I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

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Conceptual density functional theory.

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...

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

The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li–F), second- (Na–Cl), and third-row main group (K, Ca, and Ga–Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five ways. First, an extrapolation procedure is used to obtain the Hartree-Fock limit for inclusion in the total energy calculation. Second, the d-polarization sets are increased to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the latter. Third, the QCISD(T) method is replaced by the CCSD(T) method for the highest level of correlation treatment. Fourth, optimized geometries and zero-point energies are obtained with the B3LYP density functional. Fifth, two new higher level corrections are added to account for deficiencies in the energy calculations. The new method is ...

Gaussian-4 theory

It is shown that localization is necessary to preserve size consistency in nonlinear extrapolations of molecular energies. We demonstrate that the unphysical behavior of Mulliken populations obtained from extended basis set wave functions can lead to incomplete localization of orbitals by the Pipek–Mezey population localization method, and introduce a modification to correct this problem. The new localization procedure, called minimum population localization, is incorporated into the CBS-QB3 and the new CBS-4M model chemistries, and their performance is assessed on the G2/97 test set. The errors found for CBS-QB3 are comparable with those for the G3 and G3(MP2) (mean absolute deviation of 1.10, 0.94, and 1.21 kcal/mol, respectively, on the G2/97 test set). The CBS-4M is less accurate than the other models (mean absolute deviation of 3.26 kcal/mol on the G2/97 test set), but can be applied to much larger systems. The modified localization method resolves several problem cases found with CBS-4 and improves the reliability of CBS-QB3.

A complete basis set model chemistry. VII. Use of the minimum population localization method

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.

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Development of density functionals for thermochemical kinetics

Two new schemes for computing molecular total atomization energies (TAEs) and/or heats of formation (ΔHf∘) of first- and second-row compounds to very high accuracy are presented. The more affordable scheme, W1 (Weizmann-1) theory, yields a mean absolute error of 0.30 kcal/mol and includes only a single, molecule-independent, empirical parameter. It requires CCSD (coupled cluster with all single and double substitutions) calculations in spdf and spdfg basis sets, while CCSD(T) (i.e., CCSD with a quasiperturbative treatment of connected triple excitations) calculations are only required in spd and spdf basis sets. On workstation computers and using conventional coupled cluster algorithms, systems as large as benzene can be treated, while larger systems are feasible using direct coupled cluster methods. The more rigorous scheme, W2 (Weizmann-2) theory, contains no empirical parameters at all and yields a mean absolute error of 0.23 kcal/mol, which is lowered to 0.18 kcal/mol for molecules dominated by dynami...

Towards standard methods for benchmark quality ab initio thermochemistry :w1 and w2 theory

The energetics of the gas-phase SN2 reactions Y- + CH3X- → CH3Y + X- (where X,Y = F,Cl,Br), were studied using (variants on) the recent W1 and W2 ab initio computational thermochemistry methods. These calculations involve CCSD and CCSD(T) coupled cluster methods, basis sets of up to spdfgh quality, extrapolations to the one-particle basis set limit, and contributions of inner-shell correlation, scalar relativistic effects, and (where relevant) first-order spin−orbit coupling. Our computational predictions are in excellent agreement with experimental data where these have small error bars; in a number of other instances reexamination of the experimental data may be in order. Our computed benchmark data (including cases for which experimental data are unavailable altogether) are used to assess the quality of a number of compound thermochemistry schemes such as G2 theory, G3 theory, and CBS-QB3, as well as a variety of density functional theory methods. Upon applying some modifications to the level of theory...

Benchmark ab Initio Energy Profiles for the Gas-Phase SN2 Reactions Y- + CH3X → CH3Y + X- (X,Y = F,Cl,Br). Validation of Hybrid DFT Methods

The energetics of the gas-phase S$_N$2 reactions Y$^-$ + CH$_3$X $\longrightarrow$ CH$_3$Y + X$^-$ (where X,Y = F, Cl, Br), were studied using (variants on) the recent W1 and W2 {\em ab initio} computational thermochemistry methods. Our computed benchmark data (including cases for which experimental data are unavailable altogether) are used to assess the quality of a number of semiempirical compound thermochemistry schemes such as G2 theory, G3 theory, and CBS-QB3, as well as a variety of density functional theory methods. Upon applying some modifications to the level of theory used for the reference geometry (adding diffuse functions, replacing B3LYP by the very recently proposed mPW1K functional), the compound methods appear to perform well. Only the 'half-and-half' functionals BHH the other functionals fail to find a transition state in the F/Br case. BHH this problem is resolved in HCTH-120. mPW1K appears to exhibit the best performance of the functionals considered, although its energetics are still inferior to the compound thermochemistry methods.

Benchmark {\em ab initio} energy profiles for the gas-phase S$_N$2 reactions Y$^-$ + CH$_3$X $\to$ CH$_3$Y + X$^-$ (X,Y = F,Cl,Br). Validation of hybrid DFT methods

A benchmark ab initio and density-functional theory (DFT) study has been carried out on the electron affinities of the first- and second-row atoms. The ab initio study involves basis sets of $\mathrm{spdfgh}$ and $\mathrm{spdfghi}$ quality, extrapolations to the one-particle basis set limit, and a combination of the coupled cluster with all single, double (and triple) excitations [CCSD(T)], CCSDT, and full configuration-interaction electron correlation methods. Scalar relativistic and spin-orbit coupling effects were taken into account. On average, the best ab initio results agree to better than 0.001 eV with the most recent experimental results. Correcting for imperfections in the CCSD(T) method improves the mean absolute error by an order of magnitude, while for accurate results on the second-row atoms inclusion of relativistic corrections is essential. The latter are significantly overestimated at the self-consistent-field level; for accurate spin-orbit splitting constants of second-row atoms, inclusion of $2s,2p$ correlation is essential. In the DFT calculations it is found that results for the first-row atoms are very sensitive to the exchange functional, while those for second-row atoms are rather more sensitive to the correlation functional. While the Lee-Yang-Parr (LYP) correlation functional works best for first-row atoms, its PW91 counterpart appears to be preferable for second-row atoms. Among ``pure DFT'' (nonhybrid) functionals, G96PW91 (Gill 1996 exchange combined with Perdew-Wang 1991 correlation) puts in the best overall performance, actually slightly better than the popular hybrid B3LYP functional. B3PW91 outperforms B3LYP, while the recently proposed one-parameter hybrid functionals such as B1LYP seem clearly superior to B3LYP and B3PW91 for first-row atoms. The best results overall are obtained with the one-parameter hybrid modified Perdew-Wang (mPW1) exchange functionals of Adamo and Barone [J. Chem. Phys. 108, 664 (1998)], with $\mathrm{mPW}1\mathrm{LY}p$ yielding the best results for first-row, and mPW1PW91 for second-row atoms. Indications are that a hybrid of the type a $\mathrm{mPW}1\mathrm{LYP}+(1\ensuremath{-}a)$ mPW1PW91 yields better results than either of the constituent functionals.

Electron affinities of the first- and second-row atoms: Benchmark ab initio and density-functional calculations

Two new schemes for computing molecular total atomization energies (TAEs) and/or heats of formation ($\Delta H^\circ_f$) of first-and second-row compounds to very high accuracy are presented. The more affordable scheme, W1 (Weizmann-1) theory, yields a mean absolute error of 0.30 kcal/mol and includes only a single, molecule-independent, empirical parameter. It requires CCSD (coupled cluster with all single and double substitutions) calculations in $spdf$ and $spdfg$ basis sets, while CCSD(T) [i.e. CCSD with a quasiperturbative treatment of connected triple excitations] calculations are only required in $spd$ and $spdf$ basis sets. On workstation computers and using conventional coupled cluster algorithms, systems as large as benzene can be treated, while larger systems are feasible using direct coupled cluster methods. The more rigorous scheme, W2 (Weizmann-2) theory, contains no empirical parameters at all and yields a mean absolute error of 0.23 kcal/mol, which is lowered to 0.18 kcal/mol for molecules dominated by dynamical correlation. It involves CCSD calculations in $spdfg$ and $spdfgh$ basis sets and CCSD(T) calculations in $spdf$ and $spdfg$ basis sets. On workstation computers, molecules with up to three heavy atoms can be treated using conventional coupled cluster algorithms, while larger systems can still be treated using a direct CCSD code. Both schemes include corrections for scalar relativistic effects, which are found to be vital for accurate results on second-row compounds.

Glênisson de Oliveira

Papers

Towards standard methods for benchmark quality ab initio thermochemistry :w1 and w2 theory

Benchmark ab Initio Energy Profiles for the Gas-Phase SN2 Reactions Y- + CH3X → CH3Y + X- (X,Y = F,Cl,Br). Validation of Hybrid DFT Methods

Benchmark {\em ab initio} energy profiles for the gas-phase S$_N$2 reactions Y$^-$ + CH$_3$X $\to$ CH$_3$Y + X$^-$ (X,Y = F,Cl,Br). Validation of hybrid DFT methods

Electron affinities of the first- and second-row atoms: Benchmark ab initio and density-functional calculations

Towards standard methods for benchmark quality ab initio thermochemistry --- W1 and W2 theory