Double-hybrid functionals for thermochemical kinetics

We propose two new double-hybrid functionals, denoted B2K-PLYP and mPW2K-PLYP, which yield thermochemical performance comparable to existing double-hybrid functionals but offer superior performance for barrier heights of various kinds. We show that the new functionals yield excellent performance for all of the following: (a) main-group thermochemistry; (b) main-group thermochemical kinetics; (c) late transition metal reactions. In addition, B2K-PLYP performs well for weak interactions.     

Development of density functionals for thermochemical kinetics

A density functional theory exchange-correlation functional for the exploration of reaction mechanisms is proposed. This functional, denoted BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for transition state barriers but, unlike previous attempts at such a functional, this improved accuracy does not come at the expense of equilibrium properties. This makes it a general-purpose functional whose domain of applicability has been extended to transition states, rather than a specialized functional for kinetics. The improvement in BMK rests on the inclusion of the kinetic energy density together with a large value of the exact exchange mixing coefficient. For this functional, the kinetic energy density appears to correct "back" the excess exact exchange mixing for ground-state properties, possibly simulating variable exchange.     

Local hybrid functionals based on density matrix products

We present a novel similarity metric comparing exact and semilocal density functional theory (DFT) exchange holes in real space. This metric is obtained from the product of the one-particle density matrix and the uniform electron gas model density matrix. The metric is bound between 0 and 1, 1 in the uniform electron gas, 0 in regions asymptotically far from finite systems, and can detect delocalization of the exact exchange hole and effective fractional occupations. We also present a parameter-free local hybrid functional that uses this similarity metric to locally mix exact and semilocal DFT exchange energy densities. The resulting functional gives better thermochemistry and reaction barrier heights than our original local hybrids [Jaramillo et al., J. Chem. Phys. 118, 1068 (2003)], while retaining moderate accuracy for symmetric radical cation dimers.     

Hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound: implementation via local hybrids and thermochemical assessment

In 2009 Odashima and Capelle (OC) showed a way to design a correlation-only density functional that satisfies a Lieb-Oxford bound on the correlation energy, without empirical parameters and even without additional theoretical parameters. However, they were only able to test a size-inconsistent version of it that employs total energies. Here, we show that their alternative size-consistent form that employs energy densities, when combined with exact or semilocal exchange, is a local hybrid (lh) functional. We test several variants of this nonempirical OC-lh functional on standard molecular test sets. Although no variant yields enthalpies of formation with the accuracy of the semilocal Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation, OC-lh correlation with exact exchange yields rather accurate energy barriers for chemical reactions. Our purpose here is not to advocate for a new density functional, but to explore a previously published idea. We also discuss the importance of near-self-consistency for fully nonlocal functionals.     

Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions

This paper develops two new hybrid meta exchange-correlation functionals for thermochemistry, thermochemical kinetics, and nonbonded interactions. The new functionals are called PW6B95 (6-parameter functional based on Perdew-Wang-91 exchange and Becke-95 correlation) and PWB6K (6-parameter functional for kinetics based on Perdew-Wang-91 exchange and Becke-95 correlation). The resulting methods were comparatively assessed against the MGAE109/3 main group atomization energy database, against the IP13/3 ionization potential database, against the EA13/3 electron affinity database, against the HTBH38/4 and NHTBH38/04 hydrogen-transfer and non-hydrogen-transfer barrier height databases, against the HB6/04 hydrogen bonding database, against the CT7/04 charge-transfer complex database, against the DI6/04 dipole interaction database, against the WI7/05 weak interaction database, and against the new PPS5/05 pi-pi stacking interaction database. From the assessment and comparison of methods, we draw the following conclusions, based on an analysis of mean unsigned errors: (i) The PW6B95, MPW1B95, B98, B97-1, and TPSS1KCIS methods give the best results for a combination of thermochemistry and nonbonded interactions. (ii) PWB6K, MPWB1K, BB1K, MPW1K, and MPW1B95 give the best results for a combination of thermochemical kinetics and nonbonded interactions. (iii) PWB6K outperforms the MP2 method for nonbonded interactions. (iv) PW6B95 gives errors for main group covalent bond energies that are only 0.41 kcal (as measured by mean unsigned error per bond (MUEPB) for the MGAE109 database), as compared to 0.56 kcal/mol for the second best method and 0.92 kcal/mol for B3LYP.     

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

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. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Evaluation of a combination of local hybrid functionals with DFT-D3 corrections for the calculation of thermochemical and kinetic data

Due to their position-dependent exact exchange admixture, local hybrid functionals offer a higher flexibility and thus the potential for more universal and accurate exchange correlation functionals compared to global hybrids with a constant admixture, as has been demonstrated in previous work. Yet, the local hybrid constructions used so far do not account for the inclusion of dispersion-type interactions. As a first exploratory step toward a more general approach that includes van der Waals-type interactions with local hybrids, the present work has added DFT-D3-type corrections to a number of simple local hybrid functionals. Optimization of only the s(8) and s(r,6) parameters for the S22 set provides good results for weak interaction energies but deteriorates the excellent performance of the local hybrids for G3 atomization energies and for classical reaction barriers. A combined optimization of the two DFT-D3 parameters with one of the two parameters of the spin-polarized local mixing function (LMF) of a local hybrid for a more general optimization set provides simultaneously accurate dispersion energies, improved atomization energies, and accurate reaction barriers, as well as excellent alkane protobranching ratios. For other LMFs, the improvements of such a combined optimization for the S22 energies have been less satisfactory. The most notable advantage of the dispersion-corrected local hybrids over, for example, a B3LYP-D3 approach, is in the much more accurate reaction barriers.     

Analytic derivatives for the XYG3 type of doubly hybrid density functionals: Theory,implementation, and assessment

We present a theoretical development of the equations required to perform an analytic geometry optimization of a molecular system using the XYG3 type of doubly hybrid (xDH) functionals. In contrast to the well‐established B2PLYP type of DH functionals, the energy expressions in the xDH functionals are constructed by using density and orbital information from another standard Kohn–Sham (KS) functional (e.g., B3LYP) for doing the self‐consistent field calculations. Thus, the xDH functionals are nonvariational in both the hybrid density functional part and the second‐order perturbation part, each of which requires formally to solve a coupled‐perturbed KS equation. An implementation is reported here which combines the two parts by defining a total Lagrangian such that only a single set of the Z‐vector equations need to be solved. The computational cost with our implementation is of the same order as those for the conventional Møller–Plesset theory to the second order (MP2) and B2PLYP. Systematic test calculations are provided for covalently bonded molecules as well as compounds involving the intramolecular nonbonded interactions for the main group elements. Satisfactory performance of the xDH functionals demonstrates that the extra computer time on top of the conventional KS procedure is well‐invested, in particular, when the standard KS functionals and MP2 as well, are problematic. © 2013 Wiley Periodicals, Inc.     

Dibenzofuran and methyldibenzofuran derivatives: assessment of thermochemical data

Thermochemical data of dibenzofuran, a compound of considerable industrial and environmental significance, obtained from experimental calorimetric and computational techniques are reported in this work. The enthalpy of fusion, (19.4 ± 1.0) kJ mol^?1, at the temperature of fusion, (355.52 ± 0.02) K, was determined by differential scanning calorimetry measurements of dibenzofuran. From the standard (p° = 0.1 MPa) molar enthalpies of formation of crystalline dibenzofuran, (?29.2 ± 3.8) kJ mol^?1, and of sublimation, (84.5 ± 1.0) kJ mol^?1, determined at T = 298.15 K by static bomb combustion calorimetry and by vacuum drop microcalorimetry, respectively, it was possible to calculate the enthalpy of formation of the gaseous compound, (55.0 ± 3.9) kJ mol^?1, at the same temperature. The enthalpy of formation in the gaseous phase was also determined from G3(MP2)//B3LYP calculations. The same computational strategy was employed in the calculation of the standard molar enthalpies of formation, at T = 298.15 K, in the gas-phase, of single methylated derivatives of benzofuran and dibenzofuran.     

The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals

Hybrid functionals are responsible for much of the utility of modern Kohn-Sham density functional theory. When rigorously applied to solid-state metallic and small band gap systems, however, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally challenging and introduces unphysical effects. This can be remedied by using a range-separated hybrid which only keeps short-range nonlocal exchange, as in the functional of Heyd et al. [J. Chem. Phys. 118, 8207 (2003)]. On the other hand, many molecular properties require full long-range nonlocal exchange, which can also be included by means of a range-separated hybrid such as the recently introduced LC-omegaPBE functional [O. A. Vydrov and G. E. Scuseria, J. Chem. Phys. 125, 234109 (2006)]. In this paper, we show that a three-range hybrid which mainly includes middle-range Hartree-Fock-type exchange and neglects long- and short-range Hartree-Fock-type exchange yields excellent accuracy for thermochemistry, barrier heights, and band gaps, emphasizing that the middle-range part of the 1/r potential seems crucial to accurately model these properties.     

Molecular dynamics simulation of liquid water: hybrid density functionals

The structure, dynamical, and electronic properties of liquid water utilizing different hybrid density functionals were tested within the plane wave framework of first-principles molecular dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calculations of the structural and bonding properties of the water dimer and cyclic water trimer. Liquid water simulations were performed at the state point of 350 K at the experimental density. Simulations included three different hybrid functionals, a meta-functional, four gradient-corrected functionals, and the local density and Hartree-Fock approximations. It is found that hybrid functionals are superior in reproducing the experimental structure and dynamical properties as measured by the radial distribution function and self-diffusion constant when compared to the pure density functionals. The local density and Hartree-Fock approximations show strongly over- and understructured liquids, respectively. Hydrogen bond analysis shows that the hybrid functionals give slightly smaller average numbers of hydrogen bonds than pure density functionals but similar hydrogen bond populations. The average molecular dipole moments in the liquid from the three hybrid functionals are lower than those of the corresponding pure density functionals.     

Parameterized local hybrid functionals from density-matrix similarity metrics

We recently proposed a real-space similarity metric comparing the Kohn-Sham one-particle density matrix to the local spin-density approximation model density matrix [Janesko and Scuseria, J. Chem. Phys. 127, 164117 (2007)]. This metric provides a useful ingredient for constructing local hybrid density functionals that locally mix exact exchange and semilocal density functional theory exchange. Here we present two lines of inquiry: An approximate similarity metric comparing exact versus generalized gradient approximation (GGA), exchange and parameterized mixing functions using these similarity metrics. This approach yields significantly improved thermochemistry, including GGA local hybrids whose thermochemical performance approaches GGA global hybrids.     

Systematic optimization of long-range corrected hybrid density functionals

A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid density functionals.