Projection between basis sets: A means of defining the electronic structure of functional subunits

The general problem of the transfer of the representation of a set of orthonormal functions from one basis to a different, nonequivalent one is considered and specialized to a matrix formulation convenient for use in molecular electronic structure calculations. A procedure is suggested for treating problems where the transfer of representation breaks into a subset of most interest and one of less interest as for example the occupied and virtual orbitals of a Hartree-Fock SCF calculation. These techniques are then applied to obtain a representation of a methyl group from an SCF wave function for methane.     

Salting coefficients for gases in seawater from scaled-particle theory

Experimental values of the salting coefficients for He, Ne, Ar, O₂, and N₂ in seawater are compared with values calculated from scaled-particle theory. The agreement is reasonably good; the average difference between calculated and observed values at 25°C is 0.007. Scaled-particle theory predicts correctly thatk _s should decrease as the temperature increases and that this effect should be most pronounced at low temperatures. However, the predicted magnitude ofdK _s/dt is only about half of that observed.     

Synthesis and Reaction Chemistry of the Disodium Alkoxide of 2,6-Bis(trifluoromethyl)-2,6-dihydroxy-3,3,4,4,5,5-hexafluorooxane

The disodium alkoxide of 2,6-bis(trifluoromethyl)-2,6-dihydroxy-3,3,4,4,5,5-hexafluorooxane, C(7)F(12)O(3)Na(2), 1, was prepared by reaction of the corresponding diol with MeONa in MeOH. This cyclic alkoxide readily mimics the reaction chemistry of the lithium and sodium alkoxides of perfluoropinacol. The reaction of the alkoxide 1 with covalent dichlorides and metallocene dichlorides yields a series of novel bicyclic ring systems. The crystal structure of the trioxasilane, 3, formed from (CH(3))(2)SiCl(2) was determined to provide structural information about these ring systems. Crystal data: C(9)H(6)O(3)F(12)Si, fw = 418.21 u, orthorhombic space group, Pnma (No. 62), a = 15.822(3) ?, b = 12.163(3) ?, c = 7.373(2) ?, V = 1418.9(4) ?(3), and D(calc) = 1.96 g cm(-)(3) for Z = 4 (molecule possesses mirror symmetry). Least-squares refinement on 1075 observed reflections (I > 3sigma(I)) converged with R = 0.0357 and R(w) = 0.0478.     

Constrained phosphite ester complexes of π-cyclopentadienylmolybdenum tricarbonyl halides

The synthesis of complexes of the type π-C₅H₅Mo(CO)₂LX and π-C₅H₅Mo(CO)L₂X, where XCl, Br, or I and LP(OCH₂)₃CR (RCH₃, C₂H₅, or C₃H₇), is reported. Infrared and conductance data verified that all compounds existed as covalent species in solution. Each of the three π-C₅H₅Mo(CO)₂LCl complexes was isolated as an inseparable mixture of cis and trans isomeric forms. Only the trans forms of the remaining π-C₅H₅Mo(CO)₂LX complexes were observed in solution, as indicated by infrared and PMR spectra. All of the π-C₅H₅Mo(CO)L₂X compounds apparently exist in primarily one isomeric form in solution; their PMR spectra, which exhibited a sharp triplet resonance for the ?OCH₂? protons of the phosphite ligands and a single sharp π-C₅H₅ proton signal, indicated a predominantly trans arrangement of the phosphite ligands at room temperature.     

Reversible subsets of certain linear transformations

Summary Suppose U is a set,F is a field of subsets of U, p_AB is the set of all real-valued bounded finitely additive functions defined onF, and for each in p_AB, A()={: in p_AB, absolutely continuous with respect to }. SupposeM is a linear subspace of p_AB such that . A generalisation of a previously discussed collection of linear transformations (see J. London Math. Soc., vol. 44 (1969), pp. 385–396) is treated by letting C_M denote the set to which T belongs iff T is a linear transformation from M into p_AB such that for some K inR and all in M and V inF, . Certain theorems of the aforementioned reference are generalized, as well as one of Trans. Amer. Math. Soc., vol. 199, (1974), pp. 131–140. The principal result of the present paper is the following generalisation of a reversibility characterisation in the first mentioned reference: Theorem: If T is in C_M, then (, T()): in M A(T()) is the only reversible subset T⁰ if T such that: i) the domain M⁰ of T⁰ is a linear subspace of M and , and ii) the range of T⁰ is the range of T.     

Ont ∞ quasi-similarity of linear systems

Summary Conti defined t similarity of systems (1)x=tA(t)xand (2)y=B(t)y, and showed that it is an equivalence relation which preserves uniform and strict stability. Here the definition is weakened by imposing less stringent integrability conditions, some in terms of perhaps conditionally convergent improper integrals, on the matrix function relating A and B. The extended relation, t quasi-similarity, is not symmetric or transitive; however, it is shown that if (2) is t quasi-similar to (1)and (1)is uniformly, uniformly asymptotically, or strictly stable, then so is (2).Results are also given concerning linear asymptotic equilibrium of (2)in the case where (1)is stricly stable or has linear asymptotic equilibrium.     

The physics of detecting torsion and placing limits on its effects

We present the essential principles of torsion-detection physics and evaluate several conceivable types of experiments and observations for actually detecting torsion fields, reemphasizing also the evident impossibility of successfully searching for its manifestations among cosmological relics. In particular, a polarized body, with net intrinsic (fundamental-particle) spin, is essential for detecting a torsion field. One which possesses only orbital angular momentum—rotation—or an unpolarized intrinsic spin density will not feel torsion. The fundamental problem in searching for such fields is the extremely small basic unit of the coupling or interaction energy between the torsion field and spin,(8G/c ²)( ²/4). The best way of maximizing the total interaction energy is to increase the spin density of the source _s, and, at the same time the spin numberS _D of the detector.This essay was awarded an honorable mention in 1984 by the Gravity Research Foundation—Ed.     

Very long-lived doubly vibrationally excited states above dissociation threshold: non-RRKM behavior in model triatomic systems

For couplings and mass ratios appropriate to molecules such as H₂O, D₂O, and CH₂ large volumes of the classical vibrational phase space are found to be non-dissociating even well above threshold. Fully quantum calculations yield families of exceptionally long-lived quantum states corresponding to these trapped volumes.     

Facile homogeneous hydrogenations of hindered olefins with [Ir(cod)py(PCy3)]PF6

The title complex readily hydrogenates a number of hindered steroidal olefin groups from the α face, without reducing ketone carbonyl groups, carbon—halogen bonds or cyclopropane rings.