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.

Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 molecules representing (nearly) all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, density functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.

Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy

We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993

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A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions.

A new hybrid density functional for general chemistry applications is proposed. It is based on a mixing of standard generalized gradient approximations GGAs for exchange by Becke B and for correlation by Lee, Yang, and Parr LYP with Hartree-Fock HF exchange and a perturbative second-order correlation part PT2 that is obtained from the Kohn-Sham GGA orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixture of HF and GGA exchange ax and of the PT2 and GGA correlation c, respectively. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large 53% with c=27% which at least in part explains the success for many problematic molecular systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 standard benchmark set, a second test suite of atoms, molecules, and reactions that are considered as electronically very difficult including transition-metal compounds, weakly bonded complexes, and reaction barriers and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose density functional for molecules e.g., a mean absolute deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, respectively, for the best other density functionals. Very importantly, also the maximum and minium errors outliers are strongly reduced by about 10‐20 kcal/mol. Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equilibrium properties. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for diatomic molecules and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chemical systems emphasizes the need of virtual orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chemical method of general purpose. © 2006 American Institute of Physics. DOI: 10.1063/1.2148954

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Semiempirical hybrid density functional with perturbative second-order correlation

A set of f-polarization functions for pseudo-potential basis sets of the transition metals ScCu, YAg and LaAu

Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M(Z−28)+-core orbitals of the second row transition elements and the M(Z−60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Recently published nonrelativistic and quasirelativistic energy-adjustedab initio pseudopotentials representing the M(Z−28)+ cores of the second row transition metal atoms and the M(Z−60)+ cores of the third row transition metal atoms have been tested in SCF, CI(SD) and CEPA1 calculations of the spectroscopic constants (R

 e
 ,D

 e
 , and ω
 e
 ) of the ground states of the neutral and singly charged silver and gold dimers, and in state averaged CASSCF and multi-reference CI(SD) calculations of the spectroscopic constants (R

 e
 ,D

 e
 , ω
 e
 , μ
 e
 , ∂μ/∂R). Comparison is made with experimental and reliable theoretical data where available; in the case of the hydrides, additional calculations with pseudopotentials published by other groups have been made for comparison.

Energy-adjustedab initio pseudopotentials for the second and third row transition elements: Molecular test for M2 (M=Ag, Au) and MH (M=Ru, Os)

Abstract A diglyme solution of Na[cyclo‐P5] (1) reacts with alkynes and isolobal nitriles and phosphaalkynes to afford the otherwise elusive (aza)phospholide anions 2  a–c, 4  a,b, and 6. The reaction of Na[cyclo‐P5] with alkynes and nitriles was studied by means of DFT methods, which suggested a concerted mechanism for the formation of 2  a and 4  b. The anions 2  a–c, 4  a,b, and 6 coordinate in an η 5‐fashion towards FeII to give the sandwich (aza)phosphametallocenes 3  a–c, 5  a,b and 7 in moderate to good yields. The new compounds were characterized by means of multinuclear NMR spectroscopy, single‐crystal X‐ray diffraction and cyclic voltammetry.

D. Andrae

Papers

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Energy-adjustedab initio pseudopotentials for the second and third row transition elements: Molecular test for M2 (M=Ag, Au) and MH (M=Ru, Os)

Reactivity of Sodium Pentaphospholide Na[cyclo‐P5] towards C≡E (E=C, N, P) Triple Bonds

Comment on “spectroscopic constants and potential energy curves of OsH” by M. Benavides-Garcia and K. Balasubramanian