There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The relatively small diffuse function-augmented basis set, 3-21+G, is shown to describe anion geometries and proton affinities adequately. The diffuse sp orbital exponents are recommended for general use to augment larger basis sets.

Efficient diffuse function‐augmented basis sets for anion calculations. III. The 3‐21+G basis set for first‐row elements, Li–F

A. Water Exchange 2326 B. Proton Exchange 2327 C. Electronic Relaxation 2327 D. Relaxivity 2331 E. Outerand Second-Sphere Relaxivity 2334 F. Methods of Improving Relaxivity 2336 V. Macromolecular Conjugates 2336 A. Introduction 2336 B. General Conjugation Methods 2336 C. Synthetic Linear Polymers 2336 D. Synthetic Dendrimer-Based Agents 2338 E. Naturally Occurring Polymers (Proteins, Polysaccharides, and Nucleic Acids) 2339

https://mriquestions.com/uploads/3/4/5/7/34572113/lauffer_1999_review.pdf

Gadolinium(III) Chelates as MRI Contrast Agents: Structure, Dynamics, and Applications

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

/pdf/conceptual-density-functional-theory-btz9wwrxv9.pdf

Conceptual density functional theory.

Asymmetric enamine catalysis.

The 1,3-dipolar cycloadditions of a thiocarbonyl ylide to dimethyl 2,3-dicyanofumarate and 2,3-dicyanomaleate have been studied with DFT computations. The first C−C bond is formed via an anti attack to produce a very polar, zwitterionic diradical. The low stereoselectivity of the reaction was found to arise from rotations about single bonds in the intermediates that compete with cyclization. A distortion−interaction energy analysis was performed to compare the stepwise and concerted mechanisms, and to explain why the stepwise mechanism is favored in this unusual case.

Mechanism and stereoselectivity of the stepwise 1,3-dipolar cycloadditions between a thiocarbonyl ylide and electron-deficient dipolarophiles: a computational investigation.

There are few biocatalytic transformations that produce fluorine-containing molecules prevalent in modern pharmaceuticals. To expand the scope of biocatalysis for organofluorine synthesis, we have developed an enzymatic platform for highly enantioselective carbene B-H bond insertion to yield versatile α-trifluoromethylated (α-CF3) organoborons, an important class of organofluorine molecules that contain stereogenic centers bearing both CF3 and boron groups. In contrast to current "carbene transferase" enzymes that use a limited set of simple diazo compounds as carbene precursors, this system based on Rhodothermus marinus cytochrome c (Rma cyt c) can accept a broad range of trifluorodiazo alkanes and deliver versatile chiral α-CF3 organoborons with total turnovers up to 2870 and enantiomeric ratios up to 98.5:1.5. Computational modeling reveals that this broad diazo scope is enabled by an active-site environment that directs the alkyl substituent on the heme CF3-carbene intermediate toward the solvent-exposed face, thereby allowing the protein to accommodate diazo compounds with diverse structural features.

/pdf/a-biocatalytic-platform-for-synthesis-of-chiral-a-3qcsuwhuou.pdf

A Biocatalytic Platform for Synthesis of Chiral α- Trifluoromethylated Organoborons

Transition structures, activation energies, and reaction energies were calculated by ab initio quantum mechanical methods for the Claisen rearrangements of five hydroxy-substituted allyl vinyl ethers. The RHF, DFT(Becke3LYP), and CASSCF methods with the 6-31G* basis set were carried out. There is good agreement with activation energies measured for alkoxy-substituted compounds. The activation energies were separated into thermodynamic and intrinsic effects using Marcus theory as adapted by Murdoch for pericyclic reactions. Intrinsic effects were analyzed by frontier molecular orbital theory. The deuterium kinetic isotope effects calculated at the CASSCF/6-31G* level for the 2-OH allyl vinyl ether are in good agreement with the experimental results for the 2-OSiMe3 derivative, and these calculated isotope effects show much more bond-breaking and less bond-making than those at both the RHF/6-31G* and Becke3LYP/6-31G* levels.

K. N. Houk

Papers

Mechanism and stereoselectivity of the stepwise 1,3-dipolar cycloadditions between a thiocarbonyl ylide and electron-deficient dipolarophiles: a computational investigation.

A Biocatalytic Platform for Synthesis of Chiral α- Trifluoromethylated Organoborons

Theory of Substituent Effects on Pericyclic Reaction Rates: Alkoxy Substituents in the Claisen Rearrangement

Secondary Kinetic Isotope Effects of Diastereotopic Protons in Pericyclic Reactions: A New Mechanistic Probe

Mechanism of Permanganate Oxidation of Alkanes: Hydrogen Abstraction and Oxygen “Rebound”