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.

A new hybrid density functional for general chemistry applications is proposed. It is based on a mixing of standard generalized gradient approximations GGAs for exchange by Becke B and for correlation by Lee, Yang, and Parr LYP with Hartree-Fock HF exchange and a perturbative second-order correlation part PT2 that is obtained from the Kohn-Sham GGA orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixture of HF and GGA exchange ax and of the PT2 and GGA correlation c, respectively. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large 53% with c=27% which at least in part explains the success for many problematic molecular systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 standard benchmark set, a second test suite of atoms, molecules, and reactions that are considered as electronically very difficult including transition-metal compounds, weakly bonded complexes, and reaction barriers and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose density functional for molecules e.g., a mean absolute deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, respectively, for the best other density functionals. Very importantly, also the maximum and minium errors outliers are strongly reduced by about 10‐20 kcal/mol. Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equilibrium properties. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for diatomic molecules and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chemical systems emphasizes the need of virtual orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chemical method of general purpose. © 2006 American Institute of Physics. DOI: 10.1063/1.2148954

/pdf/semiempirical-hybrid-density-functional-with-perturbative-1i3y04gu68.pdf

Semiempirical hybrid density functional with perturbative second-order correlation

I. Introduction and Scope 231A. Definitions of Atomic Electron Affinities 233B. Definitions of Molecular Electron Affinities 233II. Experimental Photoelectron Electron Affinities 235A. Historical Background 235B. The Photoeffect 236C. Experimental Methods 237D. Time-of-Flight Negative Ion PhotoelectronSpectroscopy239E. Some Thermochemical Uses of ElectronAffinities241F. Layout of Table 10: ExperimentalPhotoelectron Electron Affinities242III. Theoretical Determination of Electron Affinities 242A. Historical Background 2421. Theoretical Predictions of Atomic ElectronAffinities2422. Theoretical Predictions of MolecularElectron Affinities243B. Present Status of Theoretical Electron AffinityPredictions243C. Basis Sets and Theoretical Electron Affinities 244D. Density Functional Theory (DFT) andElectron Affinities245E. Layout of Tables 8 and 9: Theoretical DFTElectron Affinities247F. Details of Density Functional MethodsEmployed in Tables 8 and 9247IV. Discussion and Observations 248A. Statistical Analysis of DFT Results ThroughComparisons to Experiment and OtherTheoretical Methods248B. Theoretical EAs for Species with UnknownExperimental EAs251C. On the Applicability of DFT to Anions and theFuture of DFT EA Predictions251D. Specific Theoretical Successes 251E. Interesting Problems 2521. C

/pdf/atomic-and-molecular-electron-affinities-photoelectron-3x4vklpj6q.pdf

Atomic and molecular electron affinities: photoelectron experiments and theoretical computations.

Molecular Clusters of π-Systems: Theoretical Studies of Structures, Spectra, and Origin of Interaction Energies

The hybrid meta density functionals M05-2X and M06-2X have been shown to provide broad accuracy for main group chemistry. In the present article we make the functional form more flexible and improve the self-interaction term in the correlation functional to improve its self-consistent-field convergence. We also explore the constraint of enforcing the exact forms of the exchange and correlation functionals through second order (SO) in the reduced density gradient. This yields two new functionals called M08-HX and M08-SO, with different exact constraints. The new functionals are optimized against 267 diverse main-group energetic data consisting of atomization energies, ionization potentials, electron affinities, proton affinities, dissociation energies, isomerization energies, barrier heights, noncovalent complexation energies, and atomic energies. Then the M08-HX, M08-SO, M05-2X, and M06-2X functionals and the popular B3LYP functional are tested against 250 data that were not part of the original training ...

Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions

The energetics of the station- ary points of the gas-phase reactions CH3X F CH3F X (X F, Cl, CN, OH, SH, NH2 and PH2) have been definitively computed using focal point analyses. These analyses entailed extrap- olation to the one-particle limit for the Hartree ± Fock and MP2 energies using basis sets of up to aug-cc-pV5Z quality, inclusion of higher-order electron corre- lation (CCSD and CCSD(T)) with basis sets of aug-cc-pVTZ quality, and addi- tion of auxiliary terms for core correla- tion and scalar relativistic effects. The final net activation barriers for the forward reactions are: E b

http://theop11.chem.elte.hu/main_index_files/2003_Gonzales_CEJ_SN2.pdf

Definitive Ab Initio Studies of Model SN2 Reactions CH3X+F− (X=F, Cl, CN, OH, SH, NH2, PH2)

The B3LYP, BLYP, and BP86 variants of density functional theory, in conjunction with double and triple ζ basis sets, have been examined for SN2 reactions of the type CH3X + F- → CH3F + X- (X = F, C...

Assessment of Density Functional Theory for Model SN2 Reactions: CH3X + F- (X = F, Cl, CN, OH, SH, NH2, PH2)

The structures of seven gas phase identity SN2 reactions of the form CH3X + X- have been characterized with seven distinct theoretical methods:  RHF, B3LYP, BLYP, BP86, MP2, CCSD, and CCSD(T), in conjunction with basis sets of double and triple ζ quality. Additionally, the energetics of said reactions have been definitively computed using focal point analyses utilizing extrapolation to the one-particle limit for the Hartree−Fock and MP2 energies using basis sets of up to aug-cc-pV5Z quality, inclusion of higher order correlation effects [CCSD and CCSD(T)] with basis sets of aug-cc-pVTZ quality, and additional auxiliary terms for core correlation and scalar relativistic effects. Final net activation barriers for the reactions are = −0.8, = 1.6, = 28.7, = 14.3, = 13.8, = 28.6, and = 25.7 kcal mol-1. General trends in the energetics, specifically the performance of the density functionals, and the component energies of the focal point analyses are discussed. The utility of classic Marcus theory as a techniqu...

Model identity SN2 reactions CH3X + X- (X = F, Cl, CN, OH, SH, NH2, PH2): Marcus theory analyzed.

Second-order Moller-Plesset perturbation theory (MP2) and density functional theory (DFT) were employed to optimize two cyclic conformations of the methanol trimer, denoted “bowl” and “chair,” as well as a third noncyclic, “open-chain” conformation. This is the first time all three methanol trimer conformations have been studied at the same level of theory. Harmonic vibrational frequencies confirm that all stationary points are minima on the intermolecular potential energy hypersurface. The chair is consistently predicted to be the most stable conformer. The bowl and open-chain conformers are only slightly less stable and lie within 3 kcal/mol. Results indicate that the bowl structure contains a threefold rotational axis of symmetry which resolves a discrepancy over its symmetry in previous theoretical investigations. Further, this finding precludes the possibility that only the cyclic conformers of (CH3OH)3 are the source of the five bands observed in the OH stretching spectrum of the methanol trimer rec...

Assignment of the infrared spectra of the methanol trimer

We have optimized geometries for various electronic states of both neutral and anionic ScO and ScO2 using density functional theory (DFT) and coupled cluster theory. Adiabatic and vertical separation energies have been computed using both DFT and coupled cluster theory. For the ScO− anion the 1Σ+ state is predicted to lie lower than the 3Δ state by 1.48 eV. In fact, the anion 3Δ state is higher in energy than the 2Σ+ neutral ground state. This contradicts the assignment of the ScO− ground state made by Wu and Wang, in their recent report of photoelectron spectroscopy experiments. The CCSD(T) adiabatic electron affinity for the ground state of ScO is 1.30 eV, while the vertical detachment energy is 1.33 eV. This compares favorably with the experimental value of 1.35 eV. For ScO2 the 2B2 ground state with a CCSD(T) bond angle of 140.5° is lower in energy than the 2A1 state with a bond angle of 48.4° by 1.13 eV. The anion minima include two 1A1 states, with the CCSD(T) global minimum corresponding to 140.9° ...

Jason M. Gonzales

Papers

Definitive Ab Initio Studies of Model SN2 Reactions CH3X+F− (X=F, Cl, CN, OH, SH, NH2, PH2)

Assessment of Density Functional Theory for Model SN2 Reactions: CH3X + F- (X = F, Cl, CN, OH, SH, NH2, PH2)

Model identity SN2 reactions CH3X + X- (X = F, Cl, CN, OH, SH, NH2, PH2): Marcus theory analyzed.

Assignment of the infrared spectra of the methanol trimer

Analyses of the ScO− and ScO2− photoelectron spectra