Chemical potential for harmonically interacting particles in a harmonic potential

The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin-½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.     

An ab initio study of the geometry,harmonic and anharmonic force fields,and fundamental vibrational frequencies of cis- and trans- thiolformic acid

The geometry, harmonic and anharmonic force fields, and fundamental vibrational frequencies of cis- and trans-thiolformic acid are studied ab initio in the 4-31G basis set. An extensive comparison is made between changes in diagonal and off-diagonal quadratic and cubic force constants and diagonal stretching quartic constants in going from the chain to the ring structure in thiolformic acid and formic acid. The changes in the force constants are indicative of a much weaker interaction in the trans conformer between S? H and O?C, compared with O–H and O?C, in keeping with the weaker hydrogenbonding property of the S? H group in general.     

Conversions between ordered and disordered cellulose. Effects of mechanical treatment followed by cyclic wetting and drying

An investigation into the effects of mechanical treatment and hydration on the order of cellulose substrates (microcrystalline cellulose and Cladophora cellulose) was performed by the use of ball milling followed by cyclic wetting and drying. The results, monitored by¹³C-CP/MAS NMR-spectroscopy, were evaluated by calculation of the crystallinity indices and principal component analysis of the NMR data acquired. The results showed that a large part of the disorder induced by the mechanical treatment of cellulose by ball milling is reversible and reordering upon hydration leads to the cellulose I form initially present. The C4 signals corresponding to the reversibly disordered cellulose chains are observed in the amorphous region between 79 and 86 ppm in the¹³C-CP/MAS NMR-spectra together with signals from cellulose chains on the surface of ordered regions. The peak cluster which contains the C2, C3 and C5 ring carbons can be divided into two specific spectral regions; one between 74 and 77 ppm largely originates from ring carbons within disordered cellulose structures, and one between 70 and 74 ppm contains larger contributions from ordered cellulose. The behaviour of the celluloses upon milling is in accordance with a concept of ordered cellulose fibrils containing amorphous cellulose mainly as surface layers and induced reversible lattice distortions.     

Cyclophanes—13: Crystal and molecular structure of [2.2][2,5]furano(1,4)naphthalenophane

The crystal and molecular structure of [2.2](2,5)furano(1,4)naphthalenophane (1) was determined by X-ray crystallography. The molecule exists in the anti-conformation and the study represents the first instance in which the structural features of a naphthalenoid ring within a cyclophane were determined. Crystals of cyclophane 1 are orthorhombic, space group Pbca, with a = 7.859(2). b = 11.482(3) and c = 28.818(8) Å. While the nonbridged portion of the naphthalenoid ring is planar, the portion which is bridged to the furanoid ring through its 1 and 4 C atoms is puckered and boat-shaped. These C atoms are positioned 14° out of the plane of the other four C atoms of this ring. The furanoid ring is essentially planar but is not parallel to the naphthalenoid ring. It is inclined 22° to the least squares plane of the bridged portion of the naphthalenoid ring. This angle of inclination staggers the atoms of the furanoid and bridged naphthalenoid ring and positions the 3 and 4 C atoms, the 2 and 5 C atoms and the 0 atom of the furanoid ring 3.4. 2.9 and 2.6 Å. respectively, from the least squares plane of the bridged portion of the naphthalenoid ring. While the internal angles around the bridging C atoms α- to the naphthalenoid ring are 109°, those α- to the furanoid ring are 113°. In addition unusually large bond angles ($\text{\$}\text{?}$137°) at the 2 and 5 C atoms of the furanoid ring, external to the ring, are also observed. The distortions are considered with respect to the strain within the cyclophane macrocycle and are compared with other similar systems.     

On the question of allene formation from tricyclic cyclopropylidenes

The carbenoid or carbene derived from $\text{8}$ undergoes dimerization or trapping with DPIBF. The allene mechanism previously proposed was made doubtful by the finding that stereoisomeric carbenes

and

give stereoisomeric products without crossover.     

1,2-Shift of a Carboxyl Group in a Wagner-Meerwein Rearrangement

On treatment with HSO₃F in SO₂C1F at 0°, 3-hydroxy-2,2-dimethyl-3-phenyl-propionic acid ( 1a ) is transformed into 2-phenyl-3-methyl-2-butenoic acid ( 2a ) (isolated yield: 40–44%). Using monolabelled [3-¹³C]- 1a ( 1a *) and doubly labelled [1,3-¹³C₂]- 1a ( 1a **), the migration of HOOC (or a mechanistically equivalent group) was proved; a cross experiment established the intramolecular character of the rearrangement. By following the reaction at low temperature in an NMR. spectrometer, the formation of intermediates and side products was demonstrated.     

Synthesis and characterization of the non-Kekulé, singlet biradicaloid Ar'Ge(micro-NSiMe(3))(2)GeAr' (Ar' = 2,6-Dipp(2)C(6)H(3), Dipp = 2,6-i-Pr(2)C(6)H(3))

Reaction of Ar'GeGeAr' (1) with an excess of Me3SiN3 gives the non-Kekulé, biradicaloid Ar'Ge(mu-NSiMe3)2GeAr' (3, Ar' = 2,6-Dipp2C6H3, Dipp = 2,6-i-Pr2C6H3) which has a planar Ge2N2Si2 array and pyramidal geometry at the germaniums. DFT calculations for the model MeGe(mu-NSiH3)2GeMe indicate no Ge-Ge bonding and a singlet ground state. The calculated energy difference between the optimized singlet and triplet states is 17.51 kcal/mol.     

The [2 + 4] Diels-Alder cycloadditon product of a probable dialuminene,Ar'AlAlAr' (Ar' = C(6)H(3)- 2,6-dipp(2); dipp = C(6)H(3)-2,6-Pr(i)(2)), with toluene

Reduction of Ar'AlI2 (Ar' = Ar'= C6H3-2,6-Dipp2; Dipp = C6H3-2,6-Pri2) with KC8 in diethyl ether most probably affords the first "dialuminene", Ar'AlAlAr'; it was characterized by its reaction with toluene which yielded a [2 + 4] cycloaddition product incorporating the Ar'AlAlAr' unit.     

Nucleic acid related compounds. 31. Smooth and efficient palladium-copper catalyzed coupling of terminal alkynes with 5-iodouracil nucleosides

Coupling of terminal alkynes with protected 5-iodouracil nucleosides in the presence of dichlorobis(triphenylphosphine)palladium and copper(I) iodide in triethylamine gives the corresponding 5-(alkyn-1-yl)uracil nucleosides in 72–92% yields.