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

An ab initio investigation of the electric-field-gradient-induced birefringence of H2, N2, C2H2, and CH4 is presented. All linear and nonlinear optical properties contributing to the induced anisotropy of the refractive index are computed by means of coupled cluster singles and doubles response theory. For systems of cubic or icosahedral symmetry, the only nonvanishing contribution to the induced birefringence within the semiclassical approach is due to the frequency-dependent dipole–dipole–quadrupole and dipole–dipole–magnetic dipole hyperpolarizabilities. These hyperpolarizabilities are important for accurate experimental determinations of the molecular quadrupole moment from electric-field-gradient-induced birefringence measurements.

Coupled cluster investigation of the electric-field-gradient-induced birefringence of h2, n2, c2h2, and ch4

Expressions for the frequency‐dependent polarizability, the Verdet constant, and the energy sum rules have been derived consistent through third order in the electronic repulsion using an analytical polarization propagator method. In this approach, the second order optical properties are obtained directly from the propagator without calculating the individual excitation energies and transition moments which appear in the sum‐over‐states procedures.

Polarization propagator calculations of frequency‐dependent polarizabilities, Verdet constants, and energy weighted sum rules

The analytical calculation of molecular dipole‐moment derivatives for MCSCF wave functions is described. The formalism is based on exponential unitary transformation of the wave function and symmetric orthonormalization of the molecular orbitals. The response equations are solved using an iterative, direct technique to allow for large configuration expansions. Translational and rotational symmetries of the dipole moment are used to minimize computational costs. Sample calculations involving several thousand configurations are presented for H2O and ONF.

Analytical calculation of MCSCF dipole‐moment derivatives

Erratum: Second‐order Mo/ller–Plesset perturbation theory as a configuration and orbital generator in multiconfiguration self‐consistent‐field calculations [J. Chem. Phys. 88, 3834 (1988)]

We report an implementation of the linear response function for singlet excited states for the coupled cluster models CCS, CC2 and CCSD The implementation is based on the derivation of excited state response functions as derivatives of excited state quasienergy Lagrangians Secular divergencies are explicitly eliminated and response equations and response functions therefore are numerical stable in the static limit Calculations are performed for the polarizabilities of pyrimidine and s-tetrazine in their lowest singlet excited states We find that the results for the excited state polarizabilities are sensitive to the accuracy of the excitation energies and that a qualitative correct description of the dispersion is first obtained at a correlated level

Poul Jo

Papers

Coupled cluster investigation of the electric-field-gradient-induced birefringence of h2, n2, c2h2, and ch4

Polarization propagator calculations of frequency‐dependent polarizabilities, Verdet constants, and energy weighted sum rules

Analytical calculation of MCSCF dipole‐moment derivatives

Erratum: Second‐order Mo/ller–Plesset perturbation theory as a configuration and orbital generator in multiconfiguration self‐consistent‐field calculations [J. Chem. Phys. 88, 3834 (1988)]

Static and frequency-dependent polarizabilities of excited singlet states using coupled cluster response theory