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The recently developed multiconfiguration pair-density functional theory (MC-PDFT) combines multiconfiguration wave function theory with a density functional that depends on the on-top pair density of an electronic system. In an MC-PDFT calculation, there are two steps: a conventional multiconfiguration self-consistent-field (MCSCF) calculation and a post-MCSCF evaluation of the energy with an on-top density functional. In this work, we present the details of the MC-PDFT algorithm that avoids steeply scaling steps that are present in other post-self-consistent-field multireference calculations of dynamic correlation energy. We demonstrate the favorable scaling by considering systems of H2 molecules with active spaces of several different sizes. We then apply the MC-PDFT method to calculate the heterolytic dissociation enthalpy of ferrocene. We find that MC-PDFT yields results that are at least as accurate as complete active space second-order perturbation theory and are more stable with respect to basis set, but at a fraction of the cost in both time and memory. [ABSTRACT FROM AUTHOR]

We extend our recent SOGGA11 approximation to the exchange-correlation functional to include a percentage of Hartree-Fock exchange. The new functional, called SOGGA11-X, has better overall performance for a broad chemical database than any previously available global hybrid generalized gradient approximation, and in addition it satisfies an extra physical constraint in that it is correct to second order in the density-gradient. [ABSTRACT FROM AUTHOR]

In the present study, we comparatively assessed the newly developed M05 functional against a data set of reaction energies for transition-metal chemistry. The functionals to which we compare are BLYP, B3LYP, B97-2, MPWLYP1M, TPSS, and TPSSh. We draw the following conclusions: (1) TPSS gives the best performance for calculating the binding energies of three transition-metal dimers (Sc2, Ni2, and V2) that have severe multireference character, (2) B97-2 gives the best performance for calculating the binding energies of the nine metal-ligand diatomics (three monohydrides, three monoxide, and three monofluorides), and (3) M05 gives the overall best performance for all 18 data in the assessment, and it has a mean unsigned error 55% lower than the popular B3LYP functional. Since the M05 functional also gives good performance for main-group thermochemistry, for noncovalent chemistry, and for calculating barrier heights, M05 can be applied to a wide range of problems where nonhybrid functionals or functionals designed for kinetics fail. [ABSTRACT FROM AUTHOR]

The performance of the M06-L density functional has been tested for band gaps in seven semiconductors plus diamond and MgO. Comparison with the local spin density approximation (LSDA), Becke-Lee-Yang-Parr (BLYP), Perdew-Burke-Eernzerhof (PBE), Tao-Perdew-Staroverov-Scuseria (TPSS), and Heyd-Scuseria-Ernzerhof (HSE) functionals shows that M06-L has improved performance for calculating band gaps as compared to other local functionals, but it is less accurate than the screened hybrid HSE functional for band gaps. [ABSTRACT FROM AUTHOR]

Time-dependent density functional theory (TDDFT) holds great promise for studying photochemistry because of its affordable cost for large systems and for repeated calculations as required for direct dynamics. The chief obstacle is uncertain accuracy. There have been many validation studies, but there are also many formulations, and there have been few studies where several formulations were applied systematically to the same problems. Another issue, when TDDFT is applied with only a single exchange-correlation functional, is that errors in the functional may mask successes or failures of the formulation. Here, to try to sort out some of the issues, we apply eight formulations of adiabatic TDDFT to the first valence excitations of ten molecules with 18 density functionals of diverse types. The formulations examined are linear response from the ground state (LR-TDDFT), linear response from the ground state with the Tamm-Dancoff approximation (TDDFT-TDA), the original collinear spin-flip approximation with the Tamm-Dancoff (TD) approximation (SF1-TDDFT-TDA), the original noncollinear spin-flip approximation with the TDA approximation (SF1-NC-TDDFT-TDA), combined self-consistent-field (SCF) and collinear spin-flip calculations in the original spin-projected form (SF2-TDDFT-TDA) or non-spin-projected (NSF2-TDDFT-TDA), and combined SCF and noncollinear spin-flip calculations (SF2-NC-TDDFT-TDA and NSF2-NC-TDDFT-TDA). Comparing LR-TDDFT to TDDFT-TDA, we observed that the excitation energy is raised by the TDA; this brings the excitation energies underestimated by full linear response closer to experiment, but sometimes it makes the results worse. For ethylene and butadiene, the excitation energies are underestimated by LR-TDDFT, and the error becomes smaller making the TDA. Neither SF1-TDDFT-TDA nor SF2-TDDFT-TDA provides a lower mean unsigned error than LR-TDDFT or TDDFT-TDA. The comparison between collinear and noncollinear kernels shows that the noncollinear kernel drastically reduces the spin contamination in the systems considered here, and it makes the results more accurate than collinear spin-flip TDDFT for functionals with a low percentage of Hartree-Fock exchange and sometimes for functionals with a higher percentage of Hartree-Fock exchange, but it yields less accurate results than ground-state TDDFT. [ABSTRACT FROM AUTHOR]

The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps. [ABSTRACT FROM AUTHOR]

We report a test of 30 density functionals, including several recent ones, for their predictions of 69 singlet-to-singlet excitation energies of 11 molecules. The reference values are experimental results collected by Caricato et al. for 30 valence excitations and 39 Rydberg excitations. All calculations employ time-dependent density functional theory in the adiabatic, linear-response approximation. As far as reasonable, all of the assignments are performed by essentially the same protocol as used by Caricato et al., and this allows us to merge our mean unsigned errors (MUEs) with the ones they calculated for both density functional and wave function methods. We find 21 of the 30 density functionals calculated here have smaller MUEs for the 30 valence states than what they obtained (0.47 eV) for the state-of-the-art EOM-CCSD wave function. In contrast, for all of density functionals the MUE for 39 Rydberg states is larger than that (0.11 eV) of EOM-CCSD. Merging the 30 density functionals calculated here with the 26 calculated by Caricato et al. makes a set of 56 density functionals. Averaging the unsigned errors over both the valence excitations and the Rydberg excitations, none of the 56 density functionals shows a lower mean unsigned error than that (0.27 eV) of EOM-CCSD. Nevertheless, two functionals are successful in having an overall mean unsigned error of 0.30 eV, and another nine are moderately successful in having overall mean unsigned errors in the range 0.32-0.36 eV. Successful or moderately successful density functionals include seven hybrid density functionals with 41% to 54% Hartree-Fock exchange, and four range-separated hybrid density functionals in which the percentage of Hartree-Fock exchange increases from 0% to 19% at small interelectronic separation to 65%-100% at long range. [ABSTRACT FROM AUTHOR]

Molecular fragmentation algorithms provide a powerful approach to extending electronic structure methods to very large systems. Here we present a method for including charge transfer between molecular fragments in the explicit polarization (X-Pol) fragment method for calculating potential energy surfaces. In the conventional X-Pol method, the total charge of each fragment is preserved, and charge transfer between fragments is not allowed. The description of charge transfer is made possible by treating each fragment as an open system with respect to the number of electrons. To achieve this, we applied Mermin's finite temperature method to the X-Pol wave function. In the application of this method to X-Pol, the fragments are open systems that partially equilibrate their number of electrons through a quasithermodynamics electron reservoir. The number of electrons in a given fragment can take a fractional value, and the electrons of each fragment obey the Fermi-Dirac distribution. The equilibrium state for the electrons is determined by electronegativity equalization with conservation of the total number of electrons. The amount of charge transfer is controlled by re-interpreting the temperature parameter in the Fermi-Dirac distribution function as a coupling strength parameter. We determined this coupling parameter so as to reproduce the charge transfer energy obtained by block localized energy decomposition analysis. We apply the new method to ten systems, and we show that it can yield reasonable approximations to potential energy profiles, to charge transfer stabilization energies, and to the direction and amount of charge transferred. [ABSTRACT FROM AUTHOR]

A database containing 17 multiplicity-changing valence and Rydberg excitation energies of p-block elements is used to test the performance of density functional theory (DFT) with approximate density functionals for calculating relative energies of spin states. We consider only systems where both the low-spin and high-spin state are well described by a single Slater determinant, thereby avoiding complications due to broken-symmetry solutions. Because the excitations studied involve a spin change, they require a balanced treatment of exchange and correlation, thus providing a hard test for approximate density functionals. We test three formalisms for predicting the multiplicity-changing transition energies. First is the ΔSCF method; we also test time-dependent density functional theory (TDDFT), both in its conventional form starting from the low-spin state and in its collinear spin-flip form starting from the high-spin state. Very diffuse basis functions are needed to give a qualitatively correct description of the Rydberg excitations. The scalar relativistic effect needs to be considered when quantitative results are desired, and we include it in the comparisons. With the ΔSCF method, most of the tested functionals give mean unsigned errors (MUEs) larger than 6 kcal/mol for valence excitations and MUEs larger than 3 kcal/mol for Rydberg excitations, but the performance for the Rydberg states is much better than can be obtained with time-dependent DFT. It is surprising to see that the long-range corrected functionals, which have 100% Hartree-Fock exchange at large inter-electronic distance, do not improve the performance for Rydberg excitations. Among all tested density functionals, ΔSCF calculations with the O3LYP, M08-HX, and OLYP functionals give the best overall performance for both valence and Rydberg excitations, with MUEs of 2.1, 2.6, and 2.7 kcal/mol, respectively. This is very encouraging since the MUE of the CCSD(T) coupled cluster method with quintuple zeta basis sets is 2.0 kcal/mol; however, caution is advised since many popular density functionals give poor results, and there can be very significant differences between the ΔSCF predictions and those from TDDFT. [ABSTRACT FROM AUTHOR]

As gold clusters increase in size, the preferred structure changes from planar to three-dimensional and, for anionic clusters, Aun-, the two-dimensional(2D)→three-dimensional (3D) transition is found experimentally to occur between n=11 and n=12. Most density functionals predict that planar structures are preferred up to higher n than is observed experimentally, an exception being the local spin density approximation. Here we test four relatively new functionals for this feature, in particular, M05, M06-L, M06, and SOGGA. We find that M06-L, M06, and SOGGA all predict the 2D→3D transition at the correct value of n. Since the M06-L and M06 functionals have previously been shown to be reasonably accurate for transition metal bond energies, main group atomization energies, barrier heights, and noncovalent interaction energies, and, since they are here shown to perform well for the s-d excitation energy and ionization potential of Au atoms and for the size of Aun- clusters at which the 2D→3D transition occurs, they are recommended for simulating processes catalyzed by gold clusters. [ABSTRACT FROM AUTHOR]

The adsorption of CO on Mg(001) constitutes a challenge for current density functional approximations because of its weak interaction character. In the present work we show that the M06-2X and M06-HF exchange-correlation functionals are the first ones to provide a simultaneously satisfactory description of adsorbate geometry, vibrational frequency shift, and adsorption energy of CO on MgO(001). For a sufficiently large embedded cluster model, the three functionals of the M06 family—which contain a nonzero percentage of Hartree–Fock exchange (M06, M06-2X, and M06-HF)—all predict positive C–O vibrational shifts, in agreement with the experimental findings, while the local M06-L functional gives large negative shifts. Moreover, the shifts computed with the M06-2X and M06-HF potentials are in good agreement with the experimental shift of +14 cm-1. The interaction energy (De) calculated with M06-2X and M06-HF is ∼6.0 kcal/mol, which agrees well with the De value (∼4 kcal/mol) deduced from the D0 obtained in thermal desorption measurements on single-crystal surfaces. [ABSTRACT FROM AUTHOR]

The abstraction and addition reactions of H with trans-N2H2 are studied by high-level ab initio methods and density functional theory. Rate constants were calculated for these two reactions by multistructural variational transition state theory with multidimensional tunneling and including torsional anharmonicity by the multistructural torsion method. Rate constants of the abstraction reaction show large variational effects, that is, the variational transition state yields a smaller rate constant than the conventional transition state; this results from the fact that the variational transition state has a higher zero-point vibrational energy than the conventional transition state. The addition reaction has a classical barrier height that is about 1 kcal/mol lower than that of the abstraction reaction, but the addition rates are lower than the abstraction rates due to vibrational adiabaticity. The calculated branching ratio of abstraction to addition is 3.5 at 200 K and decreases to 1.2 at 1000 K and 1.06 at 1500 K. [ABSTRACT FROM AUTHOR]

The purpose of the present investigation is to calculate partition functions and thermodynamic quantities, viz., entropy, enthalpy, heat capacity, and Gibbs free energies, for 1-butanol, 2-methyl-1-propanol, and butanal in the vapor phase. We employed the multi-structural (MS) anharmonicity method and electronic structure calculations including both explicitly correlated coupled cluster theory and density functional theory. The calculations are performed using all structures for each molecule and employing both the local harmonic approximation (MS-LH) and the inclusion of torsional anharmonicity (MS-T). The results obtained from the MS-T calculations are in excellent agreement with experimental data taken from the Thermodynamics Research Center data series and the CRC Handbook of Chemistry and Physics, where available. They are also compared with Benson's empirical group additivity values, where available; in most cases, the present results are more accurate than the group additivity values. In other cases, where experimental data (but not group additivity values) are available, we also obtain good agreement with experiment. This validates the accuracy of the electronic structure calculations when combined with the MS-T method for estimating the thermodynamic properties of systems with multiple torsions, and it increases our confidence in the predictions made with this method for molecules and temperatures where experimental or empirical data are not available. [ABSTRACT FROM AUTHOR]

Thirty four density functional approximations are tested against two diverse databases, one with 18 bond energies and one with 24 barriers. These two databases are chosen to include bond energies and barrier heights which are relevant to catalysis, and in particular the bond energy database includes metal-metal bonds, metal-ligand bonds, alkyl bond dissociation energies, and atomization energies of small main group molecules. Two revised versions of the Perdew–Burke–Ernzerhof (PBE) functional, namely the RPBE and revPBE functionals, widely used for catalysis, do improve the performance of PBE against the two diverse databases, but give worse results than B3LYP (which denotes the combination of Becke's 3-parameter hybrid treatment with Lee–Yang–Parr correlation functional). Our results show that the Minnesota functionals, M05, M06, and M06-L give the best performance for the two diverse databases, which suggests that they deserve more attention for applications to catalysis. We also obtain notably good performance with the τ-HCTHhyb, ωB97X-D, and MOHLYP functional (where MOHLYP denotes the combination of the OptX exchange functional as modified by Schultz, Zhao, and Truhlar with half of the LYP correlation functional). [ABSTRACT FROM AUTHOR]

The performance of the M06 family of exchange-correlation potentials for describing the electronic structure and the Heisenberg magnetic coupling constant (J) is investigated using a set of representative open-shell systems involving two unpaired electrons. The set of molecular systems studied has well defined structures, and their magnetic coupling values are known experimentally. As a general trend, the M06 functional is about equally as accurate as B3LYP or PBE0. The performance of local functionals is important because of their economy and convenience for large-scale calculations; we find that M06-L local functional of the M06 family largely improves over the local spin density approximation and the generalized gradient approximation. [ABSTRACT FROM AUTHOR]

Presents corrections to the article, entitled `Density functional solvation model based on CM2 atomic charges' published in the volume 109 issue of the `Journal of Chemical Physics'.