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

6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

A new implementation of the conductor-like screening solvation model (COSMO) in the GAUSSIAN94 package is presented. It allows Hartree−Fock (HF), density functional (DF) and post-HF energy, and HF and DF gradient calculations:  the cavities are modeled on the molecular shape, using recently optimized parameters, and both electrostatic and nonelectrostatic contributions to energies and gradients are considered. The calculated solvation energies for 19 neutral molecules in water are found in very good agreement with experimental data; the solvent-induced geometry relaxation is studied for some closed and open shell molecules, at HF and DF levels. The computational times are very satisfying:  the self-consistent energy evaluation needs a time 15−30% longer than the corresponding procedure in vacuo, whereas the calculation of energy gradients is only 25% longer than in vacuo for medium size molecules.

Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model

This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at ??HOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The ??HOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential

Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold

A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initioMO methods. Since the computation time for analytical energy gradients is approximately the same as for the energy, the optimization algorithm evaluates and utilizes the gradients each time the energy is computed. The second derivative matrix, rather than its inverse, is updated employing the gradients. At each step, a one-dimensional minimization using a quartic polynomial is carried out, followed by an n-dimensional search using the second derivative matrix. By suitably controlling the number of negative eigenvalues of the second derivative matrix, the algorithm can also be used to locate transition structures. Representative timing data for optimizations of equilibrium geometries and transition structures are reported for ab initioSCF–MO calculations.

Optimization of equilibrium geometries and transition structures

Ab initio calculations of all the nuclear magnetic resonance (NMR) indirect nuclear spin–spin coupling constants in the HN3 molecule and in four isomers of CH2N2 are described. For each molecule, SCF and two multiconfiguration self‐consistent field (MCSCF) wave functions that take into account valence shell correlation effects are applied. All mechanisms contributing to the coupling constants are included. While the SCF results are meaningless, the agreement of the correlated values with those known from experiment is satisfactory. Our most accurate calculations are carried out with the wave functions previously used successfully to compute the NMR shielding constants. All parameters determining the NMR spectra of these molecules have thus been obtained at uniform accuracy from the same reference wave function.

Multiconfigurational self‐consistent field calculations of nuclear magnetic resonance indirect spin–spin coupling constants

The dependence of the electronic energy of a multiconfigurational self‐consistent field wave function on molecular geometry is currently receiving a great deal of attention. In this manuscript, analytical expressions are derived which permit the evaluaton of the third and fourth derivatives of the energy the respect to geometrical displacements. Although the resultant expressions do requires higher order derivatives of the atomic‐orbital‐level one‐ and two‐electron integrals, there are no other substantial increases in computational difficulty when compared to the first (gradient) and second (Hessian) energy derivatives obtained earlier. (AIP)

First and second anharmonicities of the MCSCF energy

We have shown that equivalence between dipole length and dipole velocity transition moments is obtained in an order by order polarization propagator calculation of excitation energies and transition moments. Also, the Thomas–Reiche–Kuhn sum rule is shown to be fulfilled order by order. Numerical examples show good agreement between dipole length and velocity transition moments both in first and second order polarization propagator calculations using finite basis sets with approximately 50 Slater type orbitals for atoms and diatomic molecules.

Equivalence between perturbatively calculated transition moments

The quartic force field and the cubic dipole moment surface are calculated for trans‐2,3‐ dideuteriooxirane at the self‐consistent field and the second order Moller–Plesset levels of theory using a triple zeta plus two polarization functions basis set. Contact transformation theory is used to determine the corresponding anharmonic vibrtional frequencies and intensities. Inclusion of anharmonicity improves agreement of the calculated frequencies and intensities with their experimental counterparts. The anharmonic corrections are much more sensitive to correlation effects for intensities than for frequencies.

Ab initio calculations of anharmonic vibrational transition intensities of trans‐2,3‐dideuteriooxirane

We discuss implementation of cubic contributions in multiconfigurational self‐consistent field (MCSCF) calculations. We explicitly demonstrate that, far from convergence, an iterative cubic technique can often eliminate the need for constraint procedures. Chebyshev (perturbative) and recursive (two‐point fixed Hessian) cubic techniques are shown to be useful for local, but not global convergence.

Poul Jo

Papers

Multiconfigurational self‐consistent field calculations of nuclear magnetic resonance indirect spin–spin coupling constants

First and second anharmonicities of the MCSCF energy

Equivalence between perturbatively calculated transition moments

Ab initio calculations of anharmonic vibrational transition intensities of trans‐2,3‐dideuteriooxirane

Cubic contributions in multiconfigurational self‐consistent‐field (MCSCF) calculations