bluuebunny/crossref_metadata_2025_split huggingface dataset:
Chemistry of (Carbonyl)(nitrosyl)[bis(phosphorus donor)]rhenium Complexes
Authors: Hund Hans‐Ulrich , Ruppli Urs , Berke Heinz 
Published: December 2004

AbstractThe chemistry of [Re(CO)(NO)L2] fragments (L  phosphorus donor) was explored. Starting from [Re(CO)5Cl] the synthesis of [Re2Cl2(μ‐Cl)2(CO)4(NO)2] (1) was accomplished via the preparation of [Et4N]2[Re2Cl2(μ‐Cl)2(CO)6] and nitrosylation of this compound with [NO][BF4]. Complex 1 was converted to [RecL2(CO)(NO)L2] complexes 2 (a L = (MeO)3P; b L = (EtO)3P; c L = (i‐PrO)3P; d L  Me3P; e L  Et3P; f L  Cy3P) by heating with L in MeCN. In the case of the reaction of L = (MeO)3P, a trisubstitued compound mer‐{ReCl2(NO)[P(OMe)3]3} 3 was also obtained. Replacement of the Cl ligands in 2a–e with Me groups was achieved by reacting them with MeLi in Et2O yielding cis, trans‐[Re(CO)(NO)Me2L2]complexes 4a–e. Reaction of 2a–e with Li[BHEt3] led to substitution of one Cl by an H ligand with formation of [ReCl(CO)H(NO)L2] compounds 5a–;e, displaying trans‐H,NO geometries. The hydride‐transfer agent Na[AlH2(OCH2CH2OCH3)2] transformed 2 into the cis‐dihydride systems [Re(CO)H2(NO)L2] 6a–f. Reductive carbonylation of 2a–d in the presence of Na/Hg and CO gave pentacoordinate [Re(CO)2(NO)L2] complexes 7b–d, and under comparable conditions the Cl substituents of 2b–f were replaced by tolane using Mg or t‐BuLi giving trigonal bipyramidal [Re(CO)(NO)L2(PhCCPh)] compounds 8b–f. Complexes 5c, 6a, and 8d were characterized by X‐ray crystal‐structure analysis.
Synthetische Analoga von niedermolekularen Spinnentoxinen mit Acyl‐polyamin‐Struktur
Authors: Fiedler Wolfgang J. , Guggisberg Armin , Hesse Manfred 
Published: December 2004

Synthetic Analogues of Low‐Molecular‐Weight Acyl‐polyamine Spider ToxinsLow‐molecular‐weight spider and wasp toxins are selective inhibitors of glutamate receptors of the central nervous system and consist of a polyamine backbone and one or several carboxylic acids and/or amino acids linked by a peptide‐like bond. The syntheses of twelve analogues of spider and wasp toxins are described (10a–c, 15a–c, 20a–c, 25a–c) having the general structure of acyl, arylacyl, or heteroarylacyl → DL‐alanyl → ω‐aminoacyl → N1‐spermidine, with variation in the acyl and the ω‐aminoacyl part.
Transient Radicals Formed by Electron Transfer between inorganic ions and excited aromatic molecules in polar solvents
Authors: Mac Marek , Wirz Jakob , Najbar Jan 
Published: December 2004

AbstractFluorescence quenching of aromatic molecules by inorganic anions has been the subject of many investigations, yet the nature of the quenching mechanism is not fully understood. The fluorescence‐quenching rate constants correlate with electrochemical data, but the radicals expected to form upon transfer of an electron to the excited aromatic molecules have escaped observation. We report the first observation of radical‐ion species formed by electron‐transfer quenching with inorganic anions in acetonitrile. A decisive step leading to formation of separated radical ions is the trapping of the primary charge‐transfer complex by a second inorganic ion.
Radical Ions of a Bishomobinaphthylene Containing two 1,6‐methano[10]annulene moieties: An ESR and ENDOR study
Authors: Bachmann Rainer , Gerson Fabian , Kusch Andreas , Vogel Emanuel 
Published: December 2004

AbstractThe radical cation and the radical anion of ‘syn’‐cyclobuta[1,2‐c:3,4‐c′]di‐1,6‐methano[10]annulene (‘syn’‐4a,12a:6a, 10a‐bishomobinaphthylene; 3) have been characterized by their hyperfine data. The highly resolved ESR spectrum of \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{+ \atop \dot{}} $\end{document} is dominated by a triplet splitting from the outer pair of methano β‐protons (Ho). In contrast, the ESR spectrum of \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document} is poorly resolved with the largest coupling constants arising from perimeter α‐protons. The different hyperfine features of \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{+ \atop \dot{}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document} are rationalized by MO models. The SOMO of \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{+ \atop \dot{}} $\end{document} ψSA(b1), has substantial LCAO coefficients of the same sign at the bridged atoms C(1), C(6), C(11), and C(16), whereas in the SOMO of \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document}, ψSS(a1), the four atoms lie in the vertical nodal planes. The large width and the reluctance to saturation of the lines in the ESR spectrum of \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document} are attributed to the near‐degeneracy of the lowest antibonding MO's. Due to their similar nodal properties, the SOMO's of \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document} and the radical anions of binaphthylene (4), 1,6‐methano[10]annulene (1), and naphthalene (2) are interrelated. Moreover, because the cyclic π‐systems in 3 and 1 deviate in the same way from planarity, the effect of such distortions on the coupling constants, aHμ, of the perimeter α‐protons in \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{- \atop \dot{}} $\end{document} should be comparable. Indeed, on going from \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} to \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document}, the |aHμ| values are reduced exactaly by half as much as the corresponding values on passing from \documentclass{article}\pagestyle{empty}\begin{document}$ 2^{- \atop \dot{}} $\end{document} to \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document}, of which the cyclic π‐systems are twice contained in \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{- \atop \dot{}} $\end{document} respectively.
Intramolecular Dynamics of Tetranuclear Iridium Carbonyl Cluster Compounds. Part IV. Derivatives with monodentate ligands and edge‐bridging bidentate ligands
Authors: Strawczynski Andrès , Suardi Gianfranco , Ros Renzo , Roulet Raymond 
Published: December 2004

AbstractThe fluxionality of [Ir4(CO)8(μ2‐CO)3L] (L = Br−, I−, SCN−, NO2−, P(4‐ClC6H4)3, PPh3, P(4‐MeOC6H4)3, P(4‐Me2NC6H4)3), as studied by 2D‐13C‐NMR in solution, is due to two successive scrambling processes: the merry‐go‐round of six basal CO's and CO bridging to alternative faces of the Ir4 tetrahedron. The basicity of the ligand L has no significant effect on the activation parameters. The scrambling process of lowest activation energy in [Ir4(CO)7(μ2‐CO)3(PMePh2)2] correspond to the two possible synchronous CO bridging about a unique face of the metal tetrahedron swapping the relative axial and radial positions of the ligands L. The disubstituted clusters [Ir4(CO)10(μ2‐LL)] with one edge‐bridging ligand have a ground‐state geometry with three edge‐bridging CO's (LL = bis(diphenylphosphino)methane, bis(diphenylarsino)methane, bis(diphenylphosphino)propane) or with all terminal CO's (LL = CH3SCH2SCH3). In all cases, the fluxional process of lowest activation energy in the merry‐go‐round of six CO's about a unique triangular face. For the P and As donor ligands, this process is followed by the rotation of terminal CO's bonded to two Ir‐atoms residing on the mirror plane of the unbridged intermediate.
Homogeneous Catalysis with Dicationic PdII Complexes: Aldol reaction of methyl isocyanoacetate with benzaldehyde
Authors: Nesper Reinhard , Pregosin Paul S. , Püntener Kurt , Wörle Michael 
Published: December 2004

AbstractA series of dicationic PdII‐acetonitrile complexes containing bi‐ and tridentate nitrogen and bidentate phosphine ligands (some of which are chiral) has been prepared as their BF4 salts. The molecular structures for two of these, [Pd(CH3CN)2(bipy)] (BF4)2 (4) and [Pd(CH3CN)((pybox)(i‐Pr))] (BF4)2((S,S)‐pybox(i‐Pr) = 2,6‐bis[(S)‐4′‐isopropyloxazolin‐2′‐yl]pyridine, 5) have been determined by X‐ray diffraction. All of these complexes are shown to be effective homogeneous catalysts for the aldol‐type condensation of the isonitrile, methyl isocyanoacetate, with benzaldehyde. Two isonitrile complexes, [Pd(2,2′‐bipyridyl)(CNCH2COOCH3)2] (BF4)2 and [Pd((S,S)‐pybox(i‐Pr))(CNCH2COOCH3)] (BF4)2, have also been prepared.
Ringerweiterung von sechs‐ zu neungliedrigen Heterocyclen: Umsetzung von 3‐(Dimethylamino)‐2,2‐dimethyl‐2H‐azirin mit 3,4‐Dihydro‐2H‐1,2,4‐benzothiadiazin‐3‐on‐1,1‐dioxiden
Authors: Schläpfer‐Dähler Marlise , Heimgartner Heinz 
Published: December 2004

Ring Enlargement of Six‐ to Nine‐Membered Heterocycles: Reaction of 3‐(Dimethylamino)‐2,2‐dimethyl‐2H‐azirine with 3,4‐Dihydro‐2H‐1,2,4‐benzothiadiazin‐3‐one 1,1‐DioxidesReaction of 3‐(dimethylamino)‐2,2‐dimethyl‐2H‐azirine (1) and N‐substituted 3,4‐dihydro‐2H‐1,2,4‐benzothiadiazin‐3‐one 1,1‐dioxides (4) in CHCl3 yields 3‐(dimethylamino)‐4,5,6,7‐tetrahydro‐1,2,5,7‐benzothiatriazonin‐6‐one 1,1‐dioxides 5, a novel nine‐membered heterocyclic system, by ring enlargement (Schemes 2 and 4). In refluxing MeOH, the heterocycle 5a rearranges to give the N‐[1‐methyl‐1‐(1,1‐dioxo‐4H‐1,2,4‐benzothiadiazin‐3‐yl)ethyl]‐N′, N′‐dimethylurea 10. The three isomeric 2‐(methylamino)benzenesufonamides 8,9, and 11 (Scheme 3) are obtained by naBH4 reduction of 5a and 10, respectively. Mechanisms for the thermal isomerization 5a → 10 and the NaBH4 reduction of 5a are proposed in Schemes 5 and 6.
Synthesis of Certain 5‐Substituted 2′‐Deoxytubercidin Derivatives
Authors: Seela Frank , Thomas Horst 
Published: December 2004

AbstractThe synthesis of the 7‐deaza‐2′‐deoxy‐adenine derivatives 7b–3 with chloro, bromo, or methyl substituents at C(5) is described. Glycosylation of the 5‐substituted 4‐chloropyrrolo[2,3‐d]pyrimidines 4b–d with 2‐deoxy‐3,5‐di‐O‐(4‐toluoyl)‐α‐D‐erythro‐pentofuranosyl chloride (3) gave the β‐D‐nucleosides 5b–d, exclusively. They were deblocked (→6b–d) and converted into the tubercidin derivatives 7b–d.
Herstellung von Analoga von Polyamin‐Spinnentoxinen
Authors: Benz Herbert , Hesse Manfred 
Published: December 2004

Synthesis of Polyamine Analoga of Spider ToxinsWithin the last few years, polyamine toxins derived from various arthropods raised increasing interest due to their interaction with glutamate receptors of insects and invertebrates. Compounds 51 and 52 (Scheme 5) were prepared together with 53–58 to study a new pathway to Ala‐, Lys‐, and Gln‐derived polyamine toxins according to Scheme 6.
Photocycloaddition of Benzothiazole‐2‐thiones to Alkenes
Authors: Nishio Takehiko , Mori Yo‐Ichi , Iida Ikuo , Hosomi Akira 
Published: December 2004

AbstractThe photocycloaddition of benzothiazole‐2‐thiones to electron‐rich and aryl‐substituted alkenes are described. Irradiation of N‐unsubstituted benzothiazole‐2‐thione (1) in the presence of alkenes 3 gave 2‐(2′‐mercaptoalkyl)benzothiazoles 4, and 2‐substituted benzothiazoles 5 and 6 (in the case of 3a and 3h, resp.) through the ring cleavage of an intermediate 2‐aminothietane (Schemes 1 and 3). The latter was formed by [2+2] cycloaddition of the CS bond of 1 and the CC bond of 3. Irradiation of N‐methylbenzothiazole‐2‐thione (2) and 2‐methylpropene (3a) gave the spiro‐1,3‐dithiane 8, 1,2,6‐benzodithiazocin‐5‐one 9, and disulfide 10. The structure of 9 was established by X‐ray crystal‐structure analysis.
Efficient Preparation and X‐Ray Structure Analyses of (2R)‐N‐pyruvoyl‐ and (2R)‐N‐(phenylglyoxyloyl)bornane‐10,2‐sultam
Authors: Bauer Tomasz , Chapuis Christian , Kiegiel Jaroslaw , Krajewski Janusz W. , Piechota Katarzyna , Urbanczyk‐Lipkowska Zofia , Jurczak Janusz 
Published: December 2004

AbstractAn efficient synthesis of the two title compounds is reported, as well as their X‐ray crystal‐structure analyses. A discussion based on stereoelectronic considerations rationalizes the first example of a crystalline SO2/C(O) syn‐periplanar conformer of a N‐acylbornane‐10,2‐sultam.
Glycosylidene Carbenes. Part 23. Regioselective glycosidation of deoxy‐ and fluorodeoxy‐myo‐inositol derivatives
Authors: Zapata Amparo , Bernet Bruno , Vasella Andrea 
Published: December 2004

AbstractTo demonstrate the relevance of the kinetic acidity of individual OH groups for the regioselectivity of glycosylation by glycosylidene carbenes, we compared the glycosylation by 1 of the known triol 2 with the glycosylation of the diol D‐3 and the fluorodiol L‐4. Deoxygenation with Bu3SnH of the phenoxythiocarbonyl derivative of 5 (Scheme 1) or the carbonothioate 6 gave the racemic alcohol (±)‐7. The enantiomers were separated via the allophanates 9a and 9b, and desilylated to the deoxydiols D‐ and L‐3, respectively. The assignment of their absolute configuration is based upon the CD spectra of the bis(4‐bromobenzoates) D‐ and L‐10. The (+)‐(R)‐1‐phenylethylcarbamates 13a and 13b (Scheme 2) were prepared from the fluoroinositol (±)‐11 via (±)‐4 and the silyl ether (±)‐12 and separated by chromatography. The absolute configuration of 13a was established by X‐ray analysis. Decarbamoylation of 13a ( → L‐12) and desilylation afforded the fluorodiol L‐4. The H‐bonds of D‐3 and L‐4 in chlorinated solvents and in dioxane were studied by IR and 1H‐NMR spectroscopy (Fig. 2). In both diols, HOC(2) forms an intramolecular, bifurcated H‐bond. There is an intramolecular H‐bond between HOC(6) and F in solutions of L‐4 in CH2Cl2, but not in 1,4‐dioxane; the solubility of L‐4 in CH2Cl2 is too low to permit a meaningful glycosidation in this solvent. Glycosidation of D‐3 in dioxane by the carbene derived from 1 (Scheme 3) followed by acetylation gave predominantly the pseudodisaccharides 18/19 (38%), derived from glycosidation of the axial OH group besides the pseudodisaccharides 16/17 (13%) and the epoxides 20/21 (7%), derived from protonation of the carbene by the equatorial OH group. Similarly, the reaction of L‐4 with 1 (Scheme 4) led to the pseudodisaccharides 28/29 (46%) and 26/27 (14%), derived from deprotonation of the axial and equatorial OH groups, respectively. Formation of the epoxides involved deprotonation of the intramolecularly H‐bonded tautomer, followed by intramolecular alkylation, elimination, and substitution (Scheme 4). The regio‐ and diastereoselectivities of the glycosidation correlate with the H‐bonds in the starting diols.
Synthesis and transformations of methyl (E)‐2‐(acetylamino)‐3‐cyanoprop‐2‐enoate und methyl (E)‐2‐(benzoylamino)‐3‐cyanoprop‐2‐enoate, versatile reagents for the preparation of polyfunctional heterocyclic systems
Authors: Pizzioli Lucija , Ornik Brina , Svete Jurij , Stanovnik Branko 
Published: December 2004

AbstractMethyl (E)‐2‐(acetylamino)‐3‐cyanoprop‐2‐enoate (2a), and its 2‐benzoyl analog 2b ere prepared from the corresponding methyl (Z)‐2‐(acylamino)‐3‐(dimethylamino)propenoates 1 Multifunctional compounds 2 are versatile synthons for preparation of polysubstituted heterocyclic systems such as pyrroles 4, pyrimidines 5 and 6, pyridazines 7, pyrazoles 8, 9, and 11, and isoxazoles 10.
Intrinsic and Intramolecular Lipophilicity Effects in O‐Glucuronides
Authors: Giroud Yvan , Carrupt Pierre‐Alain , Pagliara Alessandra , Testa Bernard , Dickinson Ronald G. 
Published: December 2004

AbstractIn this study, we compared the lipophilicity of O‐glucuronides and their aglycones. Distribution coefficients (log D) and P values of neutral species (log P) were determined by centrifugal partition chromatography (CPC) in octanol/buffer systems. Two‐phase potentiometry was also used to measure the log P value of some lipophilic solutes. The experimentally determined global influence of glucuronidation on lipophilicity, obtained as the difference (decrement) log P(glucuronide) − log P(aglycone), was found to be −1.30 ± 0.16 (n = 4) for glucuronides of alcohols (methyl, menthyl, neomenthyl, and chloramphenicol O‐glucuronide). The mean decrement was −2.06 ± 0.31 (n = 9) for glucuronides of phenols (phenyl, p‐nitrophenyl, 1‐naphthyl, 6‐bromo‐2‐naphthyl, 4‐methylumbelliferyl, 3‐coumarinyl, phenolphthalein, 4′‐benzophenonyl O‐glucuronide, and diflunisal phenolic glucuronide). For the acylglucuronide of diflunisal and its rearrangement isomers, the mean decrement was −1.80 ± 0.08 (n = 4; range −1.7 to −1.9). Differences in through‐bond proximity effects as parametrized in the CLOGP algorithm seem to account for much of this difference. Conformational factors may also play a role, although it appears modest and unassessable for the glucuronides investigated here. The results imply that in vivo glucuronidation should have a stronger influence on the excretion of phenols than on that of alcohols.
Zur Krystallstruktur einiger Sterine und verwandter Verbindungen. 2. Hochtemperatur‐Modifikation von 17‐Iso‐desoxy‐corticosteron‐acetat
Authors: Nowacki W. 
Published: December 2004

AbstractDie Hochtemperatur‐Modifikation von 17‐Iso‐desoxy‐corticosteron‐acetat krystallisiert in der Raumgruppe D–P212121 mit den Gitterkonstanten a = 19,267 ± 0,05, b = 9,888 ± 0,027, c = 10,664 ± 0,015 Å und Z = 4 Molekeln pro Zelle [d(röntgen.) = 1,210]. Der Strukturvorschlag ist in Fig. 2 abgebildet worden. Eine Beziehung zur Struktur von Desoxy‐corticosteron‐acetat hat sich nicht ergeben. Die Frage nach der Stellung der langen Seitenkette am C17 bleibt offen.
Notice sur la prise, en photographie en couleurs, de spectres d'émission, de spectres d'absorption et spécialement de spectres Raman
Authors: Briner E. , Kundig J. J. , Berenstein M. 
Published: December 2004

AbstractOn expose les résultats observés dans la prise en couleur de divers spectres: spectres d'émission, spectres d'absorption et spécialement de spectres Raman.
The electronic structures and spectra of proflavine, acridine orange, and their DNA complexes
Authors: Ito Hirotoshi , I'Haya Y. J. 
Published: December 2004

AbstractThe electronic structure of the proflavine cation is studied by the SCF–ASMO–CI method using the Pariser–Parr–Pople approximations. It is shown that the band at 445 mμ may be assigned to the 1A1 → 1B1, transition polarized along the long axis of the molecule. The bands in the neighbourhood of 260 mμ, which are composed of three absorption bands, are tentatively assigned to the 1A1 → 1B1, 1A1 → 1B1, and 1A1 → 1A1 transitions, respectively, in order of decreasing wavelength. The spectrum of the acridine orange cation may be understood to have the same assignment as that of the proflavine cation.The acridine dye cations are well known for their dimerization with concentration. The intermolecular distances in these dimers are estimated from the band shifts due to the formation of dimers, using the exciton theory. The main contribution to the molecular interaction is shown to be the electrostatic dipole–dipole interaction.Since the first excitation band of the dye molecule which exhibits a remarkable change due to the formation of the DNA–acridine dye complex, is suggested to be polarized along the long axis, preference of the outside stacking or the intercalation model is qualitatively discussed from the spectral shift of the acridine dye bound to the DNA, assuming simple models.
Factorization of the secular determinant by constants of the motion
Authors: Gallup G. A. 
Published: December 2004

AbstractA discussion of the factorization by constants of the motion of the secular equation is given and formulas are obtained which relate these factors to the traces of certain operators. These traces are independent of the specific basis in the vector space, and, hence, so are the factors of the secular equation. The results are also applied to the case of factoring by a finite symmetry group.
Computation of derivatives for parameter optimization in least‐squares fitting of linear combinations of Slater‐type orbitals by Gaussians
Authors: Lesk Arthur M. 
Published: December 2004

AbstractThe approximation of a linear combination of Slater‐type orbitals in terms of Gaussian functions is a many‐parameter optimization problem. Formulas for computation of the gradient of the overlap in parameter space are reported. An alternative method of computing the gradient is described, which is of general applicability. This technique permits the exact evaluation of a derivative, without derivation and programming of its analytic expression.
The effect of electric field on the electronic structure of DNA. I. Calculation of the polarizability and of the permanent dipole moment for the nucleotide bases and base pairs
Authors: Seprödi L. , Biczó G. , Ladik J. 
Published: December 2004

AbstractGeneralizing the method of Hirschfelder, Curtiss and Bird for the calculation of the polarizability of molecules, we have calculated both the diagonal and off‐diagonal polarizability tensor elements of the nucleotide bases and base pairs. In the course of calculations also the components of the permanent dipole moments have been computed for these systems.On the basis of the results obtained we have determined also the critical field strengths necessary to break off a base pair and thus to induce the unwinding of the DNA double helix. According to the data obtained, a field strength of the order 108 V/cm can induce the unwinding of DNA if its direction lies in the plane of the base pairs.
Theoretical study of the derivative hydrocarbons of biphenylene. I. Electronic spectrum of the biphenylene
Authors: Peradejordi F. , Domingo R. , Ferńndez‐Alonso J. I. 
Published: December 2004

AbstractThe electronic spectrum of biphenylene has been studied theoretically. The investigation is based on the semi‐empirical LCAO SCF MO method with various degrees of approximations. The results have been analysed with regard to the following two factors: (a) The difference in effective electronegativity between the carbon atoms in the four‐membered ring and the other carbon atoms in the molecule. (b) The inclusion of doubly excited configurations in the description of the π‐electronic molecular states. The theory satisfactorily interprets the excitation energies and the nature of the electronic transitions. The predictions are particularly affected by the inclusion of the doubly excited configurations. On the basis of these results, the empirical parameters used are discussed.
Brackets to the eigenvalues of the Schrödinger equation, part 1. Tridiagonal matrices
Authors: Weltin E. 
Published: December 2004

AbstractThe problem of upper and lower bounds to the first few eigenvalues of a very large or infinite tridiagonal matrix H is studied. Those eigenvalues of a comparison‐matrix Mn which are lower than a characteristic limit, together with the corresponding eigenvalues of the variational matrix Hn are shown to bracket exact eigenvalues of H. Mn differs from Hn only in the last off‐diagonal element and is easily obtained from H. Sufficient conditions for lower bounds are based on a low estimate of the characteristic limit. For increasing dimensions n, the lower bounds approach the exact eigenvalues from below. As a numerical illustration, brackets to the known eigenvalues of the harmonic oscillator with a linear perturbation are calculated.
A perturbed generalized eigenvalue equation for the helium atom
Authors: Laughlin C. , Amos A. T. 
Published: December 2004

AbstractThe Schrödinger equation for helium is written as a generalized eigenvalue equation and this is solved perturbatively for the ground state. The zero order equation is taken to be that of a “six‐dimensional hydrogen atom” since, in generalized eigenvalue form, this has a discrete spectrum. Although the zero‐order wave function is very poor and gives only 86% of the energy the perturbation procedure is able to improve this to 99% through third‐order.