We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

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The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

A method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results The method, Dmol for short, uses fast convergent three‐dimensional numerical integrations to calculate the matrix elements occurring in the Ritz variation method The flexibility of the integration technique opens the way to use the most efficient variational basis sets A practical choice of numerical basis sets is shown with a built‐in capability to reach the LDF dissociation limit exactly Dmol includes also an efficient, exact approach for calculating the electrostatic potential Results on small molecules illustrate present accuracy and error properties of the method Computational effort for this method grows to leading order with the cube of the molecule size Except for the solution of an algebraic eigenvalue problem the method can be refined to quadratic growth for large molecules

An all‐electron numerical method for solving the local density functional for polyatomic molecules

We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation-strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001

Chemistry with ADF

A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approximate Coulomb energies in conjunction with orbital basis sets of split valence, triple zeta valence and quadruple zeta valence quality with errors of typically below ca. 0.15 kJ mol−1 per atom; this was demonstrated in conjunction with the recently developed orbital basis sets of types def2-SV(P), def2-TZVP and def2-QZVPP for a large set of small molecules representing (nearly) each element in all of its common oxidation states. These auxiliary bases are slightly more than three times larger than orbital bases of split valence quality. Compared to non-approximated treatments, computation times for the Coulomb part are reduced by a factor of ca. 8 for def2-SV(P) orbital bases, ca. 25 for def2-TZVP and ca. 100 for def2-QZVPP orbital bases.

Accurate Coulomb-fitting basis sets for H to Rn

An approximate Xα functional is proposed from which the charge density fitting equations follow variationally. LCAO Xα calculations on atomic nickel and diatomic hydrogen show the method independent of the fitting (auxiliary) bases to within 0.02 eV. Variational properties associated with both orbital and auxiliary basis set incompleteness are used to approach within 0.2 eV the Xα total energy limit for the nitrogen molecule.

On some approximations in applications of Xα theory

A new theory of cluster expansions has been derived, which allows one, for the first time, to estimate the energy of a disordered system from first principles. The cluster variables are derived from a series of density-functional calculations on ordered compounds. The disordering temperatures calculated with this theory show the correct trends for binary alloys of $4d$ transition metals, and are in excellent agreement with the experimental phase diagrams in most cases.

Density-functional theory applied to phase transformations in transition-metal alloys

The total Xα energy accurate to 0.3 eV is computed for H2, B2, C2, N2, O2, CO, and F2. Relative to experiment, the Xα model (α=0.7) is accurate to within ΔRe=0.1 bohr, ΔDe=2 eV, and Δωe=300 cm−1 for these molecules. Except for the lightest first‐row diatomic molecules, the Xα and experimental dissociation energies are bracketed by those of the Hartree–Fock model (from below) and the Local Spin Density model (from above).

On first‐row diatomic molecules and local density models

From the Publisher: 
Cliff Stoll was an astronomer turned systems manager at Lawrence Berkeley Lab when a 75-cent accounting error alerted him to the presence of an unauthorized user on his system. The hacker's code name was "Hunter"a mystery invader hiding inside a twisting electronic labyrinth, breaking into U.S. computer systems and stealing sensitive military and security information. Stoll began a one-man hunt of his own, spying on the spyand plunged into an incredible international probe that finally gained the attention of top U.S. counterintelligence agents. The Cookoo's Egg is his wild and suspenseful true storya year of deception, broken codes, satellites, missile bases, and the ultimate sting operationand how one ingenious American trapped a spy ring paid in cash and cocaine, and reporting to the KGB.

The Cuckoo's Egg: Tracking a Spy Through the Maze of Computer Espionage

The energy bands in ferromagnetic nickel have been calculated within the framework of the unrestricted Hartree-Fock scheme, in which the exchange terms were approximated by a local potential. The augmented-plane-wave method was used to find the eigenvalues of the approximate Hamiltonian, and self-consistency was achieved after several iterations of this method. It was found that the use of the averaged free-electron exchange potential, i.e., ${{\overline{V}}_{x}}^{(s)}=\ensuremath{-}6{(\frac{6{\ensuremath{\rho}}_{s}}{8\ensuremath{\pi}})}^{\frac{1}{3}}$, gave results in qualitative disagreement with experiment. Reducing the exchange potential by a factor of $\frac{2}{3}$ gave more realistic results. Comparisons with the experimental data are presented which show that the unrestricted Hartree-Fock scheme may be an acceptable model for the ground state of a ferromagnetic solid.

John W. D. Connolly

Papers

On some approximations in applications of Xα theory

Density-functional theory applied to phase transformations in transition-metal alloys

On first‐row diatomic molecules and local density models

The Cuckoo's Egg: Tracking a Spy Through the Maze of Computer Espionage

Energy Bands in Ferromagnetic Nickel