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

A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

https://www.tddft.org/TDDFT2004/PracticalSessions/papers/ahlrichs_casida.pdf

Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory

Time-dependent density-functional (TDDFT) methods are applied within the adiabatic approximation to a series of molecules including C70. Our implementation provides an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules. We also present a new algorithm for the diagonalization of large non-Hermitian matrices which is needed for hybrid functionals and is also faster than the widely used Davidson algorithm when employed for the Hermitian case appearing in excited energy calculations. Results for a few selected molecules using local, gradient-corrected, and hybrid functionals are discussed. We find that for molecules with low lying excited states TDDFT constitutes a considerable improvement over Hartree–Fock based methods (like the random phase approximation) which require comparable computational effort.

An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules

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

Second-order perturbation theory based on a CASSCF reference state is derived and implemented. The first-order wave function includes the full space of interacting states. Expressions for the contributions to the second-order energy are obtained in terms of up to four-particle density matrices for the CASSCF reference state. The zeroth-order Hamiltonian reduces to the MOller-Plesset Hamiltonian for a closed-shell reference state. The limit of the implementation is given by the number of active orbitals, which determines the size of the density matrices. It is presently around 13 orbitals. The method is illustrated in a series of calculations on H 2 , H 2 O, CH 2 , and F - , and the results are compared with corresponding full CI results

Second-order perturbation theory with a CASSCF reference function

The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.

Medium-size polarized basis sets for high-level correlated calculations of molecular electric properties

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

The perturbation equations of the self-consistent density matrix perturbation theory are derived for open-shell configurations in the restricted Hartree-Fock approximation. It is assumed that the b...

Self-consistent perturbation theory: Open-shell states in perturbation-dependent non-orthogonal basis sets This work was partly supported by the Institute of Low Temperatures and Structure Research of the Polish Academy of Sciences under contract No. MR-I.9.4.3/2.

A method for the iterative algebraic generation of the numerically accurate two-component Hamiltonian for the use in relativistic quantum chemistry is presented. The separation of the electronic and positronic states of the Dirac Hamiltonian is accomplished by the algebraic solution for the Foldy–Wouthuysen transformation. This leads to the two-component formalism whose accuracy is primarily limited by the choice of basis functions. Its performance is tested in calculations of the most sensitive 1s1/2 energy for increasing values of the nuclear charge. These calculations show that the electronic part of the Dirac eigenspectrum can be obtained from the two-component theory to arbitrarily high accuracy. Moreover, if needed, the positronic states can be separately determined in a similar way. Thus the present method can be also used for the evaluation of quantum electrodynamic corrections in the finite basis set approximation.

Andrzej J. Sadlej

Papers

Second-order perturbation theory with a CASSCF reference function

Medium-size polarized basis sets for high-level correlated calculations of molecular electric properties

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Self-consistent perturbation theory: Open-shell states in perturbation-dependent non-orthogonal basis sets This work was partly supported by the Institute of Low Temperatures and Structure Research of the Polish Academy of Sciences under contract No. MR-I.9.4.3/2.

Infinite-order two-component theory for relativistic quantum chemistry