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.

/pdf/the-m06-suite-of-density-functionals-for-main-group-1748swzp1l.pdf

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

/pdf/quantum-mechanical-continuum-solvation-models-3edv963g14.pdf

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

We describe multiconfiguration linear-response (MCLR) approaches to the calculation of absolute photoionization cross sections. Three algorithms are described: (i) one in which the MCLR equations are used to derive the primitive spectrum of excitation energies and oscillator strengths; (ii) one in which the solutions of the MCLR equations are used to provide the even negative moments of the photoexcitation-photoionization spectrum; and (iii) one in which a pseudospectrum is obtained directly in the iterative procedure used to solve the MCLR equations. Either the primitive spectra (i), the moments (ii), or the pseudospectra (iii) are used as basic quantities in Stieltjes imaging to obtain the photoionization cross sections. Numerical demonstrations with large multiconfigurational self-consistent field reference spaces are given for the photoionization of HF, ${\mathrm{H}}_{2}$O, and Ne. Comparative calculations are performed in the random-phase approximation. Results are analyzed with respect to the fulfillment of gauge invariance, sum rules, basis-set completeness, and choice of correlating orbital spaces. Results for absolute photoionization cross sections from the MCLR algorithms agree very well with Stieltjes-imaging cross sections obtained from the semiempirically determined spectral moments of Meath and co-workers [Can. J. Phys. 55, 2080 (1977); 63, 1616 (1985)], and distinguish the raw experimental cross sections.

Multiconfiguration linear-response approaches to the calculation of absolute photoionization cross sections: HF, H2O, and Ne.

The molecular electric dipole and quadrupole moments of HF have been calculated in Mo/ller–Plesset perturbation theory through 20th order. From comparison with full configuration interaction results, the Mo/ller–Plesset series is found to diverge for both properties. Within the Mo/ller–Plesset series, only the second-order correction should be calculated. For higher accuracy, one should use coupled-cluster methods instead of proceeding to higher-order perturbation theory.

Divergent behavior of Mo/ller–Plesset perturbation theory for molecular electric dipole and quadrupole moments

A multiconfiguration self‐consistent reaction field method is presented for calculating isotropic hyperfine coupling constants of solvated molecules. The solvent model is based on generalizations of Kirkwood’s model for describing solvation effects. Isotropic hyperfine coupling constants are calculated for the methyl and ClO2 radicals in different solvents.

Theory of hyperfine coupling constants of solvated molecules: Applications involving methyl and ClO2 radicals in different solvents

We have demonstrated how Hessian update methods may easily be implemented into an MCSCF calculation. We have shown that the Hessian update methods constitute the most efficient iterative methods for obtaining local convergence of an MCSCF calculation and we have further shown that Hessian update methods, when implemented with step size and sign control, have very promising global convergence properties.

Update methods in multiconfigurational self‐consistent field calculations

The one‐ and two‐photon dipole transitions between the X 1Σ+ and the A 1Π states of CO have been studied by means of multiconfiguration self‐consistent‐field linear and quadratic response methods. The vibrationally averaged oscillator strength for the 0–0 one‐photon dipole transition between the X 1Σ+ and A 1Π states obtained using the linear response method is 1.31×10−2 as compared to the experimental results of 0.96(14)×10−2, 1.08(7)×10−2, and 1.11×10−2. The two‐photon transition probability rate constant, obtained using the quadratic response method, for the 0–1 vibrational band of the X–A transition of 7×10−59 cm4 s is more than six orders of magnitude smaller than the experimental result of 3.5×10−52 cm4 s. We suggest that the experiment should be reconsidered. The dipole moment of the A 1Π state obtained from quadratic response calculations on the ground state at R=2.332 a.u. is −0.0441 a.u. suggesting an anomalous polarity also for the A 1Π state. The experimental value is ±0.059(20) a.u.

Poul Jo

Papers

Multiconfiguration linear-response approaches to the calculation of absolute photoionization cross sections: HF, H2O, and Ne.

Divergent behavior of Mo/ller–Plesset perturbation theory for molecular electric dipole and quadrupole moments

Theory of hyperfine coupling constants of solvated molecules: Applications involving methyl and ClO2 radicals in different solvents

Update methods in multiconfigurational self‐consistent field calculations

A multiconfiguration self‐consistent‐field response study of one‐ and two‐photon dipole transitions between the X 1Σ+ and A 1Π states of CO