Analytic quantum mechanics of the morse oscillator

The approximate eigenfunctions of the Morse oscillator, expressed in terms of Laguerre polynomials, are shown to form an approximately orthogonal basis. Analytic expressions for the matrix elements of common operators are obtained within this representation. With such matrix elements in closed form, the Morse oscillator becomes, as the harmonic oscillator has been, a practical building block in molecular theory.     

Statistical mechanical theory of liquid entropy

The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but, rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and of the hard-sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher-order correlation entropy, due to n-particle irreducible correlations for n ≥ 3, is significant in only a few liquid metals, and its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, we discover the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and we discover the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. We clarify the relation among different entropy expansions in the recent literature. © 1994 John Wiley & Sons, Inc.     

Origin of the acidity enhancement of formic acid over methanol: resonance versus inductive effects

Density functional theory calculations were employed to study the relative contribution of resonance versus inductive effects toward the 37 kcal/mol enhanced gas-phase acidity (DeltaH degrees (acid)) of formic acid (1) over methanol (2). The gas-phase acidities of formic acid, methanol, vinyl alcohol (5), and their vinylogues (6, 8, and 9) were calculated at the B3LYP/6-31+G level of theory. Additionally, acidities were calculated for the formic acid and vinyl alcohol vinylogues in which the formyl group and the vinyl group, respectively, were perpendicular to the rest of the conjugated system. Comparisons among these calculated acidities suggest that inductive effects are the predominant effects responsible for the enhanced acidity of formic acid over methanol, accounting for between roughly 62% and 65% of the total enhanced acidity; the remaining 38% to 35% of the acidity enhancement appears to be due to resonance effects. Further comparisons suggest that resonance effects are between roughly 58% and 65% of the 26 kcal/mol calculated acidity enhancement of vinyl alcohol over methanol, and the remaining 42% to 35% are due to inductive effects.     

Design and characterization of a homodimeric antiparallel coiled coil

We report the first successful design of a self-associating antiparallel coiled coil, APH. The simultaneous application of Coulombic and hydrophobic components results in a decided preference for the antiparallel alignment as judged by HPLC, sedimentation equilibrium, and chemical denaturation data. The designed peptide is of comparable stability to naturally occurring leucine zipper peptides and can be expressed in bacteria. These properties of APH suggest potential in vivo protein fusion and biomaterials applications.     

Five-coordinate Fe(III)NO and Fe(II)CO porphyrinates: where are the electrons and why does it matter?

Recent years have seen dramatic growth in our understanding of the biological roles of nitric oxide (NO). Yet, the fundamental underpinnings of its reactivities with transition metal centers in proteins and enzymes, the stabilities of their structures, and the relationships between structure and reactivity remains, to a significant extent, elusive. This is especially true for the so-called ferric heme nitrosyls ([FeNO](6) in the Enemark-Feltham scheme). The Fe-CO and C-O bond strengths in the isoelectronic ferrous carbonyl complexes are widely recognized to be inversely correlated and sensitive to structural, environmental, and electronic factors. On the other hand, the Fe-NO and N-O bonds in [FeNO](6) heme complexes exhibit seemingly inconsistent behavior in response to varying structure and environment. This report contains resonance Raman and density functional theory results that suggest a new model for FeNO bonding in five-coordinate [FeNO](6) complexes. On the basis of resonance Raman and FTIR data, a direct correlation between the nu(Fe)(-)(NO) and nu(N)(-)(O) frequencies of [Fe(OEP)NO](ClO(4)) and [Fe(OEP)NO](ClO(4)).CHCl(3) (two crystal forms of the same complex) has been established. Density functional theory calculations show that the relationship between Fe-NO and N-O bond strengths is responsive to FeNO electron density in three molecular orbitals. The highest energy orbital of the three is sigma-antibonding with respect to the entire FeNO unit. The other two comprise a lower-energy, degenerate, or nearly degenerate pair that is pi-bonding with respect to Fe-NO and pi-antibonding with respect to N-O. The relative sensitivities of the electron density distributions in these orbitals are shown to be consistent with all published indicators of Fe-N-O bond strengths and angles, including the examples reported here.     

Palladium-catalyzed amidation of enol triflates: a new synthesis of enamides

[reaction: see text] The palladium-catalyzed coupling of a range of enol triflates with amides, carbamates, and sulfonamides has been developed. This offers a simple and widely applicable synthesis of enamides, which may not be readily available by other means.     

Dyeing uric acid crystals with methylene blue

The growth of anhydrous uric acid (UA) and uric acid dihydrate (UAD) crystals from supersaturated aqueous solutions containing methylene blue, a cationic organic dye, has been investigated. Low concentrations of dye molecules were found to be included in both types of crystal matrixes during the growth process. Incorporation of dye into UA crystals occurs with high specificity, affecting primarily [001] and [201] growth sectors, while UAD crystals grown from solutions of similar dye concentration show inclusion but little specificity. The orientation of the UA-trapped species was determined from polarization data obtained from visible light microspectrometry. To achieve charge neutrality, a second anionic species must also be included with the methylene blue into UA and UAD crystal matrices. Under high pH conditions, crystallization of 1:1 stoichiometric mixtures of methylene blue and urate yields methylene blue hexahydrate (MBU.6(H2O). The crystal structure of MBU.6(H2O) reveals continuous pi-pi stacks of planes of dye cations and urate anions mediated by water molecules. This structure provides an optimal geometry for methylene blue-urate pairs and additional support for the incorporation of these dimers in uric acid single-crystal matrices. The strikingly different inclusion patterns in UA and UAD demonstrate that subtle changes in the crystal surfaces and/or growth dynamics can greatly affect recognition events.     

The structure and maximum number of maximum independent sets in trees

A subset of vertices is a maximum independent set if no two of the vertices are joined by an edge and the subset has maximum cardinality. in this paper we answer a question posed by Herb Wilf. We show that the greatest number of maximum independent sets for a tree of n vertices is We give the families of trees on which these maxima are achieved. Proving which trees are extremal depends upon the structure of maximum independent sets in trees. This structure is described in terms of adjacency rules between three types of vertices, those which are in all, no, or some maximum independent sets. We show that vertices that are in some but not all maximum independent sets of the tree are joined in pairs by the α-critical edges (edges whose removal increases the size of a maximum independent set). The number of maximum independent sets is shown to depend on the structure within the tree of the α-critical edges.     

Assay development and high-throughput screening of caspases in microfluidic format

Caspase proteases are familiar targets in drug discovery. A common format for screening to identify caspase inhibitors employs fluorogenic or colorimetric tetra-peptide substrates in 96, 384, or 1536 -well microtiter plates. The primary motivation for increasing the number of wells per plate is to reduce the reagent cost per test and increase the throughput of HTS operations. There are significant challenges, however, to moving into or beyond the 1536-well format, such as submicroliter liquid handling, liquid evaporation, increased surface area-to-volume ratios, and the potential for artifacts and interference from small air-borne particles such as lint. Therefore, HTS scientists remain keenly interested in technologies that offer alternatives to the ever-shrinking microtiter plate well. Microfluidic assay technology represents an attractive option that, in theory, consumes only subnanoliter volumes of reagents per test. We have successfully employed a microfluidic assay technology in fluorogenic screening assays for several caspase isoforms utilizing the Caliper Technologies Labchip platform. Caspase-3 is used as a representative case to describe microfluidic assay development and initial high-throughput screening results. In addition, microfluidic screening and plate-based screening are compared in terms of reagent consumption, data quality, and ease of operation.