rev. A 50, 2138 (1994)]. HFKS calculations using these ZMP potentials quantitatively reproduce the distortion, giving dispersion forces in good agreement with BD(T). The dimer ZMP correlation potential is partitioned into two parts, one equal to the sum of two unperturbed spherical atomic correlation potentials and the other representing an interaction potential. HFKS calculations using the former do not generate the distortion; forces are close to Hartree-Fock. Calculations using the latter do generate the distortion, giving forces essentially identical to those from the full dimer potential. The origin of the distortion is traced to the asymmetric structure of the interaction correlation potential in the vicinity of each nucleus.

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Helium dimer dispersion forces and correlation potentials in density functional theory.

The energies of the gauche and anti conformers of 2-fluoroethylamine, 2-fluoroethanol and their protonated analogues are calculated using density functional theory. Unlike the non protonated systems, the protonated systems show a strong gauche effect where the C–F and the C–+NH3 or C–F and C–+OH2 bonds are gauche rather than anti to each other. Single crystal X-ray diffraction studies of 2-fluoroethylammonium compounds identify the same conformational preference.

The observation of a large gauche preference when 2-fluoroethylamine and 2-fluoroethanol become protonated.

The energy of the excess electron state has been determined for six nonpolar liquids by a photoelectric injection method. The functional dependence of the photocurrents on wavelength is the same in the liquid as in the vacuum and work functions can be evaluated from Fowler plots. For several liquids the work functions are less than the vacuum value and these lowerings are characteristic for each liquid. For tetramethylsilane, neopentane, cyclopentane, and 2,2,4‐trimethylpentane the work functions are lowered by 0.62, 0.43, 0.28, and 0.18 eV, respectively. For n‐pentane and n‐hexane the work functions are close to the vacuum value. The magnitude of the lowering is correlated with the energy of the first electronic absorption band. A variation of electron mobility with the work function changes is noted and discussed relative to the trap theory. The photocurrents measured in the liquids increase with voltage, and at the voltage employed the currents in neopentane and tetramethylsilane are comparable to the ...

Energy of Excess Electrons in Nonpolar Liquids by Photoelectric Work Function Measurements

Kohn—Sham eigenvalues are determined from coupled cluster electron densities. The calculated HOMO—LUMO eigenvalue differences are compared with those from conventional generalized gradient approximation (GGA) exchange-correlation functionals for a range of small molecules. In all cases, GGA HOMO—LUMO differences are smaller than those calculated from the coupled cluster densities. When the GGA HOMO—LUMO differences are explicitly corrected—such that they equal those calculated from electron densities—significant improvements in NMR shielding constants are obtained. The eigenvalues calculated from electron densities are also used to approximate the magnitude of the integer discontinuity in the exact exchange-correlation potential. The value of the Kohn—Sham HOMO eigenvalue is then considered. Although HOMO eigenvalues from high quality, asymptotically vanishing, exchange-correlation potentials are close to the negative of the ionization potential, HOMO eigenvalues from the GGA functionals are shifted upwar...

Mark J. Allen

Papers

Helium dimer dispersion forces and correlation potentials in density functional theory.

The observation of a large gauche preference when 2-fluoroethylamine and 2-fluoroethanol become protonated.

Energy of Excess Electrons in Nonpolar Liquids by Photoelectric Work Function Measurements

Eigenvalues, integer discontinuities and NMR shielding constants in Kohn-Sham theory

Improved NMR chemical shifts in density functional theory