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

Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by medium-range correlation energy, such as van der Waals attraction, aromatic−aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid)...

Density functionals with broad applicability in chemistry.

We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993

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A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions.

We present a new hybrid meta exchange-correlation functional, called M05-2X, for thermochemistry, thermochemical kinetics, and noncovalent interactions. We also provide a full discussion of the new M05 functional, previously presented in a short communication. The M05 functional was parametrized including both metals and nonmetals, whereas M05-2X is a high-nonlocality functional with double the amount of nonlocal exchange (2X) that is parametrized only for nonmetals. In particular, M05 was parametrized against 35 data values, and M05-2X is parametrized against 34 data values. Both functionals, along with 28 other functionals, have been comparatively assessed against 234 data values:  the MGAE109/3 main-group atomization energy database, the IP13/3 ionization potential database, the EA13/3 electron affinity database, the HTBH38/4 database of barrier height for hydrogen-transfer reactions, five noncovalent databases, two databases involving metal−metal and metal−ligand bond energies, a dipole moment databas...

/pdf/design-of-density-functionals-by-combining-the-method-of-3dsa6vb61i.pdf

Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions.

Scale factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zeropoint vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory. Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP, PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency scale factors were determined by a comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing a standard set of 1066 individual vibrations. ZPVE scale factors were generally obtained from a comparison of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the scale factors for a wide range of levels of theory, we have also probed the effect on scale factors of varying the percentage of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has revealed a near-linear relationship between the magnitude of the scale factor and the proportion of exact exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK scale factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.

An Evaluation of Harmonic Vibrational Frequency Scale Factors

A new hybrid Hartree−Fock−density functional (HF-DF) model called the modified Perdew−Wang 1-parameter model for kinetics (MPW1K) is optimized against a database of 20 forward barrier heights, 20 r...

Adiabatic connection for kinetics

https://www.chem.ccu.edu.tw/~hu/Web_Lib/papers/MCG3_1999.pdf

Multi-coefficient Gaussian-3 method for calculating potential energy surfaces

Twelve general parameterizations of the SAC (scaling-all-correlation) method for semiempirical extrapolation of electronic structure calculations are presented. The methods are based on Moeller-Plesset perturbation theory and coupled-cluster theory with correlation-consistent basis sets, and the parameterizations are based on 49 equilibrium atomization energies. This paper also presents an optimized scale factor for estimating the total anharmonic zero-point vibrational energy of a molecule with a root-mean-square accuracy of 0.17 kcal/mol.

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Optimized Parameters for Scaling Correlation Energy

This paper presents a multi-coefficient correlation method based on quadratic configuration interaction with single and double excitations (MC-QCISD) and basis sets using segmented contraction and having the same exponential parameters in the s and p spaces. The results are comparable to a previous multi-coefficient correlation method based on coupled cluster theory with less efficient correlation-consistent basis sets, and they are better than a previous multi-coefficient correlation method based on Moller−Plesset fourth order perturbation theory with single, double, and quadruple excitations with correlation-consistent basis functions. The mean unsigned error per bond of the MC-QCISD method is 0.72 kcal/mol. The new method should be very efficient for computing geometries of open-shell transition states.

MC-QCISD: Multi-coefficient correlation method based on quadratic configuration interaction with single and double excitations

We have developed a database of 29 molecules for which we have estimated the complete-one-electron-basis-set limit of the zero-point-exclusive atomization energy for five levels of electronic structure theory: Hartree–Fock (HF) theory, Mo/ller–Plesset second- and fourth-order perturbation theory, coupled cluster theory based on single and double excitations (CCSD), and CCSD plus a quasiperturbative treatment of triple excitations [CCSD(T)], all at a single set of standard geometries. Convergence checks indicate that the estimates are within a few tenths of a kcal/mol of the n=infinity limit of the cc-pVnZ basis set sequence. This data is then used to obtain optimized power-law exponents for extrapolating to the basis-set-limit from correlation-consistent polarized valence double and triple zeta (cc-pVDZ and cc-pVTZ) basis sets. This allows one to get thermochemical accuracy comparable to polarized quadruple or quintuple zeta (cc-pVQZ or cc-pV5Z) basis sets with a cost very comparable to polarized triple z...

Patton L. Fast

Papers

Adiabatic connection for kinetics

Multi-coefficient Gaussian-3 method for calculating potential energy surfaces

Optimized Parameters for Scaling Correlation Energy

MC-QCISD: Multi-coefficient correlation method based on quadratic configuration interaction with single and double excitations

Infinite basis limits in electronic structure theory