The Hellmann-Feynman theorem applied to long-range forces

The relations between the Hellmann-Feynman forces in laboratory fixed (L-) and relative (R-) coordinate systems are clarified. In the usualL-coordinate system, the force is interpreted as force on nucleus, while in theR-coordinate system, it means force on whole particles consisting of the electrons and nuclei of each interacting subsystem. From a perturbation theoretical viewpoint, the concept of the force on whole particles correctly corresponds to the perturbation energy and is superior to the force on the nucleus.     

Momentum density interpretation of the H(1s)–H+ long-range force

The recently proposed method of using momentum densities for interatomic interactions is applied to the long-range force between the ground-state hydrogen atom and the proton, and the results are compared with those from using the position density based on the electrostatic Hellmann–Feynaman theorem. A new physical interpretation of the long-range force is obtained, which is complementary to that in position space. It is found that some perturbative changes in the position density do not accompany changes in the momentum density.     

Laser-ionization mass-spectrometric studies on laser ablation of a nitrogen-rich polymer at 532 nm and 1064 nm

Laser-ionization Time-Of-Flight (TOF) mass-spectrometric studies have been carried out on the 532 nm and 1064 nm laser ablation products from a nitrogen-rich polymer. The polymer used had an elemental composition of C_6.0N_8.9H_3.4 and consisted of C=N, C-N, and N-H chemical bonds. The TOF mass spectra observed were composed of various peaks (150 amu) depending on the ablation laser wavelength. The primary peaks were assigned to C⁺, CN⁺, CHnN⁺ ₂ (n=1–3) and C₂H₂N⁺ ₃ for 532 nm ablation, and C⁺, C⁺ ₃, HCN⁺, HCCN⁺, CH₂NH⁺, HNCN⁺, H₃NCN⁺, and C₄H₄N⁺ ₇ for 1064 nm ablation. The flight velocity distributions with peak velocities ranging from 8.6×10³ cm/s to 3.8×10⁴ cm/s were measured for these products. The distinct velocity distributions observed between small and large products indicate the presence of two origins in the fragment ejection process from the polymer for both 532 nm and 1064 nm ablation. Furthermore, we suggest an importance of the translational energy of the fragments for the product generation in the laser plume.     

Biomimetic studies using artificial systems. IV. Biomimetic peptide synthesis by using multifunctionalized crown ethers as a novel enzyme model. A new concept in mimicking of enzyme-catalyzed bond-forming reactions

A novel approach to the mimicking of enzyme-catalyzed bond-forming reactions has been examined using multifunctionalized chiral crown ethers. In addition to the 18-crown-6 moiety as a binding site, the host have one thiol and one thio ester with an N-protected alpha-amino acid or a peptide, and have successfully achieved peptide synthesis in an enzyme-mimetic reaction mode. This new method involves the following three key reactions. (1) Intra-complex thiolysis: the host carries out the rapid intra-complex thiolysis of alpha-amino acid ester salts to form the dithioester, corresponding to the assembly of two guests by the host. (2) Amide formation: intramolecular aminolysis occurs between the bound guests to form the amide bond. (3) Peptide chain elongation: as the thiol reactive group is regenerated, the above two reactions are repeated to elongate the peptide chain. Formal turnover of the enzyme model has been demonstrated by the synthesis of a tetrapeptide derivative by the repetition of the above processes.     

pH-regulated formation of amyloid-like beta-sheet assemblies from polyglutamate grafted polyallylamine

A novel artificial protein with simple primary structure, poly(gamma-methyl-L-glutamate)-grafted polyallylamine, has been prepared and the resultant peptide has shown a unique property of pH-regulated conformation and morphology.     

Preparation and properties of poly(imide-oxoisoindolobenzothiadiazine dioxides)

New thermally stable poly(imide-oxoisoindolobenzothiadiazine dioxides) (PIOD) have been prepared by the three-step cyclopolycondensation reaction of diaminobenzenesulfonamides with aromatic tetracarboxylic dianhydrides. The polymerization proceeded through the formation of poly(amic acid-sulfonamides) (PAAS), followed by cyclodehydration to yield polyimide-sulfonamides (PIS), which were subsequently converted to PIOD at 300°C. PAAS having inherent viscosities in the range of 0.1–0.5 in N-methyl-2-pyrrolidone (NMP) were obtained in approximately quantitative yield. PIOD were insoluble in most organic solvents, whereas PAAS and PIS were soluble in NMP and dimethyl sulfoxide. Differential thermal analysis and thermogravimetric analysis indicated that PIOD began to decompose at 460°C in air. The cyclodehydration of the model compounds was also investigated.     

Atomic one- and two-electron subshell moments in position and momentum spaces

For 357 subshells of the 53 neutral atoms He through Xe in their ground states, the two-electron intracule (relative motion) <u ^k > _nl and extracule (center-of-mass motion) <R ^k > _nl subshell moments in position space are examined as well as their counterparts <v ^k > _nl and <P ^k > _nl in momentum space, where n and l are the principal and azimuthal quantum numbers of the atomic subshell, respectively. It is clarified that between the intracule and extracule moments the “2 ^k -rule” is strictly valid, which means <u ^k > _nl = 2 ^k <R ^k > _nl and <v ^k > _nl = 2 ^k <P ^k > _nl for any nl subshell. Theoretical analysis also proves that for a particular case of k = +2, two relations <u ²> _nl = (N _nl −1)<r ²> _nl and <v ²> _nl = (N _nl −1)<p ²> _nl hold exactly, where N _nl (≥2) is the number of electrons in the subshell nl, and <r ^k > _nl and <p ^k > _nl are the familiar one-electron subshell moments in position and momentum spaces, respectively. The latter equality establishes a new and rigorous relation between the second electron-pair moments in momentum space and the total energy of an atom through the virial theorem. For k=+1, −1, and −2, the numerical Hartree-Fock results for the 357 subshells show that there are approximate but accurate linear relations between <u ^k > _nl and <r ^k > _nl and between <v ^k > _nl and <p ^k > _nl , in which the proportionality constant in each space depends on n,l, and k. Received: 27 April 1998 / Accepted: 29 May 1998 / Published online: 28 August 1998     

A Kinetic Aspect of the Thermal Dehydration of Dilithium Tetraborate Trihydrate

The reaction process of the thermal dehydration of dilithium tetraborate trihydrate, Li₂B₄O₇3H₂O, was reinvestigated from a viewpoint of reaction kinetics. On the basis of the results of thermogravimetry, constant rate thermal analysis, powder X-ray diffractometry, infrared spectroscopy and scanning electron microscopy, it was confirmed that the reaction proceeds via three consecutive kinetic steps characterized by different activation energies. The first and second kinetic steps, accompanied by the destruction of the original crystal structure of the reactant, seem to be assigned to the surface and internal reactions, respectively. During the third kinetic step, the thermal dehydration of hydrated amorphous intermediate, produced at the second kinetic step, and crystallization of the final dehydration product, Li₂B₄O₇, are likely to take place concurrently.This revised version was published online in November 2005 with corrections to the Cover Date.     

Cyclophanes as hosts for aromatic and aliphatic guests

A series of water-soluble cyclophanes, made by connecting two diarylmethane units and two bridging chains via four nitrogens, were found to provide hydrophobic cavities of definite shape and size for forming inclusion complexes with various organic compounds in aqueous solution. Some chemical modifications of these cyclophanes are described.This paper is dedicated to Professor D. J. Cram to celebrate his honor in receiving the 1987 Nobel Prize in Chemistry.