Structural, optical, and photophysical properties of nickel(II) alkylthioporphyrins: insights from experimental and DFT/TDDFT studies

The ground- and excited-state properties of a Ni(II) porphyrin bearing peripheral alkylthio group, NiOMTP (OMTP = 2,3,7,8,12,13,17,18-octakis methylthio porphyrinate) have been investigated by steady-state and time-resolved absorption spectrometry and DFT/TDDFT theoretical methods. Several conformations corresponding to different deformations of the porphyrin core and to different orientations of the alkylthio groups have been theoretically explored. The nearly degenerate, purely ruffled D(2d) and hybrid (ruffled with a modest degree of saddling) D(2) conformations, both characterized by an up-down (ud) orientation of the vicinal methylthio groups are by far the preferred conformations in the "gas phase". In contrast to NiOEP, it is the orientation of the peripheral substituents rather than the type and degree of distortions of the porphyrin core that determines the stability of the NiOMTP conformers. The ground-state electronic absorption spectra of NiOMTP exhibit significant changes compared to its parent NiP and beta-alkylated analogues, such as NiOEP, resulting in a considerable red shift of the B and the Q bands, intensification and broadening of the Q band, and additional weak absorptions in the region between the Q and B bands. These spectral changes can be understood in terms of the electronic effects of the methylthio groups with nonplanar distortions of the porphyrin ring playing a very minor role. Transient absorption measurements with sub-picosecond resolution performed in toluene and TDDFT calculations reveal that following photoexcitation, NiOMTP deactivates by the pathway 1(pi,pi) --> 3(d(z2),d(x2-y2))--> ground state. The (d,d) state exhibits complex spectral evolution over ca. 8 ps, interpreted in terms of vibrational relaxation and cooling. The cold ligand-field excited state decays with a lifetime of 320 ps. At variance with the highly distorted nickel porphyrins but similar to the planar analogues, the (d,d) spectrum of NiOMTP has transient absorption bands immediately to the red of the bleaching of the ground-state Q and B bands.     

Photophysical investigation of neutral and diprotonated free-base bis(arylethynyl)porphyrins

The photophysical properties for a series of free-base arylethynyl porphyrins and the corresponding trans-disubstituted tetraphenylporphyrin (H(2)TPP) derivatives lacking arylethynyl functionalities have been studied via electronic absorption and emission spectroscopy in both neutral and diacid forms. Enhanced substituent effects on porphyrin absorption spectra are observed in the arylethynyl porphyrins relative to the H(2)TPP derivatives, owing to the presence of the ethynyl spacer that allows for a coplanar geometry between the porphyrin macrocycle and the appended phenyl substituents. Upon protonation, both series of porphyrins exhibit substantially red shifted absorption and emission spectra and enhanced oscillator strengths, with the magnitude of the spectral shifts being more substantial in the presence of the ethynyl functionalities. Spectral features of the arylethynyl porphyrin bearing p-dimethylamino substituents closely resemble those previously classified as "hyperporphyrin spectra" and are indicative of excited-state charge-transfer character. Protonation of both series of porphyrins results in reduced fluorescence lifetimes and enhanced nonradiative decay rates, and the impact of protonation on these parameters is attenuated in the presence of the arylethynyl functionalities. Our results coupled with previous structural data showing that arylethynyl porphyrins exhibit less structural distortion upon diacid formation relative to H(2)TPP further substantiate the proposal that significant alteration of porphyrin photophysical properties upon diacid formation can be attributed to nonplanar structural distortions induced by protonation.     

Origin of the red shifts in the optical absorption bands of nonplanar tetraalkylporphyrins

The view that the large red shifts seen in the UV-visible absorption bands of peripherally crowded nonplanar porphyrins are the result of nonplanar deformations of the macrocycle has recently been challenged by the suggestion that the red shifts arise from substituent-induced changes in the macrocycle bond lengths and bond angles, termed in-plane nuclear reorganization (IPNR). We have analyzed the contributions to the UV-visible band shifts in a series of nickel or zinc meso-tetraalkylporphyrins to establish the origins of the red shifts in these ruffled porphyrins. Structures were obtained using a molecular mechanics force field optimized for porphyrins, and the nonplanar deformations were quantified by using normal-coordinate structural decomposition (NSD). Transition energies were calculated by the INDO/S semiempirical method. These computational studies demonstrate conclusively that the large Soret band red shifts ( approximately 40 nm) seen for very nonplanar meso-tetra(tert-butyl)porphyrin compared to meso-tetra(methyl)porphyrin are primarily the result of nonplanar deformations and not IPNR. Strikingly, nonplanar deformations along the high-frequency 2B(1u) and 3B(1u) normal coordinates of the macrocycle are shown to contribute significantly to the observed red shifts, even though these deformations are an order of magnitude smaller than the observed ruffling (1B(1u)) deformation. Other structural and electronic influences on the UV-visible band shifts are discussed and problems with the recent studies are examined (e.g., the systematic underestimation of the 2B(1u) and 3B(1u) modes in artificially constrained porphyrin structures that leads to a mistaken attribution of the red shift to IPNR). The effect of nonplanar deformations on the UV-visible absorption bands is then probed experimentally with a series of novel bridled nickel chiroporphyrins. In these compounds, the substituent effect is essentially invariant and the amount of nonplanar deformation decreases as the length of the straps connecting adjacent meso-cyclopropyl substituents decreases (the opposite of the effect observed for conventional strapped porphyrins). Several spectroscopic markers for nonplanarity (UV-visible bands, resonance Raman lines, and (1)H NMR resonances) are found to correlate with time-averaged deformations obtained from an NSD analysis of molecular dynamics snapshot structures. These results suggest that UV-visible band shifts of tetrapyrroles in proteins are potentially useful indicators of changes in nonplanarity provided other structural and electronic factors can be eliminated.     

Complexes of Formaldehyde and α-Dicarbonyls with Hydroxylamine: FTIR Matrix Isolation and Theoretical Study

The interactions of formaldehyde (FA), glyoxal (Gly) and methylglyoxal (MGly) with hydroxylamine (HA) isolated in solid argon and nitrogen were studied using FTIR spectroscopy and ab initio methods. The spectra analysis indicates the formation of two types of hydrogen-bonded complexes between carbonyl and hydroxylamine in the studied matrices. The cyclic planar complexes are stabilized by O–H⋯O(C), and C–H⋯N interactions and the nonplanar complexes are stabilized by O–H⋯O(C) bond. Formaldehyde was found to form with hydroxylamine, the cyclic planar complex and methylglyoxal, the nonplanar one in both argon and nitrogen matrices. In turn, glyoxal forms with hydroxylamine the most stable nonplanar complex in solid argon, whereas in solid nitrogen, both types of the complex are formed.     

Urea: an ab initio and force field study of the gas and solid phases

We have studied the gaseous and solid phases of urea using both quantum mechanics calculation and force field simulation methods. Our ab initio calculations confirmed experimental observations that urea structure is planar in the crystal, but nonplanar in the gas phase. Based on electron structure analysis, we suggest that the significant difference between these two structures in different environments can be qualitatively explained by two resonance structures. The planar structure is more polarized than the nonplanar one, and the former is stabilized in the solid phases due to strong electrostatic interactions. We found classical force field method is incapable to represent such strong polarization effect. Using molecular dynamics simulations with a force field optimized for condensed phases, we calculated the crystalline structures of urea in the temperature range of 12 to 293 K. The densities as well as cell parameters are within 2% deviation from the experimental data in the temperature range.     

Microwave spectrum and conformational composition of 1-vinylimidazole

The microwave spectrum of 1-vinylimidazole has been investigated in the 21-80 GHz spectral region. The spectra of two conformers have been assigned. One of these forms is planar, while the other is nonplanar with the imidazole ring and the vinyl group forming an angle of 15(4)° from coplanarity. The planar form is found to be 5.7(7) kJ/mol more stable than the nonplanar rotamer by relative intensity measurements. The spectra of 10 vibrationally excited states of the planar form and one excited-state spectrum of the nonplanar form were assigned. The vibrational frequencies of several of these states were determined by relative intensity measurements. The microwave work has been augmented by quantum chemical calculations at the CCSD/cc-pVTZ, MP2/cc-pVTZ, and B3LYP/cc-pVTZ levels of theory. The B3LYP calculations predict erroneously that both forms of 1-vinylimidazole are planar, whereas the MP2 and CCSD calculations correctly predict the existence of a planar and a nonplanar conformer of this compound.     

On the negligible impact of ruffling on the electronic spectra of porphine, tetramethylporphyrin, and perfluoroalkylporphyrins.

In the first part of this paper, the syntheses, structural characterization, molecular modeling, and electronic spectra for planar and nonplanar perfluoroalkylated porphyrins, (R(f))(4)P's, are reported. These studies demonstrate that the intrinsic substituent effect of the perfluoroalkyl group on the long-wavelength electronic spectrum of porphyrins is substantial, and similar (in magnitude) to that of a phenyl ring. Moreover, it is shown that out-of-plane distortion of (R(f))(4)P's has a negligible impact on their electronic spectra. These data bolster the findings of our earlier work and demonstrate that nonplanarity of (R(f))(4)P's does not result in a red-shift in their optical spectra. In the second part of this paper, time-dependent density functional spectral calculations (B3LYP/6-311G/TD) for porphine, 5,10,15,20-tetrakis(trifluoromethyl)porphyrin, and 5,10,15,20-tetramethylporphyrin in a variety of ruffled conformations are reported. The results of these studies indicate that (1) substantial ruffling of porphyrins has a negligible effect upon their electronic spectra, (2) similarly small effects upon electronic spectra are predicted if electron-withdrawing or electron-releasing groups decorate the porphyrin periphery, (3) for sterically encumbered porphyrins, ruffling can actually result in hypsochromic shifts in various absorption bands, and (4) the bulk of the red-shift commonly thought to be due to nonplanar distortion actually arises from other substituent effects. These results pose serious challenges to previous theoretical and empirical studies that have sought to find a cause-and-effect relationship between nonplanarity and electronic spectra in porphyrins.     

Thermochromism in polydiacetylene solutions

A novel planar ? nonplanar visual thermochromic conformational transition of polydiacetylene molecules in poor solvents is reported. The conformational transition is associated with both a color change (blue or red ? yellow) and a change in the state; the yellow solution (liquid) transforms to a blue or red gel (solid). The color transition occurs within a narrow range of temperature and has a large associated hysteresis. The enthalpy of the conformational transition is 29 kJ/mole of repeat unit. Fourier-transform infrared studies show that molecules acquire a planar conformation in red or blue gels by formation of intramolecular H bonds between the adjacent substituent groups. Virtually all H bonds break (a nonplanar conformation) when the gels turn into yellow solutions.     

Influence of electronic and structural effects on the oxidative behavior of nickel porphyrins

With the aim of better understanding the electronic and structural factors which govern electron-transfer processes in porphyrins, the electrochemistry of 29 nickel(II) porphyrins has been examined in dichloromethane containing either 0.1 M tetra-n-butylammonium perchlorate (TBAP) or tetra-n-butylammonium hexafluorophosphate (TBAPF(6)) as supporting electrolyte. Half-wave potentials for the first oxidation and first reduction are only weakly dependent on the supporting electrolyte, but E(1/2) for the second oxidation varies considerably with the type of supporting electrolyte. E(1/2) values for the first reduction to give a porphyrin pi-anion radical are effected in large part by the electronic properties of the porphyrin macrocycle substituents, while half-wave potentials for the first oxidation to give a pi-cation radical are affected by the substituents as well as by nonplanar deformations of the porphyrin macrocycle. The potential difference between the first and second oxidations (Delta/Ox(2) - Ox(1)/) is highly variable among the 29 investigated compounds and ranges from 0 mV (two overlapped oxidations) to 460 mV depending on the macrocycle substituents and the anion of the supporting electrolyte. The magnitude of Delta/Ox(2) - Ox(1)/ is generally smaller for compounds with very electron-withdrawing substituents and when TBAP is used as the supporting electrolyte. This behavior is best explained in terms of differences in the binding strengths of anions from the supporting electrolyte (ClO(4)(-) or PF(6)(-)) to the doubly oxidized species. A closer analysis suggests two factors which are important in modulating Delta/Ox(2) - Ox(1)/ and thus the binding affinity of the anion to the porphyrin dication. One is the type of pi-cation radical (a proxy for the charge distribution in the dication), and the other is the conformation of the porphyrin macrocycle (either planar or nonplanar). These findings imply that the redox behavior of porphyrins can be selectively tuned to display separate or overlapped oxidation processes.     

Aspects of prewetting at nonplanar surfaces

We employ Monte Carlo simulations in the grand canonical ensemble (GCEMC) to investigate the impact of nonplanarity of a solid substrate on the locus of the prewetting phase transition. The substrate is modelled as a periodic sequence of furrows of depth D and periodicity sx in the x direction; the furrows are infinitely long in the y direction. Our results indicate that a necessary prerequisite for a prewetting transition is the formation of a(n approximately) planar interface between molecularly thin films and an adjacent (bulk) gas. Thus, in general the prewetting transition is shifted to larger chemical potentials because the formation of a planar film-gas interface is more difficult next to a nonplanar compared with a planar solid surface. However, this shift turns out to be nonmonotonic depending on D on account of subtle packing effects manifested in the deviation of the local density Deltarho(x,Deltaz;D) at the nonplanar solid surface from that at a planar substrate. If D becomes sufficiently large prewetting as a discontinuous phase transition is suppressed because inside the furrow a highly ordered film forms that prevents a planar film-gas interface from forming.     

Planar and Nonplanar Free‐Base Tetraarylporphyrins: β‐Pyrrole Substituents and Geometric Effects on Electrochemistry,Spectroelectrochemistry, and Protonation/Deprotonation Reactions in Nonaqueous Media

A series of planar and nonplanar free‐base β‐pyrrole substituted meso‐tetraarylporphyrins were characterized by electrochemistry, spectroelectrochemistry, and protonation or deprotonation reactions in neutral, acidic, and basic solutions of CH₂Cl₂. The neutral compounds are represented as H₂(P), in which P represents a porphyrin dianion with one of several different sets of electron‐withdrawing or ‐donating substituents at the messo and/or β‐pyrrole positions of the macrocycle. The conversion of H₂(P) to [H₄(P)]²⁺ in CH₂Cl₂ was accomplished by titration of the neutral porphyrin with trifluoroacetic acid (TFA) while the progress of the protonation was monitored by UV/Vis spectroscopy, which was also used to calculate logβ₂ for proton addition to the core nitrogen atoms of the macrocycle. Cyclic voltammetry was performed after each addition of TFA or TBAOH to CH₂Cl₂ solutions of the porphyrin and half‐wave potentials for reduction were evaluated as a function of the added acid or base concentration. Thin‐layer spectroelectrochemistry was used to obtain UV/Vis spectra of the neutral and protonated or deprotonated porphyrins under the application of an applied reducing potential. The magnitude of the protonation constants, the positions of λ_max in the UV/Vis spectra and the half‐wave or peak potentials for reduction are then related to the electronic properties of the porphyrin and the data evaluated as a function of the planarity or nonplanarity of the porphyrin macrocycle. Surprisingly, the electroreduction of the diprotonated nonplanar porphyrins in acid media leads to H₂(P), whereas the nonplanar H₂(P) derivatives are reduced to [(P)]^2? in CH₂Cl₂ containing 0.1 M tetra‐n‐butylammonium perchlorate (TBAP). Thus, in both cases an electrochemically initiated deprotonation is observed.     

Nonplanar heme deformations and excited state displacements in nickel porphyrins detected by Raman spectroscopy at soret excitation

We have correlated the Raman intensities of out-of-plane modes of nickel porphyrins with the nonplanar deformations of specific symmetries, i.e., static normal coordinate deformations (SNCDs) expressed in terms of irreducible representations of the unperturbed D(4h) point group. The model porphyrins Ni(II) octaethyltetraphenylporphyrin (NiOETPP), Ni(II) tetra(isopropyl)porphyrin (NiT((i)Pr)P), Ni(II) tetra(tert-butyl)porphyrin (NiT((t)Bu)P), and Ni(II) meso-tetraphenylporphyrin (NiTPP) were chosen because they exhibit significant out-of-plane deformations of different symmetries. At B-band excitation, the Raman scattering of out-of-plane modes becomes activated mostly via the Franck-Condon mechanism. Some characteristic bands from out-of-plane modes in the spectra were identified as reliable predictors of the type and magnitude of out-of-plane deformation. The gamma(10)-gamma(13) bands are indicators of ruffling (B(1u)) deformations for porphyrins, as confirmed by data for NiTPP, NiT((i)Pr)P, and NiT((t)Bu)P, where the Raman intensity increases with the magnitude of the ruffling deformation. The gamma(15)-gamma(17) bands are indicators of saddling (B(2u)) deformations, as shown by data for NiOETPP, which is highly saddled. By comparing the relative intensities of these prominent Raman bands we estimated the vibronic coupling parameters using a self-consistent analysis, and showed that they reproduce the respective B-band absorption profiles. We also identified the deformations along the lowest wavenumber normal coordinates as the predominant reason for the Raman activity of out-of-plane modes. Our results suggest that some of the normal coordinates (gamma(10) and gamma(13)) may be used as tools to quantitatively probe the nonplanar deformations of metalloporphyrins with alkyl substituents at the meso-positions. Out-of-plane deformations also increase the vibronic coupling strength of some low frequency in-plane Raman modes, namely, nu(7) and nu(8). Generally, the Raman data suggest that the excited B-state is substantially more nonplanar than the ground state. The overall larger vibronic coupling of ruffled porphyrins yields substantially larger dipole strengths for the vibronic sidebands associated with the B-state transition, so that the relative absorptivity of the B(v) band can be used as a convenient tool to probe the nonplanarity of the porphyrin macrocycle.     

Porphyrin protonation studied by magnetic circular dichroism

Magnetic circular dichroism (MCD) spectroscopy provides valuable information about electronic excited states in molecules. The interpretation of spectra is however difficult, often requiring additional theoretical calculations to rationalize the observed signal. Recent developments in time-dependent density functional theory (TDDFT) bring hope that the applicability of MCD spectroscopy for chemical problems may be significantly extended. In this study, two modern analytical TDDFT implementations are compared and used to understand experimental MCD spectra of a model porphyrin system upon protonation. Changes in porphyrin geometry and electronic structure are related to MCD intensities by comparing the spectra of 5,10,15,20-tetraphenyl-21H,23H-porphyrintetrasulfonic acid (TPPS) measured at different pH values with the TDDFT calculations. Although the theoretical results slightly depended on the chosen exchange-correlation functional, the computations provided MCD curves that could well rationalize the experimental data. The protonation of the porphyrin core causes marked changes in the MCD spectrum, whereas the role of the substituents is limited. Also, different conformations of the porphyrin substituents cause relatively minor changes of the MCD pattern, mostly in the Soret region, where the porphine and phenyl electronic transitions start to mix. The solvent environment simulated by the dielectric model caused a shift (~20 nm) of the absorption bands but only minor variations in the absorption and MCD spectral shapes. The study thus demonstrates that the recently available first-principles interpretations of MCD spectra significantly enhance the applicability of the technique for molecular structural studies.     

Amphiphilic meso-disubstituted porphyrins: synthesis and the effect of the hydrophilic group on absorption spectra at the air-water interface

Five amphiphilic meso-disubstituted porphyrins bearing one polar group were synthesized, and their monolayer films were prepared. Their limiting molecular areas obtained from pi-A isotherms were 0.5-0.6 nm2, which were smaller than those of the corresponding meso-tetrasubstituted porphyrins. At the air-water interface, the disubstituted porphyrins showed a broad band in visible absorption spectra compared with the solution state, and the red shift of the Soret band exhibited a significant dependence on the kind of hydrophilic groups at the meso positions. Interestingly, the monolayer of the disubstituted porphyrin bearing a carboxyphenyl group (1-CO2H) showed a blue shift of the Soret band by adding cadmium chloride to the subphase, and the spectra varied upon multilayer deposition. The observed phenomena were interpreted by using the exciton theory. The effect of hydrophilic substituents on the absorption spectra of disubstituted porphyrin monolayers is discussed.     

Facile meso Functionalization of Porphyrins by Nucleophilic Substitution with Organolithium Reagents

The ruffle of the porphyrin increases with the number of meso substituents. (Octaethylporphyrin)nickel(II ) undergoes nucleophilic substitution reactions upon treatment with alkylating reagents such as butyllithium, hydrolysis with water, and oxidation with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone [DDQ; Eq. (a)]. Alkylation can be achieved at all four meso positions, and access is provided to new nonplanar porphyrins and asymmetrically substituted systems.     

卟啉、酞菁L-B膜中取代基的定向作用研究

由Π-A 曲线研究了五种具有不同取代基的卟啉、酞菁金属配合物不溶物膜的水/空气界面性质, 根据分子截面积和分子模型推断了单层膜中卟啉、酞菁环的可能取向及取代基的定向作用. 以偏振紫外测定了L-B 多层膜中大环的取向, 结果表明卟啉, 酞菁环以与它们在亚相表面相同的取向转移到固体基片上, 证明了取代基的性质和致目不同对分子大环的定向作用不同.     

Synthesis of Novel Symmetric Porphyrin Schiff Base Dimers by Solid–Liquid Reaction Methodology

A new convenient solid–liquid condensation reaction procedure for the synthesis of novel asymmetric and symmetric meso‐tetraarylporphyrin and metalloporphyrin Schiff bases is reported. The condensation reaction between β‐formyl porphyrin or metalloporphyrins and aromatic amines was carried out at solid–liquid interface by using neutral alumina powder as a solid support for β‐formyl porphyrin or metalloporphyrins and absolute ethanol as the carrier solvent for aromatic amines. Six different asymmetric porphyrin/metalloporphyrin Schiff bases were synthesized via solid–liquid interface reaction methodology. The same solid–liquid synthetic methodology was applied for the synthesis of six novel symmetric Schiff base porphyrin/metalloporphyrin dimers. The comparison of UV–visible spectra of porphyrin Schiff base monomers and dimers revealed that some degree of electronic perturbation has occurred upon dimerization as the Soret bands of the monomers underwent peak broadening along with red shifts. Column chromatography and crystallization were used to purify the compounds. Fourier transform infrared, UV–visible, elemental analysis, ¹H NMR, and mass spectrometry were used to characterize the newly synthesized compounds.     

The application of Fourier-transform Raman spectroscopy to the determination of conformation in poly(ε-caprolactam) chains

The Fourier-transform Raman spectra of various structural forms of poly(ε-caprolactam) have been obtained and the Raman bands characterizing planar and nonplanar conformation of the ε-caprolactam units have been defined. These bands have been used for the investigation of the conformational composition of ε-caprolactam sequences in several ε-caprolactam-butadiene block copolymers.     

Probing the structural and electronic effects to stabilize nonplanar forms of thioamide derivatives: A computational study

Density functional calculations have been performed to examine the stability of nonplanar conformations of thioamide derivatives. Electrostatic, orbital, and ring strain effects were invoked to stabilize the nonplanar conformations of thioamide systems 2 – 7 . Electrostatic interactions helped to achieve the twisted forms of thioamide derivatives; however, pyramidal forms predicted to be the global minimum. Negative hyperconjugative type interactions enhanced the stability of the twisted form 4b when compared with the planar form 4a . The influence of ring strain effect to achieve the twisted form of thioamide was observed with azirine ring. The predictions made with B3LYP/cc‐pVDZ+ level of theory was found to be in good agreement with more accurate CBS‐QB3 method. The solvent calculations performed with polarized continuum solvation model suggest that the relative stabilities of the nonplanar forms of thioamide derivatives are in general similar to the gas phase results. The importance of hydrogen bonding interactions between the solvent molecules and thioamide derivatives was observed toward the enhanced stability of twisted forms using a combination of explicit solvent molecules and continuum model. The natural bond orbital analysis confirmed the participation of n_N → π*_C?S delocalizations in the planar forms and corroborated the earlier reports on larger delocalizations in thioamide systems. Furthermore, the influence of electrostatic and ring strain effects on the amide, natural amides, and selenoamide has also been studied. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Characteristic features of excess charge localization in stepwise three-electron reduction of Ni-octaethylporphin

We have investigated the electronic structure of Ni-octaethylporphin anions (NiOEP) by¹H NMR. We have established that in (NiOEP)–, the excess electron is localized in the orbital of the nickel, while the second and third extra electrons in (NiOEP)^2- and (NiOEP)^3- are localized in the orbitals of the ligand. We conclude that spin density is transferred between the d orbitals of the Ni and the orbitals of the porphyrin ligand.Institute of Molecular and Atomic Physics, Academy of Sciences of Belarus, 70 Prospekt Frantsiska Skoriny, Minsk 220072, Belarus. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 6, pp. 345–347, November–December, 1996. Original article submitted February 22, 1996.