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

The identification of poles in approximate electron propagator calculations on open shell systems has been analyzed. The electron propagator consistent through second order in electronic repulsion has been derived for a 2Σ reference state. Calculations are performed on Li, Na, and BeH and the accuracy of the result is comparable to the one obtained for closed shell systems.

Ionization potentials and electron affinites for a spacially nondegenerate doublet state in a second-order electron propagator approach

In standard multiconfigurational Hartree–Fock (MCSCF) theory, a two electron integral transformation is performed before application of the equation defining the MCSCF approach in each iterative cycle. It is shown how the two electron integral transformation may be replaced by an approximate orbital transformation introduced directly into the equation that defines the second order MCSCF approach. In this way, the number of two electron integral transformations required to obtain a set of MCSCF orbitals is reduced considerably. Numerical examples for the 3Σ−g, 1Δg, and 1Σ+g states of O2 indicate that an accuracy of 10−6 a.u. in the total energy may be obtained by carrying out 2–3 two electron integral transformations, which is about half the number of transformations required to obtain the same accuracy in the second order MCSCF approach. An accuracy of 10−10 a.u. is obtained after one further iteration is carried out with a second order MCSCF scheme.

A method to reduce the number of two electron integral transformations in a second order multiconfigurational Hartree–Fock procedure

We choose H2CO+ and its deuterated species to demonstrate the potential for using second‐order multiconfigurational self‐consistent field theory to optimize structures and calculate properties of ionized and excited states. We focus on the calculation of multidimensional vibronic spectra using only the local information of the potential hypersurface, viz. the molecular energy, gradient, and Hessian. Second‐order multiconfigurational self‐consistent field optimization on lowest excited states using the trust radius algorithm is found to give the same stable convergence as for neutral ground states, while for higher lying states, the problem of multidimensional potential crossings renders the calculations more difficult.

Excited state structures and vibronic spectra of H2CO+, HDCO+, and D2CO+ using molecular gradient and Hessian techniques

In J. Chem. Phys. [107, 10823 (1997)], Rozyczko and Bartlett report an open-ended formula for equation-of-motion coupled cluster (EOM-CC) hyperpolarizabilities. We demonstrate that this formula is incompatible with the generic definition of EOM-CC properties and converges to a wrong full configuration limit. We derive the correct expressions for the EOM-CC quadratic and cubic response functions.

Comment on “Frequency-dependent equation-of-motion coupled cluster hyperpolarizabilities: Resolution of the discrepancy between theory and experiment for HF?” [J. Chem. Phys. 107, 10823 (1997)]

The system density operator is expanded in powers of an arbitrary perturbation which may be electronic correlation and an efficient formalism is obtained for evaluating the matrix elements required to perform molecular property calculations. A generalized Brillouin condition is derived and used to define a Fock potential. The problem of assigning the poles of the polarization propagator to transitions of pure space and spin symmetry is discussed and the polarization propagator is expanded through second order in correlation for a spatially nondegenerate doublet state. Preliminary results for the Li(2S) and BeH(2Σ) systems indicate that agreement with experimental excitation energies is as favorable for open shell systems as for closed shells.

Poul Jo

Papers

Ionization potentials and electron affinites for a spacially nondegenerate doublet state in a second-order electron propagator approach

A method to reduce the number of two electron integral transformations in a second order multiconfigurational Hartree–Fock procedure

Excited state structures and vibronic spectra of H2CO+, HDCO+, and D2CO+ using molecular gradient and Hessian techniques

Comment on “Frequency-dependent equation-of-motion coupled cluster hyperpolarizabilities: Resolution of the discrepancy between theory and experiment for HF?” [J. Chem. Phys. 107, 10823 (1997)]

An open shell polarization propagator: Doublet-doublet transitions