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

6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Moller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT:  B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vib...

Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors

This article introduces MMFF94, the initial published version of the Merck molecular force field (MMFF). It describes the objectives set for MMFF, the form it takes, and the range of systems to which it applies. This study also outlines the methodology employed in parameterizing MMFF94 and summarizes its performance in reproducing computational and experimental data. Though similar to MM3 in some respects, MMFF94 differs in ways intended to facilitate application to condensed-phase processes in molecular-dynamics simulations. Indeed, MMFF94 seeks to achieve MM3-like accuracy for small molecules in a combined “organic/protein” force field that is equally applicable to proteins and other systems of biological significance. A second distinguishing feature is that the core portion of MMFF94 has primarily been derived from high-quality computational data—ca. 500 molecular structures optimized at the HF/6-31G* level, 475 structures optimized at the MP2/6-31G* level, 380 MP2/6-31G* structures evaluated at a defined approximation to the MP4SDQ/TZP level, and 1450 structures partly derived from MP2/6-31G* geometries and evaluated at the MP2/TZP level. A third distinguishing feature is that MMFF94 has been parameterized for a wide variety of chemical systems of interest to organic and medicial chemists, including many that feature frequently occurring combinations of functional groups for which little, if any, useful experimental data are available. The methodology used in parameterizing MMFF94 represents a fourth distinguishing feature. Rather than using the common “functional group” approach, nearly all MMFF parameters have been determined in a mutually consistent fashion from the full set of available computational data. MMFF94 reproduces the computational data used in its parameterization very well. In addition, MMFF94 reproduces experimental bond lengths (0.014 A root mean square [rms]), bond angles (1.2° rms), vibrational frequencies (61 cm−1 rms), conformational energies (0.38 kcal/mol/rms), and rotational barriers (0.39 kcal/mol rms) very nearly as well as does MM3 for comparable systems. MMFF94 also describes intermolecular interactions in hydrogen-bonded systems in a way that closely parallels that given by the highly regarded OPLS force field. © 1996 John Wiley & Sons, Inc.

Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94

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.

Mechanism of halogen-catalyzed Mukaiyama aldol reactions: concerted or stepwise?

Preparation and Chemistry of an Unexpectedly Stable α‐Oxoketene−Pyridine Zwitterion, 2,2‐Bis(tert‐butylcarbonyl)‐1‐[4‐(dimethylamino)pyridinio]ethen‐1‐olate

High-level ab initio molecular orbital calculations were employed to explore the potential energy hypersurface of hexasulfur, S6. Twelve isomeric structures of S6 have been identified: two unbranched rings (chair and boat), one trigonal prism of D3h symmetry, two singly branched rings (S5=S), three triplet chains, one singlet chain, and three doubly branched rings (S=S4=S). The prism structure is essentially a cluster of three S2 molecules connected via a six-center π*-π*-π* interaction. It is by 51 kJ mol−1 less stable than the lowest-energy chair form. The reactions to generate the boat, the prism, and the singly branched isomers from the chair form are predicted to have lower barriers than the ring opening reaction of cyclo-S6, which requires an activation energy of 149 kJ mol−1. The prism and singly branched isomers are found to be more reactive species than the chair form and they are potential sources of S2 in chemical reactions involving elemental sulfur.

Novel isomers of hexasulfur: Prediction of a stable prism isomer and implications for the thermal reactivity of elemental sulfur

Conformations of 4,4-bisphenylsulfonyl-N,N-dimethylbutylamine (BSDBA) were examined by ab initio calculations. Intramolecular C–H···N, C–H···O, and π···π interactions are found to play an important role in governing the conformational properties. This finding is supported by charge density analysis based on the theory of atoms in molecules. The calculated molecular structure and 1H chemical shifts of the methyl derivative (BSTBA) are in excellent agreement with experimental findings. The intramolecular C–H···N hydrogen bond in BSDBA is estimated to have a significant interaction energy of 25 kJ mol–1. The sulfonyl oxygens in BSDBA interact readily with neighbouring methylene, methyl and phenyl hydrogens via C–H···O=S hydrogen bonds. In agreement with experiment, solvent effect calculations indicate that these weaker intramolecular interactions prevail in an aprotic polar medium.

Structure of 4,4-Bisphenylsulfonyl-N,N-dimethylbutylamine: Interplay of Intramolecular C-H ··· N, C-H ··· O=S, and π ··· π Interactions

The novel iminopropadienones RN=C=C=C=O (8) and the corresponding thione 21 have been synthesized by FVP of isoxazole or Meldrum's acid derivatives. Bisimhes 16 and the unusual, linear ketenimine 18 were generated in related reactions. In the Meldrum's acid series, a competing fragmentation leads to imidoylketenes (R"=CR-CR"=C=O) (28). a-Oxoketenes (MR-CR'=C=O) (22), imidoylketenes (28), and vinylketenes (39c) undergo reversible interconversion with a-oxoketenes (23), oxoketenimines (29), and acylallenes (~OC), respectively, via a thermal 1,3-shifi of the group R. This is favored by electron-donating substituents R by means of interaction with the ketene LUMO.

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Ming Wah Wong

Papers

Mechanism of halogen-catalyzed Mukaiyama aldol reactions: concerted or stepwise?

Preparation and Chemistry of an Unexpectedly Stable α‐Oxoketene−Pyridine Zwitterion, 2,2‐Bis(tert‐butylcarbonyl)‐1‐[4‐(dimethylamino)pyridinio]ethen‐1‐olate

Novel isomers of hexasulfur: Prediction of a stable prism isomer and implications for the thermal reactivity of elemental sulfur

Structure of 4,4-Bisphenylsulfonyl-N,N-dimethylbutylamine: Interplay of Intramolecular C-H ··· N, C-H ··· O=S, and π ··· π Interactions

Novel heterocumulene (RN=C=C=C=X) and ketene rearrangements