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.

Experimental Geometry of the Epoxidation Transition State

Transition-state modeling with empirical force fields

Computational chemistry and biochemistry began with Isaac Newton’s classical mechanics in the 17th century and the establishment of quantum mechanics in the 1920s. Enabled by extraordinary advances in computers, in the last half century, this field has become a robust partner with experiment. The challenges facing computational chemists and biochemists, the Holy Grails of the field, are described. These include the development of a highly accurate density functional, ideally one that has universal chemical accuracy, and accurate polarizable force fields, as well as methods to handle efficiently the massive number of computations that must be performed for molecular dynamics and for the computation of flexible systems such as proteins. We estimate when the breakthroughs that will make computation a powerful engine for chemical discovery and design will be achieved. The Holy Grails of this field involve methods to enable the accurate and efficient prediction of structures and properties of complex biologica...

Holy Grails for Computational Organic Chemistry and Biochemistry

Pericyclic reactions-which proceed in a concerted fashion through a cyclic transition state-are among the most powerful synthetic transformations used to make multiple regioselective and stereoselective carbon-carbon bonds. They have been widely applied to the synthesis of biologically active complex natural products containing contiguous stereogenic carbon centres. Despite the prominence of pericyclic reactions in total synthesis, only three naturally existing enzymatic examples (the intramolecular Diels-Alder reaction, and the Cope and the Claisen rearrangements) have been characterized. Here we report a versatile S-adenosyl-l-methionine (SAM)-dependent enzyme, LepI, that can catalyse stereoselective dehydration followed by three pericyclic transformations: intramolecular Diels-Alder and hetero-Diels-Alder reactions via a single ambimodal transition state, and a retro-Claisen rearrangement. Together, these transformations lead to the formation of the dihydropyran core of the fungal natural product, leporin. Combined in vitro enzymatic characterization and computational studies provide insight into how LepI regulates these bifurcating biosynthetic reaction pathways by using SAM as the cofactor. These pathways converge to the desired biosynthetic end product via the (SAM-dependent) retro-Claisen rearrangement catalysed by LepI. We expect that more pericyclic biosynthetic enzymatic transformations remain to be discovered in naturally occurring enzyme 'toolboxes'. The new role of the versatile cofactor SAM is likely to be found in other examples of enzyme catalysis.

https://escholarship.org/content/qt8nm707zd/qt8nm707zd.pdf?t=qaf0ra

SAM-dependent enzyme-catalysed pericyclic reactions in natural product biosynthesis

Diels-Alder reactions of substituted dienes and dienophiles have been found to cccur by both concerted and stepwise mechanisms.’.* The nature of the mechanism of the prototype Diels-Alder reaction of butadiene with ethylene to form cyclohexene is not only of fundamental interest but has generated fervid fulminations for favorite We wish to report new experimental evidence that is compatible only with the concerted mechanism, as well as further theoretical evidence for the synchronicity of this concerted mechanism.6 The reactions of 1,1,4,4-tetradeuterio-1,3-butadiene with cisor trans-1,2-dideuterioethylene were carried out at 185 “ C for 36 h at a pressure of 1800 psi in a stainless steel b~mb.~-’O Infrared spectra of the unreacted dideuterioethylenes indicate that they do not isomerize under the conditions of the reaction. Each cyclohexene product was separated from butadiene dimers by preparative GLC” and was then epoxidized with m-chloroperbenzoic acid (Figure 1). The N M R spectrum of cyclohexene oxide (Figure 2A) has resonances for the protons at C, and C, at 6 1.19 and 1.38, corresponding to protons that are cis and trans to the epoxide oxygen.12 The proton NMR spectra of the epoxides obtained from the reactions of cis and trans-dideuterioethylenes are clearly different. The DH couplings were partially eliminated by irradiation of the C3 and C6 deuteriums to give the spectra shown in Figure 2. The cis-dideuterio compound has a singlet resonance at d 1.19, due to the product with C4 and Cs hydrogens cis to the epoxide, and a second singlet a t 6 1.38, due to the

K. N. Houk

Papers

Experimental Geometry of the Epoxidation Transition State

Transition-state modeling with empirical force fields

Holy Grails for Computational Organic Chemistry and Biochemistry

SAM-dependent enzyme-catalysed pericyclic reactions in natural product biosynthesis

Evidence for the concerted mechanism of the Diels-Alder reaction of butadiene with ethylene.